Data Converter circuits

Data Converter circuits
Converters
CHAPTER 6: CONVERTERS
INTRODUCTION
SECTION 6.1: DIGITAL-TO-ANALOG CONVERTER
ARCHITECTURES
DIGITAL-TO ANALOG CONVERTERS (DACs OR D/As) INTRODUCTION
KELVIN DIVIDER (STRING DACs)
SEGMENTED DACs
DIGITAL POTS
THERMOMETER (FULLY DECODED) DACs
BINARY WEIGHTED CURRENT SOURCES
R-2R LADDER
MULTIPLING DACs
SEGMENTED DACs
SIGMA-DELTA DACs
I/V CONVERTERS
DIFFERENTIAL TO SINGLE-ENDED CONVERSION TECHNIQUES
SINGLE-ENDED CURRENT-TO-VOLTAGE CONVERSION
DIFFERENTIAL CURRENT-TO-VOLTAGE CONVERSION
DIGITAL INTERFACES
DATA CONVERTER LOGIC: TIMING AND OTHER ISSUES
INTERPOLATING DACs (INTERPOLATING TxDACs)
RECONSTRUCTION FILTERS
SIN(X)/(X) (SINC)
INTENTIONALLY NONLINEAR DACs
SECTION 6.2: ANALOG-TO-DIGITAL CONVERTER
ARCHITECTURES
THE COMPARATOR: A 1-BIT ADC
SUCCESSIVE APPROXIMATION ADCs
FLASH CONVERTERS
SUBRANGING, ERROR CORRECTED, AND PIPELINED ADCs
SERIAL BIT-PER-STAGE BINARY AND GRAY CODED (FOLDING) ADCs
COUNTING AND INTEGRATING ADC ARCHITECTURES
CHARGE RUN-DOWN ADCs
RAMP RUN-UP ADCs
TRACKING ADCs
VOLTAGE-TO-FREQUENCY CONVERTERS (VFCs)
DUAL-SLOPE/MULTISLOPE ADCs
RESOLVER-TO-DIGITAL CONVERTERS (RDCs) AND SYNCHROS
6.1
6.3
6.3
6.4
6.5
6.7
6.9
6.12
6.14
6.18
6.20
6.22
6.23
6.24
6.27
6.27
6.28
6.33
6.33
6.35
6.36
6.37
6.40
6.44
6.45
6.50
6.52
6.58
6.64
6.65
6.65
6.66
6.68
6.73
6.76
BASIC LINEAR DESIGN
SECTION 6.2: ANALOG-TO-DIGITAL CONVERTER
ARCHITECTURES (cont.)
REFERENCES
SECTION 6.3: SIGMA-DELTA (ΣΔ) CONVERTERS
HISTORICAL PERSPECTIVE
BASICS OF SIGMA-DELTA ADCs
IDLE TONE CONSIDERATIONS
HIGHER ORDER LOOP CONSIDERATIONS
MULTIBIT SIGMA-DELTA CONVERTERS
DIGITAL FILTER IMPLICATIONS
HIGH RESOLUTION MEASUREMENT SIGMA-DELTA ADCs
BAND-PASS SIGMA-DELTA CONVERTERS
SIGMA-DELTA DACs
SUMMARY
REFERENCES
SECTION 6.4: DEFINING THE SPECIFICATIONS
SECTION 6.5: DAC AND ADC STATIC TRANSFER FUNCTIONS
AND DC ERRORS
SECTION 6.6: DATA CONVERTER AC ERRORS
NOISE IN PRACTICAL ADCs
EQUIVALENT INPUT REFERRED NOISE
NOISE-FREE (FLICKER-FREE) CODE RESOLUTION
DYNAMIC PERFORMANCE OF DATA CONVERTERS
INTEGRAL AND DIFFERENTIAL NONLINEARITY DISTORTION EFFECTS
HARMONIC DISTORTION, WORST HARMONIC, TOTAL HARMONIC
DISTORTION (THD), TOTAL HARMONIC DISTORTION PLUS NOISE
(THD + N)
SIGNAL-TO-NOISE-AND-DISTORTION RATIO (SINAD), SIGNAL-TO-NOISE
RATIO (SNR) AND EFFECTIVE NUMBER OF BITS (ENOB)
ANALOG BANDWIDTH
SPURIOUS-FREE DYNAMIC RANGE (SFDR)
TWO TONE INTERMODULATION DISTORTION (IMD)
MULTITONE SPURIOUS-FREE DYNAMIC RANGE
SECOND- AND THIRD-ORDER INTERCEPT POINTS, 1 dB COMPRESSION
POINT
WIDEBAND CDMA (W-CDMA) ADJACENT CHANNEL POWER RATIO
(ACPR) AND ADJACENT CHANNEL LEAKAGE RATIO (ADLR)
NOISE POWER RATIO (NPR)
NOISE FACTOR (F) AND NOISE FIGURE (NF)
6.80
6.85
6.85
6.90
6.96
6.98
6.98
6.100
6.102
6.107
6.108
6.110
6.111
6.115
6.117
6.129
6.131
6.131
6.132
6.133
6.133
6.135
6.136
6.137
6.138
6.141
6.142
6.143
6.145
6.146
6.149
Converters
SECTION 6.6: DATA CONVERTER AC ERRORS (cont.)
APERTURE TIME, APERTURE DELAY TIME, AND APERTURE JITTER
A SIMPLE EQUATION FOR THE TOTAL SNR OF AN ADC
ADC TRANSIENT RESPONSE AND OVERVOLTAGE RECOVERY
ADC SPARKLE CODES, METASTABLE STATES, AND BIT ERROR RATE
(BER)
DAC DYNAMIC PERFORMANCE
DAC SETTLING TIME
GLITCH IMPULSE AREA
DAC SFDR AND SNR
MEASURING DAC SNR WITH AN ANALOG SPECTRUM ANALYZER
OTHER AC SPECIFICATIONS
REFERENCES
SECTION 6.7: TIMING SPECIFICATIONS
SECTION 6.8: HOW TO READ A DATA SHEET
THE FRONT PAGE
THE SPECIFICATION TABLES
THE ABSOLUTE MAXIMUMS
THE ORDERING GUIDE
PIN DESCRIPTION
DEFINING THE SPECIFICATIONS
EQUIVALENT CIRCUITS
THE GRAPHS
THE MAIN BODY
CIRCUIT DESCRIPTION
INTERFACE
REGISTER DESCRIPTION
APPLICATIONS CIRCUITS
EVALUATION BOARDS
SUMMARY
SECTION 6.9: CHOOSING A DATA CONVERTER
DETERMINE THE PARAMETERS
PRIORITIZING THE PARAMETERS
SELECTING THE PART
6.156
6.160
6.161
6.163
6.167
6.167
6.168
6.170
6.172
6.173
6.175
6.177
6.181
6.181
6.181
6.188
6.189
6.191
6.192
6.193
6.194
6.198
6.198
6.199
6.201
6.202
6.203
6.203
6.205
6.205
6.206
6.206
BASIC LINEAR DESIGN
CONVERTERS
INTRODUCTION
CHAPTER 6: CONVERTERS
Introduction
There are two basic type of converters, digital-to-analog (DACs or D/As) and analog-todigital (ADCs or A/Ds). Their purpose is fairly straightforward. In the case of DACs,
they output an analog voltage that is a proportion of a reference voltage, the proportion
based on the digital word applied. In the case of the ADC, a digital representation of the
analog voltage that is applied to the ADCs input is outputted, the representation
proportional to a reference voltage.
In both cases the digital word is almost always based on a binarily weighted proportion.
The digital input or output is arranged in words of varying widths, referred to as bits,
typically anywhere from 6 bits to 24 bits. In a binarily weighted system each bit is worth
half of the bit to its left and twice the bit to its right. The greater the number of bits in the
digital word, the finer the resolution. These bits are typically arranged in groups of four,
called bytes, for convenience.
For a better understanding of the relationship between the digital domain and the analog
domain please refer to the section on sampling theory.
As stated earlier, we shall look at the operation of converters primarily from a “black
box” view. We will concern ourselves less with the internal construction of the converter
and more with its operation. We cannot, however, completely ignore the internal
architecture because in many cases it is relevant to operational advantages or limitations.
There are a number of works that cover the internal workings of the converters in much
more detail (see References).
Another point that should be kept in mind is the difference between accuracy and
resolution. The resolution of a converter is the number of bits in its digital word. The
accuracy is the number of those bits that meet the specifications. For instance, a DAC
might have 16 bits of resolution, but might only be monotonic to 14 bits. This means that
the assured accuracy of the DAC will be no better than 14 bits. Also, an audio ADC
might have a digital word width of 16 bits, but the SNR may be only 70 dB. This means
that the accuracy will only be at the 12-bit level. This is not to say that the other bits are
irrelevant. With further processing, typically filtering, often the accuracy can be
improved. While these terms are similar and sometimes used interchangeably, the
distinction between the two should be remembered.
We shall examine the DAC first.
6.1
BASIC LINEAR DESIGN
6.2
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
SECTION 6.1: DIGITAL-TO-ANALOG CONVERTER
ARCHITECTURES
Digital-to-Analog Converters (DACs or D/As) Introduction
What we commonly refer to as a DAC today is typically quite a bit more. The DAC will
typically have the converter itself and a collection of support circuitry built into the chip.
The first DACs were board level designs, built from discrete components, including
vacuum tubes as the switching elements. Monolithic DACs began to appear in the early
’70s. These early examples were actually sub-blocks of the DAC. An example of this
would be the AD550, which was a 4 bit binarily weighted current source. This current
source block would be mated to a separate part, such as the AD850, which contained a
resistor array and CMOS switches. Together these would form the basic DAC. As we
moved on in time these functions were integrated on the same die, additional digital
circuitry, specifically latches to store the digital input, were added. Then a second rank of
latches was often added. The purpose of the second rank was to allow the microprocessor
or microcontroller to write to many DACs in a system and the updated them all at the
same time. The input rank of latches could also be a shift register, which would allow a
serial interface.
VDD
(ANALOG)
REFERENCE
INPUT
VREF
DIGITAL
INPUT
DAC
VSS
GROUND
(MAY BE INTERNALLY
CONNECTED TO VSS)
Figure 6.1: The Basic DAC
6.3
BASIC LINEAR DESIGN
On the back end, since the output of the DAC is often a current, an op amp is often added
to perform the current-to-voltage (I/V) conversion. On the front end a voltage reference is
often added.
Process limitations did not allow the integration of all these sub-blocks to occur at once.
Initially, the processes used to make the various sub-blocks were not compatible. The
process that made the best switches was typically not the best for the amplifier and the
reference. As the processes became more advanced these limitations became less. Today
CMOS can make acceptable amplifiers and processes combining bipolar and CMOS
together exist.
There are several advantages to including all this additional circuitry in one package. The
first is the obvious advantage of reducing the chip count. This reduces the size of the
circuitry and increases the reliability. Probably more important is that the circuit designer
now doesn’t have to concern himself with the accuracy of several parts in a system. The
system is now one part and tested by the manufacturer as a unit.
Next we will look at the various DAC architectures. When we refer to DACs here we are
referring to the basic converter rather than the complete system.
Kelvin Divider (String DAC)
The simplest structure of all is the Kelvin divider or string DAC as shown in Figure 6.2.
An N-bit version of this DAC simply consists of 2N equal resistors in series and 2N
switches (usually CMOS), one between each node of the chain and the output. The output
is taken from the appropriate tap by closing just one of the switches (there is some slight
digital complexity involved in decoding to 1 of 2N switches from N-bit data).
This architecture is simple, has a voltage output and is inherently monotonic—even if a
resistor is accidentally short-circuited, output n cannot exceed output n + 1. It is linear if
all the resistors are equal, but may be made deliberately nonlinear if a nonlinear DAC is
required. The output is a voltage, but it has the disadvantage of having a relatively large
output impedance. This output impedance is also code dependant (the impedance changes
with changes to the digital input). In many cases it will be beneficial to follow the output
of the DAC with an op amp to buffer this output impedance and present a low impedance
source to the following circuitry.
Since only two switches operate during a transition it is a low glitch architecture (the
concept of glitch will be examined in a following section). Also, the switching glitch is
not code-dependent, making it ideal for low distortion applications. Because the glitch is
constant regardless of the code transition, the frequency content of the glitch is at the
DAC update rate and its harmonics—not at the harmonics of the DAC output signal
frequency. The major drawback of the Kelvin DAC is the large number of resistors and
switches required for high resolution. There are 2N resistors required, so a 10 bit DAC
would require 1024 switches and resistors, and as a result it was not commonly used as a
simple DAC architecture until the recent advent of very small IC feature sizes made it
very practical for low and medium resolution (typically up to 10 bits) DACs.
6.4
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
VREF
R
R
3-TO-8
DECODER
R
8
R
TO
SWITCHES
R
3-BIT
DIGITAL
INPUT
ANALOG
OUTPUT
R
R
R
CIRCA 1920
SWITCHES WERE
RELAYS OR VACUUM TUBES
Figure 6.2: Simplest Voltage-Output Thermometer DAC:
The Kelvin Divider
As we mentioned in the section on sampling theory, the output of a DAC for an all 1s
code is 1 LSB below the reference, so a Kelvin divider DAC intended for use as a
general-purpose DAC has a resistor between the reference terminal and the first switch as
shown in Figure 6.2.
Segmented String DACs
A variation of the Kelvin divider is the segmented string DAC. Here we reduce the
number of resistors required by segmenting. Figure 6.3 shows two varieties of segmented
voltage-output DAC. The architecture in Figure 6.3A is sometimes called a KelvinVarley Divider. Since there are buffers between the first and second stages, the second
string DAC does not load the first, and the resistors in the second string do not need to
have the same value as the resistors in the first. All the resistors in each string, however,
do need to be equal to each other or the DAC will not be linear. The examples shown
have 3-bit first and second stages but for the sake of generality, let us refer to the first
(MSB) stage resolution as M-bits and the second (LSB) as K-bits for a total of N = M +
K bits. The MSB DAC has a string of 2M equal resistors and a string of 2K equal resistors
in the LSB DAC. As an example, if we make a 10-bit string DAC out of two 5-bit
sections, each segment would have 25 or 32 resistors, for a total of 64, as opposed to the
1024 required for a standard Kelvin divider. This is an obvious advantage.
6.5
BASIC LINEAR DESIGN
(A)
VREF
KELVIN-VARLEY DIVIDER
("STRING DAC")
A
B
(B)
A
VREF
KELVIN DIVIDER AND
R-2R LADDER NETWORK
OUTPUT
B
A
B
OUTPUT
A
B
NOTE:
MSB OF LADDER
ON RIGHT
A
B
A
A
B
IF THE LADDER NETWORK
IS MONOTONIC, THE
WHOLE DAC IS
MONOTONIC
Figure 6.3: Segmented Voltage-Output DACs
Buffer amplifiers can have offset, of course, and this can cause nonmonotonicity in a
buffered segmented string DAC.
In the simpler configuration of a buffered Kelvin-Varley divider buffer (Figure 6.3A),
buffer A is always “below” (at a lower potential than) buffer B, and the extra tap labeled
“A” on the LSB string DAC is not necessary. The data decoding is just two priority
encoders.
But if the decoding of the MSB string DAC is made more complex so that buffer A can
only be connected to the taps labeled “A” in the MSB string DAC, and buffer B to the
taps labeled “B,” then it is not possible for buffer offsets to cause nonmonotonicity. Of
course, the LSB string DAC decoding must change direction each time one buffer
“leapfrogs” the other, and taps A and B on the LSB string DAC are alternately not
used—but this involves a fairly trivial increase in logic complexity and is justified by the
increased performance.
Rather than using a second string of resistors, a binary R-2R DAC can be used to
generate the three LSBs as shown in Figure 6.3B. This voltage-output DAC (Figure 6.3B)
consists of a 3-bit string DAC followed by a 3-bit buffered voltage-mode ladder network.
Again the number of resistors require for the DAC is reduced.
An unbuffered version of the segmented string DAC is shown in Figure 6.4. This version
is more clever in concept. Here, the resistors in the two strings must be equal, except that
the top resistor in the MSB string must be smaller—1/2K of the value of the others—and
the LSB string has 2K – 1 resistors rather than 2K. Because there are no buffers, the LSB
string appears in parallel with the resistor in the MSB string that it is switched across and
loads it. This drops the voltage across that MSB resistor by 1 LSB of the LSB DAC—
which is exactly what is required. The output impedance of this DAC, being unbuffered,
6.6
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
varies with changing digital code. This circuit is intrinsically monotonic since it is
unbuffered (and, of course, can be manufactured on CMOS processes which make
resistors and switches but not high precision amplifiers, so it may be cheaper as well).
VREF
R
8
R
63 V
64 REF
55
64
48
64
R
R
R
R
R
R
R
R
40 V
64 REF
32 V
64 REF
24 V
64 REF
16 V
64 REF
8 V
64 REF
VREF
R
VREF
R
R
R
R
R
55 V
64 REF
54 V
64 REF
53 V
64 REF
52 V
64 REF
51 V
64 REF
OUTPUT
50 V
64 REF
49 V
64 REF
48 V
64 REF
Dennis Dempsey and Christopher Gorman, "Digital-to-Analog Converter,"
U.S. Patent 5,969,657, filed July 27, 1997, issued October 19, 1999.
Figure 6.4: Segmented Unbuffered String DACs Use Patented Architecture
In order to understand this clever concept better, the actual voltages at each of the taps
has been worked out and labeled for the 6-bit segmented DAC composed of two 3-bit
string DACs shown in Figure 6.4. The reader is urged to go through this simple analysis
with the second string DAC connected across any other resistor in the first string DAC
and verify the numbers. A detailed mathematical analysis of the unbuffered segmented
string DAC can be found in the relevant patent filed by Dennis Dempsey and Christopher
Gorman of Analog Devices in 1997 (Reference 14).
Digital Potentiometers
Another variation of the string DAC is the digital potentiometer. A simple digital
potentiometer is shown in Figure 6.5.
The major difference is that the lower arm of the potentiometer (terminal B) is not
connected to ground, but is instead left floating. The absolute values of the resistors in a
Kelvin DAC typically are not critical. They are limited by the available material. They
must, of course, be the same as each other. In a digital potentiometer the end-to-end
resistance is specified. The accuracy of the end to end resistance is on the order of a
6.7
BASIC LINEAR DESIGN
mechanical potentiometer. Digital potentiometers are typically available in end-to-end
resistance values from 10 kΩ to 1 MΩ. Lower values of end-to-end resistance are
difficult since the on resistance of the CMOS switches is on the order of the resistor
segment, so the linearity of the pot suffers at the low end.
TERMINAL A
3-TO-8
DECODER
R
R
8
R
TO
SWITCHES
3-BIT
DIGITAL
INPUT
TAP
R
R
R
R
TERMINAL B
Figure 6.5: A Slight Modification to a Kelvin DAC Yields a "Digital Potentiometer"
The advantages to digital potentiometers are many. Even the lowest resolution digital
potentiometers have better setability than their mechanical counterparts. Also, they are
immune to mechanical vibration and oxidation of the wiper contact. Obviously,
adjustments can be made without human intervention.
In most digital potentiometers the voltage on the input pins can not exceed the supplies
(typically 3 V or 5 V) due to the CMOS switches used in their construction, but certain
models are designed for ±15 V operation.
Another design feature on many of the digital potentiometers is that on power up
(sometimes from an internal timer, sometimes controlled by an external pin) the wiper is
shorted to one of the terminals. This is useful since output on power up is undefined until
it is written to. Since it might take a while (relatively) for the micro-controller to initialize
itself and then get around to initializing the rest of the system, having the digital
potentiometer in a known state can be useful. Some digital potentiometers incorporate
nonvolatile logic so that their settings are retained when they are turned off.
One time programmable (OTP) versions of digital potentiometers have become available.
Here the digital code is locked into the potentiometer once the setting had been
determined. The technology used is fuseable links. A variation on this theme is the two
6.8
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
times programeable (TTP) digital potentiometer. This allows the nonvolatile settings to
be modified one time. The block diagram of a TTP digital potentiometer is shown in
Figure 6.6.
A
VDD
1
AD1
SDA
SCL
FUSE
LINKS
B
2
RDAC
REGISTER
GND
AD0
W
ADDRESS
DECODE
/8
SERIAL INPUT
REGISTER
Figure 6.6: Two Times Programmable (TTP) Digital Potentiometer Block
Diagram
Thermometer (Fully Decoded) DACs
There is a current-output DAC architecture analogous to a string DAC which consists of
2N – 1 switchable current sources (which may be resistors and a voltage reference or may
be active current sources) connected to an output terminal. This output must be at, or
close to, ground. Figure 6.7 shows a thermometer DAC which use resistors connected to
a reference voltage to generate the currents.
If active current sources are used as shown in Figure 6.8, the output may have more
compliance (the allowable voltage on the output pin which still guarantees performance),
and a resistive load is typically used to develop an output voltage. The load resistor must
be chosen so that at maximum output current the output terminal remains within its rated
compliance voltage
Once a current in a thermometer DAC is switched into the circuit by increasing the
digital code, any further increases do not switch it out again. The structure is thus
inherently monotonic, irrespective of inaccuracies in the currents. Again, like the Kelvin
divider, only the advent of high density IC processes has made this architecture practical
for general purpose medium resolution DACs, although a slightly more complex
version—shown in the next diagram—is quite widely used in high speed applications.
Unlike the Kelvin divider, this type of current-mode DAC does not have a unique name,
although both types may be referred to as fully decoded DACs or thermometer DACs.
6.9
BASIC LINEAR DESIGN
VREF
R
R
R
R
R
R
R
3-TO-7
DECODER
7
CURRENT
OUTPUT INTO
VIRTUAL
GROUND
(USUALLY AN
OP-AMP I-V
CONVERTER)
TO
SWITCHES
3-BIT
DIGITAL
INPUT
Figure 6.7: The Simplest Current-Output Thermometer (Fully Decoded) DAC
A DAC where the currents are switched between two output lines—one of which is often
grounded, but may, in the more general case, be used as the inverted output—is more
suitable for high speed applications because switching a current between two outputs is
far less disruptive, and so causes a far lower glitch than simply switching a current on and
off. This architecture is shown in Figure 6.9.
I
I
I
I
I
I
I
3-TO-7
DECODER
7
TO
SWITCHES
3-BIT
DIGITAL
INPUT
Figure 6.8: Current Sources Improve the Basic
Current-Output Thermometer DAC
6.10
CURRENT
OUTPUT
MAY HAVE
COMPLIANCE
OF 1 OR 2 V
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
A
C
B
I
I
D
I
E
I
F
I
G
I
I
3-TO-7
DECODER
7
OUTPUT
3-BIT
DIGITAL
INPUT
TO
SWITCHES
CURRENT
OUTPUTS
MAY HAVE
COMPLIANCE
OF 1 OR 2 V
OUTPUT
Figure 6.9: High Speed Thermometer DAC with
Complementary Current Outputs
But the settling time of this DAC still varies with initial and final code, giving rise to
intersymbol distortion (ISI). This can be addressed with even more complex switching
where the output current is returned to zero before going to its next value. Note that
although the current in the output is returned to zero it is not “turned off”—the current is
dumped to ground when it is not being used, rather than being switched on and off. The
techniques involved are too complex to discuss in detail here but can be found in the
references.
In the normal (linear) version of this DAC, all the currents are nominally equal. Where it
is used for high speed reconstruction, its linearity can also be improved by dynamically
changing the order in which the currents are switched by ascending code. Instead of code
001 always turning on current A; code 010 always turning on currents A and B, code 011
always turning on currents A, B, and C; etc. the order of turn-on relative to ascending
code changes for each new data point. This can be done quite easily with a little extra
logic in the decoder. The simplest way of achieving it is with a counter which increments
with each clock cycle so that the order advances: ABCDEFG, BCDEFGA, CDEFGAB,
etc., but this algorithm may give rise to spurious tones in the DAC output. A better
approach is to set a new pseudo-random order on each clock cycle—this requires a little
more logic, but even complex logic is now very cheap and easily implemented on CMOS
processes. There are other, even more complex, techniques which involve using the data
itself to select bits and thus turn current mismatch into shaped noise. Again they are too
complex for a book of this sort. (See references for a more detailed discussion).
6.11
BASIC LINEAR DESIGN
Binary Weighted Current Source
The voltage-mode binary-weighted resistor DAC shown in Figure 6.10 is usually the
simplest textbook example of a DAC. However, this DAC is not inherently monotonic
and is actually quite hard to manufacture successfully at high resolutions due to the large
spread in component (resistor) values. In addition, the output impedance of the voltagemode binary DAC changes with the input code.
V
OUT
R/8
R/4
LSB
R/2
R
MSB
VREF
Adapted from: B. D. Smith, "Coding by Feedback Methods," Proceedings of the
I. R. E., Vol. 41, August 1953, pp. 1053-1058
Figure 6.10: Voltage-Mode Binary-Weighted Resistor DAC
Current-mode binary weighted DACs are shown in Figure 6.11A (resistor-based), and
Figure 6.11B (current-source based). An N-bit DAC of this type consists of N weighted
current sources (which may simply be resistors and a voltage reference) in the ratio
1:2:4:8:....:2N–1. The LSB switches the 2N–1 current, the MSB the 1 current, etc. The
theory is simple but the practical problems of manufacturing an IC of an economical size
with current or resistor ratios of even 128:1 for an 8-bit DAC are enormous, especially as
they must have matched temperature coefficients. This architecture is virtually never
used on its own in integrated circuit DACs, although, again, 3-bit or 4-bit versions have
been used as components in more complex structures. For example, the AD550
mentioned at the beginning of this section is an example of a binary-weighted DAC.
If the MSB current is slightly low in value, it will be less than the sum of all the other bit
currents, and the DAC will not be monotonic (the differential nonlinearity of most types
of DAC is worst at major bit transitions).
However, there is another binary-weighted DAC structure which has recently become
widely used. This uses binary-weighted capacitors as shown in Figure 6.12. The problem
with a DAC using capacitors is that leakage causes it to lose its accuracy within a few
milliseconds of being set. This may make capacitive DACs unsuitable for generalpurpose DAC applications, but it is not a problem in successive approximation ADCs,
6.12
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
since the conversion is complete in a few µs or less—long before leakage has any
appreciable effect.
(A) RESISTOR
(B) CURR ENT SOURCE
VREF
R
2R
4R
LSB
MSB
I
2
I
8R
I
4
I
8
LSB
MSB
CURR ENT OUTPUTS
INTO VIRTUAL GROUND S
DIFFICULT TO FABRICATE IN IC
FORM DUE TO LARGE RESISTOR OR CURRENT
RATIOS FOR HIGH RESOLUTIONS
Figure 6.11: Current-Mode Binary-Weighted DACs
BIT1
(MSB)
BIT2
SC
BIT3
(LSB)
A
CTOTAL = 2C
C
C/ 2
C/ 4
_
C/ 4
+
S1
S2
S3
S4
AIN
SIN
VREF
SWITCHES SHOWN IN TRACK (SAMPLE) MODE
Figure 6.12: Capacitive Binary-Weighted DAC in
Successive Approximation ADC
The use of capacitive charge redistribution DACs offers another advantage as well—the
DAC itself behaves as a sample-and-hold circuit (SHA), so not only is an external SHA
6.13
BASIC LINEAR DESIGN
unnecessary with these ADCs, there is no need to allocate separate chip area for a
separate integral SHA.
R-2R Ladder
One of the most common DAC building-block structures is the R-2R resistor ladder
network shown in Figure 3.15. It uses resistors of only two different values, and their
ratio is 2:1. An N-bit DAC requires 2N resistors, and they are quite easily trimmed. There
are also relatively few resistors to trim.
R
2R
2R
R
2R
R
2R
2R
Figure 6.13: 4-Bit R-2R Ladder Network
This structure is the basis of a large family of DACs. Figure 6.14 is the block diagram of
the AD7524, which is typical of a basic current output CMOS DAC. The diagram shows
the structure of the DAC.
DATA LATCHES
AD7524
Figure 6.14: AD7524 CMOS DAC Block Diagram
6.14
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
The input impedance (basically the value of the resistors) is not a closely specified
parameter. The specified range is 4:1 (5 kΩ min, 20 kΩ max, although it is typically
closer than that). It is the relative accuracy, not the absolute accuracy of the resistors that
is of interest. In most applications the absolute value is not important. Certain
applications exist where the value does matter. In these instances, the parts must be
selected at test.
Note the extra resistor added at the RFEEDBACK pin. This is designed to be the feedback
resistor for the I/V op amp. This resistor is trimmed along with the rest of the resistors so
it tracks. Also, since it is made of the same material as the rest of the resistors, therefore
having the same temperature coefficient, and is on the same substrate, hence at the same
temperature, it will track over temperature.
Figure 6.15 shows a more modern example of a CMOS DAC, the AD7394. Several
trends are obvious here. First off, the output is voltage, not current. Advancements in
process technology have allowed reasonable quality CMOS op amps to be created. Also
note the two ranks of latches. The purpose of these latches is to allow the microcontroller to write to all converters in a system and then update them all at the same time.
This will be covered on more detail in a later section. Note also the power on reset
circuit. Since the wake up state of a CMOS DAC is undefined and not repeatable, many
modern DACs include a circuit to force the output to either half scale of minimum scale,
depending on whether the intended application is unipolar or bipolar. Probably the most
obvious difference is that this is a multiple DAC package. Shrinking device geometries
have allowed more circuitry to be included, even with the smaller packages in use today.
Figure 6.15: AD7394 Quad CMOS DAC Block Diagram
6.15
BASIC LINEAR DESIGN
The previous examples were CMOS devices, that is to say, that the switches were
implemented with CMOS switches. The switches could also be implemented with bipolar
transistors (BJT). An example of this is the classic DAC-08. Its block diagram is shown
in Figure 6.16. One major difference in the BJT implementation is that the switch allows
current in one direction, versus the CMOS switch, which can allow bidirectional current.
This limits the BJT DAC to 2-quadrant operation while the CMOS version can be
4-quadrant. Supplies tend to be different as well.
V+
13
VLC
MSB
B1
1
5
B2
6
B3
7
B4
8
B5
9
B6
10
B7
11
(LSB)
B8
12
DAC08
VREF (+)
VREF (–)
BIAS
NETWORK
CURRENT
SWITCHES
14
4
2
IOUT
IOUT
15
REFERENCE
AMPLIFIER
16
3
COMP
V–
Figure 6.16: DAC-08 Block Diagram
There are two ways in which the R-2R ladder network may be used as a DAC—known
respectively as the voltage mode and the current mode (they are sometimes called
“normal” mode and “inverted” mode, but as there is no consensus on whether the voltage
mode or the current mode is the “normal” mode for a ladder network this nomenclature
can be misleading, although in most cases the current mode would be considered the
“normal” mode). Each mode has its advantages and disadvantages.
In the current-mode R-2R ladder DAC shown in Figure 6.17, the gain of the DAC may be
adjusted with a series resistor at the VREF terminal, since in the current mode, the end of
the ladder, with its code-independent impedance, is used as the VREF terminal; and the
ends of the arms are switched between ground and an output line which must be held at
ground potential. The normal connection of a current-mode ladder network output is to an
op amp’s inverting input (virtual ground), but stabilization of this op amp is complicated
by the DAC output impedance variation with digital code.
6.16
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
VREF
*
R
R
R
<< R
2R
2R
MSB
2R
2R
2R
LSB
CURRENT
OUTPUT
INTO
VIRTUAL
GROUND
* GAIN TRIM IF REQUIRED
Figure 6.17: Current-Mode R-2R Ladder Network DAC
Current-mode operation has a larger switching glitch than voltage mode since the
switches connect directly to the output line(s). However, since the switches of a currentmode ladder network are always at ground potential, their design is less demanding and,
in particular, their voltage rating does not affect the reference voltage rating. If switches
capable of carrying current in either direction (such as CMOS devices) are used, the
reference voltage may have either polarity, or may even be ac. Such a structure is one of
the most common types used as a multiplying DAC (MDAC) which will be discussed
later in this section.
Since the switches are always at, or very close to, ground potential, the maximum
reference voltage may greatly exceed the logic voltage, provided the switches are makebefore-break—which they are in this type of DAC. It is not unknown for a CMOS
MDAC to accept a ±30 V reference (or even a 60-V peak-to-peak ac reference) while
working from a single 5 V supply.
In the voltage mode R-2R ladder DAC shown in Figure 6.18, the “rungs” or arms of the
ladder are switched between VREF and ground, and the output is taken from the end of the
ladder. The output may be taken as a voltage, but the output impedance is independent of
code, so it may equally well be taken as a current into a virtual ground.
The voltage output is an advantage of this mode, as is the constant output impedance,
which eases the stabilization of any amplifier connected to the output node. Additionally,
the switches switch the arms of the ladder between a low impedance VREF connection and
ground, which is also, of course, low impedance, so capacitive glitch currents tend not to
flow in the load. On the other hand, the switches must operate over a wide voltage range
(VREF to ground), which is difficult from a design and manufacturing viewpoint, and the
reference input impedance varies widely with code, so that the reference input must be
driven from a very low impedance. In addition, the gain of the DAC cannot be adjusted
by means of a resistor in series with the VREF terminal.
6.17
BASIC LINEAR DESIGN
R
2R
2R
R
2R
LSB
V
OUT
R
2R
2R
MSB
VREF
Adapted from: B. D. Smith, "Coding by Feedback Methods," Proceedings of the
I. R. E., Vol. 41, August 1953, pp. 1053-1058
Figure 6.18: Voltage-Mode R-2R Ladder Network DAC
Probably the most important advantage to the voltage mode is that it allows single-supply
operation. This is because the op amp that is commonly used as I/V converter in the
current mode converter is in the inverting configuration so would require a negative
output for a positive input, assuming ground reference. Of course you could bias
everything up to a rail-splitter ground, but that introduces other issues into the system.
Multiplying DACs (MDACs)
In most cases the reference to a DAC is a highly stable dc voltage. In some instances,
however, it is useful to have a variable reference. The R-2R ladder structure using CMOS
switches can easily handle a bipolar signal on its input. Having the ability to have bipolar
(positive and negative) signals on the input allows construction of 2-quadrant and
4-quadrant Multiplying DACs. Figure 6.19 shows the schematic and Table I outlines the
operation of a 2-quadrant MDAC and Figure 6.20 shows the schematic and Table II
outlines the operation of a 4-quadrant MDAC for an 8-bit DAC.
DACs utilizing bipolar transistors as switches, such as the DAC-08 above, cannot
accommodate bipolar signals on the reference. Therefore they can only implement
2-quadrant MDACs. In addition, the reference voltage can not go all the way to 0 V. The
maximum allowable range is typically from 10% to 100% of the allowable reference
voltage range.
One of the main applications of the MDAC is as a variable gain amplifier, where the gain
is controlled by the digital word applied to the MDAC.
6.18
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
Figure 6.19: 2-Quadrant Multiplying DAC
Figure 6.20: 4-Quadrant Multiplying DAC
6.19
BASIC LINEAR DESIGN
The frequency response of the MDAC is limited by the parasitic capacitance across the
switches in the off condition. As the frequency goes up the impedance of the capacitors
goes down, effectively bypassing the switch. This reduces the off isolation at higher
frequencies. Typically the frequency response of an MDAC will be on the order of
1 MHz.
Segmented DACs
So far we have considered mostly basic DAC architectures. When we are required to
design a DAC with a specific performance, it may well be that no single architecture is
ideal. In such cases, two or more DACs may be combined in a single higher resolution
DAC to give the required performance. These DACs may be of the same type or of
different types and need not each have the same resolution. For example, the segmented
string DAC is a segmented DAC where 2 Kelvin DACs are cascaded.
Typically, one DAC handles the MSBs, another handles the LSBs, and their outputs are
added in some way. The process is known as “segmentation,” and these more complex
structures are called “segmented DACs.” There are many different types of segmented
DACs and some, but by no means all, will be illustrated in the next few diagrams. It is
sometimes not obvious from looking at the data sheet that a particular DAC is segmented.
- MSB THERMOMETER DAC
3-BIT
4- BIT R- 2R DAC
VREF
(A)
R
R
R
R
R
R
R
2R
R
R
R
2R
2R
2R
2R
RESISTOR
BASED
CURRENT
OUTPUT
IOUT
IOUT
- MSB THERMOMETER DAC
3-BIT
(B)
CURRENTSOURCE
BASED
I
I
I
I
I
I
4- BIT BINARY DAC
I
I
2
I
4
I
8
I
16
CURRENT
OUTPUT
IOUT
IOUT
Figure 6.21: Segmented Current-Output DACs:
(A) Resistor-Based, (B) Current-Source Based
Very high speed DACs for video, communications, and other HF reconstruction
applications are often built with arrays of fully decoded current sources. The two or three
6.20
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
LSBs may use binary-weighted current sources. It is extremely important that such DACs
have low distortion at high frequency, and there are several important issues to be
considered in their design.
Two examples of segmented current-output DAC structures are shown in Figure 6.21.
Figure 6.21A shows a resistor-based approach for the 7-bit DAC where the 3 MSBs are
fully decoded, and the 4 LSBs are derived from an R-2R network. Figure 6.21B shows a
similar implementation using current sources. The current source implementation is by
far the most popular for today's high-speed reconstruction DACs.
It is also often desirable to utilize more than one fully decoded thermometer section to
make up the total DAC. Figure 6.22 shows a 6-bit DAC constructed from two fully
decoded 3-bit DACs. As previously discussed, these current switches must be driven
simultaneously from parallel latches in order to minimize the output glitch.
- MSB THERMOMETER DAC
3-BIT
I
I
I
I
I
I
3- BIT LSB THERMOMETER DAC
I
I
8
I
8
I
8
I
8
I
8
I
8
I
8
CURRENT
OUTPUT
IOUT
IOUT
Figure 6.22: 6-Bit Current-Output Segmented DAC
Based on Two 3-Bit Thermometer DACs
The AD9775 14-bit, 160-MSPS (input)/400-MSPS (output) TxDAC™ uses three sections
of segmentation as shown in Figure 6.23. Other members of the AD977x-family and the
AD985x-family also use this same basic core.
The first 5 bits (MSBs) are fully decoded and drive 31 equally weighted current switches,
each supplying 512 LSBs of current. The next 4 bits are decoded into 15 lines which
drive 15 current switches, each supplying 32 LSBs of current. The 5 LSBs are latched
and drive a traditional binary-weighted DAC which supplies 1 LSB per output level. A
total of 51 current switches and latches are required to implement this ultra low glitch
architecture.
6.21
BASIC LINEAR DESIGN
5
31
31
BITS 1-5
DECODE
14
14-BIT
LATCH
5-TO-31
4
15
51-BIT
LATCH
I = 512 LSB
15
BITS 6-9
DECODE
CLOCK
15
CURRENT
SWITCHES
I = 32 LSB
4-TO-15
5
31
CURRENT
SWITCHES
5
5
5 BINARY
CURRENT
SWITCHES
I = 1 LSB
CURRENT
OUTPUT
FS =
2mA20mA
NOTE: Differential Outputs Not Shown
Figure 6.23: AD9775 TxDAC 14-Bit CMOS DAC Core
Decoding must be done before the new data is applied to the DAC so that all the data is
ready and can be applied simultaneously to all the switches in the DAC. This is generally
implemented by using a separate parallel latch for the individual switches in fully
decoded array. If all switches were to change state instantaneously and simultaneously
there would be no skew glitch—by very careful design of propagation delays around the
chip and time constants of switch resistance and stray capacitance the update
synchronization can be made very good, and hence the glitch-related distortion is very
small.
Sigma-Delta DACs
Sigma-Delta DACs will be discussed in detail in the Sigma-Delta section.
6.22
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
I/V Converters
Modern IC DACs provide either voltage or current outputs. Figure 6.24 below shows
three fundamental configurations, all with the objective of using an op amp for a buffered
output voltage.
(A)
+
N
+
R2
VOUT 1 + R1
–
VOUT
R1
(B)
R2
(C)
R2
IOUT•RL
+
N
–
N
–
IOUT
RL
1 + R2
R1
R2
IOUT
+
–IOUT•R2
R1
Figure 6.24: Buffering DAC Outputs with Op Amps
Figure 6.24A shows a buffered voltage output DAC. In many cases, the DAC output can
be used directly, without additional buffering. If an additional op amp is needed, it is
usually configured in a noninverting mode, with gain determined by R1 and R2.
There are two basic methods for dealing with a current output DAC.
A direct method to convert the output current into a voltage is shown in Figure 6.24C.
This circuit is usually called a current-to-voltage converter, or I/V. In this circuit, the
DAC output drives the inverting input of an op amp, with the output voltage developed
across the R2 feedback resistor. In this approach the DAC output always operates at
virtual ground (which may give a linearity improvement vis-à-vis Fig. 6.24B).
In Figure 6.24B, a voltage is simply developed across external load resistor, RL. This is
typically done with high speed op amps. An external op amp can be used to buffer and/or
amplify this voltage if required. The output current is dumped into a resistor instead of
into an op amp directly since the fast edges may exceed the slew rate of the amplifier and
cause distortion. Many DACs supply full-scale currents of 20 mA or more, thereby
allowing reasonable voltages to be developed across fairly low value load resistors. For
instance, fast settling video DACs typically supply nearly 30 mA full-scale current,
6.23
BASIC LINEAR DESIGN
allowing 1 V to be developed across a source and load terminated 75 Ω coaxial cable
(representing a dc load of 37.5 Ω to the DAC output).
The general selection process for an op amp used as a DAC buffer is that the performance
of the op amp should not compromise the performance of the DAC. The basic
specifications of interest are DC accuracy, noise, settling time, bandwidth, distortion, etc.
Differential to Single-Ended Conversion Techniques
A general model of a modern current output DAC is shown in Figure 6.25. This model is
typical of the AD976X and AD977X TxDAC series (see Reference 1).
Current output is more popular than voltage output, especially at audio frequencies and
above. If the DAC is fabricated on a bipolar or BiCMOS process, it is likely that the
output will sink current, and that the output impedance will be less than 500 Ω (due to the
internal R/2R resistive ladder network). On the other hand, a CMOS DAC is more likely
to source output current and have a high output impedance, typically greater than 100 kΩ.
IFS – I
IOUT
ROUT
I
ROUT
IOUT
RSET
Figure 6.25: Model of High Speed DAC Output
Another consideration is the output compliance voltage—the maximum voltage swing
allowed at the output in order for the DAC to maintain its linearity. This voltage is
typically 1 V to 1.5 V, but will vary depending upon the DAC. Best DAC linearity is
generally achieved when driving a virtual ground, such as an op amp I/V converter.
Modern current output DACs usually have differential outputs, to achieve high CM
rejection and reduce the even-order distortion products. Full-scale output currents in the
range of 2 to 20 mA are common.
In most applications, it is desirable to convert the differential output of the DAC into a
single-ended signal, suitable for driving a coax line. This can be readily achieved with an
6.24
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
RF transformer, provided low frequency response is not required. Figure 6.26 shows a
typical example of this approach. The high impedance current output of the DAC is
terminated differentially with 50 Ω, which defines the source impedance to the
transformer as 50 Ω.
The resulting differential voltage drives the primary of a 1:1 RF transformer, to develop a
single-ended voltage at the output of the secondary winding. The output of the 50 Ω LC
filter is matched with the 50 Ω load resistor RL, and a final output voltage of 1 V p-p is
developed.
MINI-CIRCUITS
T1-1T
1:1
0 TO 20mA
VLOAD = ± 0.5V
LC
FILTER
IOUT
RDIFF
= 50Ω
CMOS
DAC
RLOAD
= 50Ω
± 10mA
IOUT
20 TO 0mA
Figure 6.26: Differential Transformer Coupling
The transformer not only serves to convert the differential output into a single-ended
signal, but it also isolates the output of the DAC from the reactive load presented by the
LC filter, thereby improving overall distortion performance.
1kΩ
0 TO 20mA
0V TO +0.5V
500Ω
+5V
–
IOUT
25Ω
CMOS
DAC
± 1V
AD8055
CFILTER
+
–5V
500Ω
IOUT
20 TO 0mA
+0.5V TO 0V
f3dB =
25Ω
1kΩ
1
2π • 50Ω • CFILTER
Figure 6.27: Differential DC Coupled Output Using a Dual Supply Op Amp
6.25
BASIC LINEAR DESIGN
An op amp connected as a differential to single-ended converter can be used to obtain a
single-ended output when frequency response to DC is required. In Figure 6.28 the
AD8055 op amp is used to achieve high bandwidth and low distortion (see Reference 2).
The current output DAC drives balanced 25 Ω resistive loads, thereby developing an outof-phase voltage of 0 V to +0.5 V at each output. The AD8055 is configured for a gain of
8, to develop a final single-ended ground-referenced output voltage of 2 V p-p. Note that
because the output signal swings above and below ground, a dual-supply op amp is
required.
The CFILTER capacitor forms a differential filter with the equivalent 50 Ω differential
output impedance. This filter reduces any slew induced distortion of the op amp, and the
optimum cutoff frequency of the filter is determined empirically to give the best overall
distortion performance.
A modified form of the Figure 6.26 circuit can also be operated on a single supply,
provided the CM voltage of the op amp is set to mid-supply (+2.5 V). This is shown in
Figure 6.28. The output voltage is 2 V p-p centered around a CM voltage of +2.5 V. This
CM voltage can be either developed from the +5 V supply using a resistor divider, or
directly from a +2.5 V voltage reference. If the +5 V supply is used as the CM voltage, it
must be heavily decoupled to prevent supply noise from being amplified.
0 TO 20mA
0V TO +0.5V
500 Ω
+5V
–
IOUT
25Ω
CMOS
DAC
+2.5V
± 1V
AD8055
CFILTER
+
500 Ω
IOUT
+5V
2kΩ
20 TO 0mA
+0.5V TO 0V
25Ω
2kΩ
+5V
f3dB =
1
2π • 50Ω • CFILTER
1kΩ
+2.5V
REF
SEE TEXT
Figure 6.28: Differential DC Coupled Output Using a Single-Supply Op Amp
6.26
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
Single-Ended Current-to-Voltage Conversion
Single-ended current-to-voltage conversion is easily performed using a single op amp as
an I/V converter, as shown in Figure 6.29. The 10 mA full-scale DAC current from the
AD768 (see Reference 3) develops a 0 V to +2 V output voltage across the 200 Ω RF.
Driving the virtual ground of the AD8055 op amp minimizes any distortion due to
nonlinearity in the DAC output impedance. In fact, most high resolution DACs of this
type are factory trimmed using an I/V converter.
It should be recalled, however, that using the single-ended output of the DAC in this
manner will cause degradation in the CM rejection and increased second-order distortion
products, compared to a differential operating mode.
CF
RF = 200Ω
0 TO 10mA
IOUT
AD768
16-BIT
BiCMOS
DAC
+5V
–
RDAC||CDAC
CIN
0 TO +2.0V
AD8055
+
–5V
fu = Op Amp Unity
Gain-Bandwidth Product
IOUT
For RDAC ≈ RF, make CF ≈
For RDAC >> RF, make CF ≈
RDAC (CDAC + CIN)
RF
CDAC + CIN
2π RF fu
Figure 6.29: Single-Ended I/V Op Amp Interface for Precision 16-bit
AD768 DAC
The CF feedback capacitor should be optimized for best pulse response in the circuit. The
equations given in the diagram should only be used as guidelines. A more detailed
analysis of this circuit is given in the References.
Differential Current-to-Differential Voltage Conversion
If a buffered differential voltage output is required from a current output DAC, the
AD813X-series of differential amplifiers can be used as shown in Figure 6.30.
6.27
BASIC LINEAR DESIGN
The DAC output current is first converted into a voltage that is developed across the 25 Ω
resistors. The voltage is amplified by a factor of 5 using the AD813X. This technique is
used in lieu of a direct I/V conversion to prevent fast slewing DAC currents from
overloading the amplifier and introducing distortion. Care must be taken so that the DAC
output voltage is within its compliance rating.
2.49kΩ
0 TO 20mA
0 TO +0.5V
499Ω
+
IOUT
25Ω
CMOS
DAC
AD813X
5V p-p
DIFFERENTIAL
OUTPUT
499Ω
IOUT
–
20 TO 0mA
+0.5 TO 0V
2.49kΩ
25Ω
VOCM
Figure 6.30: Buffering High Speed DACs using AD813X Differential Amplifier
The VOCM input on the AD813X can be used to set a final output CM voltage within the
range of the AD813X. If transmission lines are to be driven at the output, adding a pair of
75 Ω resistors will allow this.
Digital Interfaces
The earliest monolithic DACs contained little, if any, logic circuitry, and parallel data had
to be maintained on the digital input to maintain the digital output. Today almost all
DACs are latched and data need only be written to them, not maintained. Some even have
nonvolatile latches and remember settings while turned off.
There are innumerable variations of DAC digital input structure, which will not be
discussed here, but the nearly all are described as “double-buffered.” A double-buffered
DAC has two sets of latches. Data is initially latched in the first rank and subsequently
transferred to the second as shown in Figure 6.31. There are two reasons why this
arrangement is useful.
The first is that it allows data to enter the DAC in many different ways. A DAC without a
latch, or with a single latch, must be loaded in parallel with all bits at once, since
otherwise its output during loading may be totally different from what it was or what it is
to become. A double-buffered DAC, on the other hand, may be loaded with parallel data,
or with serial data, or with 4-bit or 8-bit words, or whatever, and the output will be
6.28
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
unaffected until the new data is completely loaded and the DAC receives its update
instruction.
DIGITAL
INPUT
INPUT STRUCTURE:
MAY BE SERIAL,
PARALLEL, BYTE-WIDE,
ETC.
OUTPUT LATCH
TRANSFERS DATA
TO DAC TIMING IS
INDEPENDENT OF
INPUT
OUTPUT
DAC
fc = SAMPLING FREQUENCY
OUTPUT STROBE MAY GO TO MANY DACs
Figure 6.31: Double-Buffered DAC Permits Complex
Input Structures and Simultaneous Update
The other convenience of the double-buffered structure is that many DACs may be
updated simultaneously: data is loaded into the first rank of each DAC in turn, and when
all is ready, the output buffers of all the DACs are updated at once. There are many DAC
applications where the output of a number of DACs must change simultaneously, and the
double-buffered structure allows this to be done very easily.
Most early monolithic high resolution DACs had parallel or byte-wide data ports and
tended to be connected to parallel data buses and address decoders and addressed by
microprocessors as if they were very small write-only memories. (Some parallel DACs
are not write-only, but can have their contents read as well—this is convenient for some
applications, but is not very common.) A DAC connected to a data bus is vulnerable to
capacitive coupling of logic noise from the bus to the analog output Serial interfaces are
less vulnerable to such noise (since fewer noisy pins are involved), use fewer pins, and
therefore take less board space, and are frequently more convenient for use with modern
microprocessors, most of which have serial data ports. Some, but not all, of such serial
DACs have data outputs as well as data inputs so that several DACs may be connected in
series and data clocked to them all from a single serial port. This arrangement is often
referred to as "daisy-chaining."
Of course, serial DACs cannot be used where high update rates are involved, since the
clock rate of the serial data would be too high. Some very high speed DACs actually have
two parallel data ports and use them alternately in a multiplexed fashion (sometimes this
is called a “ping-pong” input) to reduce the data rate on each port as shown in
Figure 6.32. The alternate loading (ping-pong) DAC in the diagram loads from port A
and port B alternately on the rising and falling edges of the clock, which must have a
mark-space ratio close to 50:50. The internal clock multiplier ensures that the DAC itself
is updated with data A and data B alternately at exactly 50:50 time ratio, even if the
external clock is not so precise.
6.29
BASIC LINEAR DESIGN
DATA PORT A
N
N
LATCH
A
N
×2 CLOCK
MULTIPLIER
CLOCK
(50% DUTY
CYCLE)
DATA
MULTIPLEXER
N
OUTPUT
DAC
DATA PORT B
N
DAC
LATCH
LATCH
B
N
OUTPUT
Figure 6.32: Alternate Loading (Ping-Pong) High Speed DAC
Historically integrated circuit logic circuitry (with the exception of emitter coupled logic
or ECL) operated from 5 V supplies and had compatible logic levels—with a few
exceptions 5 V logic would interface with other 5 V logic. Today, with the advent of low
voltage logic operating with supplies of 3.3 V, 2.7 V, or even less, it is important to
ensure that logic interfaces are compatible. There are several issues which must be
considered—absolute maximum ratings, worst case logic levels, and timing. The logic
inputs of integrated circuits generally have absolute maximum ratings, as do most other
inputs, of 300 mV outside the power supply. Note that these are instantaneous ratings. If
an IC has such a rating and is currently operating from a +5 V supply then the logic
inputs may be between –0.3 V and +5.3 V—but if the supply is not present then that
input must be between +0.3 V and –0.3 V, not the –0.3 V to +5.3 V which are the limits
once the power is applied—ICs cannot predict the future.
The reason for the rating of 0.3 V is to ensure that no parasitic diode inside the IC is ever
turned on by a voltage outside the IC’s absolute maximum rating. It is quite common to
protect an input from such over-voltage with a Schottky diode clamp. At low
temperatures the clamp voltage of a Schottky diode may be a little more than 0.3 V, and
so the IC may see voltages just outside its absolute maximum rating. Although, strictly
speaking, this subjects the IC to stresses outside its absolute maximum ratings and so is
forbidden, this is an acceptable exception to the general rule provided the Schottky diode
is at a similar temperature to the IC that it is protecting (say within ±10°C).
Some low voltage devices, however, have inputs with absolute maximum ratings which
are substantially greater than their supply voltage. This allows such circuits to be driven
by higher voltage logic without additional interface or clamp circuitry. But it is important
to read the data sheets and ensure that both logic levels and absolute maximum voltages
are compatible for all combinations of high and low supplies.
This is the general rule when interfacing different low-voltage logic circuitry—it is
always necessary to check both that at the lowest value of its power supply the logic 1
6.30
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
output from the driving circuit applied to its worst-case load is greater than the specified
minimum logic 1 input for the receiving circuit, and that, again with its lowest value of
power supply and with its output sinking maximum allowed current, the logic 0 output is
less than the specified logic 0 input of the receiver. If the logic specifications of your
chosen devices do not meet these criteria it will be necessary to select different devices,
use different power supplies, or use additional interface circuitry to ensure that the
required levels are available. Note that additional interface circuitry will introduce extra
delays in timing.
It is not sufficient to build an experimental set-up and test it. In general, logic thresholds
are generously specified and usually logic circuits will work correctly well outside their
specified limits—but it is not possible to rely on this in a production design. At some
point a batch of devices near the limit on low output swing will be required to drive some
devices needing slightly more drive than usual—and will be unable to do so.
One of the latest developments in high speed logic interface is LVDS. Low voltage
differential signaling (LVDS) presents a solution to the high speed converter interface
problem by mitigating the effects of CMOS single-ended interfaces and accommodating
higher data rates. The LVDS standard specifies a p-p voltage swing of 350 mV around a
common-mode voltage of 1.2 V, which facilitates transmission of high-speed differential
digital signals with balanced current, thereby reducing the slew rate requirement.
Reducing the slew rate eliminates the gradients that result in noise from ground bounce
that are present in conventional CMOS drivers. Ground-bounce noise can couple back
into sensitive analog circuits and degrade the converter's dynamic range. Parallel LVDS
interfaces enable much higher data rates and optimum dynamic performance, in highspeed data converters.
LVDS also offers some benefit in reduced EMI. The EMI fields generated by the
opposing currents will tend to cancel each other (for matched edge rates). Trace length,
skew, and discontinuities will reduce this benefit and should be avoided.
LVDS also offers simpler timing constraints compared to a demuxed CMOS solution at
similar data rates. A demuxed databus requires a synchronization signal that is not
required in LVDS. In demuxed CMOS buses, a clock equal to one-half the ADC sample
rate is needed, adding cost and complexity, that is not required in LVDS. In general, the
LVDS is more forgiving and can lead to a simpler, cleaner design.
+1.2 V
350 mV
Figure 6.33: LVDS Output Levels
The LVDS specification (IEEE Standard 1596.3) was developed as an extension to the
1992 SCI protocol (IEEE Standard 1596-1992). The original SCI protocol was suitable
for high speed packet transmissions in high end computing and used ECL levels.
6.31
BASIC LINEAR DESIGN
However, for low end and power sensitive applications, a new standard was needed.
LVDS signals were chosen because the voltage swing is smaller than that of ECL
outputs, allowing for lower power supplies in power sensitive designs.
Unlike CMOS, which is typically a voltage output, LVDS is a current output technology.
LVDS outputs for high performance converters should be treated differently than
standard LVDS outputs used in digital logic. While standard LVDS can drive 1 m to
10 m in high speed digital applications (dependent on data rate), it is not recommended to
let a high performance converters drive that distance. It is recommended to keep the
output trace lengths short (<2 in.), minimizing the opportunity for any noise coupling
onto the outputs from the adjacent circuitry, which may get back to the analog outputs.
The differential output traces should be routed close together, maximizing common-mode
rejection with the 100 Ω termination resistor close to the receiver. Users should pay
attention to PCB trace lengths to minimize any delay skew.
A typical differential microstrip PCB trace cross section is shown in Figure 6.34.
Layout Guidelines
Keep TW, TS, and D constant over the trace length
Keep TS ~ < 2 TW
Avoid use of vias where possible
Keep D > 2 TS
Avoid 90° bends if possible
Design TW and TG for ~50 Ω
Figure 6.34: PCB Trace Spacing
Power supply decoupling is very important with these fast (<0.5 ns) edge rates. A low
inductance, surface-mount capacitor should be placed at every power supply and ground
pin as close to the converter as possible. Placing the decoupling caps on the other side of
the PCB is not recommended, since the via inductance will reduce the effective
decoupling. The differential ZO will tend to be slightly lower than twice the single-ended
ZO of each conductor due to proximity effects—the ZO of each line should be designed to
be slightly higher than 50 Ω. Simulation can be used in critical applications to verify
impedance matching. In short runs, this should not be critical.
6.32
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
Data Converter Logic: Timing and other Issues
It is not the purpose of this brief section to discuss logic architectures, so we shall not
define the many different data converter logic interface operations and their timing
specifications except to note that data converter logic interfaces may be more complex
than you expect—do not expect that because there is a pin with the same name on
memory and interface chips it will behave in exactly the same way in a data converter.
Unfortunately, there is not a standard nomenclature for pin functionality, even for the
same manufacturer. The data sheet should always be consulted to determine the operation
of all control pins. Also some data converters reset to a known state on power-up but
many more do not.
But it is very necessary to consider general timing issues. The new low voltage processes
which are used for many modern data converters have a number of desirable features.
One which is often overlooked by users (but not by converter designers!) is their higher
logic speed. DACs built on older processes frequently had logic which was orders of
magnitude slower than the microprocessors that they interfaced with and it was
sometimes necessary to use separate buffers, or multiple WAIT instructions, to make the
two compatible. Today it is much more common for the write times of DACs to be
compatible with those of the fast logic with which they interface.
Nevertheless not all DACs are speed compatible with all logic interfaces and it is still
important to ensure that minimum data set-up times and write pulse widths are observed.
Again, experiments will often show that devices work with faster signals than their
specification requires—but at the limits of temperature or supply voltage some may not
and interfaces should be designed on the basis of specified rather than measured timing.
Interpolating DACs (Interpolating TxDACs)
The concept of oversampling, to be discussed in another section (on sampling theory),
can be applied high speed DACs typically used in communications applications.
Oversampling relaxes the requirements on the output filter as well as increasing the SNR
due to process gain.
Assume a traditional DAC is driven at an input word rate of 30 MSPS (see
Figure 6.35A). Assume the DAC output frequency is 10 MHz. The image frequency
component at 30 MHz – 10 MHz = 20 MHz must be attenuated by the analog
reconstruction filter, and the transition band of the filter is therefore 10 MHz to 20 MHz.
Assume that the image frequency must be attenuated by 60 dB. The filter must therefore
go from a passband of 10 MHz to 60 dB stopband attenuation over the transition band
lying between 10 MHz and 20 MHz (one octave). Filter gives 6 dB attenuation per
octave for each pole. Therefore, a minimum of 10 poles is required to provide the desired
attenuation. This is a fairly aggressive filter and would involve high Q sections which
would be difficult to align and manufacture. Filters become even more complex as the
transition band becomes narrower.
6.33
BASIC LINEAR DESIGN
Assume that we increase the DAC update rate to 60 MSPS and insert a "zero" between
each original data sample. The parallel data stream is now 60 MSPS, but we must now
determine the value of the zero-value data points. This is done by passing the 60 MSPS
data stream with the added zeros through a digital interpolation filter which computes the
additional data points. The response of the digital filter relative to the 2-times
oversampling frequency is shown in Figure 6.35B. The analog antialiasing filter
transition zone is now 10 MHz to 50 MHz (the first image occurs at 2fc – fo = 60 – 10 =
50 MHz). This transition zone is a little greater than 2 octaves, implying that a 5-pole or
6-pole Butterworth filter is sufficient.
A
ANALOG LPF
fCLOCK = 30MSPS
dB
fo
IMAGE
IMAGE
10
20
30
40
IMAGE
50
IMAGE
60
70
80
FREQUENCY (MHz)
B
fCLOCK = 60MSPS
dB
fo
ANALOG
LPF
IMAGE
IMAGE
10
20
30
40
50
60
70
80
Figure 6.35: Analog Filter Requirements for fo = 10 MHz:
(A) fc = 30 MSPS, and (B) fc = 60 MSPS
The AD9773/AD9775/AD9777 (12-/14-/16-bit) series of Transmit DACs (TxDAC) are
selectable 2×, 4×, or 8× oversampling interpolating dual DACs, and a simplified block
diagram is shown in Figure 6.36. These devices are designed to handle 12-/14-/16-bit
input word rates up to 160 MSPS. The output word rate is 400 MSPS maximum. For an
output frequency of 50 MHz, an input update rate of 160 MHz, and an oversampling ratio
of 2×, the image frequency occurs at 320 MHz – 50 MHz = 270 MHz. The transition
band for the analog filter is therefore 50 MHz to 270 MHz. Without 2× oversampling, the
image frequency occurs at 160 MHz – 50 MHz = 110 MHz, and the filter transition band
is 60 MHz to 110 MHz.
6.34
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
N
fc
LATCH
N
PLL
DIGITAL
N
INTERPOLATION
FILTER
N
LATCH
K•fc
DAC
LPF
TYPICAL APPLICATION: fc = 160MSPS
fo = 50MHz
fo
K=2
Image Frequency = 320 – 50 = 270MHz
Figure 6.36: Oversampling Interpolating TxDAC Simplified Block Diagram
Reconstruction Filters
The output of a DAC is not a continuously varying waveform, but instead a series of dc
levels. This output must be passed through a filter to remove the high frequency
components and smooth waveform into a more truly analog waveform.
The concept of filtering is discussed in more detail in Chapter 8.
In general, to preserve spectral purity, the images of the DAC output must be attenuated
below the resolution of DAC. To use the example sited above, we assume that the DAC
output pass-band is 10 MHz. The sample rate is 30 MHz. Therefore the image of the
pass-band that must be attenuated is 30 MHz – 10 MHz = 20 MHz. This is the sample
rate minus the pass-band frequency. The DAC in this example is a 10-bit device, which
would indicate a distortion level of −60 dB. So a reconstruction filter should reduce the
image by 60 dB while not attenuating the fundamental at all. Since a filter attenuates at
6 dB/pole, this would indicate that a 10th order filter would be required.
There are several other considerations that must be taken into account.
First is that most filter cutoffs are measured at the −3 dB point. Therefore, if we do not
want the fundamental attenuated, some margin in the filter is required. The graphs in the
filter section will help illustrate this point. This will cause the transition band to become
narrower and thus the order of the filter to increase.
Secondly, there is a phenomenon called “sinc.”
6.35
BASIC LINEAR DESIGN
Sin(x)/(x) (sinc)
volts
The output of a D/A converter is not a continually varying wave form bit instead a series
of DC levels. The DAC puts out a dc level until it is told to put out a new level. This is
illustrated in Figure 6.37.
1
fs
τ=
tim e
τ
τ
τ
Figure 6.37: Output of a DAC
The width of the pulses is 1/FS. The spectrum of each pulse is the sin (x)/x curve. This is
also known as the sinc curve. This response is added to the response of the reconstruction
filter to provide the overall response of the converter. This will cause an amplitude error
as the output frequency approaches the Nyquist frequency (FS/2). The value of the sinc
function is shown in Figure 6.38. Some high speed DACs incorporate an inverse filter
(in the digital domain) to compensate for this rolloff.
0.00
-5.00
-10.00
-15.00
dB
-20.00
dB
-25.00
-30.00
-35.00
-40.00
-45.00
2.75
2.5
2.25
2
1.75
1.5
1.25
1
0.75
0.5
0.25
f
-50.00
FREQUENCY
Figure 6.38: Sinc (sin x/x) Curve (Normalized to FS)
6.36
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
Intentionally Nonlinear DACs
Thus far, we have emphasized the importance of maintaining good differential and
integral linearity. However, there are situations where ADCs and DACs which have been
made intentionally nonlinear (but maintaining good differential linearity) are useful,
especially when processing signals having a wide dynamic range. One of the earliest uses
of nonlinear data converters was in the digitization of voice-band signals for pulse code
modulation (PCM) systems. Major contributions were made at Bell Labs during the
development of the T1 carrier system. The motive for the nonlinear ADCs and DACs was
to reduce the total number of bits (and therefore the serial transmission rate) required to
digitize voice channels. Straight linear encoding of a voice channel required 11-bits or
12-bits at an 8 kSPS per channel sampling rate. In the 1960s Bell Labs determined that
7-bit nonlinear encoding was sufficient, and later in the 1970s went to 8-bit nonlinear
encoding for better performance.
The nonlinear transfer function allocates more quantization levels out of the total range
for small signals and fewer for large amplitude signals. In effect, this reduces the
quantization noise associated with small signals (where it is most noticeable) and
increases the quantization noise for larger signals (where it is less noticeable). The term
companding is generally used to describe this form of encoding.
The logarithmic transfer function chosen is referred to as the “Bell µ-255” standard, or
simply “µ-law.” A similar standard developed in Europe is referred to as “A-law.” The
Bell µ-law allows a dynamic range of about 4000:1 using 8 bits, whereas an 8-bit linear
data converter provides a range of only 256:1.
The first generation channel bank (D1) used temperature controlled resistor-diode
networks for “compressors” ahead of a 7-bit linear ADC in the transmitter to generate the
logarithmic transfer function. Corresponding resistor-diode “expandors” having an
inverse transfer function followed the 7-bit linear DAC in the receiver. The next
generation D2 channel banks used nonlinear ADCs and DACs to accomplish the
compression/expansion functions in a much more reliable and cost-effective manner and
eliminated the need for the temperature-controlled diode networks.
In his 1953 classic paper, B. D. Smith proposed that the transfer function of a successive
approximation ADC utilizing a nonlinear internal DAC in the feedback path would be the
inverse transfer function of the DAC (Reference 8). The same basic DAC could therefore
be used in the ADC and also for the reconstruction DAC. Later in the 1960s and early
1970s, nonlinear ADC and DAC technology using piecewise linear approximations of the
desired transfer function allowed low cost, high volume implementations (References 1823). These nonlinear 8-bit, 8-kSPS data converters became popular telecommunications
building blocks.
The nonlinear transfer function of the 8-bit DAC is first divided into 16 segments
(chords) of different slopes—the slopes are determined by the desired nonlinear transfer
function. The 4 MSBs determine the segment containing the desired data point, and the
individual segment is further subdivided into 16 equal quantization levels by the 4 LSBs
of the 8-bit word. This is shown in Figure 6.39 for a 6-bit DAC, where the first three bits
identify one of the eight possible chords, and each chord is further subdivided into eight
6.37
BASIC LINEAR DESIGN
equal levels defined by the 3 LSBs. The 3 MSBs are generated using a nonlinear string
DAC, and the 3 LSBs are generated using a 3-bit binary R-2R DAC.
V
REF
128R
NONLINEAR DIVIDER
R-2R DAC
LSB
128mV
V
REF = 2.048V
OUTPUT
LSB
64mV
LSB
32mV
64R
32R
LSB
16mV
16R
LSB
8mV
LSB
4mV
8R
LSB
2mV
4R
2R
R
LSB
1mV
DYNAMIC RANGE = 2048:1
(LINEARLY CODED 6-BIT
DYNAMIC RANGE = 64:1)
001000
011000
101000
111000
010000
100000
110000
111111
DIGITAL CODE
Figure 6.39: Nonlinear 6-Bit Segmented DAC
In 1982, Analog Devices introduced the LOGDAC™ AD7111 monolithic multiplying
DAC featuring wide dynamic range using a logarithmic transfer function. The basic DAC
in the LOGDAC is a linear 17-bit voltage-mode R-2R DAC preceded by an 8-bit input
decoder (A functional diagram of the LOGDAC is shown in Figure 6.40). The LOGDAC
can attenuate an analog input signal, VIN, over the range 0 dB to 88.5 dB in 0.375 dB
steps. The degree of attenuation across the DAC is determined by a nonlinear-coded 8-bit
word applied to the onboard decode logic. This 8-bit word is mapped into the appropriate
17-bit word which is then applied to a 17-bit, R-2R ladder. In addition to providing the
logarithmic transfer function, the LOGDAC also acts as a full four-quadrant multiplying
DAC.
With the introduction of high resolution linear ADCs and DACs, the method used in the
LOGDAC is widely used today to implement various nonlinear transfer functions such as
the µ-law and A-law companding functions required for telecommunications and other
applications. Figure 6.41 shows a general block diagram of the modern approach. The
µ-law or A-law companded input data is mapped into data points on the transfer function
of a high resolution DAC. This mapping can be easily accomplished by a simple lookup
table in either hardware, software, or firmware. A similar nonlinear ADC can be
constructed by digitizing the analog input signal using a high resolution ADC and
mapping the data points into a shorter word using the appropriate transfer function. A big
advantage of this method is that the transfer curve does not have to be approximated with
straight line segments as in the earlier method, thereby providing more accuracy.
6.38
CONVERTERS
DIGITAL-TO-ANALOG CONVERTER ARCHITECTURES
VIN
R
R
2R
2R
R
2R
2R
MSB
2R
RFB
LSB
IOUT
AGND
Figure 6.40: AD7111 LOGDAC (Released 1982)
M>N
INPUT
DATA
N-BITS
LOW RESOLUTION
NONLINEARLY
CODED DATA
DECODE
LOGIC
(LOOKUP
TABLE)
M-BITS
M-BITS
M-BIT
LATCH
DECODE LOGIC
CAN BE HARDWARE,
SOFTWARE,
OR FIRMWARE
M-BIT
LINEAR
DAC
HIGH RESOLUTION
LINEAR DAC
VOUT
NONLINEAR
ANALOG OUTPUT
Figure 6.41: General Nonlinear DAC
6.39
BASIC LINEAR DESIGN
SECTION 6.2: ANALOG-TO-DIGITAL CONVERTER
ARCHITECTURES
The basic ADC function is shown in Figure 6.42. This could also be referred to as a
quantizer. Most ADC chips also include some of the support circuitry, such as clock
oscillator for the sampling clock, reference (REF), the sample and hold function, and
output data latches. In addition to these basic functions, some ADCs have additional
circuitry built in. These functions could include multiplexers, sequencers, auto-calibration
circuits, programmable gain amplifiers (PGAs), etc.
VDD
SAMPLING
CLOCK
VREF
ANALOG
INPUT
ADC
DIGITAL
OUTPUT
EOC, DATA READY, ETC.
VSS
GROUND
(MAY BE INTERNALLY
CONNECTED TO VSS)
Figure 6.42: Basic ADC Function
Similar to DACs, some ADCs use external references and have a reference input
terminal, while others have an output from an internal reference. In some instances, the
ADC may have an internal reference that is pinned out through a resistor. This
connection allows the reference to be filtered (using the internal R and an external C) or
by allowing the internal reference to be overdriven by an external reference. The
AD789X family of parts is an example of ADC that use this type of connection. The
simplest ADCs, of course, have neither—the reference is on the ADC chip and has no
external connections.
If an ADC has an internal reference, its overall accuracy is specified when using that
reference. If such an ADC is used with a perfectly accurate external reference, its
absolute accuracy may actually be worse than when it is operated with its own internal
reference. This is because it is trimmed for absolute accuracy when working with its own
actual reference voltage, not with the nominal value. Twenty years ago it was common
for converter references to have accuracies as poor as ±5% since these references were
trimmed for low temperature coefficient rather than absolute accuracy, and the
inaccuracy of the reference was compensated in the gain trim of the ADC itself. Today
the problem is much less severe, but it is still important to check for possible loss of
6.40
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
absolute accuracy when using an external reference with an ADC which has a built-in
one.
ADCs which have reference terminals must, of course, specify their behavior and
parameters. If there is a reference input the first specification will be the reference input
voltage—and of course this has two values, the absolute maximum rating, and the range
of voltages over which the ADC performs correctly.
Most ADCs require that their reference voltage is within quite a narrow range whose
maximum value is less than or equal to the ADC's VDD.
The reference input terminal of an ADC may be buffered as shown in Figure 6.43, in
which case it has input impedance (usually high) and bias current (usually low)
specifications, or it may connect directly to the ADC. In either case, the transient currents
developed on the reference input due to the internal conversion process need good
decoupling with external low inductance capacitors. Good ADC data sheets recommend
appropriate decoupling networks.
Any, all or none of these pins may be
connected internally or brought off the chip.
VDD
SAMPLING
CLOCK
VREF
BUFFER
AMP
ANALOG
INPUT
ADC
VOLTAGE
REFERENCE
DATA
OUTPUT
EOC, DATA READY, ETC.
VSS
GROUND
(MAY BE INTERNALLY
CONNECTED TO VSS)
Figure 6.43: ADC with Reference and Buffer
The reference output may be buffered or unbuffered. If it is buffered, the maximum
output current will probably be specified. In general such a buffer will have a
unidirectional output stage which sources current but does not allow current to flow into
the output terminal. If the buffer does have a push-pull output stage (not as common), the
output current will probably be defined as ±(SOME VALUE) mA. If the reference output
is unbuffered, the output impedance may be specified, or the data sheet may simply
advise the use of a high input impedance external buffer.
There are some instances where the power supply is the reference. In these cases it is
imperative to make sure the power supply is clean.
6.41
BASIC LINEAR DESIGN
The sampling clock input is a critical function in an ADC and a source of some
confusion. It could truly be the sampling clock. This frequency would typically be
several times higher than the sampling rate of the converter. It could also be a convert
start (or encode) command which would happen once per conversion. Pipeline
architecture devices and sigma delta (Σ-Δ) converters are continuously converting and
have no convert start command.
Regardless of the ADC, it is extremely important to read the data sheet and determine
exactly what the external clock requirements are, because they can vary widely from one
ADC to another.
At some point after the assertion of the sampling clock, the output data is valid. This data
may be in parallel or serial format depending upon the ADC. Early successive
approximation ADCs such as the AD574 simply provided a STATUS output (STS)
which went high during the conversion, and returned to the low state when the output
data was valid. In other ADCs, this line is variously called busy, end-of-conversion
(EOC), data ready, etc. Regardless of the ADC, there must be some method of knowing
when the output data is valid—and again, the data sheet is where this information can
always be found.
Another detail which can cause trouble is the difference between EOC and DRDY (data
ready). EOC indicates that conversion has finished, DRDY that data is available at the
output. In some ADCs, EOC functions as DRDY—in others, data is not valid until
several tens of nanoseconds after the EOC has become valid, and if EOC is used as a data
strobe, the results will be unreliable.
There are one or two other practical points which are worth remembering about the logic
of ADCs. On power-up, many ADCs do not have logic reset circuitry and may enter an
anomalous logical state. Several conversions may be necessary to restore their logic to
proper operation so: (a) the first few conversions after power-up should never be trusted,
and (b) control outputs (EOC, data ready, etc.) may behave in unexpected ways at this
time (and not necessarily in the same way at each power-up), and (c) care should be taken
to ensure that such anomalous behavior cannot cause system latch-up. For example, EOC
(end-of-conversion) should not be used to initiate conversion if there is any possibility
that EOC will not occur until the first conversion has taken place, as otherwise initiation
will never occur.
Some low-power ADCs now have power-saving modes of operation variously called
standby, power-down, sleep, etc. When an ADC comes out of one of these low-power
modes, there is a certain recovery time required before the ADC can operate at its full
specified performance. The data sheet should therefore be carefully studied when using
these modes of operation.
As a final example, some ADCs use CS (Chip Select) edges to reset internal logic, and it
may not be possible to perform another conversion without asserting or reasserting CS
(or it may not be possible to read the same data twice, or both).
For more detail, it is important to read the whole data sheet before using an ADC since
there are innumerable small logic variations from type to type. Unfortunately, many data
6.42
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
sheets are not as clear as one might wish, so it is also important to understand the general
principles of ADCs in order to interpret data sheets correctly. That is one of the purposes
of this section.
There are a couple of general trend in ADCs that should be addressed. The first is the
general trend toward lower supply voltages. This is partially due to the processes,
particularly CMOS, which are used to manufacture the chips. Increasing demand for
speed has driven the feature size of the processes down. This typically results in lower
breakdown voltages for the transistors. This, in turn, requires lower supply voltages. Very
few new parts are developed with the legacy ±15 V supplies and ±10 V input range.
Since the input signal range of the ADCs is shrinking, there is also a trend towards
differential inputs. This helps improve the dynamic range of a converter, typically by
6 dB. There could be even further improvement since the common-mode ground
referenced noise is rejected. In many cases the differential input can be driven single
endedly (with the resultant reduction of SNR). Occasionally the REF input might also be
differential.
6.43
BASIC LINEAR DESIGN
The Comparator: A 1-Bit ADC
A comparator is a 1-bit ADC (see Figure 6.44). If the input is above a threshold, the
output has one logic value, below it has another. There is no ADC architecture which
does not use at least one comparator of some sort. So while a 1 bit ADC is of very
limited usefulness it is a building block for other architectures.
LATCH
ENABLE
+
DIFFERENTIAL
ANALOG INPUT
LOGIC
OUTPUT
–
COMPARATOR
OUTPUT
"1"
VHYSTERESIS
"0"
0
DIFFERENTIAL ANALOG INPUT
Figure 6.44: The Comparator: A 1-Bit ADC
Comparators used as building blocks in ADCs need good resolution which implies high
gain. This can lead to uncontrolled oscillation when the differential input approaches
zero. In order to prevent this, hysteresis is often added to comparators using a small
amount of positive feedback. Figure 6.44 shows the effects of hysteresis on the overall
transfer function. Many comparators have a millivolt or two of hysteresis to encourage
“snap” action and to prevent local feedback from causing instability in the transition
region. Note that the resolution of the comparator can be no less than the hysteresis, so
large values of hysteresis are generally not useful.
6.44
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
Successive Approximation ADCs
The successive approximation ADC has been the mainstay of data acquisition for many
years. Recent design improvements have extended the sampling frequency of these ADCs
into the megahertz region.
The basic successive approximation ADC is shown in Figure 6.45. It performs
conversions on command. On the assertion of the CONVERT START command, the
sample-and-hold (SHA) is placed in the hold mode, and all the bits of the successive
approximation register (SAR) are reset to “0” except the MSB which is set to “1.” The
SAR output drives the internal DAC. If the DAC output is greater than the analog input,
this bit in the SAR is reset, otherwise it is left set. The next most significant bit is then set
to “1.” If the DAC output is greater than the analog input, this bit in the SAR is reset,
otherwise it is left set. The process is repeated with each bit in turn. When all the bits
have been set, tested, and reset or not as appropriate, the contents of the SAR correspond
to the value of the analog input, and the conversion is complete. These bit “tests” can
form the basis of a serial output version SAR-based ADC.
CONVERT
START
TIMING
ANALOG
INPUT
COMPARATOR
SHA
DAC
CONTROL
LOGIC:
SUCCESSIVE
APPROXIMATION
REGISTER
(SAR)
EOC,
DRDY,
OR BUSY
OUTPUT
Figure 6.45: Basic Successive Approximation ADC
(Feedback Subtraction ADC)
The fundamental timing diagram for a typical SAR ADC is shown in Figure 6.46. The
end of conversion is generally indicated by an end-of-convert (EOC), data-ready
(DRDY), or a busy signal (actually, not-BUSY indicates end of conversion). The
polarities and name of this signal may be different for different SAR ADCs, but the
fundamental concept is the same. At the beginning of the conversion interval, the signal
goes high (or low) and remains in that state until the conversion is completed, at which
time it goes low (or high). The trailing edge is generally an indication of valid output
6.45
BASIC LINEAR DESIGN
data, but the data sheet should be carefully studied—in some ADCs additional delay is
required before the output data is valid.
SAMPLE X+1
SAMPLE X
SAMPLE X+2
CONVST
CONVERSION
TIME
TRACK/
ACQUIRE
CONVERSION
TIME
TRACK/
ACQUIRE
EOC,
BUSY
OUTPUT
DATA
DATA
X
DATA
X+1
Figure 6.46: Typical SAR ADC Timing
An N-bit conversion takes N steps. It would seem on superficial examination that a 16-bit
converter would have twice the conversion time of an 8-bit one, but this is not the case.
In an 8-bit converter, the DAC must settle to 8-bit accuracy before the bit decision is
made, whereas in a 16-bit converter, it must settle to 16-bit accuracy, which takes a lot
longer. In practice, 8-bit successive approximation ADCs can convert in a few hundred
nanoseconds, while 16-bit ones will generally take several microseconds.
While there are some variations, the fundamental timing of most SAR ADCs is similar
and relatively straightforward. The conversion process is initiated by asserting a
CONVERT START signal. This signal is typically named something like CONVST or
CS. This signal is a usually a negative-going pulse whose positive-going edge actually
initiates the conversion. The internal sample-and-hold (SHA) amplifier is placed in the
hold mode on this edge, and the various bits are determined using the SAR algorithm.
The negative-going edge of the CONVST pulse causes a signal typically called E OC
(End Of Conversion) or BUSY to go high. When the conversion is complete, the BUSY
line goes low (or E OC goes high), indicating the completion of the conversion process.
In most cases the trailing edge of the BUSY line can be used as an indication that the
output data is valid and can be used to strobe the output data into an external register.
There may also be other control lines. And sometimes control lines have dual function.
This is primarily done when the chip is pin limited. Because of the many variations in
terminology and design, the individual data sheet should always be consulted when using
a specific ADC.
6.46
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
It should also be noted that some SAR ADCs require an external high frequency clock in
addition to the CONVERT START command. In most cases, there is no need to
synchronize the two. The frequency of the external clock, if required, generally falls in
the range of 1 MHz to 30 MHz depending on the conversion time and resolution of the
ADC. Other SAR ADCs have an internal oscillator which is used to perform the
conversions and only require the CONVERT START command. Because of their
architecture, SAR ADCs generally allow single-shot conversion at any repetition rate
from dc to the converter's maximum conversion rate.
Notice that the overall accuracy and linearity of the SAR ADC is determined primarily by
the internal DAC. Until recently, most precision SAR ADCs used laser-trimmed thin-film
DACs to achieve the desired accuracy and linearity. The thin-film resistor trimming
process adds cost, and the thin-film resistor values may be affected when subjected to the
mechanical stresses of packaging.
For these reasons, switched capacitor (or charge-redistribution) DACs have become
popular in newer SAR ADCs. The advantage of the switched capacitor DAC is that the
accuracy and linearity is primarily determined by photolithography, which in turn
controls the capacitor plate area and the capacitance as well as matching. In addition,
small capacitors can be placed in parallel with the main capacitors which can be switched
in and out under control of autocalibration routines to achieve high accuracy and linearity
without the need for thin-film laser trimming. Temperature tracking between the switched
capacitors can be better than 1 ppm/ºC, thereby offering a high degree of temperature
stability.
BIT1
(MSB)
BIT2
SC
BIT3
(LSB)
A
CTOTAL = 2C
C
C/ 2
C/ 4
_
C/ 4
+
S1
S2
S3
S4
AIN
SIN
VREF
SWITCHES SHOWN IN TRACK (SAMPLE) MODE
Figure 6.47: 3-Bit Switched Capacitor DAC
6.47
BASIC LINEAR DESIGN
A simple 3-bit capacitor DAC is shown in Figure 6.47. The switches are shown in the
track, or sample mode where the analog input voltage, AIN, is constantly charging and
discharging the parallel combination of all the capacitors. The hold mode is initiated by
opening SIN, leaving the sampled analog input voltage on the capacitor array. Switch SC
is then opened allowing the voltage at node A to move as the bit switches are
manipulated. If S1, S2, S3, and S4 are all connected to ground, a voltage equal to –AIN
appears at node A. Connecting S1 to VREF adds a voltage equal to VREF/2 to –AIN. The
comparator then makes the MSB bit decision, and the SAR either leaves S1 connected to
VREF or connects it to ground depending on the comparator output (which is high or low
depending on whether the voltage at node A is negative or positive, respectively). A
similar process is followed for the remaining two bits. At the end of the conversion
interval, S1, S2, S3, S4, and SIN are connected to AIN, SC is connected to ground, and the
converter is ready for another cycle.
Note that the extra LSB capacitor (C/4 in the case of the 3-bit DAC) is required to make
the total value of the capacitor array equal to 2C so that binary division is accomplished
when the individual bit capacitors are manipulated.
The operation of the capacitor DAC (cap DAC) is similar to an R-2R resistive DAC.
When a particular bit capacitor is switched to VREF, the voltage divider created by the bit
capacitor and the total array capacitance (2 C) adds a voltage to node A equal to the
weight of that bit. When the bit capacitor is switched to ground, the same voltage is
subtracted from node A.
An example of charge redistribution successive approximation ADCs is Analog Devices’
PulSAR™ series. The AD7677 is a 16-bit, 1-MSPS, PulSAR, fully differential, ADC that
operates from a single 5 V power supply (see Figure 6.48). The part contains a high speed
16-bit sampling ADC, an internal conversion clock, error correction circuits, and both
serial and parallel system interface ports. The AD7677 is hardware factory calibrated and
comprehensively tested to ensure such ac parameters as signal-to-noise ratio (SNR) and
total harmonic distortion (THD), in addition to the more traditional dc parameters of gain,
offset, and linearity. It features a very high sampling rate mode (Warp) and, for
asynchronous conversion rate applications, a fast mode (Normal) and, for low power
applications, a reduced power mode (Impulse) where the power is scaled with the
throughput.
The operation of a successive approximation ADC is as follows. Using Figure 6.49 as an
example, one side of the balance is loaded with half scale (in this case 32 lbs.). Call this
the proof mass. The test mass is then put on the other side of the balance. If the test mass
is greater, as it is in this case, the proof mass is retained, otherwise it is discarded. Next a
proof mass equal to ¼ scale is added. Again, if the test mass is still greater the proof mass
is retained, otherwise it is rejected. It the example it is rejected. This process is continued,
each time cutting the proof mass in half, until the desired resolution is reached. The proof
masses are added up. This will equal the mass of the test mass, to the resolution of the
test.
6.48
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
Figure 6.48: AD7677 16-Bit 1-MSPS Switched Capacitor PulSAR ADC
In a SAR ADC the proof mass is a voltage provided by the DAC. It is compared to the
input, corresponding to the test mass, by the comparator. Keeping track of output of each
test and setting the DAC is accomplished by the successive approximation register.
The digital output is basically serial in nature, but SAR ADCs are generally available in
both serial and parallel output formats.
TEST
TOTALS:
X
ASSUME X = 45
IS X ≥ 32 ?
YES Î RETAIN 32 Î
1
IS X ≥ (32 +16) ?
NO Î REJECT 16 Î
0
IS X ≥ (32 +8) ?
YES Î RETAIN 8 Î
1
IS X ≥ (32 +8 + 4) ?
YES Î RETAIN 4 Î
1
IS X ≥ (32 +8 + 4 + 2) ?
NO Î REJECT 2 Î
0
IS X ≥ (32 +8 + 4 + 2 + 1) ?
YES Î RETAIN 1
1
X = 32 + 8 + 4 + 1 = 4510
=
Î
1011012
Figure 6.49: Successive Approximation ADC Algorithm
6.49
BASIC LINEAR DESIGN
Flash Converters
Flash ADCs (sometimes called parallel ADCs) are the fastest type of ADC and use large
numbers of comparators. An N-bit flash ADC consists of 2N resistors and 2N–1
comparators arranged as in Figure 6.50. Each comparator has a reference voltage which
is 1 LSB higher than that of the one below it in the chain. For a given input voltage, all
the comparators below a certain point will have their input voltage larger than their
reference voltage and a “1” logic output, and all the comparators above that point will
have a reference voltage larger than the input voltage and a “0” logic output. The 2N–1
comparator outputs therefore behave in a way analogous to a mercury thermometer, and
the output code at this point is sometimes called a thermometer code. Since 2N–1 data
outputs are not really practical, they are processed by a decoder to generate an N-bit
binary output.
STROBE
ANALOG
INPUT
+VREF
1.5R
R
R
R
PRIORITY
ENCODER
AND LATCH
N
DIGITAL
OUTPUT
R
R
R
0.5R
Figure 6.50: 3-Bit All-Parallel (Flash) Converter
The input signal is applied to all the comparators at once, so the thermometer output is
delayed by only one comparator delay from the input, and the encoder N-bit output by
only a few gate delays on top of that, so the process is very fast. However, the
architecture uses large numbers of resistors and comparators and is limited to low
resolutions, and if it is to be fast, each comparator must run at relatively high power
levels. Hence, the problems of flash ADCs include limited resolution, high power
dissipation because of the large number of high speed comparators (especially at
sampling rates greater than 50 MSPS), and relatively large (and therefore expensive) chip
sizes. In addition, the resistance of the reference resistor chain must be kept low to supply
6.50
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
adequate bias current to the fast comparators, so the voltage reference has to source quite
large currents (typically > 10 mA).
Each comparator has a voltage-variable junction capacitance, and this signal-dependent
capacitance results in most flash ADCs having reduced ENOB and higher distortion at
high input frequencies. For this reason, most flash converters must be driven with a
wideband op amp which is tolerant to the capacitive load presented by the converter as
well as high speed transients developed on the input.
Power dissipation is always a big consideration in flash converters, especially at
resolutions above eight bits. A clever technique was used AD9410 10-bit, 210 MSPS
ADC called interpolation to minimize the number of preamplifiers in the flash converter
comparators and also reduce the power (2.1 W). The method is shown in Figure 6.51 (see
reference).
ANALOG
INPUT
B
+
A2
V2
B
-
V2
LATCH
2
V1A
DECODE
V1A = V1 + V2
2
A1
V1
-
LATCH
1A
A
+
A
ANALOG
INPUT
V1
B
A
A
B
A
B
B
A
LATCH
1
LATCH
STROBE
AD9410: 10-Bits, 210MSPS
Figure 6.51: “Interpolating” Flash Reduces the Number
of Preamplifiers by Factor of Two
The preamplifiers (labeled “A1,” “A2,” etc.) are low-gain gm stages whose bandwidth is
proportional to the tail currents of the differential pairs. Consider the case for a positivegoing ramp input which is initially below the reference to AMP A1, V1. As the input
signal approaches V1, the differential output of A1 approaches zero (i.e., A = A ), and the
decision point is reached. The output of A1 drives the differential input of LATCH 1. As
the input signals continues to go positive, A continues to go positive, and B begins to go
negative. The interpolated decision point is determined when A = B . As the input
continues positive, the third decision point is reached when B = B . This novel
architecture reduces the ADC input capacitance and thereby minimizes its change with
signal level and the associated distortion. The AD9410 also uses an input sample-andhold circuit for improved ac linearity.
6.51
BASIC LINEAR DESIGN
Subranging, Error Corrected, and Pipelined ADCs
A basic, two-stage N-bit subranging ADC is shown in Figure 6.52. The ADC is based on
two separate conversions—a coarse conversion (N1 bits) in the MSB sub-ADC (SADC)
followed by a fine conversion (N2 bits) in the LSB sub-ADC. Early subranging ADCs
nearly always used flash converters as building blocks, but a number of recent ADCs
utilize other architectures for the individual ADCs.
The conversion process begins placing the sample-and-hold in the hold mode followed by
a coarse N1-bit sub-ADC (SADC) conversion of the MSBs. The digital outputs of the
MSB converter drive an N1-bit sub-DAC (SDAC) which generates a coarsely quantized
version of the analog input signal. The N1-bit SDAC output is subtracted from the held
analog signal, amplified, and applied to the N2-bit LSB SADC. The amplifier provides
gain, G, sufficient to make the “residue” signal exactly fill the input range of the
N2 SADC. The output data from the N1 SADC and the N2 SADC are latched into the
output registers yielding the N-bit digital output code, where N = N1 + N2.
ANALOG
INPUT
RESIDUE
SIGNAL
–
SAMPLE
AND HOLD
N1-BIT
SADC
N1-BIT
SDAC
+
Σ
G
N2-BIT
SADC
SAMPLING
CLOCK
CONTROL
OUTPUT REGISTER
N1 MSBs
DATA OUTPUT,
N2 LSBs
N-BITS = N1 + N2
See: R. Staffin and R. Lohman, "Signal Amplitude Quantizer,"
U.S. Patent 2,869,079, Filed December 19, 1956, Issued January 13, 1959
Figure 6.52: N-bit Two-Stage Subranging ADC
In order for this simple subranging architecture to work satisfactorily, both the N1 SADC
and SDAC (although they only have N1 bits of resolution) must be better than N-bits
accurate. The residue signal offset and gain must be adjusted such that it precisely fills
the range of the N2 SADC as shown in Figure 3.66A. If the residue signal drifts by more
than 1 LSB (referenced to the N2 SADC), then there will be missing codes as shown in
Figure 3.66B where the residue signal enters the out-of-range regions labeled “X” and
“Y.” Any nonlinearity or drift in the N1 SADC will also cause missing codes if it exceeds
1 LSB referenced to N-bits. In practice, an 8-bit subranging ADC with N1 = 4 bits and
N2 = 4 bits represents a realistic limit to this architecture in order to maintain no missing
codes over a reasonable operating temperature range.
6.52
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
0
1
2
2N1–2 2N1–1
3
(A)
IDEAL
N1 SADC
R = RANGE
OF N2 SADC
MISSING CODES
0
1
(B)
NONLINEAR
N1 SADC
2
X
R
3
Y
MISSING CODES
Figure 6.53: Residue Waveforms at Input of N2 Sub-ADC
When the interstage alignment is not correct, missing codes will appear in the overall
ADC transfer function as shown in Figure 6.54. If the residue signal goes into positive
overrange (the “X” region), the output first “sticks” on a code and then “jumps” over a
region leaving missing codes. The reverse occurs if the residue signal is negative
overrange.
"STICKS"
"JUMPS"
DIGITAL
OUTPUT
MISSING CODES
"JUMPS"
MISSING CODES
"STICKS"
ANALOG INPUT
Figure 6.54: Missing Codes Due to MSB SADC Nonlinearity or
Interstage Misalignment
6.53
BASIC LINEAR DESIGN
In order to reliably achieve higher than 8-bit resolution using the subranging approach, a
technique generally referred to as digital corrected subranging, digital error correction,
overlap bits, redundant bits, etc. is utilized.
Figure 6.55 shows two methods that can be used to design a pipeline stage in a
subranging ADC. Figure 6.55A shows two pipelined stages which use an interstage T/H
in order to provide interstage gain and give each stage the maximum possible amount of
time to process the signal at its input. In Figure 6.55B a multiplying DAC is used to
provide the appropriate amount of interstage gain as well as the subtraction function.
(A)
+
T/H
–
SADC
N1 BITS
SDAC
N1 BITS
–
+
Σ
+
T/H,
G
–
+
SADC
N2 BITS
SDAC
N2 BITS
–
Σ
TO ERROR CORRECTING LOGIC
(B)
+
T/H
–
SADC
N1 BITS
S MDAC
N1 BITS
+
T/H
–
SADC
N2 BITS
S MDAC
N2 BITS
TO ERROR CORRECTING LOGIC
Figure 6.55: Generalized Pipeline Stages in a
Subranging ADC with Error Correction
The term “pipelined” architecture refers to the ability of one stage to process data from
the previous stage during any given clock cycle. At the end of each phase of a particular
clock cycle, the output of a given stage is passed on to the next stage using the T/H
functions and new data is shifted into the stage. Of course this means that the digital
outputs of all but the last stage in the “pipeline” must be stored in the appropriate number
of shift registers so that the digital data arriving at the correction logic corresponds to the
same sample.
Figure 6.56 shows a timing diagram of a typical pipelined subranging ADC. Notice that
the phases of the clocks to the T/H amplifiers are alternated from stage to stage such that
when a particular T/H in the ADC enters the hold mode it holds the sample from the
preceding T/H, and the preceding T/H returns to the track mode. The held analog signal
is passed along from stage to stage until it reaches the final stage in the pipelined ADC—
in this case, a flash converter. When operating at high sampling rates, it is critical that the
differential sampling clock be kept at a 50% duty cycle for optimum performance. Duty
6.54
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
cycles other than 50% affect all the T/H amplifiers in the chain—some will have longer
than optimum track times and shorter than optimum hold times; while others suffer
exactly the reverse condition. Several newer pipelined ADCs including the 12-bit, 65MSPS AD9235 and the 12-bit, 210-MSPS AD9430 have on-chip clock conditioning
circuits to control the internal duty cycle while allowing some variation in the external
clock duty cycle.
CLOCK
CLOCK
VIN
T
H
INPUT
T/H
T
H
STAGE 1
T/H
T
H
STAGE 2
T/H
T
H
STAGE 3
T/H
H
FLASH
CLOCK
INPUT T/H
T
H
T
H
T
H
T
H
T
STAGE 1
H
T
H
T
H
T
H
T
H
STAGE 2
T
H
T
H
T
H
T
H
T
STAGE 3
H
T
H
T
H
T
H
T
H
FLASH
T
H
T
H
T
H
T
H
T
DATA OUT
DATA OUT
DATA OUT
DATA OUT
PIPELINE DELAY
Figure 6.56: Clock Issues in Pipelined ADCs
The effects of the “pipeline” delay (sometimes called latency) in the output data as shown
in Figure 6.57 for the AD9235 12-bit 65-MSPS ADC where there is a 7-clock cycle
pipeline delay.
PIPELINE DELAY (LATENCY) = 7 CLOCK CYCLES
Figure 6.57: Typical Pipelined ADC Timing for AD9235 12-Bit, 65-MSPS ADC
6.55
BASIC LINEAR DESIGN
Note that the pipeline delay is a function of the number of stages and the particular
architecture of the ADC under consideration—the data sheet should always be consulted
for the exact details of the relationship between the sampling clock and the output data
timing. In many applications the pipeline delay will not be a problem, but if the ADC is
inside a feedback loop the pipeline delay may cause instability. The pipeline delay can
also be troublesome in multiplexed applications or when operating the ADC in a "singleshot" mode. Other ADC architectures—such as successive approximation—may be better
suited to these types of applications.
The pipelined error correcting ADC has become very popular in modern ADCs requiring
wide dynamic range and low levels of distortion. There are many possible ways to design
a pipelined ADC, and we will now look at just a few of the tradeoffs. Figure 6.58A shows
a pipelined ADC designed with identical stages of k-bits each. This architecture uses the
same core hardware in each stage, offers a few other advantages, but does necessarily
optimize the ADC for best possible performance. Figure 6.58B shows the simplest form
of this architecture where k = 1.
+
VIN
k-BIT
ADC
T/H
+
Σ
2k
k-BIT
ADC
T/H
–
(A)
k-BITS
PER STAGE
2k
T/H
–
k-BIT
DAC
k
Σ
k
k-BIT
ADC
k-BIT
DAC
k
MSBs
LSBs
+
VIN
1-BIT
ADC
T/H
Σ
+
2
T/H
1-BIT
ADC
–
(B)
1-BIT
PER STAGE
1-BIT
DAC
Σ
2
T/H
–
1-BIT
DAC
MSB
1-BIT
ADC
LSB
Figure 6.58: Basic Pipelined ADC with Identical Stages
In order to optimize performance at the 12-bit level, for example, 1-bit per stage pipeline
is more commonly used with a multibit front-end and back-end ADC as shown in
Figure 6.59.
Another less popular type of error corrected subranging architecture is the recirculating
subranging ADC. The concept is similar to the error corrected subranging architecture
previously discussed, but in this architecture, the residue signal is recirculated through a
single ADC and DAC stage using switches and a programmable gain amplifier (PGA).
6.56
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
The major problem with this technique is the PGA. Its gain bandwidth product will limit
the frequency response at higher gains. Also matching of the various gains could be
problematic.
+
VIN
Σ
k-BIT
ADC
T/H
2k
–
k-BIT
DAC
k
MSBs
+
1-BIT
ADC
T/H
+
Σ
2
T/H
1-BIT
ADC
–
Σ
2
T/H
m-BIT
ADC
–
1-BIT
DAC
1-BIT
DAC
LSBs
1-BIT PIPELINED STAGES
Figure 6.59: Multibit and 1-Bit Pipelined Core Combined
ANALOG
INPUT
–
SAMPLE
AND HOLD
+
Σ
PGA
SAMPLING
CLOCK
3-BIT
FLASH
ADC
3-BIT
DAC
REG.
CONTROL
Adapted from:
D.J. Kinniment, D. Aspinall, and D.B.G. Edwards,
"High-Speed Analogue-Digital Converter,"
IEE Proceedings, Vol. 113, pp. 2061-2069, Dec. 1966
REG.
REG.
REG.
REG.
REG.
ADDER
OUTPUT REGISTER
DATA OUTPUT
Figure 6.60: Kinniment, et. al., 1966 Pipelined 7-bit, 9-MSPS
Recirculating ADC Architecture
6.57
BASIC LINEAR DESIGN
Serial Bit-Per-Stage Binary and Gray Coded (Folding) ADCs
Various architectures exist for performing A/D conversion using one stage per bit.
Figure 6.61 shows the overall concept. In fact, a multistage subranging ADC with one bit
per stage and no error correction is one form as previously discussed. In this approach,
the input signal must be held constant during the entire conversion cycle. There are
N stages, each of which has a bit output and a residue output. The residue output of one
stage is the input to the next. The last bit is detected with a single comparator as shown.
VREF
ANALOG
INPUT
STAGE
1
SHA
R1
BIT 1
MSB
STAGE
2
R2
STAGE
N-1
-
BIT N-1
BIT 2
+
BIT N
LSB
DECODE LOGIC AND OUTPUT REGISTERS
N
B. D. Smith, "An Unusual Electronic Analog-Digital Conversion Method,"
IRE Transactions on Instrumentation, June 1956, pp. 155-160.
Figure 6.61: Generalized Bit-Per-Stage ADC Architecture
+VR
RESIDUE
INPUT
Σ
G=2
INPUT
t
0
+
-VR
-
+VR
+VR
SWITCH POSITION
SHOWN FOR
NEGATIVE INPUT
BIT OUTPUT
(BINARY CODE)
-VR
RESIDUE
0
-VR
Figure 6.62: Single-Stage Transfer Function for Binary ADC
6.58
t
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
The basic stage for performing a single binary bit conversion is shown in Figure 6.62. It
consists of a gain-of-two amplifier, a comparator, and a 1-bit DAC. Assume that this is
the first stage of the ADC. The MSB is simply the polarity of the input, and that is
detected with the comparator which also controls the 1-bit DAC. The 1-bit DAC output is
summed with the output of the gain-of-two amplifier. The resulting residue output is then
applied to the next stage. In order to better understand how the circuit works, the diagram
shows the residue output for the case of a linear ramp input voltage which traverses the
entire ADC range, –VR to +VR. Notice that the polarity of the residue output determines
the binary bit output of the next stage.
A simplified 3-bit serial-binary ADC is shown in Figure 6.63, and the residue outputs are
shown in Figure 6.64. Again, the case is shown for a linear ramp input voltage whose
range is between –VR and +VR. Each residue output signal has discontinuities which
correspond to the point where the comparator changes state and causes the DAC to
switch. The fundamental problem with this architecture is the discontinuity in the residue
output waveforms. Adequate settling time must be allowed for these transients to
propagate through all the stages and settle at the final comparator input. As presented
here, the prospects of making this architecture operate at high speed are dismal. However
using the 1.5-bit-per stage pipelined architecture previously discussed in this section
makes it much more attractive at high speeds.
±VR
ANALOG
ANALOG
INPUT
INPUT
R1
SHA
STAGE
1
BIT 1
R2
STAGE
2
+
-
BIT 2
BIT 3
OUTPUT
REGISTER
OUTPUT
REGISTER
3
Figure 6.63: 3-Bit Serial ADC with Binary Output
Although the binary method is discussed in his paper, B. D. Smith also describes a much
preferred bit-per-stage architecture based on absolute value amplifiers (magnitude
amplifiers, or simply MagAMPs™). This scheme has often been referred to as serialGray (since the output coding is in Gray code), or folding converter because of the shape
of the transfer function. Performing the conversion using a transfer function that produces
an initial Gray code output has the advantage of minimizing discontinuities in the residue
output waveforms and offers the potential of operating at much higher speeds than the
binary approach.
6.59
BASIC LINEAR DESIGN
+VR
INPUT
t
0
–VR
R1
+VR
+VR
0
t
–VR
–VR
+VR
R2
+VR
0
t
–VR
–VR
BINARY
CODE
000
001
010
011
100
101
110
111
Figure 6.64: Input and Residue Waveforms of 3-Bit Binary Ripple ADC
The basic folding stage is shown functionally in Figure 6.65 along with its transfer
function. The input to the stage is assumed to be a linear ramp voltage whose range is
between –VR and +VR. The comparator detects the polarity of the input signal and
provides the Gray bit output for the stage. It also determines whether the overall stage
gain is +2 or –2. The reference voltage VR is summed with the switch output to generate
the residue signal which is applied to the next stage. The polarity of the residue signal
determines the Gray bit for the next stage. The transfer function for the folding stage is
also shown in Figure 6.65.
VR
INPUT
+VR
G = +2
INPUT
Σ
RESIDUE
0
t
G = -2
SWITCH POSITION
SHOWN FOR
NEGATIVE INPUT
-VR
+VR
+
RESIDUE
0
BIT OUTPUT
(GRAY CODE)
-VR
Figure 6.65: Folding Stage Functional Equivalent Circuit
6.60
t
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
A 3-bit MagAMP folding ADC is shown in Figure 6.66, and the corresponding residue
waveforms in Figure 6.67. As in the case of the binary ripple ADC, the polarity of the
residue output signal of a stage determines the value of the Gray bit for the next stage.
The polarity of the input to the first stage determines the Gray MSB; the polarity of R1
output determines the Gray bit-2; and the polarity of R2 output determines the Gray bit-3.
Notice that unlike the binary ripple ADC, there is no abrupt transition in any of the
folding stage residue output waveforms. This makes operation at high speeds quite
feasible.
±VR
ANALOG
INPUT
MAGAMP
2
MAGAMP
1
SHA
BIT 1
+
-
BIT 2
BIT 3
GRAY CODE REGISTER
3
GRAY-TO-BINARY CONVERTER
3
OUTPUT REGISTER
3
Figure 6.66: 3-bit Folding ADC Block Diagram
+VR
INPUT
t
0
–VR
R1
+VR
0
t
–VR
–VR
+VR
R2
+VR
0
t
–VR
GRAY
CODE
–VR
–VR
000
001
011
010
110
111
101
100
Figure 6.67: Input and Residue Waveforms for 3-Bit Folding ADC
6.61
BASIC LINEAR DESIGN
Modern IC circuit designs implement the transfer function using current-steering openloop gain techniques which can be made to operate much faster. Fully differential stages
(including the SHA) also provide speed, lower distortion, and yield 8-bit accurate folding
stages with no requirement for thin film resistor laser trimming.
An example of a fully differential gain-of-two MagAMP folding stage is shown in
Figure 6.68. The differential input signal is applied to the degenerated-emitter differential
pair Q1, Q2 and the comparator. The differential input voltage is converted into a
differential current which flows in the collectors of Q1, Q2. If +IN is greater than –IN,
cascode-connected transistors Q3, Q6 are on, and Q4, Q6 are off. The differential signal
currents therefore flow through the collectors of Q3, Q6 into level-shifting transistors Q7,
Q8, and into the output load resistors, developing the differential output voltage between
+OUT and –OUT. The overall differential voltage gain of the circuit is two.
If +IN is less than –IN (negative differential input voltage), the comparator changes stage
and turns Q4, Q5 on and Q3, Q6 off. The differential signal currents flow from Q5 to Q7
and from Q4 to Q8, thereby maintaining the same relative polarity at the differential
output as for a positive differential input voltage. The required offset voltage is developed
by adding a current IOFF to the emitter current of Q7 and subtracting it from the emitter
current of Q8.
The differential residue output voltage of the stage drives the next stage input, and the
comparator output represents the Gray code output for the stage.
2I - IOFF
2I + IOFF
Q7
VBIAS
Q3
Q8
VBIAS
Q4
Q5
Q6
+OUT
-OUT
i+
GRAY
GRAY
-
+
+IN
i-
-IN
Q2
Q1
R
I
R
R
I
Figure 6.68: A Modern Current-Steering MagAMP Stage
6.62
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
The MagAMP architecture offers lower power and can be extended to sampling rates
previously dominated by flash converters. For example, the AD9054A 8-bit, 200 MSPS
ADC is shown in Figure 6.69. The first five bits (Gray code) are derived from five
differential MagAMP stages. The differential residue output of the fifth MagAMP stage
drives a 3-bit flash converter, rather than a single comparator.
The Gray-code output of the five MagAMPs and the binary-code output of the 3-bit flash
are latched, all converted into binary, and latched again in the output data register.
Because of the high data rate, a demultiplexed output option is provided.
ANALOG
INPUT
SHA
DIFFERENTIAL
OUTPUTS ON
BITS 1 - 5
MAGAMP
1
MAGAMP
2
MAGAMP
3
MAGAMP
4
MAGAMP
5
BIT
1
GRAY
BIT
2
GRAY
BIT
3
GRAY
BIT
4
GRAY
BIT
5
GRAY
3-BIT
FLASH
ADC
3
BINARY
REGISTER
5
GRAY-TO-BINARY CONVERTER
3
5
OUTPUT REGISTERS
8
Figure 6.69: AD9054A 8-bit, 200-MSPS ADC Functional Diagram
6.63
BASIC LINEAR DESIGN
Counting and Integrating ADC Architectures
Although counting-based ADCs are not well suited for high speed applications, they are
ideal for high resolution, low frequency applications, especially when combined with
integrating techniques.
VOICE
INPUT
PULSE WIDTH
MODULATOR
SAMPLING
PULSE
6 kSPS
5-BIT
CK COUNTER
CLOCK
600 kHz
÷ 100
RESET
DATA
OUTPUT
READ-OUT PULSE
6 kSPS
Adapted from: Alec Harley Reeves, "Electric Signaling System,"
U.S. Patent 2,272,070, Filed November 22, 1939, Issued February 3, 1942
Figure 6.70: A. H. Reeves' 5-bit Counting ADC
The counting ADC technique (see Figure 6.70) basically uses a sampling pulse to take a
sample of the analog signal, set an R/S flip-flop, and simultaneously start a controlled
ramp voltage. The ramp voltage is compared with the input, and when they are equal, a
pulse is generated which resets the R/S flip-flop. The output of the flip-flop is a pulse
whose width is proportional to the analog signal at the sampling instant. This pulse width
modulated (PWM) pulse controls a gated oscillator, and the number of pulses out of the
gated oscillator represents the quantized value of the analog signal. This pulse train can
be easily converted to a binary word by driving a counter. In Reeves' system, a master
clock of 600 kHz was used, and a 100:1 divider generated the 6-kHz sampling pulses.
The system uses a 5-bit counter, and 31 counts (out of the 100 counts between sampling
pulses) therefore represents a full-scale signal. The technique can obviously be extended
to higher resolutions.
6.64
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
Charge Run-Down ADCs
The charge run-down ADC architecture shown in Figure 6.71 first samples the analog
input and stores the voltage on a fixed capacitor. The capacitor is then discharged with a
constant current source, and the time required for complete discharge is measured using a
counter. Notice that in this approach, the overall accuracy is dependent on the magnitude
of the capacitor, the magnitude of the current source, as well as the accuracy of the
timebase.
ANALOG
INPUT
+
–
C
I
COUNTER
CK
R
DIGITAL
OUTPUT
TIMER
AND
CONTROL
OSC.
Figure 6.71 Charge Run-Down ADC
Ramp Run-Up ADCs
In the ramp run-up architecture shown in Figure 6.71, a ramp generator is started at the
beginning of the conversion cycle. The counter then measures the time required for the
ramp voltage to equal the analog input voltage. The counter output is therefore
proportional to the value of the analog input. In an alternate version (shown dotted in
Figure 6.72), the ramp voltage generator is replaced by a DAC which is driven by the
counter output. The advantage of using the ramp is that the ADC is always monotonic,
whereas overall monotonicity is determined by the DAC when it is used as a substitute.
The accuracy of the ramp run-up ADC depends on the accuracy of the ramp generator (or
the DAC) as well as the oscillator.
6.65
BASIC LINEAR DESIGN
ANALOG
INPUT
+
–
* ALTERNATE
DAC
* RAMP
GENERATOR
COUNTER
CK
R
DIGITAL
OUTPUT
TIMER
AND
CONTROL
OSC.
Figure 6.72: Ramp Run-Up ADC
Tracking ADCs
The tracking ADC architecture shown in Figure 6.73 continually compares the input
signal with a reconstructed representation of the input signal. The up/down counter is
controlled by the comparator output. If the analog input exceeds the DAC output, the
counter counts up until they are equal. If the DAC output exceeds the analog input, the
counter counts down until they are equal. It is evident that if the analog input changes
slowly, the counter will follow, and the digital output will remain close to its correct
value. If the analog input suddenly undergoes a large step change, it will be many
hundreds or thousands of clock cycles before the output is again valid. The tracking ADC
therefore responds quickly to slowly changing signals, but slowly to a quickly changing
one.
The simple analysis above ignores the behavior of the ADC when the analog input and
DAC output are nearly equal. This will depend on the exact nature of the comparator and
counter. If the comparator is a simple one, the DAC output will cycle by 1 LSB from just
above the analog input to just below it, and the digital output will, of course, do the same
—there will be 1 LSB of flicker. Note that the output in such a case steps every clock
cycle, irrespective of the exact value of analog input, and hence always has unity
Mark/Space ratio. In other words, there is no possibility of taking a mean value of the
digital output and increasing resolution by oversampling.
6.66
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
ANALOG
INPUT
+
U/D
–
UP/DOWN
COUNTER
OSC.
DIGITAL
OUTPUT
CK
DAC
Figure 6.73: Tracking ADC
A more satisfactory, but more complex arrangement would be to use a window
comparator with a window 1-2 LSB wide. When the DAC output is high or low the
system behaves as in the previous description, but if the DAC output is within the
window, the counter stops. This arrangement eliminates the flicker, provided that the
DAC DNL never allows the DAC output to step across the window for 1 LSB change in
code.
Tracking ADCs are not very common. Their slow step response makes them unsuitable
for many applications, but they do have one asset: their output is continuously available.
Most ADCs perform conversions: i.e., on receipt of a “start convert” command (which
may be internally generated), they perform a conversion and, after a delay, a result
becomes available. Providing that the analog input changes slowly, the output of a
tracking ADC is always available. This is valuable in synchro-to-digital and resolver to
digital converters (SDCs and RDCs), and this is the application where tracking ADCs are
most often used. Another valuable characteristic of tracking ADCs is that a fast transient
on the analog input causes the output to change only one count. This is very useful in
noisy environments. Notice the similarity between a tracking ADC and a successive
approximation ADC. Replacing the up/down counter with SAR logic yields the
architecture for a successive approximation ADC.
6.67
BASIC LINEAR DESIGN
Voltage-to-Frequency Converters (VFCs)
A voltage-to-frequency converter (VFC) is an oscillator whose frequency is linearly
proportional to a control voltage (a high accuracy VCO). The VFC/counter ADC is
monotonic and free of missing codes, integrates noise, and can consume very little power.
It is also very useful for telemetry applications, since the VFC, which is small, cheap, and
low-powered can be mounted on the experimental subject (patient, wild animal, artillery
shell, etc.) and communicate with the counter by a telemetry link as shown in
Figure 6.74.
There are two common VFC architectures: the current- steering multivibrator VFC and
the charge-balance VFC. The charge-balanced VFC may be made in asynchronous or
synchronous (clocked) forms. There are many more VFO (variable frequency oscillator)
architectures, including the ubiquitous 555 timer, but the key feature of VFCs is
linearity—few VFOs are very linear.
ANALOG
INPUT
VFC
FREQUENCY
COUNTER
OUTPUT
‹ CONNECTION NEED NOT BE DIRECT
‹ CIRCUIT IS IDEAL FOR TELEMETRY
Figure 6.74: Voltage-to-Frequency Converter (VFC) and Frequency Counter
Make a Low Cost, Versatile, High-Resolution ADC
The current-steering multivibrator VFC is actually a current-to-frequency converter
rather than a VFC, but, as shown in Figure 6.75, practical circuits invariably contain a
voltage-to-current converter at the input. The principle of operation is evident: the current
discharges the capacitor until a threshold is reached, and when the capacitor terminals are
reversed, the half-cycle repeats itself. The waveform across the capacitor is a linear
tri-wave, but the waveform on either terminal with respect to ground is the more complex
waveform shown.
Practical VFCs of this type have linearities around 14-bits, and comparable stability,
although they may be used in ADCs with higher resolutions without missing codes. The
performance limits are set by comparator threshold noise, threshold temperature
coefficient, and the stability and dielectric absorption (DA) of the capacitor, which is
generally a discrete component. The comparator/voltage reference structure shown in the
diagram is more of a representation of the function performed than the actual circuit used,
which is much more integrated with the switching, and correspondingly harder to
analyze.
6.68
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
Figure 6.75: A Current Steering VFC
This type of VFC is simple, inexpensive, and low powered, and most run from a wide
range of supply voltages. They are ideally suited for low cost medium accuracy (12 bit)
ADC and data telemetry applications.
The charge balance VFC shown in Figure 6.76 is more complex, more demanding in its
supply voltage and current requirements, and more accurate. It is capable of 16-bit to
18-bit linearity.
ANALOG
INPUT
–
DIGITAL
OUTPUT
PRECISION
ONE-SHOT
+
FREQUENCY
COUNTER
VREF
FREQUENCY
OUTPUT
I
PRECISION
CURRENT
SOURCE
Figure 6.76: Charge Balance Voltage-to-Frequency Converter (VFC)
6.69
BASIC LINEAR DESIGN
The integrator capacitor charges from the signal as shown in Figure 6.76. When it passes
the comparator threshold, a fixed charge is removed from the capacitor, but the input
current continues to flow during the discharge, so no input charge is lost. The fixed
charge is defined by the precision current source and the pulse width of the precision
monostable. The output pulse rate is thus accurately proportional to the rate at which the
integrator charges from the input.
At low frequencies, the limits on the performance of this VFC are set by the stability of
the current source and the monostable timing (which depends on the monostable
capacitor, among other things). The absolute value and temperature stability of the
integration capacitor do not affect the accuracy, although its leakage and dielectric
absorption (DA) do. At high frequencies, second-order effects, such as switching
transients in the integrator and the precision of the monostable when it is retriggered very
soon after the end of a pulse, take their toll on accuracy and linearity.
The changeover switch in the current source addresses the integrator transient problem.
By using a changeover switch instead of the on/off switch more common on older VFC
designs: (a) there are no on/off transients in the precision current source and (b) the
output stage of the integrator sees a constant load—most of the time the current from the
source flows directly in the output stage; during charge balance, it still flows in the output
stage, but through the integration capacitor.
The stability and transient behavior of the precision monostable present more problems,
but the issue may be avoided by replacing the monostable with a clocked bistable
multivibrator. This arrangement is known as a synchronous VFC or SVFC and is shown
in Figure 6.77.
ANALOG
INPUT
CLOCK INPUT
–
DIGITAL
OUTPUT
+
D
D
FLIP-FLOP
FREQUENCY
COUNTER
VREF
FREQUENCY
OUTPUT
I
PRECISION
CURRENT
SOURCE
Figure 6.77: Synchronous VFC (SVFC)
6.70
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
The difference from the previous circuit is quite small, but the charge balance pulse
length is now defined by two successive edges of the external clock. If this clock has low
jitter, the charge will be very accurately defined. The output pulse will also be
synchronous with the clock. SVFCs of this type are capable of up to 18-bit linearity and
excellent temperature stability.
This synchronous behavior is convenient in many applications, since synchronous data
transfer is often easier to handle than asynchronous. It does mean, however, that the
output of an SVFC is not a pure tone (plus harmonics, of course) like a conventional
VFC, but contains components harmonically related to the clock frequency. The display
of an SVFC output on an oscilloscope is especially misleading and is a common cause of
confusion—a change of input to a VFC produces a smooth change in the output
frequency, but a change to an SVFC produces a change in probability density of output
pulses N and N+1 clock cycles after the previous output pulse, which is often
misinterpreted as severe jitter and a sign of a faulty device (see Figure 6.78).
Another problem with SVFCs is nonlinearity at output frequencies related to the clock
frequency. If we study the transfer characteristic of an SVFC, we find nonlinearities close
to sub-harmonics of the clock frequency FC as shown in Figure 6.79. They can be found
at FC/3, FC/4, and FC/6. This is due to stray capacitance on the chip (and in the circuit
layout!) and coupling the clock signal into the SVFC comparator which causes the device
to behave as an injection-locked, phase-locked loop (PLL). This problem is intrinsic to
SVFCs, but is not often serious: if the circuit card is well laid out, and clock amplitude
and dv/dts kept as low as practical, the effect is a discontinuity in the transfer
characteristic of less than 8 LSBs (at 18-bit resolution) at FC/3 and FC/4, and less at other
sub-harmonics. This is frequently tolerable, since the frequencies where it occurs are
known. Of course, if the circuit layout or decoupling is poor, the effect may be much
larger, but this is the fault of poor design and not the SVFC itself.
T
VFC
T VARIES SMOOTHLY WITH INPUT
T1
SVFC
T2
SVFC CLOCK
THE RELATIVE PROBABILITY OF DELAY
T1 OR T2 VARIES WITH INPUT, BUT
BOTH DELAYS DO OCCUR
Figure 6.78: VFC and SVFC Waveforms
6.71
BASIC LINEAR DESIGN
‹ NONLINEARITIES CAUSED BY
INJECTION LOCKING DUE TO CLOCK
FEEDTHROUGH
‹ SHOULD ONLY BE 6-8 LSBs AT
18-BITS WITH PROPER LAYOUT AND
DECOUPLING
‹ NONLINEARITIES OCCUR AT
SUBHARMONICS OF THE CLOCK,
WHERE FS = FCLOCK/2
Figure 6.79: SVFC Nonlinearity
It is evident that the SVFC is quantized, while the basic VFC is not. It does NOT follow
from this that the counter/VFC ADC has higher resolution (neglecting nonlinearities)
than the counter/SVFC ADC, because the clock in the counter also sets a limit to the
resolution.
When a VFC has a large input, it runs quickly and (counting for a short time) gives good
resolution, but it is hard to get good resolution in a reasonable sample time with a
slow-running VFC. In such a case, it may be more practical to measure the period of the
VFC output (this does not work for an SVFC), but of course the resolution of this system
deteriorates as the input (and the frequency) increases. However, if the counter/timer
arrangement is made “smart,” it is possible to measure the approximate VFC frequency
and the exact period of not one, but N cycles (where the value of N is determined by the
approximate frequency), and maintain high resolution over a wide range of inputs. The
AD1170 modular ADC released in 1986 is an example of this architecture.
VFCs have more applications than as a component in ADCs. Since their output is a pulse
stream, it may easily be sent over a wide range of transmission media (PSN, radio,
optical, IR, ultrasonic, etc.). It need not be received by a counter, but by another VFC
configured as a frequency-to-voltage converter (FVC). This gives an analog output, and a
VFC-FVC combination is a very useful way of sending a precision analog signal across
an isolation barrier.
6.72
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
Dual Slope/Multi-Slope ADCs
The dual-slope ADC architecture was truly a breakthrough in ADCs for high resolution
applications such as digital voltmeters (DVMs), etc. A simplified diagram is shown in
Figure 6.80, and the integrator output waveforms are shown in Figure 6.81.
ANALOG
INPUT
VIN
C
R
–
–VREF
+
TIMER AND
CONTROL
DIGITAL
OUTPUT
COUNTER
CK
R
OSC.
Figure 6.80: Dual slope ADC
SLOPE =
VIN
SLOPE =
RC
VREF
RC
(CONSTANT SLOPE)
t
0
T
tx
VIN
RC
T
=
tx
=
VREF
RC
tx
VIN
VREF
T
HIGH NORMAL MODE REJECTION AT MULTIPLES OF
1
T
Figure 6.81: Dual Slope ADC Integrator Output Waveforms
The input signal is applied to an integrator; at the same time a counter is started, counting
clock pulses. After a predetermined amount of time (T), a reference voltage having
opposite polarity is applied to the integrator. At that instant, the accumulated charge on
6.73
BASIC LINEAR DESIGN
the integrating capacitor is proportional to the average value of the input over the interval
T. The integral of the reference is an opposite-going ramp having a slope of VREF/RC. At
the same time, the counter is again counting from zero. When the integrator output
reaches zero, the count is stopped, and the analog circuitry is reset. Since the charge
gained is proportional to VIN · T, and the equal amount of charge lost is proportional to
VREF · tx, then the number of counts relative to the full scale count is proportional to tx/T,
or VIN/VREF. If the output of the counter is a binary number, it will therefore be a binary
representation of the input voltage.
Dual-slope integration has many advantages. Conversion accuracy is independent of both
the capacitance and the clock frequency, because they affect both the up-slope and the
down-slope by the same ratio.
The fixed input signal integration period results in rejection of noise frequencies on the
analog input that have periods that are equal to or a sub-multiple of the integration time
T. Proper choice of T can therefore result in excellent rejection of 50-Hz or 60-Hz line
ripple as shown in Figure 6.82.
Errors caused by bias currents and the offset voltages of the integrating amplifier and the
comparator as well as gain errors can be cancelled by using additional charge/discharge
cycles to measure “zero” and “full-scale” and using the results to digitally correct the
initial measurement, as in the quad-slope architecture.
Figure 6.82: Frequency Response of Integrating ADC
6.74
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
The triple-slope architecture retains the advantages of the dual-slope, but greatly
increases the conversion speed at the cost of added complexity. The increase in
conversion speed is achieved by accomplishing the reference integration (ramp-down) at
two distinct rates: a high-speed rate, and a “vernier” lower speed rate. The counter is
likewise divided into two sections, one for the MSBs and one for the LSBs. In a properly
designed triple-slope converter, a significant increase in speed can be achieved while
retaining the inherent linearity, differential linearity, and stability characteristics
associated with dual-slope ADCs.
6.75
BASIC LINEAR DESIGN
Resolver-to-Digital Converters (RDCs) and Synchros
Machine-tool and robotics manufacturers have increasingly turned to resolvers and
synchros to provide accurate angular and rotational information. These devices excel in
demanding factory applications requiring small size, long-term reliability, absolute
position measurement, high accuracy, and low noise operation.
A diagram of a typical synchro and resolver is shown in Figure 6.83. Both synchros and
resolvers employ single-winding rotors that revolve inside fixed stators. In the case of a
simple synchro, the stator has three windings oriented 120º apart and electrically
connected in a Y-connection. Resolvers differ from synchros in that their stators have
only two windings oriented at 90º.
S1
S2
STATOR
SYNCHRO
ROTOR
ROTOR
R1
θ
S1 TO S3 = V sin ωt sin θ
S3 TO S2 = V sin ωt sin (θ + 120°)
S2 TO S1 = V sin ωt sin (θ + 240°)
V sin ωt
R2
S3
ROTOR
S4
R1
STATOR
V sin ωt
S1 TO S3 = V sin ωt sin θ
S4 TO S2 = V sin ωt sin (θ + 90°)
= V sin ωt cos θ
S2
STATOR
R2
S3
RESOLVER
S1
Figure 6.83: Synchros and Resolvers
Because synchros have three stator coils in a 120º orientation, they are more difficult than
resolvers to manufacture and are therefore more costly. Today, synchros find decreasing
use, except in certain military and avionic retrofit applications.
Modern resolvers, in contrast, are available in a brushless form that employ a transformer
to couple the rotor signals from the stator to the rotor. The primary winding of this
transformer resides on the stator, and the secondary on the rotor. Other resolvers use
more traditional brushes or slip rings to couple the signal into the rotor winding.
Brushless resolvers are more rugged than synchros because there are no brushes to break
or dislodge, and the life of a brushless resolver is limited only by its bearings. Most
resolvers are specified to work over 2 V to 40 V rms and at frequencies from 400 Hz to
10 kHz. Angular accuracies range from 5 arc-minutes to 0.5 arc-minutes. (There are
6.76
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
60 arc-minutes in one degree, and 60 arc-seconds in one arc-minute. Hence, one
arc-minute is equal to 0.0167 degrees).
In operation, synchros and resolvers resemble rotating transformers. The rotor winding is
excited by an ac reference voltage, at frequencies up to a few kHz. The magnitude of the
voltage induced in any stator winding is proportional to the sine of the angle, θ, between
the rotor coil axis and the stator coil axis. In the case of a synchro, the voltage induced
across any pair of stator terminals will be the vector sum of the voltages across the two
connected coils.
For example, if the rotor of a synchro is excited with a reference voltage, Vsinωt, across
its terminals R1 and R2, then the stator's terminal will see voltages in the form:
S1 to S3 = V sinωt sinθ
S3 to S2 = V sinωt sin (θ + 120º)
S2 to S1 = V sinωt sin (θ + 240º),
Eq. 6.1
Eq. 6.2
Eq. 6.3
where θ is the shaft angle.
In the case of a resolver, with a rotor ac reference voltage of Vsinωt, the stator's terminal
voltages will be:
S1 to S3 = V sinωt sin θ
S4 to S2 = V sinωt sin(θ + 90º) = V sinωt cosθ.
Eq. 6.4
Eq. 6.5
It should be noted that the 3-wire synchro output can be easily converted into the
resolver-equivalent format using a Scott-T transformer. Therefore, the following signal
processing example describes only the resolver configuration.
A typical resolver-to-digital converter (RDC) is shown functionally in Figure 6.84. The
two outputs of the resolver are applied to cosine and sine multipliers. These multipliers
incorporate sine and cosine lookup tables and function as multiplying digital-to-analog
converters. Begin by assuming that the current state of the up/down counter is a digital
number representing a trial angle, ϕ. The converter seeks to adjust the digital angle, ϕ,
continuously to become equal to, and to track θ, the analog angle being measured. The
resolver's stator output voltages are written as:
V1 = V sinωt sinθ
V2 = V sinωt cosθ
Eq. 6.6
Eq. 6.7
where θ is the angle of the resolver’s rotor. The digital angle ϕ is applied to the cosine
multiplier, and its cosine is multiplied by V1 to produce the term:
V sinωt sinθ cosϕ.
Eq. 6.8
The digital angle ϕ is also applied to the sine multiplier and multiplied by V2 to product
the term:
Eq. 6.9
V sinωt cosθ sinϕ.
6.77
BASIC LINEAR DESIGN
V sin ωt
V sin ωt sin θ
ROTOR REFERENCE
COSINE
MULTIPLIER
STATOR
INPUTS
V sin ωt cos θ
V sin ωt sin θ cos ϕ
_
ϕ
SINE
MULTIPLIER
V sin ωt [sin (θ – ϕ )]
DETECTOR
+
V sin ωt cos θ sin ϕ
ERROR
ϕ
UP / DOWN
COUNTER
K sin (θ – ϕ )
INTEGRATOR
VCO
ϕ = DIGITAL ANGLE
VELOCITY
LATCHES
ϕ
WHEN ERROR = 0,
ϕ = θ ± 1 LSB
Figure 6.84: Resolver-to-Digital Converter (RDC)
These two signals are subtracted from each other by the error amplifier to yield an ac
error signal of the form:
V sinωt [sinθ cosϕ – cosθ sinϕ].
Eq. 6.10
Using a simple trigonometric identity, this reduces to:
V sinωt [sin (θ –ϕ)].
Eq. 6.11
The detector synchronously demodulates this ac error signal, using the resolver’s rotor
voltage as a reference. This results in a dc error signal proportional to sin(θ–ϕ).
The dc error signal feeds an integrator, the output of which drives a voltage-controlledoscillator (VCO). The VCO, in turn, causes the up/down counter to count in the proper
direction to cause:
Sin (θ – ϕ) → 0.
Eq. 6.12
When this is achieved,
θ – ϕ → 0,
Eq. 6.13
ϕ=θ
Eq. 6.14
and therefore
6.78
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
to within one count. Hence, the counter’s digital output,ϕ, represents the angle θ. The
latches enable this data to be transferred externally without interrupting the loop's
tracking.
This circuit is equivalent to a so-called type-2 servo loop, because it has, in effect, two
integrators. One is the counter, which accumulates pulses; the other is the integrator at the
output of the detector. In a type-2 servo loop with a constant rotational velocity input, the
output digital word continuously follows, or tracks the input, without needing externally
derived convert commands, and with no steady state phase lag between the digital output
word and actual shaft angle. An error signal appears only during periods of acceleration
or deceleration.
As an added bonus, the tracking RDC provides an analog dc output voltage directly
proportional to the shaft's rotational velocity. This is a useful feature if velocity is to be
measured or used as a stabilization term in a servo system, and it makes tachometers
unnecessary.
Since the operation of an RDC depends only on the ratio between input signal
amplitudes, attenuation in the lines connecting them to resolvers doesn’t substantially
affect performance. For similar reasons, these converters are not greatly susceptible to
waveform distortion. In fact, they can operate with as much as 10% harmonic distortion
on the input signals; some applications actually use square-wave references with little
additional error.
Tracking ADCs are therefore ideally suited to RDCs. While other ADC architectures,
such as successive approximation, could be used, the tracking converter is the most
accurate and efficient for this application.
Because the tracking converter doubly integrates its error signal, the device offers a high
degree of noise immunity (12 dB per octave rolloff). The net area under any given noise
spike produces an error. However, typical inductively coupled noise spikes have equal
positive and negative going waveforms. When integrated, this results in a zero net error
signal. The resulting noise immunity, combined with the converter’s insensitivity to
voltage drops, lets the user locate the converter at a considerable distance from the
resolver. Noise rejection is further enhanced by the detector's rejection of any signal not
at the reference frequency, such as wideband noise.
The AD2S90 is one of a number of integrated RDCs offered by Analog Devices. The
general architecture is similar to that of Figure 6.83. Further details on synchro and
resolver-to-digital converters can be found in the references.
Syncros and resolvers are also discussed in Chapter 3 (section 3.1)
6.79
BASIC LINEAR DESIGN
REFERENCES:
ADC ARCHITECTURES
1.
Walt Kester, Editor, Amplifier Applications Guide, Analog Devices, 1992, ISBN-0-916550-10-9,
Chapter 10. (An excellent discussion by James Bryant on the use of op amps as comparators).
2.
James N. Giles, “High Speed Transistor Difference Amplifier,” U.S. Patent 3,843,934, filed January
31 1973, issued October 22, 1974. (Describes one of the first high-speed ECL comparators, the
AM685).
3.
Christopher W. Mangelsdorf, A 400-MHz Input Flash Converter with Error Correction, IEEE
Journal of Solid-State Circuits, Vol. 25, No. 1, February 1990, pp. 184-191. (A discussion of the
AD770, an 8-bi,t 200 MSPS flash ADC. The paper describes the comparator metastable state problem
and how to optimize the ADC design to minimize its effects).
4.
Charles E. Woodward, A Monolithic Voltage-Comparator Array for A/D Converters, IEEE Journal of
Solid State Circuits, Vol. SC-10, No. 6, December 1975, pp. 392-399. (An early paper on a 3-bit
flash converter optimized to minimize metastable state errors).
5.
Paul M. Rainey, “Facimile Telegraph System,” U.S. Patent 1,608,527, filed July 20, 1921, issued
November 30, 1926. (Although A. H. Reeves is generally credited with the invention of PCM, this
patent discloses an electro-mechanical PCM system complete with A/D and D/A converters. The 5-bit
electro-mechanical ADC described is probably the first documented flash converter. The patent was
largely ignored and forgotten until many years after the various Reeves' patents were issued in 19391942).
6.
R. W. Sears, “Electron Beam Deflection Tube for Pulse Code Modulation,” Bell System Technical
Journal, Vol. 27, pp. 44-57, Jan. 1948. (describes an electon-beam deflection tube 7-bit, 100-kSPS
flash converter for early experimental PCM work).
7.
Frank Gray, “Pulse Code Communication,” U.S. Patent 2,632,058, filed November 13, 1947, issued
March 17, 1953. (Detailed patent on the Gray code and its application to electron beam coders).
8.
J. O. Edson and H. H. Henning, “Broadband Codecs for an Experimental 224 Mb/s PCM Terminal,”
Bell System Technical Journal, Vol. 44, pp. 1887-1940, Nov. 1965. (Summarizes experiments on
ADCs based on the electron tube coder as well as a bit-per-stage Gray code 9-bit solid state ADC. The
electron beam coder was 9-bits at 12 MSPS, and represented the fastest of its type at the time).
9.
R. Staffin and R. D. Lohman, “Signal Amplitude Quantizer,” U.S. Patent 2,869,079, filed December
19, 1956, issued January 13, 1959. (Describes flash and subranging conversion using tubes and
transistors).
10. E. Goto, et. al., “Esaki Diode High-Speed Logical Circuits,” IRE Transactions on Electronic
Computers, Vol. EC-9, March 1960, pp. 25-29. (Describes how to use tunnel diodes as logic
elements).
11. T. Kiyomo, K. Ikeda, and H. Ichiki, “Analog-to-Digital Converter Using an Esaki Diode Stack,” IRE
Transactions on Electronic Computers, Vol. EC-11, December 1962, pp. 791-792. (Description of a
low resolution 3-bit flash ADC using a stack of tunnel diodes).
12. H. R. Schindler, “Using the Latest Semiconductor Circuits in a UHF Digital Converter,” Electronics,
August 1963, pp. 37-40. (Describes a 6-bit, 50-MSPS subranging ADC using three 2-bit tunnel diode
flash converters).
13. J. B. Earnshaw, “Design for a Tunnel Diode-Transistor Store with Nondestructive Read-out of
Information,” IEEE Transactions on Electronic Computers, EC-13, 1964, pp. 710-722. (Use of
tunnel diodes as memory elements).
6.80
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
14. Willard K. Bucklen, “A Monolithic Video A/D Converter,” Digital Video, Vol. 2, Society of Motion
Picture and Television Engineers, March 1979, pp. 34-42. (Describes the revolutionary TDC1007J 8bit 20MSPS video flash converter. Originally introduced at the February 3, 1979 SMPTE Winter
Conference in San Francisco, Bucklen accepted an Emmy award for this product in 1988 and was
responsible for the initial marketing and applications support for the device).
15. J. Peterson, “A Monolithic video A/D Converter,” IEEE Journal of Solid-State Circuits, Vol. SC-14,
No. 6, December 1979, pp. 932-937. (Another detailed description of the TRW TDC1007J 8-bit, 20MSPS flash converter).
16. Yukio Akazawa et. al., A 400MSPS 8 Bit Flash A/D Converter, 1987 ISSCC Digest of Technical
Papers, pp. 98-99. (Describes a monolithic flash converter using Gray decoding).
17. A. Matsuzawa et al., An 8b 600MHz Flash A/D Converter with Multi-stage Duplex-gray Coding,
Symposium VLSI Circuits, Digest of Technical Papers, May 1991, pp. 113-114. (Describes a
monolithic flash converter using Gray decoding).
18. Chuck Lane, A 10-bit 60MSPS Flash ADC, Proceedings of the 1989 Bipolar Circuits and
Technology Meeting, IEEE Catalog No. 89CH2771-4, September 1989, pp. 44-47. (Describes an
interpolating method for reducing the number of preamps required in a flash converter).
19. W. W. Rouse Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, Thirteenth Edition,
Dover Publications, 1987, pp. 50, 51. (Describes a mathematical puzzle for measuring unknown
weights using the minimum number of weighing operations. The solution proposed in the 1500's is the
same basic successive approximation algorithm used today).
20. Alec Harley Reeves, “Electric Signaling System,” U.S. Patent 2,272,070, filed November 22, 1939,
issued February 3, 1942. Also French Patent 852,183 issued 1938, and British Patent 538,860 issued
1939. (The ground-breaking patent on PCM. Interestingly enough, the ADC and DAC proposed by
Reeves are counting types, and not successive approximation).
21. John C. Schelleng, “Code Modulation Communication System,” U.S. Patent 2,453,461, filed June 19,
1946, issued November 9, 1948. (An interesting description of a rather cumbersome successive
approximation ADC based on vacuum tube technology. This converter was not very practical, but did
illustrate the concept. Also in the patent is a description of a corresponding binary DAC).
22. W. M. Goodall, “Telephony by Pulse Code Modulation,” Bell System Technical Journal, Vol. 26, pp.
395-409, July 1947. (Describes an experimental PCM system using a 5-bit, 8 kSPS successive
approximation ADC based on the subtraction of binary weighted charges from a capacitor to
implement the internal subtraction/DAC function. It required 5 internal reference voltages).
23. Harold R. Kaiser, et al, “High-Speed Electronic Analogue-to-Digital Converter System,” U.S. Patent
2,784,396, filed April 2, 1953, issued March 5, 1957. (One of the first SAR ADCs to use an actual
binary-weighted DAC internally).
24. B. D. Smith, “Coding by Feedback Methods,” Proceedings of the I. R. E., Vol. 41, August 1953, pp.
1053-1058. (Smith uses an internal DAC and also points out that a non-linear transfer function can be
achieved by using a DAC with non-uniform bit weights, a technique which is widely used in today's
voice-band ADCs with built-in companding).
25. L.A. Meacham and E. Peterson, “An Experimental Multichannel Pulse Code Modulation System of
Toll Quality,” Bell System Technical Journal, Vol. 27, No. 1, January 1948, pp. 1-43. (Describes
non-linear diode-based compressors and expanders for generating a non-linear ADC/DAC transfer
function).
26. Bernard M. Gordon and Robert P. Talambiras, “Signal Conversion Apparatus,” U.S. Patent 3,108,266,
filed July 22, 1955, issued October 22, 1963. (Classic patent describing Gordon's 11-bit, 20 kSPS
vacuum tube successive approximation ADC done at Epsco. The internal DAC represents the first
known use of equal currents switched into an R/2R ladder network.)
6.81
BASIC LINEAR DESIGN
27. Bernard M. Gordon and Evan T. Colton, “Signal Conversion Apparatus,” U.S. Patent 2,997,704, filed
February 24, 1958, issued August 22, 1961. (Classic patent describes the logic to perform the
successive approximation algorithm in a SAR ADC).
28. J.R. Gray and S. C. Kitsopoulos, “A Precision Sample-and-Hold Circuit with Subnanosecond
Switching,” IEEE Transactions on Circuit Theory, CT11, September 1964, pp. 389-396. (One of the
first papers on the detailed analysis of a sample-and-hold circuit).
29. T.C. Verster, “A Method to Increase the Accuracy of Fast Serial-Parallel Analog-to-Digital
Converters,” IEEE Transactions on Electronic Computers, EC-13, 1964, pp. 471-473. (One of the
first references to the use of error correction in a subranging ADC).
30. G.G. Gorbatenko, “High-Performance Parallel-Serial Analog to Digital Converter with Error
Correction,” IEEE National Convention Record, New York, March 1966. (Another early reference
to the use of error correction in a subranging ADC).
31. D. J. Kinniment, D. Aspinall, and D.B.G. Edwards, “High-Speed Analogue-Digital Converter,” IEE
Proceedings, Vol. 113, pp. 2061-2069, Dec. 1966. (A 7-bit 9 MSPS three-stage pipelined error
corrected converter is described based on recirculating through a 3-bit stage three times. Tunnel
(Esaki) diodes are used for the individual comparators. The article also shows a proposed faster
pipelined 7-bit architecture using three individual 3-bit stages with error correction. The article also
describes a fast bootstrapped diode-bridge sample-and-hold circuit).
32. O. A. Horna, “A 150 Mbps A/D and D/A Conversion System,” Comsat Technical Review, Vol. 2,
No. 1, pp. 52-57, 1972. (A detailed description and analysis of a subranging ADC with error
correction).
33. J. L. Fraschilla, R. D. Caveney, and R. M. Harrison, “High Speed Analog-to-Digital Converter,” U.S.
Patent 3,597,761, filed Nov. 14, 1969, issued Aug. 13, 1971. (Describes an 8-bit, 5-MSPS subranging
ADC with switched references to second comparator bank).
34. Stephen H. Lewis, Scott Fetterman, George F. Gross, Jr., R. Ramachandran, and T. R. Viswanathan,
“A 10-b 20-Msample/s Analog-Digital Converter,” IEEE Journal of Solid-State Circuits, Vol. 27,
No. 3, March 1992, pp. 351-358. (A detailed description and analysis of an error corrected subranging
ADC using 1.5-bit pipelined stages).
35. Roy Gosser and Frank Murden, “A 12-bit 50 MSPS Two-Stage A/D Converter,” 1995 ISSCC Digest
of Technical Papers, p. 278. (A description of the AD9042 error corrected subranging ADC using
MagAMP stages for the internal ADCs).
36. B. D. Smith, “An Unusual Electronic Analog-Digital Conversion Method,” IRE Transactions on
Instrumentation, June 1956, pp. 155-160. (Possibly the first published description of the binarycoded and Gray-coded bit-per-stage ADC architectures. Smith mentions similar work partially
covered in R. P. Sallen’s 1949 thesis at M.I.T.).
37. N. E. Chasek, “Pulse Code Modulation Encoder,” U.S. Patent 3,035,258, filed November 14, 1960,
issued May 15, 1962. (An early patent showing a diode-based circuit for realizing the Gray code
folding transfer function).
38. F. D. Waldhauer, “Analog-to-Digital Converter,” U.S. Patent 3,187,325, filed July 2, 1962, issued
June 1, 1965. (A classic patent using op amps with diode switches in the feedback loops to implement
the Gray code folding transfer function).
39. J. O. Edson and H. H. Henning, “Broadband Codecs for an Experimental 224 Mb/s PCM Terminal,”
Bell System Technical Journal, Vol. 44, pp. 1887-1940, Nov. 1965. (A further description of a 9-bit
ADC based on Waldhauer's folding stage).
6.82
CONVERTERS
ANALOG-TO-DIGITAL CONVERTER ARCHITECTURES
40. Udo Fiedler and Dieter Seitzer, “A High-Speed 8-Bit A/D Converter Based on a Gray-Code Multiple
Folding Circuit,” IEEE Journal of Solid-State Circuits, Vol. SC-14, No. 3, June 1979, pp. 547-551.
(An early monolithic folding ADC).
41. Rudy J. van de Plassche and Rob E. J. van der Grift, “A High-Speed 7-Bit A/D Converter,” IEEE
Journal of Solid-State Circuits, Vol. SC-14, No. 6, December 1979, pp. 938-943. (A monolithic
folding ADC).
42. Rob. E. J. van de Grift and Rudy J. van der Plassche, “A Monolithic 8-bit Video A/D Converter,”
IEEE Journal of Solid State Circuits, Vol. SC-19, No. 3, June 1984, pp. 374-378. (A monolithic
folding ADC).
43. Rob. E. J. van der Grift, Ivo W. J. M. Rutten, and Martien van der Veen, “An 8-bit Video ADC
Incorporating Folding and Interpolation Techniques,” IEEE Journal of Solid State Circuits, Vol. SC22, No. 6, December 1987, pp. 944-953. (Another monolithic folding ADC).
44. Rudy van de Plassche, Integrated Analog-to-Digital and Digital-to-Analog Converters, Kluwer
Academic Publishers, 1994, pp. 148-187. (A good textbook on ADCs and DACs with a section on
folding ADCs indicated by the referenced page numbers).
45. Carl Moreland, “An 8-bit 150 MSPS Serial ADC,” 1995 ISSCC Digest of Technical Papers, Vol. 38,
p. 272. (A description of an 8-bit ADC with 5 folding stages followed by a 3-bit flash converter).
46. Carl Moreland, An Analog-to-Digital Converter Using Serial-Ripple Architecture, Masters' Thesis,
Florida State University College of Engineering, Department of Electrical Engineering, 1995.
(Moreland's early work on folding ADCs).
47. Frank Murden, “Analog to Digital Converter Using Complementary Differential Emitter Pairs,” U.S.
Patent 5,550,492, filed December 1, 1994, issued August 27, 1996. (A description of an ADC based
on the MagAMP folding stage).
48. Carl W. Moreland, “Analog to Digital Converter Having a Magnitude Amplifier with an Improved
Differential Input Amplifier,” U.S. Patent 5,554,943, filed December 1, 1994, issued September 10,
1996. (A description of an 8-bit ADC with 5 folding stages followed by a 3-bit flash converter).
49. Frank Murden and Carl W. Moreland, “N-bit Analog-to-Digital Converter with N-1 Magnitude
Amplifiers and N Comparators,” U.S. Patent 5,684,419, filed December 1, 1994, issued November 4,
1997. (Another patent on the MagAMP folding architecture applied to an ADC).
50. Carl Moreland, Frank Murden, Michael Elliott, Joe Young, Mike Hensley, and Russell Stop, “A 14-bit
100-Msample/s Subranging ADC,” IEEE Journal of Solid State Circuits, Vol. 35, No. 12, December
2000, pp. 1791-1798. (Describes the architecture used in the 14-bit AD6645 ADC).
51. Frank Murden and Michael R. Elliott, “Linearizing Structures and Methods for Adjustable-Gain
Folding Amplifiers,” U.S. Patent 6,172,636B1, filed July 13, 1999, issued January 9, 2001. (Describes
methods for trimming the folding amplifiers in an ADC).
52. Bernard M. Oliver and Claude E. Shannon, “Communication System Employing Pulse Code
Modulation,” U.S. Patent 2,801,281, filed February 21, 1946, issued July 30, 1957. (Charge run-down
ADC and Shannon-Rack DAC).
53. Arthur H. Dickinson, “Device to Manifest an Unknown Voltage as a Numerical Quantity,” U.S.
Patent 2,872,670, filed May 26, 1951, issued February 3, 1959. (Ramp run-up ADC).
54. K. Howard Barney, “Binary Quantizer,” U.S. Patent 2,715,678, filed May 26, 1950, issued August 16,
1955. (Tracking ADC).
55. Bernard M. Gordon and Robert P. Talambiras, “Information Translating Apparatus and Method,” U.S.
Patent 2,989,741, filed July 22, 1955, issued June 20, 1961. (Tracking ADC).
6.83
BASIC LINEAR DESIGN
56. John L. Lindesmith, “Voltage-to-Digital Measuring Circuit,” U.S. Patent 2,835,868, filed September
16, 1952, issued May 20, 1958. (Voltage-to-frequency ADC).
57. Paul Klonowski, “Analog-to-Digital Conversion Using Voltage-to-Frequency
Application Note AN-276, Analog Devices, Inc. (A good application note on VFCs).
Converters,”
58. James M. Bryant, “Voltage-to-Frequency Converters,” Application Note AN-361, Analog Devices,
Inc. (A good overview of VFCs).
59. Walt Jung, “Operation and Applications of the AD654 IC V-F Converter,” Application Note AN-278,
Analog Devices, Inc.
60. Steve Martin, “Using the AD650 Voltage-to-Frequency Converter as a Frequency-to-Voltage
Converter,” Application Note AN-279, Analog Devices, Inc. (A description of a frequency-to-voltage
converter using the popular AD650 VFC).
61. Robin N. Anderson and Howard A. Dorey, “Digital Voltmeters,” U.S. Patent 3,267,458, filed August
20, 1962, issued August 16, 1966. (Charge balance dual slope voltmeter ADC).
62. Richard Olshausen, “Analog-to-Digital Converter,” U.S. Patent 3,281,827, filed June 27, 1963, issued
October 25, 1966. (Charge balance dual slope ADC).
63. Roswell W. Gilbert, “Analog-to-Digital Converter,” U.S. Patent 3,051,939, filed May 8, 1957, issued
August 28, 1962. (Dual-slope ADC).
64. Stephan K. Ammann, “Integrating Analog-to-Digital Converter,” U.S. Patent 3,316,547, filed July 15,
1964, issued April 25, 1967. (Dual-slope ADC).
65. Ivar Wold, “Integrating Analog-to-Digital Converter Having Digitally-Derived Offset Error
Compensation and Bipolar Operation without Zero Discontinuity,” U.S. Patent 3,872,466, filed July
19, 1973, issued March 18, 1975. (Quad-slope ADC).
66. Hans Bent Aasnaes, “Triple Integrating Ramp Analog-to-Digital Converter,” U.S. Patent 3,577,140,
filed June 27, 1967, issued May 4, 1971. (Triple-slope ADC).
67. Frederick Bondzeit, Lewis J. Neelands, “Multiple Slope Analog-to-Digital Converter,” U.S. Patent
3,564,538, filed January 29, 1968, issued February 16, 1971. (Triple-slope ADC).
68. Desmond Wheable, “Triple-Slope Analog-to-Digital Converters,” U.S. Patent 3,678,506, filed
October 2, 1968, issued July 18, 1972. (Triple-slope ADC).
69. Dan Sheingold, Analog-Digital Conversion Handbook, Prentice-Hall, 1986, ISBN-0-13-032848-0,
pp. 441-471. (This chapter contains an excellent tutorial on optical, synchro, and resolver-to-digital
conversion).
70. Dennis Fu, “Circuit Applications of the AD2S90 Resolver-to-Digital Converter,” Application Note
AN-230, Analog Devices. (applications of the AD2S90 RTD).
6.84
CONVERTERS
SIGMA-DELTA CONVERTERS
SECTION 6.3: SIGMA-DELTA CONVERTERS
Historical Perspective
The sigma-delta (Σ-Δ) ADC architecture had its origins in the early development phases
of pulse code modulation (PCM) systems—specifically, those related to transmission
techniques called delta modulation and differential PCM. (An excellent discussion of
both the history and concepts of the sigma-delta ADC can be found by Max Hauser in
Reference 1).
The driving force behind delta modulation and differential PCM was to achieve higher
transmission efficiency by transmitting the changes (delta) in value between consecutive
samples rather than the actual samples themselves.
In delta modulation, the analog signal is quantized by a one-bit ADC (a comparator) as
shown in Figure 6.85A. The comparator output is converted back to an analog signal with
a 1-bit DAC, and subtracted from the input after passing through an integrator. The shape
of the analog signal is transmitted as follows: a 1 indicates that a positive excursion has
occurred since the last sample, and a 0 indicates that a negative excursion has occurred
since the last sample.
SAMPLING CLOCK
ANALOG
INPUT
+
∑
DIGITAL
OUTPUT
–
(A) DELTA MODULATION
∫
1-BIT
DAC
SAMPLING CLOCK
ANALOG
INPUT
(B) DIFFERENTIAL PCM
+
∑
N-BIT
FLASH
ADC
DIGITAL
OUTPUT
–
∫
N-BIT
DAC
Figure 6.85: Delta Modulation and Differential PCM
If the analog signal remains at a fixed dc level for a period of time, a pattern alternating
of 0s and 1s is obtained. It should be noted that differential PCM (see Figure 6.85B) uses
6.85
BASIC LINEAR DESIGN
exactly the same concept except a multibit ADC is used rather than a comparator to
derived the transmitted information.
Since there is no limit to the number of pulses of the same sign that may occur, delta
modulation systems are capable of tracking signals of any amplitude. In theory, there is
no peak clipping. However, the theoretical limitation of delta modulation is that the
analog signal must not change too rapidly. The problem of slope clipping is shown in
Figure 6.86. Here, although each sampling instant indicates a positive excursion, the
analog signal is rising too quickly, and the quantizer is unable to keep pace.
SLOPE OVERLOAD
Figure 6.86: Quantization Using Delta Modulation
Slope clipping can be reduced by increasing the quantum step size or increasing the
sampling rate. Differential PCM uses a multibit quantizer to effectively increase the
quantum step sizes at the increase of complexity. Tests have shown that in order to obtain
the same quality as classical PCM, delta modulation requires very high sampling rates,
typically 20× the highest frequency of interest, as opposed to Nyquist rate of 2×.
For these reasons, delta modulation and differential PCM have never achieved any
significant degree of popularity, however a slight modification of the delta modulator
leads to the basic sigma-delta architecture, one of the most popular high resolution ADC
architectures in use today.
The basic single and multibit first-order sigma-delta ADC architecture is shown in
Figures 6.87A and 6.87B, respectively. Note that the integrator operates on the error
signal, whereas in a delta modulator, the integrator is in the feedback loop. The basic
oversampling sigma-delta modulator increases the overall signal-to-noise ratio at low
frequencies by shaping the quantization noise such that most of it occurs outside the
bandwidth of interest. The digital filter then removes the noise outside the bandwidth of
interest, and the decimator reduces the output data rate back to the Nyquist rate.
6.86
CONVERTERS
SIGMA-DELTA CONVERTERS
SAMPLING CLOCK
+
ANALOG
INPUT
∑
DIGITAL
OUTPUT
( K•fs )
∫
DIGITAL
FILTER
–
(A) SINGLE BIT
( fs )
1-BIT
DAC
SAMPLING CLOCK
(K•fs)
+
ANALOG
INPUT
(B) MULTIBIT
∑
∫
N-BIT
FLASH
ADC
DIGITAL
OUTPUT
DIGITAL
FILTER
–
N-BIT
DAC
( fs )
Figure 6.87: Single and Multibit Sigma-Delta ADCs
The IC sigma-delta ADC offers several advantages over the other architectures,
especially for high resolution, low frequency applications. First and foremost, the singlebit sigma-delta ADC is inherently monotonic and requires no laser trimming. The sigmadelta ADC also lends itself to low cost foundry CMOS processes because of the digitally
intensive nature of the architecture. Examples of early monolithic sigma-delta ADCs are
given in References 13-21. Since that time there has been a constant stream of process
and design improvements in the fundamental architecture proposed in the early works
cited above.
6.87
BASIC LINEAR DESIGN
Sigma-Delta (Σ-Δ) or Delta-Sigma (Δ-Σ)? Editor's Notes from Analog
Dialogue Vol. 24-2, 1990, by Dan Sheingold
This is not the most earth-shaking of controversies, and many readers may wonder what
the fuss is all about—if they wonder at all. The issue is important to both editor and
readers because of the need for consistency; we’d like to use the same name for the same
thing whenever it appears. But which name? In the case of the modulation technique that
led to a new oversampling A/D conversion mechanism, we chose sigma-delta. Here’s
why.
Ordinarily, when a new concept is named by its creators, the name sticks; it should not be
changed unless it is erroneous or flies in the face of precedent. The seminal paper on this
subject was published in 1962 (References 9, 10), and its authors chose the name “deltasigma modulation,” since it was based on delta modulation but included an integration
(summation, hence Σ).
Delta-sigma was apparently unchallenged until the 1970s, when engineers at AT&T were
publishing papers using the term sigma-delta. Why? According to Hauser (Reference 1),
the precedent had been to name variants of delta modulation with adjectives preceding
the word “delta.” Since the form of modulation in question is a variant of delta
modulation, the sigma, used as an adjective—so the argument went—should precede the
delta.
Many engineers who came upon the scene subsequently used whatever term caught their
fancy, often without knowing why. It was even possible to find both terms used
interchangeably in the same paper. As matters stand today, sigma-delta is in widespread
use, probably for the majority of citations. Would its adoption be an injustice to the
inventors of the technique?
We think not. Like others, we believe that the name delta-sigma is a departure from
precedent. Not just in the sense of grammar, but also in relation to the hierarchy of
operations. Consider a block diagram for embodying an analog root-mean-square
(finding the square root of the mean of a squared signal) computer. First the signal is
squared, then it is integrated, and finally it is rooted (see Figure 6.88).
If we were to name the overall function after the causal order of operations, it would have
to be called a “square mean root” function. But naming in order of the hierarchy of its
mathematical operations gives us the familiar—and undisputed—name, root meansquare. Consider now a block diagram for taking a difference (delta), and then
integrating it (sigma).
Its causal order would give delta-sigma, but in functional hierarchy it is sigma-delta,
since it computes the integral of a difference. We believe that the latter term is correct
and follows precedent; and we have adopted it as our standard.
Dan Sheingold, 1990.
6.88
CONVERTERS
SIGMA-DELTA CONVERTERS
Root-Mean-Square:
SQUARE
MEAN
ROOT
Hierarchy of Mathematical Operations: ROOT MEAN (SQUARE)
3
2
1
Sigma-Delta:
Sigma
Delta
+
∑
∫
Hierarchy of Mathematical Operations: SIGMA (DELTA)
2
1
Figure 6.88: Sigma-Delta (Σ-Δ) or Delta-Sigma (Δ-Σ)?
6.89
BASIC LINEAR DESIGN
Basics of Sigma-Delta ADCs
Sigma-Delta Analog-Digital Converters (Σ-Δ ADCs) have been known for over thirty
years, but only recently has the technology (high density digital VLSI) existed to
manufacture them as inexpensive monolithic integrated circuits. They are now used in
many applications where a low cost, low bandwidth, low power, high resolution ADC is
required.
There have been innumerable descriptions of the architecture and theory of Σ-Δ ADCs,
but most commence with a maze of integrals and deteriorate from there. Some engineers
who do not understand the theory of operation of Σ-Δ ADCs and are convinced, from
study of a typical published article, which it is too complex to comprehend easily.
There is nothing particularly difficult to understand about Σ-Δ ADCs, as long as you
avoid the detailed mathematics, and this section has been written in an attempt to clarify
the subject. A Σ-Δ ADC contains very simple analog electronics (a comparator, voltage
reference, a switch, and one or more integrators, and analog summing circuits), and quite
complex digital computational circuitry. This circuitry consists of a digital signal
processor (DSP) which acts as a filter (generally, but not invariably, a low-pass filter). It
is not necessary to know precisely how the filter works to appreciate what it does. To
understand how a Σ-Δ ADC works, familiarity with the concepts of oversampling,
quantization noise shaping, digital filtering, and decimation is required.
Let us consider the technique of over-sampling with an analysis in the frequency domain.
Where a dc conversion has a quantization error of up to ½ LSB, a sampled data system
has quantization noise. A perfect classical N-bit sampling ADC has an rms quantization
noise of q/√12 uniformly distributed within the Nyquist band of dc to fs/2 (where q is the
value of an LSB and fs is the sampling rate) as shown in Figure 6.89A. Therefore, its
SNR with a full-scale sinewave input will be (6.02N + 1.76) dB. If the ADC is less than
perfect, and its noise is greater than its theoretical minimum quantization noise, then its
effective resolution will be less than N-bits. Its actual resolution (often known as its
Effective Number of Bits or ENOB) will be defined by:
ENOB =
SNR − 1.76dB
.
6.02dB
Eq. 6.15
If we choose a much higher sampling rate, Kfs (see Figure 6.89B), the rms quantization
noise remains q/√12, but the noise is now distributed over a wider bandwidth dc to Kfs/2.
If we then apply a digital low-pass filter (LPF) to the output, we remove much of the
quantization noise, but do not affect the wanted signal—so the ENOB is improved. We
have accomplished a high resolution A/D conversion with a low resolution ADC. The
factor K is generally referred to as the oversampling ratio. It should be noted at this point
that oversampling has an added benefit in that it relaxes the requirements on the analog
antialiasing filter.
6.90
CONVERTERS
SIGMA-DELTA CONVERTERS
A
fs
QUANTIZATION
NOISE = q / 12
q = 1 LSB
Nyquist
Operation
ADC
B
Oversampling
+ Digital Filter
Kfs
+ Decimation
ADC
C
Kfs
ΣΔ
MOD
fs
fs
2
DIGITAL FILTER
DIGITAL
DEC
FILTER
Oversampling
+ Noise Shaping
+ Digital Filter
+ Decimation
fs
REMOVED NOISE
fs
2
Kfs
2
fs
DIGITAL
DEC
FILTER
Kfs
REMOVED NOISE
fs
2
Kfs
2
Kfs
Figure 6.89: Oversampling, Digital Filtering, Noise Shaping, and Decimation
Since the bandwidth is reduced by the digital output filter, the output data rate may be
lower than the original sampling rate (Kfs) and still satisfy the Nyquist criterion. This
may be achieved by passing every Mth result to the output and discarding the remainder.
The process is known as “decimation” by a factor of M. Despite the origins of the term
(decem is Latin for ten), M can have any integer value, provided that the output data rate
is more than twice the signal bandwidth. Decimation does not cause any loss of
information (see Figure 6.89B).
If we simply use oversampling to improve resolution, we must oversample by a factor of
22N to obtain an N-bit increase in resolution. The Σ-Δ converter does not need such a
high oversampling ratio because it not only limits the signal passband, but also shapes the
quantization noise so that most of it falls outside this passband as shown in Figure 6.89C.
If we take a 1-bit ADC (generally known as a comparator), drive it with the output of an
integrator, and feed the integrator with an input signal summed with the output of a 1-bit
DAC fed from the ADC output, we have a first-order Σ-Δ modulator as shown in
Figure 6.90. Add a digital low-pass filter (LPF) and decimator at the digital output, and
we have a Σ-Δ ADC—the Σ-Δ modulator shapes the quantization noise so that it lies
above the passband of the digital output filter, and the ENOB is therefore much larger
than would otherwise be expected from the oversampling ratio.
6.91
BASIC LINEAR DESIGN
CLOCK
Kfs
INTEGRATOR
VIN
+
∫
∑
A
+
_
_
fs
DIGITAL
FILTER
AND
DECIMATOR
LATCHED
COMPARATOR
(1-BIT ADC)
B
N-BITS
fs
+VREF
1-BIT
DAC
1-BIT DATA
STREAM
1-BIT,
Kf s
–VREF
SIGMA-DELTA MODULATOR
Figure 6.90: First-Order Sigma-Delta ADC
Intuitively, a Σ-Δ ADC operates as follows. Assume a dc input at VIN. The integrator is
constantly ramping up or down at node A. The output of the comparator is fed back
through a 1-bit DAC to the summing input at node B. The negative feedback loop from
the comparator output through the 1-bit DAC back to the summing point will force the
average dc voltage at node B to be equal to VIN. This implies that the average DAC
output voltage must equal to the input voltage VIN. The average DAC output voltage is
controlled by the ones-density in the 1-bit data stream from the comparator output. As the
input signal increases towards +VREF, the number of “ones” in the serial bit stream
increases, and the number of “zeros” decreases. Similarly, as the signal goes negative
towards –VREF, the number of “ones” in the serial bit stream decreases, and the number of
“zeros” increases. From a very simplistic standpoint, this analysis shows that the average
value of the input voltage is contained in the serial bit stream out of the comparator. The
digital filter and decimator process the serial bit stream and produce the final output data.
For any given input value in a single sampling interval, the data from the 1-bit ADC is
virtually meaningless. Only when a large number of samples are averaged, will a
meaningful value result. The sigma-delta modulator is very difficult to analyze in the
time domain because of this apparent randomness of the single-bit data output. If the
input signal is near positive full-scale, it is clear that there will be more 1s than 0s in the
bit stream. Likewise, for signals near negative full-scale, there will be more 0s than 1s in
the bit stream. For signals near midscale, there will be approximately an equal number of
1s and 0s. Figure 6.91 shows the output of the integrator for two input conditions. The
first is for an input of zero (midscale). To decode the output, pass the output samples
through a simple digital low-pass filter that averages every four samples. The output of
the filter is 2/4. This value represents bipolar zero. If more samples are averaged, more
dynamic range is achieved. For example, averaging four samples gives two bits of
6.92
CONVERTERS
SIGMA-DELTA CONVERTERS
resolution, while averaging eight samples yields 4/8, or three bits of resolution. In the
bottom waveform of Figure 6.91, the average obtained for four samples is 3/4, and the
average for eight samples is 6/8.
Figure 6.91: Sigma-Delta Modulator Waveforms
Further time-domain analysis is not productive, and the concept of noise shaping is best
explained in the frequency domain by considering the simple Σ-Δ modulator model in
Figure 6.92.
The integrator in the modulator is represented as an analog low-pass filter with a transfer
function equal to H(f) = 1/f. This transfer function has an amplitude response which is
inversely proportional to the input frequency. The 1-bit quantizer generates quantization
noise, Q, which is injected into the output summing block. If we let the input signal be X,
and the output Y, the signal coming out of the input summer must be X – Y. This is
multiplied by the filter transfer function, 1/f, and the result goes to one input to the output
summer. By inspection, we can then write the expression for the output voltage Y as:
1
Y = (X − Y) + Q .
Eq. 6.16
f
This expression can easily be rearranged and solved for Y in terms of X, f, and Q:
Y=
X
Q⋅f
+
.
f +1 f +1
Eq. 6.17
6.93
BASIC LINEAR DESIGN
X
ANALOG FILTER
H(f) = 1
f
∑
+
_
Q=
QUANTIZATION
NOISE
1 (X–Y)
f
X–Y
∑
Y
Y
Y=
1 (X–Y)
+ Q
f
REARRANGING, SOLVING FOR Y:
Y=
X
+
f+1
SIGNAL TERM
Qf
f+1
NOISE TERM
Figure 6.92: Simplified Frequency Domain Linearized Model
of a Sigma-Delta Modulator
Note that as the frequency f approaches zero, the output voltage Y approaches X with no
noise component. At higher frequencies, the amplitude of the signal component
approaches zero, and the noise component approaches Q. At high frequency, the output
consists primarily of quantization noise. In essence, the analog filter has a low-pass effect
on the signal, and a high-pass effect on the quantization noise. Thus the analog filter
performs the noise shaping function in the Σ-Δ modulator model.
For a given input frequency, higher order analog filters offer more attenuation. The same
is true of Σ-Δ modulators, provided certain precautions are taken.
By using more than one integration and summing stage in the Σ-Δ modulator, we can
achieve higher orders of quantization noise shaping and even better ENOB for a given
over-sampling ratio as is shown in Figure 6.93 for both a first and second-order Σ-Δ
modulator.
The block diagram for the second-order Σ-Δ modulator is shown in Figure 6.94. Third,
and higher, order Σ-Δ ADCs were once thought to be potentially unstable at some values
of input—recent analyses using finite rather than infinite gains in the comparator have
shown that this is not necessarily so, but even if instability does start to occur, it is not
important, since the DSP in the digital filter and decimator can be made to recognize
incipient instability and react to prevent it.
6.94
CONVERTERS
SIGMA-DELTA CONVERTERS
2ND ORDER
DIGITAL
FILTER
1ST ORDER
Kfs
2
fs
2
Figure 6.93: Sigma-Delta Modulators Shape Quantization Noise
INTEGRATOR
VIN
+
∑
_
∫
CLOCK
Kfs
INTEGRATOR
+
∑
∫
+
_
_
1-BIT
DAC
1-BIT
DATA
STREAM
DIGITAL FILTER
AND
DECIMATOR
N-BITS
fs
Figure 6.94: Second-Order Sigma-Delta ADC
Figure 6.95 shows the relationship between the order of the Σ-Δ modulator and the
amount of over-sampling necessary to achieve a particular SNR. For instance, if the
oversampling ratio is 64, an ideal second-order system is capable of providing an SNR of
about 80 dB. This implies approximately 13 effective number of bits (ENOB). Although
the filtering done by the digital filter and decimator can be done to any degree of
precision desirable, it would be pointless to carry more than 13 binary bits to the outside
world. Additional bits would carry no useful signal information, and would be buried in
the quantization noise unless post-filtering techniques were employed. Additional
6.95
BASIC LINEAR DESIGN
resolution can be obtained by increasing the oversampling ratio and/or by using a higherorder modulator.
120
THIRD-ORDER LOOP*
21dB / OCTAVE
100
SECOND-ORDER LOOP
15dB / OCTAVE
80
SNR
(dB)
60
FIRST-ORDER LOOP
9dB / OCTAVE
40
* > 2nd ORDER LOOPS DO NOT
OBEY LINEAR MODEL
20
0
4
8
16
32
64
128
256
OVERSAMPLING RATIO, K
Figure 6.95: SNR vs. Oversampling Ratio for
First, Second, and Third-Order Loops
Idle Tone Considerations
In our discussion of sigma-delta ADCs up to this point, we have made the assumption
that the quantization noise produced by the sigma-delta modulator is random and
uncorrelated with the input signal. Unfortunately, this is not entirely the case, especially
for the first-order modulator. Consider the case where we are averaging 16 samples of
the modulator output in a 4-bit sigma-delta ADC.
Figure 6.96 shows the bit pattern for two input signal conditions: an input signal having
the value 8/16, and an input signal having the value 9/16. In the case of the 9/16 signal,
the modulator output bit pattern has an extra 1 every 16th output. This will produce
energy at fs/16, which translates into an unwanted tone. If the oversampling ratio is less
than 16, this tone will fall into the pass band. In audio applications these tones are
referred to as “idle tones.”
Figure 6.97 shows the correlated idling pattern behavior for a first order sigma-delta
modulator, and Figure 6.98 shows the relatively uncorrelated pattern for a second-order
modulator. For this reason, virtually all sigma-delta ADCs contain at least a secondorder modulator loop.
6.96
CONVERTERS
SIGMA-DELTA CONVERTERS
Figure 6.96: Repetitive Bit Pattern in Sigma-Delta Modulator Output
Figure 6.97: Idling Patterns for First-Order
Sigma-Delta Modulator (Integrator Output)
Figure 6.98: Idling Patterns for Second-Order Sigma-Delta Modulator
(Integrator Output)
6.97
BASIC LINEAR DESIGN
Higher Order Loop Considerations
In order to achieve wide dynamic range, sigma-delta modulator loops greater than
second-order are necessary, but present real design challenges. First of all, the simple
linear models previously discussed are no longer fully accurate. Loops of order greater
than two are generally not guaranteed to be stable under all input conditions. The
instability arises because the comparator is a nonlinear element whose effective “gain”
varies inversely with the input level. This mechanism for instability causes the following
behavior: if the loop is operating normally, and a large signal is applied to the input that
overloads the loop, the average gain of the comparator is reduced. The reduction in
comparator gain in the linear model causes loop instability. This causes instability even
when the signal that caused it is removed. In actual practice, such a circuit would
normally oscillate on power-up due to initial conditions caused by turn-on transients. As
an example, the AD1879 dual audio ADC released in 1994 by Analog Devices used a
fifth-order loop. Extensive nonlinear stabilization techniques were required in this and
similar higher order loop designs (References 22-26).
Multibit Sigma-Delta Converters
So far we have considered only sigma-delta converters which contain a single-bit ADC
(comparator) and a single-bit DAC (switch). The block diagram of Figure 6.99 shows a
multi-bit sigma-delta ADC which uses an n-bit flash ADC and an n-bit DAC. Obviously,
this architecture will give a higher dynamic range for a given oversampling ratio and
order of loop filter. Stabilization is easier, since second-order loops can generally be
used. Idling patterns tend to be more random thereby minimizing tonal effects.
CLOCK
Kfs
fs
INTEGRATOR
VIN
+
∑
∫
FLASH
ADC
n-BITS
_
n-BIT
DAC
DIGITAL
FILTER
AND
DECIMATOR
n-BITS,
n-BIT DATA
STREAM
Kfs
Figure 6.99: Multibit Sigma-Delta ADC
6.98
N-BITS
fs
CONVERTERS
SIGMA-DELTA CONVERTERS
The real disadvantage of this technique is that the linearity depends on the DAC linearity,
and thin film laser trimming is required to approach 16-bit performance levels. This
makes the multi-bit architecture extremely impractical to implement on mixed-signal ICs
using traditional binary DAC techniques.
However, fully decoded thermometer DACs coupled with proprietary data scrambling
techniques as used in a number of Analog Devices’ audio ADCs and DACs, including the
24-bit stereo AD1871 (see References 27 and 28) can achieve high SNR and low
distortion using the multibit architecture. A simplified block diagram of the AD1871
ADC is shown in Figure 6.100.
CAPLN CAPLP
AVDD
DVDD
ODVDD
CASC
LRCLK
VINLP
ANALOG
INPUT
BUFFER
MULTIBIT
Σ-∆
MODULATOR
DATA
PORT
DECIMATOR
VINLN
BCLK
DOUT
DIN
AD1871
VREF
FILTER
ENGINE
RESET
CLOCK
DIVIDER
MCLK
CLATCH (M/S)
VINRP
ANALOG
INPUT
BUFFER
MULTIBIT
Σ-∆
MODULATOR
SPI
PORT
DECIMATOR
VINRN
CCLK (256/512)
CIN/(DF1)
COUT/(DF0)
XCTRL
CAPRN CAPRP
AGND
DGND
Figure 6.100: AD1871 24-Bit, 96-kSPS Stereo Audio Multibit Sigma-Delta ADC
The AD1871’s analog Σ-Δ modulator section comprises a second-order multibit
implementation using Analog Device's proprietary technology for best performance. As
shown in Figure 6.101, the two analog integrator blocks are followed by a flash ADC
section that generates the multibit samples.
The output of the flash ADC, which is thermometer encoded, is decoded to binary for
output to the filter sections and is scrambled for feedback to the two integrator stages.
The modulator is optimized for operation at a sampling rate of 6.144 MHz (which is
128 × fs at 48-kHz sampling and 64 × fs at 96-kHz sampling). The A-weighted dynamic
range of the AD1871 is typically 105 dB.
6.99
BASIC LINEAR DESIGN
FROM
ANALOG
INPUT
SECTION
THERMOMETER
TO
BINARY
DECODER
FLASH
ADC
SCRAMBLER
FEEDBACK DACs
Figure 6.101: Details of the AD1871 Second-Order Modulator
and Data Scrambler
Digital Filter Implications
The digital filter is an integral part of all sigma-delta ADCs—there is no way to remove
it. The settling time of this filter affects certain applications especially when using sigmadelta ADCs in multiplexed applications. The output of a multiplexer can present a step
function input to an ADC if there are different input voltages on adjacent channels. In
fact, the multiplexer output can represent a full-scale step voltage to the sigma-delta ADC
when channels are switched. Adequate filter settling time must be allowed, therefore, in
such applications. This does not mean that sigma-delta ADCs shouldn’t be used in
multiplexed applications, just that the settling time of the digital filter must be
considered. Some newer sigma-delta ADCs are actually optimized for use in multiplexed
applications.
MAGNITUDE (dB)
0
–50
–100
–150
0
0.5
1.0
1.5
2.0
FREQUENCY – NORMALIZED TO f S
Figure 6.102: AD1871 24-Bit, 96-kSPS Stereo Sigma-Delta ADC
Digital Filter Characteristics
6.100
CONVERTERS
SIGMA-DELTA CONVERTERS
For example, the group delay through the AD1871 digital filter is 910 µs (sampling at
48 kSPS) and 460 µs (sampling at 96 kSPS)—this represents the time it takes for a step
function input to propagate through one-half the number of taps in the digital filter. The
total settling time is therefore approximately twice the group delay time. The input
oversampling frequency is 6.144 MSPS for both conditions. The frequency response of
the digital filter in the AD1871 ADC is shown in Figure 6.102.
In other applications, such as low frequency, high resolution 24-bit measurement sigmadelta ADCs (such as the AD77xx-series), other types of digital filters may be used. For
instance, the SINC3 response is popular because it has zeros at multiples of the
throughput rate. For instance a 10-Hz throughput rate produces zeros at 50 Hz and 60 Hz
which aid in ac power line rejection. The frequency response of a typical Σ-Δ ADC, the
AD7730 is shown if Figure 6.103.
0
–10
–20
SINC3 + 22-TAP FIR FILTER,
CHOP MODE ENABLED
–30
GAIN –40
(dB)
–50
–60
–70
–80
–90
–110
–120
–130
0
10
20
30
40
50
60
70
80
90
100
FREQUNCY (Hz)
Figure 6.103: AD7730 Digital Filter Response
6.101
BASIC LINEAR DESIGN
High Resolution Measurement Sigma-Delta ADCs
In order to better understand the capability of sigma-delta measurement ADCs and the
power of the technique, a modern example, the AD7730, will be examined in detail. The
AD7730 is a member of the AD77XX family and is shown in Figure 6.104. This ADC
was specifically designed to interface directly to bridge outputs in weigh scale
applications. The device accepts low level signals directly from a bridge and outputs a
serial digital word. There are two buffered differential inputs which are multiplexed,
buffered, and drive a PGA. The PGA can be programmed for four differential unipolar
analog input ranges: 0 V to +10 mV, 0 V to +20 mV, 0 V to +40 mV, and 0 V to +80 mV
and four differential bipolar input ranges: ±10 mV, ±20 mV, ±40 mV, and ±80 mV.
The maximum peak-to-peak, or noise-free resolution achievable is 1 in 230,000 counts,
or approximately 18-bits. It should be noted that the noise-free resolution is a function of
input voltage range, filter cutoff, and output word rate. Noise is greater using the smaller
input ranges where the PGA gain must be increased. Higher output word rates and
associated higher filter cutoff frequencies will also increase the noise.
AVDD
DVDD
REFIN(–)
REFIN(+)
REFERENCE DETECT
100nA
AIN1(+)
AIN1(–)
MUX
+
STANDBY
SIGMA-DELTA ADC
BUFFER
_
AIN2(+)/D1
AIN2(–)/D0
AD7730
+
∑
SIGMADELTA
MODULATOR
PGA
+/–
100nA
SERIAL INTERFACE
AND CONTROL LOGIC
6-BIT
DAC
PROGRAMMABLE
DIGITAL
FILTER
CLOCK
GENERATION
REGISTER BANK
VBIAS
ACX
MCLK IN
MCLK OUT
SCLK
CS
CALIBRATION
MICROCONTROLLER
ACX
SYNC
DIN
DOUT
AC
EXCITATION
CLOCK
AGND
DGND
POL
RDY
RESET
Figure 6.104: AD7730 Sigma-Delta Single-Supply Bridge ADC
The analog inputs are buffered on-chip allowing relatively high source impedances. Both
analog channels are differential, with a common-mode voltage range that comes within
1.2 V of AGND and 0.95 V of AVDD. The reference input is also differential, and the
common-mode range is from AGND to AVDD.
6.102
CONVERTERS
SIGMA-DELTA CONVERTERS
The 6-bit DAC is controlled by on-chip registers and can remove TARE (pan weight)
values of up to ±80 mV from the analog input signal range. The resolution of the TARE
function is 1.25 mV with a +2.5 V reference and 2.5 mV with a +5 V reference.
The output of the PGA is applied to the Σ-Δ modulator and programmable digital filter.
The serial interface can be configured for three-wire operation and is compatible with
microcontrollers and digital signal processors. The AD7730 contains self-calibration and
system-calibration options and has an offset drift of less than 5 nV/ºC and a gain drift of
less than 2 ppm/ºC. This low offset drift is obtained using a chop mode which operates
similarly to a chopper-stabilized amplifier.
The oversampling frequency of the AD7730 is 4.9152 MHz, and the output data rate can
be set from 50 Hz to 1200 Hz. The accuracy of the output of the ADC is dependant on the
output data rate as shown in Tables I and II of Figure 6.105. These are taken from the
AD7730. Note that the accuracy is also dependent on the PGA gain as well.
Figure 6.105: Resolution vs. Output Data Rate and Gain for the AD7730
This is easy to understand. The quantization is performed at the master clock rate
(4.9152 MHz). If the data rate is increased, there is less time for filtering, so the measured
result is noisier. Also as gain is increased, noise is increased as well.
While the output data word is 24 bits wide, there will not be a constant 24-bit data output,
even with the input grounded. As seen in Table I, the maximum accuracy is on the order
of 18 bits peak-to-peak. This gives rise to a new way of specifying accuracy. This is noise
free counts. For the AD7730 this is 230,000.
The clock source can be provided via an external clock or by connecting a crystal
oscillator across the MCLK IN and MCLK OUT pins.
6.103
BASIC LINEAR DESIGN
The AD7730 can accept input signals from a dc-excited bridge. It can also handle input
signals from an ac-excited bridge by using the ac excitation clock signals (ACX and
ACX ). These are non-overlapping clock signals used to synchronize the external
switches which drive the bridge. The ACX clocks are demodulated on the AD7730 input.
The AD7730 contains two 100 nA constant current generators, one source current from
AVDD to AIN(+) and one sink current from AIN(–) to AGND. The currents are switched
to the selected analog input pair under the control of a bit in the Mode Register. These
currents can be used in checking that a sensor is still operational before attempting to take
measurements on that channel. If the currents are turned on and a full-scale reading is
obtained, then the sensor has gone open circuit. If the measurement is 0 V, the sensor has
gone short circuit. In normal operation, the burnout currents are turned off by setting the
proper bit in the Mode Register to 0.
The AD7730 contains an internal programmable digital filter. The filter consists of two
sections: a first stage filter, and a second stage filter. The first stage is a sinc3 low-pass
filter. The cutoff frequency and output rate of this first stage filter is programmable. The
second stage filter has three modes of operation. In its normal mode, it is a 22-tap FIR
filter that processes the output of the first stage filter. When a step change is detected on
the analog input, the second stage filter enters a second mode (FASTStep™) where it
performs a variable number of averages for some time after the step change, and then the
second stage filter switches back to the FIR filter mode. The third option for the second
stage filter (SKIP mode) is that it is completely bypassed so the only filtering provided on
the AD7730 is the first stage. Both the FASTStep mode and SKIP mode can be enabled
or disabled via bits in the control register. Again, there will be an affect on accuracy.
0
–10
–20
SINC3 + 22-TAP FIR FILTER,
CHOP MODE ENABLED
–30
GAIN –40
(dB)
–50
–60
–70
–80
–90
–110
–120
–130
0
10
20
30
40
50
60
70
80
90
100
FREQUNCY (Hz)
Figure 6.106: AD7730 Digital Filter Response
Figure 6.106 shows the full frequency response of the AD7730 when the second stage
filter is set for normal FIR operation. This response is with the chop mode enabled and an
6.104
CONVERTERS
SIGMA-DELTA CONVERTERS
output word rate of 200 Hz and a clock frequency of 4.9152 MHz. The response is shown
from dc to 100 Hz. The rejection at 50 Hz ± 1 Hz and 60 Hz ± 1 Hz is better than 88 dB.
Figure 6.107 shows the step response of the AD7730 with and without the FASTStep
mode enabled. The vertical axis shows the code value and indicates the settling of the
output to the input step change. The horizontal axis shows the number of output words
required for that settling to occur. The positive input step change occurs at the 5th output.
20,000,000
FASTStep ENABLED
15,000,000
CODE
10,000,000
FASTStep DISABLED
5,000,000
0
0
5
10
15
20
25
NUMBER OF OUTPUT SAMPLES
Figure 6.107: AD7730 Digital Filter Settling Time Showing FASTStep Mode
In the normal mode (FASTStep disabled), the output has not reached its final value until
the 23rd output word. In FASTStep mode with chopping enabled, the output has settled to
the final value by the 7th output word. Between the 7th and the 23rd output, the
FASTStep mode produces a settled result, but with additional noise compared to the
specified noise level for normal operating conditions. It starts at a noise level comparable
to the SKIP mode, and as the averaging increases ends up at the specified noise level. The
complete settling time required for the part to return to the specified noise level is the
same for FASTStep mode and normal mode. The FASTStep mode gives a much earlier
indication of where the output channel is going and its new value. This feature is very
useful in weigh scale applications to give a much earlier indication of the weight, or in an
application scanning multiple channels where the user does not have to wait the full
settling time to see if a channel has changed.
Note, however, that the FASTStep mode is not particularly suitable for multiplexed
applications because of the excess noise associated with the settling time. For
multiplexed applications, the full 23-cycle output word interval should be allowed for
settling to a new channel. This points out the fundamental issue of using Σ-Δ ADCs in
6.105
BASIC LINEAR DESIGN
multiplexed applications. There is no reason why they won’t work, provided the internal
digital filter is allowed to settle fully after switching channels.
+5V
+FORCE
RLEAD
6-LEAD
BRIDGE
+SENSE
DVDD
AVDD
+ VREF
VO
– SENSE
– FORCE
+5V/+3V
AD7730
ADC
+ AIN
– AIN
24 BITS
– VREF
RLEAD
AGND
DGND
Figure 6.108: AD7730 Bridge Application (Simplified Schematic)
The AD7730 gives the user access to the on-chip calibration registers allowing an
external microprocessor to read the device's calibration coefficients and also to write its
own calibration coefficients to the part from prestored values in external E2PROM. This
gives the microprocessor much greater control over the AD7730's calibration procedure.
It also means that the user can verify that the device has performed its calibration
correctly by comparing the coefficients after calibration with prestored values in
E2PROM. Since the calibration coefficients are derived by performing a conversion on
the input voltage provided, the accuracy of the calibration can only be as good as the
noise level the part provides in the normal mode. To optimize calibration accuracy, it is
recommended to calibrate the part at its lowest output rate where the noise level is lowest.
The coefficients generated at any output rate will be valid for all selected output update
rates. This scheme of calibrating at the lowest output data rate does mean that the
duration of the calibration interval is longer.
The AD7730 requires an external voltage reference, however, the power supply may be
used as the reference in the ratiometric bridge application shown in Figure 6.108. In this
configuration, the bridge output voltage is directly proportional to the bridge drive
voltage which is also used to establish the reference voltages to the AD7730. Variations
in the supply voltage will not affect the accuracy. The SENSE outputs of the bridge are
used for the AD7730 reference voltages in order to eliminate errors caused by voltage
drops in the lead resistances.
6.106
CONVERTERS
SIGMA-DELTA CONVERTERS
Band-pass Sigma-Delta Converters
The Σ-Δ ADCs that we have described so far contain integrators, which are low-pass
filters, whose pass band extends from dc. Thus, their quantization noise is pushed up in
frequency. At present, most commercially available Σ-Δ ADCs are of this type (although
some which are intended for use in audio or telecommunications applications contain
band-pass rather than low-pass digital filters to eliminate any system dc offsets). But
there is no particular reason why the filters of the Σ-Δ modulator should be LPFs, except
that traditionally ADCs have been thought of as being baseband devices, and that
integrators are somewhat easier to construct than band-pass filters. If we replace the
integrators in a Σ-Δ ADC with band-pass filters (BPFs) as shown in Figure 6.109, the
quantization noise is moved up and down in frequency to leave a virtually noise-free
region in the pass band (see References 31, 32, and 33). If the digital filter is then
programmed to have its pass band in this region, we have a Σ-Δ ADC with a band-pass,
rather than a low-pass characteristic. Such devices would appear to be useful in direct IFto-digital conversion, digital radios, ultrasound, and other undersampling applications.
However, the modulator and the digital BPF must be designed for the specific set of
frequencies required by the system application, thereby somewhat limiting the flexibility
of this approach.
In an undersampling application of a band-pass Σ-Δ ADC, the minimum sampling
frequency must be at least twice the signal bandwidth, BW. The signal is centered around
a carrier frequency, fc. A typical digital radio application using a 455-kHz center
frequency and a signal bandwidth of 10 kHz is described in Reference 32. An
oversampling frequency Kfs = 2 MSPS and an output rate fs = 20 kSPS yielded a
dynamic range of 70 dB within the signal bandwidth.
+
Σ
-
ANALOG
BPF
+
Σ
-
CLOCK
Kfs
ANALOG
BPF
fs
DIGITAL
BPF AND
DECIMATOR
1-BIT
DAC
fc
DIGITAL BPF
RESPONSE
fs > 2 BW
BW
SHAPED
QUANTIZATION
NOISE
f
Figure 6.109: Replacing Integrators with Resonators
Gives a Band-Pass Sigma-Delta ADC
6.107
BASIC LINEAR DESIGN
Another example of a band-pass is the AD9870 IF Digitizing Subsystem having a
nominal oversampling frequency of 18 MSPS, a center frequency of 2.25 MHz, and a
bandwidth of 10 kHz to 150 kHz (see details in Reference 33).
Sigma-Delta DACs
Sigma-delta DACs operate very similarly to sigma-delta ADCs, however in a sigma-delta
DAC, the noise shaping function is accomplished with a digital modulator rather than an
analog one.
SINGLE BIT
N-BITS @ fs
N-BITS @ K fs
DIGITAL
INTERPOLATION
FILTER
1- BIT @ KfS
DIGITAL
ΣΔ
MODULATOR
ANALOG SIGNAL:
2 LEVELS
1-BIT
DAC
ANALOG
OUTPUT
FILTER
ANALOG
OUTPUT
MULTIBIT
N-BITS @ fs
N-BITS @ K fs
DIGITAL
INTERPOLATION
FILTER
M- BITS @ KfS
DIGITAL
MULTIBIT
ΣΔ
ANALOG SIGNAL:
2 M LEVELS
M-BIT
DAC
MODULATOR
ANALOG
OUTPUT
FILTER
ANALOG
OUTPUT
Figure 6.110: Sigma-Delta DACs
A Σ-Δ DAC, unlike the Σ-Δ ADC, is mostly digital (see Figure 6.110A). It consists of an
“interpolation filter” (a digital circuit which accepts data at a low rate, inserts zeros at a
high rate, and then applies a digital filter algorithm and outputs data at a high rate), a Σ-Δ
modulator (which effectively acts as a low-pass filter to the signal but as a high-pass filter
to the quantization noise, and converts the resulting data to a high speed bit stream), and a
1-bit DAC whose output switches between equal positive and negative reference
voltages. The output is filtered in an external analog LPF. Because of the high
oversampling frequency, the complexity of the LPF is much less than the case of
traditional Nyquist operation.
It is possible to use more than one bit in the Σ-Δ DAC, and this leads to the multibit
architecture shown in Figure 3.147B. The concept is similar to that of interpolating DACs
previously discussed in Chapter 2, with the addition of the digital sigma-delta modulator.
In the past, multibit DACs have been difficult to design because of the accuracy
requirement on the n-bit internal DAC (this DAC, although only n-bits, must have the
linearity of the final number of bits, N). The AD185x-series of audio DACs, however,
6.108
CONVERTERS
SIGMA-DELTA CONVERTERS
use a proprietary data scrambling technique (called data directed scrambling) which
overcomes this problem and produces excellent performance with respect to all audio
specifications (see References 27 and 28). For instance, the AD1853 dual 24-bit, 92 kSPS
DAC has greater than 104 dB THD + N at a 48 kSPS sampling rate.
One of the newest members of this family is the AD1955 multibit sigma-delta audio
DAC shown in Figure 6.111. The AD1955 also uses data directed scrambling, supports a
multitude of DVD audio formats, and has an extremely flexible serial port. THD + N is
typically 110 dB.
Figure 6.111: AD1955 Multibit Sigma-Delta Audio DAC
6.109
BASIC LINEAR DESIGN
Summary
Sigma-delta ADCs and DACs have proliferated into many modern applications including
measurement, voice-band, audio, etc. The technique takes full advantage of low cost
CMOS processes and therefore makes integration with highly digital functions such as
DSPs practical. Resolutions up to 24-bits are currently available, and the requirements on
analog antialiasing/anti-imaging filters are greatly relaxed due to oversampling. Modern
techniques such as the multibit data scrambled architecture minimize problems with idle
tones which plagued early sigma-delta products.
Many sigma-delta converters offer a high level of user programmability with respect to
output data rate, digital filter characteristics, and self-calibration modes. Multichannel
sigma-delta ADCs are now available for data acquisition systems, and most users are
well-educated with respect to the settling time requirements of the internal digital filter in
these applications.
6.110
CONVERTERS
SIGMA-DELTA CONVERTERS
REFERENCES:
SIGMA-DELTA CONVERTERS
1.
Max W. Hauser, “Principles of Oversampling A/D Conversion,” Journal Audio Engineering Society,
Vol. 39, No. 1/2, January/February 1991, pp. 3-26. (One of the best tutorials and practical discussions
of the sigma-delta ADC architecture and its history).
2.
E. M. Deloraine, S. Van Mierlo, and B. Derjavitch, “Methode et systéme de transmission par
impulsions,” French Patent 932,140, issued August, 1946. Also British Patent 627,262, issued 1949.
3.
E. M. Deloraine, S. Van Mierlo, and B. Derjavitch, “Communication System Utilizing Constant
Amplitude Pulses of Opposite Polarities,” U.S. Patent 2,629,857, filed October 8, 1947, issued
February 24, 1953.
4.
F. de Jager, “Delta Modulation: A Method of PCM Transmission Using the One Unit Code,” Phillips
Research Reports, Vol. 7, 1952, pp. 542-546. (Additional work done on delta modulation during the
same time period).
5.
H. Van de Weg, “Quantizing Noise of a Single Integration Delta Modulation System with an N-Digit
Code,” Phillips Research Reports, Vol. 8, 1953, pp. 367-385. (Additional work done on delta
modulation during the same time period).
6.
C. C. Cutler, “Differential Quantization of Communication Signals,” U.S. Patent 2,605,361, filed June
29, 1950, issued July 29, 1952. (Recognized as the first patent on differential PCM or delta
modulation, although actually first invented in the Paris labs of the International Telephone and
Telegraph Corporation by E. M. Deloraine, S. Mierlo, and B. Derjavitch a few years earlier).
7.
C. C. Cutler, “Transmission Systems Employing Quantization,” U.S. Patent 2,927,962, filed April 26,
1954, issued March 8, 1960. (A ground-breaking patent describing oversampling and noise shaping
using first and second-order loops to increase effective resolution. The goal was transmission of
oversampled noise shaped PCM data without decimation, not a Nyquist-type ADC).
8.
C. B. Brahm, “Feedback Integrating System,” U.S. Patent 3,192,371, filed September 14, 1961, issued
June 29, 1965. (Describes a second-order multibit oversampling noise shaping ADC).
9.
H. Inose, Y. Yasuda, and J. Murakami, “A Telemetering System by Code Modulation: Δ-Σ
Modulation,” IRE Transactions on Space Electronics Telemetry, Vol. SET-8, September 1962, pp.
204-209. Reprinted in N. S. Jayant, Waveform Quantization and Coding, IEEE Press and John
Wiley, 1976, ISBN 0-471-01970-4. (An elaboration on the 1-bit form of Cutler's noise-shaping
oversampling concept. This work coined the description of the architecture as 'delta-sigma
modulation').
10. H. Inose and Y. Yasuda, “A Unity Bit Coding Method by Negative Feedback,” IEEE Proceedings,
Vol. 51, November 1963, pp. 1524-1535. (Further discussions on their 1-bit 'delta-sigma' concept).
11. D. J. Goodman, “The Application of Delta Modulation of Analog-to-PCM Encoding,” Bell System
Technical Journal, Vol. 48, February 1969, pp. 321-343. Reprinted in N. S. Jayant, Waveform
Quantization and Coding, IEEE Press and John Wiley, 1976, ISBN 0-471-01970-4. (The first
description of using oversampling and noise shaping techniques followed by digital filtering and
decimation to produce a true Nyquist-rate ADC).
12. J. C. Candy, “A Use of Limit Cycle Oscillations to Obtain Robust Analog-to-Digital Converters,”
IEEE Transactions on Communications, Vol. COM-22, December 1974, pp. 298-305. (Describes a
multibit oversampling noise shaping ADC with output digital filtering and decimation to interpolate
between the quantization levels).
13. R. J. van de Plassche, “A Sigma-Delta Modulator as an A/D Converter,” IEEE Transactions on
Circuits and Systems, Vol. CAS-25, July 1978, pp. 510-514.
6.111
BASIC LINEAR DESIGN
14. B. A. Wooley and J. L. Henry, “An Integrated Per-Channel PCM Encoder Based on Interpolation,”
IEEE Journal of Solid State Circuits, Vol. SC-14, February 1979, pp. 14-20. (One of the first allintegrated CMOS sigma-delta ADCs).
15. B. A. Wooley et al, “An Integrated Interpolative PCM Decoder,” IEEE Journal of Solid State
Circuits, Vol. SC-14, February 1979, pp. 20-25.
16. J. C. Candy, B. A. Wooley, and O. J. Benjamin, “A Voice-band Codec with Digital Filtering,” IEEE
Transactions on Communications, Vol. COM-29, June 1981, pp. 815-830.
17. J. C. Candy and Gabor C. Temes, Oversampling Delta-Sigma Data Converters, IEEE Press, ISBN
0-87942-258-8, 1992.
18. R. Koch, B. Heise, F. Eckbauer, E. Engelhardt, J. Fisher, and F. Parzefall, “A 12-bit Sigma-Delta
Analog-to-Digital Converter with a 15 MHz Clock Rate,” IEEE Journal of Solid-State Circuits, Vol.
SC-21, No. 6, December 1986.
19. D. R. Welland, B. P. Del Signore and E. J. Swanson, “A Stereo 16-Bit Delta-Sigma A/D Converter for
Digital Audio,” J. Audio Engineering Society, Vol. 37, No. 6, June 1989, pp. 476-485.
20. B. Boser and Bruce Wooley, “The Design of Sigma-Delta Modulation Analog-to-Digital Converters,”
IEEE Journal of Solid-State Circuits, Vol. 23, No. 6, December 1988, pp. 1298-1308.
21. J. Dattorro, A. Charpentier, D. Andreas, “The Implementation of a One-Stage Multirate 64:1 FIR
Decimator for use in One-Bit Sigma-Delta A/D Applications,” AES 7th International Conference,
May 1989.
22. W.L. Lee and C.G. Sodini, “A Topology for Higher-Order Interpolative Coders,” ISCAS PROC.
1987.
23. P.F. Ferguson, Jr., A. Ganesan and R. W. Adams, “One-Bit Higher Order Sigma-Delta A/D
Converters,” ISCAS PROC. 1990, Vol. 2, pp. 890-893.
24. Wai Laing Lee, A Novel Higher Order Interpolative Modulator Topology for High Resolution
Oversampling A/D Converters, MIT Masters Thesis, June 1987.
25. R. W. Adams, “Design and Implementation of an Audio 18-Bit Analog-to-Digital Converter Using
Oversampling Techniques,” J. Audio Engineering Society, Vol. 34, March 1986, pp. 153-166.
26. P. Ferguson, Jr., A. Ganesan, R. Adams, et. al., “An 18-Bit 20-kHz Dual Sigma-Delta A/D Converter,”
ISSCC Digest of Technical Papers, February 1991.
27. Robert Adams, Khiem Nguyen, and Karl Sweetland, “A 113 dB SNR Oversampling DAC with
Segmented Noise-Shaped Scrambling,” ISSCC Digest of Technical Papers, vol. 41, 1998, pp. 62, 63,
413. (Describes a segmented audio DAC with data scrambling).
28. Robert W. Adams and Tom W. Kwan, “Data-directed Scrambler for Multi-bit Noise-shaping D/A
Converters,” U.S. Patent 5,404,142, filed August 5, 1993, issued April 4, 1995. (Describes a
segmented audio DAC with data scrambling).
29. Y. Matsuya, et. al., “A 16-Bit Oversampling A/D Conversion Technology Using Triple-Integration
Noise Shaping,” IEEE Journal of Solid-State Circuits, Vol. SC-22, No. 6, December 1987, pp. 921929.
30. Y. Matsuya, et. al., “A 17-Bit Oversampling D/A Conversion Technology Using Multistage Noise
Shaping,” IEEE Journal of Solid-State Circuits, Vol. 24, No. 4, August 1989, pp. 969-975.
6.112
CONVERTERS
SIGMA-DELTA CONVERTERS
31. Paul H. Gailus, William J. Turney, and Francis R. Yester, Jr., “Method and Arrangement for a Sigma
Delta Converter for Band-Pass Signals,” U.S. Patent 4,857,928, filed January 28, 1988, issued August
15, 1989.
32. S.A. Jantzi, M. Snelgrove, and P.F. Ferguson Jr., “A 4th-Order Band-Pass Sigma-Delta Modulator,”
IEEE Journal of Solid State Circuits, Vol. 38, No. 3, March 1993, pp. 282-291.
33. Paul Hendriks, Richard Schreier, Joe DiPilato, “High Performance Narrowband Receiver Design
Simplified by IF Digitizing Subsystem in LQFP,” Analog Dialogue, Vol. 35-3, June-July 2001.
available at http://www.analog.com (Describes an IF subsystem with a band-pass sigma-delta ADC
having a nominal oversampling frequency of 18MSPS, a center frequency of 2.25MHz, and a
bandwidth of 10 kHz - 150 kHz).
6.113
BASIC LINEAR DESIGN
Notes:
6.114
CONVERTERS
DEFINING THE SPECIFICATIONS
SECTION 6.4: DEFINING THE SPECIFICATONS
In specifying a converter there are basically two sets of specifications used for data
converters. They can simplistically be divided into dc and ac specifications. Which you
are more concerned with is based primarily on the application. DC specifications are
more common with lower frequency applications. Here we are measuring against a
reference. In ac specifications we are less concerned with absolute accuracy and more
concerned with relative accuracy. This is not to say the reference is unimportant. It’s just
that we are typically interested in a relative number rather than an absolute. Distortion is
always relative to the fundamental, for instance. While there is no direct conversion
between the two, it is possible to infer that you need good linearity to get good distortion.
It is rare to have a converter specified both ways.
Another point that should be made here is the difference between resolution and
accuracy. While the two terms sometimes tend to be used interchangeably, they are not
the same thing.
Resolution can be defined as the number of bits in the data word of the converter.
Accuracy is the number of those bits that meet the specifications. As an example, an
audio converter may have a data bus width of 24 bits, but only a signal to noise (SNR)
range of 120 dB. 120 dB roughly corresponds to an accuracy of 20 bits. While 120 dB is
not poor performance, it is not 24 bit performance.
You should keep in mind the magnitude in volts as well as in bits of the resolution of the
converter that you are considering. This is shown in Figure 6.112 for a full-scale level of
2 V (note that there is some rounding off of the voltages in this table). This level is not
uncommon for modern systems and is the typical standard for line level audio
measurement. Remember that Gaussian noise of the system will probably set the lower
limit of the accuracy spec. For example, 600 nV is the Johnson Noise in a 10 kHz BW of
a 2.2 kΩ resistor @ 25°C. This corresponds to approximately 21.5 bits.
And some systems use even smaller full scales. Notably the AD7730 Σ-Δ ADC system is
designed to operate with full-scale inputs down to 10 mV. With a 24-bit resolution this
means a LSB weighting of 596 µV.
6.115
BASIC LINEAR DESIGN
RESOLUTION
N
2N
VOLTAGE
(2 V FS)
ppm FS
% FS
dB FS
2-bit
4
500 mV
250,000
25
– 12
4-bit
16
125 mV
62,500
6.25
– 24
6-bit
64
31.2 mV
15,625
1.56
– 36
8-bit
256
7.81 mV
3,906
0.39
– 48
10-bit
1,024
1.95 mV
977
0.098
– 60
12-bit
4,096
488 μV
244
0.024
– 72
14-bit
16,384
122 μV
61
0.0061
– 84
16-bit
65,536
30.5 μV
15
0.0015
– 96
18-bit
262,144
7.62 μV
4
0.0004
– 108
20-bit
1,048,576
1.9 μV
1
0.0001
– 120
22-bit
4,194,304
476 nV
0.24
0.000024
– 132
24-bit
16,777,216
119 nV
0.06
0.000006
– 144
Figure 6.112: LSB size for a 2 V Full-Scale Input
6.116
CONVERTERS
DAC AND ADC STATIC TRANSFER FUNCTION AND DC ERRORS
SECTION 6.5: DAC AND ADC STATIC TRANSFER FUNCTIONS
AND DC ERRORS
The four primary dc errors in a data converter are offset error, gain error, and two types
of linearity error (differential and integral). Offset and gain errors are analogous to offset
and gain errors in amplifiers as shown in Figure 6.113 for a bipolar input range. (Though
offset error and zero error, which are identical in amplifiers and unipolar data converters,
are not identical in bipolar converters and should be carefully distinguished.)
The transfer characteristics of both DACs and ADCs may be expressed as D = K + GA,
where D is the digital code, A is the analog signal, and K and G are constants. In a
unipolar converter, K is zero, and in an offset bipolar converter, it is –1 MSB. The offset
error is the amount by which the actual value of K differs from its ideal value.
+FS
+FS
ACTUAL
ACTUAL
IDEAL
IDEAL
0
0
ZERO ERROR
OFFSET
ERROR
ZERO ERROR
NO GAIN ERROR:
ZERO ERROR = OFFSET ERROR
–FS
–FS
WITH GAIN ERROR:
OFFSET ERROR = 0
ZERO ERROR RESULTS
FROM GAIN ERROR
Figure 6.113: Data Converter Offset and Gain Error
The gain error is the amount by which G differs from its ideal value, and is generally
expressed as the percentage difference between the two, although it may be defined as the
gain error contribution (in mV or LSB) to the total error at full-scale. These errors can
usually be trimmed by the data converter user. Note, however, that amplifier offset is
trimmed at zero input, and then the gain is trimmed near to full-scale. The trim algorithm
for a bipolar data converter is not so straightforward.
The integral linearity error of a converter is also analogous to the linearity error of an
amplifier, and is defined as the maximum deviation of the actual transfer characteristic of
the converter from a straight line, and is generally expressed as a percentage of full-scale
(but may be given in LSBs). For an ADC, the most popular convention is to draw the
straight line through the mid-points of the codes, or the code centers. There are two
common ways of choosing the straight line: end point and best straight line as shown in
Figure 6.114.
6.117
BASIC LINEAR DESIGN
END POINT METHOD
BEST STRAIGHT LINE METHOD
OUTPUT
LINEARITY
ERROR = X
INPUT
LINEARITY
ERROR ≈ X/2
INPUT
Figure 6.114: Method of Measuring Integral Linearity Errors
(Same Converter on Both Graphs)
In the endpoint system, the deviation is measured from the straight line through the origin
and the full-scale point (after gain adjustment). This is the most useful integral linearity
measurement for measurement and control applications of data converters (since error
budgets depend on deviation from the ideal transfer characteristic, not from some
arbitrary “best fit”), and is the one normally adopted by Analog Devices, Inc.
The best straight line, however, does give a better prediction of distortion in ac
applications, and also gives a lower value of “linearity error” on a data sheet. The best fit
straight line is drawn through the transfer characteristic of the device using standard
curve fitting techniques, and the maximum deviation is measured from this line. In
general, the integral linearity error measured in this way is only 50% of the value
measured by end point methods. This makes the method good for producing impressive
data sheets, but it is less useful for error budget analysis. For ac applications, it is even
better to specify distortion than dc linearity, so it is rarely necessary to use the best
straight line method to define converter linearity.
The other type of converter nonlinearity is differential nonlinearity (DNL). This relates to
the linearity of the code transitions of the converter. In the ideal case, a change of 1 LSB
in digital code corresponds to a change of exactly 1 LSB of analog signal. In a DAC, a
change of 1 LSB in digital code produces exactly 1 LSB change of analog output, while
in an ADC there should be exactly 1 LSB change of analog input to move from one
digital transition to the next. Differential linearity error is defined as the maximum
amount of deviation of any quantum (or LSB change) in the entire transfer function from
its ideal size of 1 LSB.
Where the change in analog signal corresponding to 1 LSB digital change is more or less
than 1 LSB, there is said to be a DNL error. The DNL error of a converter is normally
defined as the maximum value of DNL to be found at any transition across the range of
the converter. Figure 6.115 shows the nonideal transfer functions for a DAC and an ADC
and shows the effects of the DNL error.
6.118
CONVERTERS
DAC AND ADC STATIC TRANSFER FUNCTION AND DC ERRORS
DAC
FS
ADC
111
110
ANALOG
OUTPUT
DIGITAL
OUTPUT
NON-MONOTONIC
101
100
MISSING CODE
011
010
001
000
000
001
010
011
100
101
110
ANALOG INPUT
111
FS
DIGITAL INPUT
Figure 6.115: Transfer Functions for Nonideal 3-Bit DAC and ADC
FS
d
1 LSB,
DNL = 0
BIT 2 IS 1 LSB HIGH
BIT 1 IS 1 LSB LOW
2 LSB,
DNL = +1 LSB
ANALOG
OUTPUT
1 LSB,
DNL = 0
2 LSB,
DNL = +1 LSB
1 LSB,
DNL = 0
d
000
001
–1 LSB,
DNL = –2 LSB
1 LSB,
DNL = 0
NON-MONOTONIC IF
DNL < –1 LSB
010 011
100 101 110
DIGITAL CODE INPUT
111
Figure 6.116: Details of DAC Differential Nonlinearity
The DNL of a DAC is examined more closely in Figure 6.116. If the DNL of a DAC is
less than –1 LSB at any transition, the DAC is nonmonotonic i.e., its transfer
characteristic contains one or more localized maxima or minima. A DNL greater than +1
LSB does not cause nonmonotonicity, but is still undesirable. In many DAC applications
(especially closed-loop systems where nonmonotonicity can change negative feedback to
positive feedback), it is critically important that DACs are monotonic. DAC monotonicity
6.119
BASIC LINEAR DESIGN
is often explicitly specified on data sheets, although if the DNL is guaranteed to be less
than 1 LSB (i.e., |DNL| ≤ 1 LSB) then the device must be monotonic, even without an
explicit guarantee.
MISSING CODE (DNL < –1 LSB)
DIGITAL
OUTPUT
CODE
1 LSB,
DNL = 0
0.25 LSB,
DNL = –0.75 LSB
1.5 LSB,
DNL = +0.5 LSB
0.5 LSB,
DNL = –0.5 LSB
1 LSB,
DNL = 0
ANALOG INPUT
Figure 6.117: Details of ADC Differential Nonlinearity
MISSING CODE
DIGITAL
OUTPUT
CODE
NON-MONOTONIC
ANALOG INPUT
Figure 6.118: Nonmonotonic ADC with Missing Code
6.120
CONVERTERS
DAC AND ADC STATIC TRANSFER FUNCTION AND DC ERRORS
In Figure 6.117, the DNL of an ADC is examined more closely on an expanded scale.
ADCs can be nonmonotonic, but a more common result of excess DNL in ADCs is
missing codes. Missing codes in an ADC are as objectionable as nonmonotonicity in a
DAC. Again, they result from DNL < –1 LSB.
Not only can ADCs have missing codes, they can also be nonmonotonic as shown in
Figure 6.118. As in the case of DACs, this can present major problems—especially in
servo applications.
In a DAC, there can be no missing codes—each digital input word will produce a
corresponding analog output. However, DACs can be nonmonotonic as previously
discussed. In a straight binary DAC, the most likely place a nonmonotonic condition can
develop is at midscale between the two codes: 011…11 and 100…00. If a nonmonotonic
condition occurs here, it is generally because the DAC is not properly calibrated or
trimmed. A successive approximation ADC with an internal nonmonotonic DAC will
generally produce missing codes but remain monotonic. However it is possible for an
ADC to be nonmonotonic—again depending on the particular conversion architecture.
Figure 6.118 shows the transfer function of an ADC which is nonmonotonic and has a
missing code.
(A) NON-MONOTONIC
(B) WIDE CODES
(C) MISSING CODES
NON-MONOTONIC
MISSING
CODE
WIDE
CODE
NON-MONOTONIC
MISSING
CODE
WIDE
CODE
ANALOG INPUT
Figure 6.119: Errors Associated with Improperly Trimmed Subranging ADC
ADCs which use the subranging architecture divide the input range into a number of
coarse segments, and each coarse segment is further divided into smaller segments—and
ultimately the final code is derived. This process is described in more detail in Chapter 4
of this book. An improperly trimmed subranging ADC may exhibit nonmonotonicity,
wide codes, or missing codes at the subranging points as shown in Figure 6.119 A, B, and
C, respectively. This type of ADC should be trimmed so that drift due to aging or
temperature produces wide codes at the sensitive points rather than nonmonotonic or
missing codes.
6.121
BASIC LINEAR DESIGN
Defining missing codes is more difficult than defining nonmonotonicity. All ADCs suffer
from some inherent transition noise as shown in Figure 6.120 (think of it as the flicker
between adjacent values of the last digit of a DVM). As resolutions and bandwidths
become higher, the range of input over which transition noise occurs may approach, or
even exceed, 1 LSB. High resolution wideband ADCs generally have internal noise
sources which can be reflected to the input as effective input noise summed with the
signal. The effect of this noise, especially if combined with a negative DNL error, may be
that there are some (or even all) codes where transition noise is present for the whole
range of inputs. There are therefore some codes for which there is no input which will
guarantee that code as an output, although there may be a range of inputs which will
sometimes produce that code.
CODE TRANSITION NOISE
DNL
TRANSITION NOISE
AND DNL
ADC
OUTPUT
CODE
ADC INPUT
ADC INPUT
ADC INPUT
Figure 6.120: Combined Effects of Code Transition Noise and DNL
For low resolution ADCs, it may be reasonable to define no missing codes as a
combination of transition noise and DNL which guarantees some level (perhaps 0.2 LSB)
of noise-free code for all codes. However, this is impossible to achieve at the very high
resolutions achieved by modern sigma-delta ADCs, or even at lower resolutions in wide
bandwidth sampling ADCs. In these cases, the manufacturer must define noise levels and
resolution in some other way. Which method is used is less important, but the data sheet
should contain a clear definition of the method used and the performance to be expected.
A complete discussion of effective input noise follows later in this chapter.
The discussion thus far has not dealt with the most important dc specifications associated
with data converters. Other less important specifications require only a definition.
Accuracy, Absolute. Absolute accuracy error of a DAC is the difference between actual
analog output and the output that is expected when a given digital code is applied to the
converter. Error is usually commensurate with resolution, i.e., less 1/2 LSB of full-scale,
for example. However, accuracy may be much better than resolution in some
applications; for example, a 4-bit reference supply having only 16 discrete digitally
chosen levels would have a resolution of 1/16, but it might have an accuracy to within
0.01 % of each ideal value.
6.122
CONVERTERS
DAC AND ADC STATIC TRANSFER FUNCTION AND DC ERRORS
Absolute accuracy error of an ADC at a given output code is the difference between the
actual and the theoretical analog input voltages required to produce that code. Since the
code can be produced by any analog voltage in a finite band (see Quantizing
Uncertainty), the “input required to produce that code” is defined as the midpoint of the
band of inputs that will produce that code. For example, if 5 volts, ±1.2 mV, will
theoretically produce a 12-bit half-scale code of 1000 0000 0000, then a converter for
which any voltage from 4.997 V to 4.999 V will produce that code will have absolute
error of (1/2)(4.997 + 4.999) – 5 V = +2 mV.
Sources of error include gain (calibration) error, zero error, linearity errors, and noise.
Absolute accuracy measurements should be made under a set of standard conditions with
sources and meters traceable to an internationally accepted standard.
Accuracy, Logarithmic DACs. The difference (measured in dB) between the actual
transfer function and the ideal transfer function, as measured after calibration of gain
error at 0 dB.
Accuracy, Relative. Relative accuracy error, expressed in %, ppm, or fractions of 1 LSB,
is the deviation of the analog value at any code (relative to the full analog range of the
device transfer characteristic) from its theoretical value (relative to the same range), after
the full-scale range (FSR) has been calibrated (see Full-Scale Range).
Since the discrete analog values that correspond to the digital values ideally lie on a
straight line, the specified worst case relative accuracy error of a linear
ADC or DAC can be interpreted as a measure of end-point nonlinearity (see Linearity).
The “discrete points” of a DAC transfer characteristic are measured by the actual analog
outputs. The “discrete points” of an ADC transfer characteristic are the midpoints of the
quantization bands at each code (see Accuracy, Absolute).
Temperature Coefficient. In general, temperature instabilities are expressed as %/°C,
ppm/°C, fractions of 1 LSB per degree C, or as a change in a parameter over a specified
temperature range. Measurements are usually made at room temperature and at the
extremes of the specified range, and the temperature coefficient (tempco, TC) is defined
as the change in the parameter, divided by the corresponding temperature change.
Parameters of interest include gain, linearity, offset (bipolar), and zero.
a. Gain Tempco: Two factors principally affect converter gain stability with
temperature. In fixed-reference converters, the reference voltage will vary with
temperature. The reference circuitry and switches (and comparator in aid converters) will
also contribute to the overall gain TC.
b. Linearity Tempco: Sensitivity of linearity (integral and/or differential linearity)
to temperature, in % FSR/°C or ppm FSR/°C, over the specified range. Monotonic
behavior in DACs is achieved if the differential nonlinearity is less than 1 LSB at any
temperature in the range of interest. The differential nonlinearity temperature coefficient
may be expressed as a ratio, as a maximum change over a temperature range, and/or
implied by a statement that the device is monotonic over the specified temperature range.
To avoid missing codes in noiseless ADCs, it is sufficient that the differential
6.123
BASIC LINEAR DESIGN
nonlinearity error magnitude be greater than –1 LSB at any temperature in the range of
interest. The differential nonlinearity temperature coefficient is often implied by the
statement that there are no missed codes when operating within a specified temperature
range. In DACs, the differential nonlinearity TC is often implied by the statement that the
DAC is monotonic over a specified temperature range.
c. Zero TC (unipolar converters): The temperature stability of a unipolar
fixed-reference DAC, measured in % FSR/°C or ppm FSR/°C, is principally affected by
current leakage (current-output DAC), and offset voltage and bias current of the output
op amp (voltage-output DAC). The zero stability of an ADC is dependent on the zero
stability of the DAC or integrator and/or the input buffer and the comparator. It is
typically expressed in µV/°C or in percent or ppm of full-scale range (FSR) per degree C.
d. Offset Tempco: The temperature coefficient of the all-DAC-switches-off
(minus full-scale) point of a bipolar converter (in % FSR/°C or ppm FSR/°C) depends on
three major factors—the tempco of the reference source, the voltage zero-stability of the
output amplifier, and the tracking capability of the bipolar-offset resistors and the gain
resistors. In an ADC, the corresponding tempco of the negative full-scale point depends
on similar quantities—the tempco of the reference source, the voltage stability of the
input buffer and the sample-and-hold, and the tracking capabilities of the bipolar offset
resistors and the gain-setting resistors.
Common-Mode Range. Common-mode rejection usually varies with the magnitude of the
range through which the input signal can swing, determined by the sum of the commonmode and the differential voltage. Common-mode range is that range of total input
voltage over which specified common-mode rejection is maintained. For example, if the
common-mode signal is ±5 V and the differential signal is ±5 V, the common-mode
range is ±10 V.
Common-Mode Rejection (CMR) is a measure of the change in output voltage when both
inputs are changed by equal amounts of ac and/or dc voltage. Common-mode rejection is
usually expressed either as a ratio (e.g., CMRR = 1,000,000:1), or in decibels: CMR =
20log10CMRR; if CMRR = 106, CMR = 120 dB. A CMRR of 106 means that 1 volt of
common mode is processed by the device as though it were a differential signal of 1microvolt at the input.
CMR is usually specified for a full-range common-mode voltage change (CMV), at a
given frequency, and a specified imbalance of source impedance (e.g., 1 kΩ source
unbalance, at 60 Hz). In amplifiers, the common-mode rejection ratio is defined as the
ratio of the signal gain, G, to the common-mode gain (the ratio of common-mode signal
appearing at the output to the CMV at the input.
Common-Mode Voltage (CMV). A voltage that appears in common at both input
terminals of a device, with respect to its output reference (usually "ground"). For inputs,
V1 and V2, with respect to ground, CMV = ½(V1 + V2). An ideal differential-input device
would ignore CMV. Common-mode error (CME) is any error at the output due to the
common-mode input voltage. The errors due to supply-voltage variation, an internal
common- mode effect, are specified separately.
6.124
CONVERTERS
DAC AND ADC STATIC TRANSFER FUNCTION AND DC ERRORS
Compliance-Voltage Range. For a current source (e.g., a current-output DAC), the
maximum range of (output) terminal voltage for which the device will maintain the
specified current-output characteristics.
Differential Analog Input Resistance, Differential Analog Input Capacitance, and
Differential Analog Input Impedance. The real and complex impedances measured at
each analog input port of an ADC. The resistance is measured statically and the
capacitance and differential input impedances are measured with a network analyzer.
Differential Analog Input Voltage Range. The peak-to-peak differential voltage that must
be applied to the converter to generate a full-scale response. Peak differential voltage is
computed by observing the voltage on a single pin and subtracting the voltage from the
other pin, which is 180 degrees out of phase. Peak-to-peak differential is computed by
rotating the inputs phase 180 degrees and taking the peak measurement again. Then the
difference is computed between both peak measurements.
Full-Scale Range (FSR). For binary ADCs and DACs, that magnitude of voltage, current,
or-in a multiplying DAC-gain, of which the MSB is specified to be exactly one-half or
for which any bit or combination of bits is tested against its (their) prescribed ideal
ratio(s). FSR is independent of resolution; the value of the LSB (voltage, current, or gain)
is 2–N FSR. There are several other terms, with differing meanings, that are often used in
the context of discussions or operations involving full-scale range. They are:
Full-scale—similar to full-scale range, but pertaining to a single polarity. Thus,
full-scale for a unipolar device is twice the prescribed value of the MSB and has the same
polarity. For a bipolar device, positive or negative full-scale is that positive or negative
value, of which the next bit after the polarity bit is tested to be one-half.
Span—the scalar voltage or current range corresponding to FSR.
All-1’s—All bits on, the condition used, in conjunction with all-zeros, for gain
adjustment of an ADC or DAC, in accordance with the manufacturer's instructions. Its
magnitude, for a binary device, is (l – 2–N) FSR. All-1’s is a positive-true definition of a
specific magnitude relationship; for complementary coding the “all-l's” code will actually
be all zeros. To avoid confusion, all-l’s should never be called "full-scale;" FSR and FS
are independent of the number of bits, all-l’s isn't.
All-0’s—All bits off, the condition used in offset (and gain) adjustment of a DAC
or ADC, according to the manufacturer's instructions. All-0’s corresponds to zero output
in a unipolar DAC and negative full-scale in an offset bipolar DAC with positive output
reference. In a sign-magnitude device, all-0’s refers to all bits after the sign bit.
Analogous to “all-l’s,” “all-0’s” is a positive-true definition of the all-bits-off condition;
in a complementary-coded device, it is expressed by all ones. To avoid confusion, all-0’s
should not be called “zero” unless it accurately corresponds to true analog zero output
from a DAC.
The best way of defining the critical points for an actual device is a brief table of critical
codes and the ideal voltages, currents, or gains to which they correspond, with the
conditions for measurement defined.
6.125
BASIC LINEAR DESIGN
Gain: The “gain” of a converter is that analog scale factor setting that establishes the
nominal conversion relationship, e.g., 10 volts full-scale. In a multiplying DAC or
ratiometric ADC, it is indeed a gain. In a device with fixed internal reference, it is
expressed as the full-scale magnitude of the output parameter (e.g., 10 volts or 2
milliamperes). In a fixed-reference converter, where the use of the internal reference is
optional, the converter gain and the reference may be specified separately. Gain and zero
adjustment are discussed under zero.
Impedance, Input: The dynamic load of an ADC presented to its input source. In
unbuffered CMOS switched-capacitor ADCs, the presence of current transients at the
converter's clock frequency mandates that the converter be driven from a low impedance
(at the frequencies contained in the transients) in order to accurately convert. For
buffered-input ADCs, the input impedance is generally represented by a resistive and
capacitive component.
Input-Referred Noise (Effective Input Noise): Input-referred noise can be viewed as the
net effect of all internal ADC noise sources referred to the input. It is generally expressed
in LSBs rms, but can also be expressed as a voltage. It can be converted to a peak-to-peak
value by multiplying by the factor 6.6. The peak-to-peak input-referred noise can then be
used to calculate the noise-free code resolution. (See noise-free code resolution).
Leakage Current, Output: Current which appears at the output terminal of a DAC with all
bits “off.” For a converter with two complementary outputs (for example, many fast
CMOS DACs), output leakage current is the current measured at OUT 1, with all digital
inputs low—and the current measured at OUT 2, with all digital inputs high.
Output Propagation Delay: For an ADC having a single-ended sampling (or ENCODE)
clock input, the delay between the 50% point of the sampling clock and the time when all
output data bits are within valid logic levels. For an ADC having differential sampling
clock inputs, the delay is measured with respect to the zero-crossing of the differential
sampling clock signal.
Output Voltage Tolerance: For a reference, the maximum deviation from the normal
output voltage at 25°C and specified input voltage, as measured by a device traceable to a
recognized fundamental voltage standard.
Overload: An input voltage exceeding the ADC's full-scale input range producing an
overload condition.
Overvoltage Recovery Time: Overvoltage recovery time is defined as the amount of time
required for an ADC to achieve a specified accuracy after an overvoltage (usually 50%
greater than full-scale range), measured from the time the overvoltage signal reenters the
converter's range. The ADC should act as an ideal limiter for out-of-range signals,
producing a positive or negative full-scale code during the overvoltage condition. Some
ADCs provide over- and under-range flags to allow gain-adjustment circuits to be
activated.
Overrange, Overvoltage: An input signal that exceeds the input range of an ADC, but is
less than an overload.
6.126
CONVERTERS
DAC AND ADC STATIC TRANSFER FUNCTION AND DC ERRORS
Power-Supply Rejection Ratio (PSRR: The ratio of a change in dc power supply voltage
to the resulting change in the specified device error, expressed in percentage, parts per
million, or fractions of 1 LSB. It may also be expressed logarithmically, in dB (PSR = 20
log10 (PSRR)).
Power Supply Sensitivity. The sensitivity of a converter to changes in the power supply
voltages is normally expressed in terms of percent-of-full-scale change in analog value or
fractions of 1 LSB—(DAC output, ADC output code-center) for a 1% dc change in the
power supply, e.g., 0.05%/% ΔVS. Power supply sensitivity may also be expressed in
relation to a specified maximum dc shift of power supply voltage. A converter might be
considered “good” if the change in reading at full-scale does not exceed ±½ LSB for a
3% change in power supply voltage. Even better specs are necessary for converters
designed for direct battery operation.
Ratiometric: The output of an ADC is a digital number proportional to the ratio of (some
measure of) the input to a reference voltage. Most requirements for conversions call for
an absolute measurement, i.e., against a fixed reference; but this presumes that the signal
applied to the converter is either reference independent, or in some way derived from
another fixed reference. However, real references are not truly fixed; the references for
both the converter and the signal source vary with time, temperature, loading, etc.
Therefore, if the converter is used with signal sources that also rely on references (for
example, strain-gage bridges, RTDs, thermistors), it makes sense to replace this
multiplicity of references by a single system reference; reference-caused errors will tend
to cancel out. This can be done by using the converter's internal reference (if it has one)
as the system reference. Another way is to use a separate external system reference,
which also becomes the reference for a ratiometric converter.
Over limited ranges, ratiometric conversion can also serve as a substitute for analog or
digital signal division (where the denominator changes by less than ½LSB during the
conversion). The signal input is the numerator; the reference input is the denominator.
Total Unadjusted Error: A comprehensive specification on some devices which includes
full-scale error, relative-accuracy and zero-code errors, under a specified set of
conditions.
6.127
BASIC LINEAR DESIGN
Notes:
6.128
CONVERTERS
DATA CONVERTER AC ERRORS
SECTION 6.6: DATA CONVERTER AC ERRORS
This section examines the ac errors associated with data converters. Many of the errors
and specifications apply equally to ADCs and DACs, while some are more specific to
one or the other. All possible specifications are not discussed here, only the most popular
ones.
fs
ANALOG
INPUT
fa
IDEAL
N-BIT
ADC
N
BUFFER
MEMORY
M-WORDS
M POINT
M-POINT
2
FFT
PROCESSOR SPECTRAL
OUTPUT
Figure 6.121: Dynamic Performance Analysis of an Ideal N-bit ADC
In most applications, the input to the ADC is a band of frequencies (usually summed with
some noise), so the quantization noise tends to be random. In spectral analysis
applications (or in performing FFTs on ADCs using spectrally pure sinewaves—see
Figure 6.121), however, the correlation between the quantization noise and the signal
depends upon the ratio of the sampling frequency to the input signal. This is
demonstrated in Figure 6.122, where an ideal 12-bit ADCs output is analyzed using a
4096-point FFT. In the left-hand FFT plot, the ratio of the sampling frequency to the
input frequency was chosen to be exactly 32, and the worst harmonic is about 76 dB
below the fundamental. The right hand diagram shows the effects of slightly offsetting
the ratio to 4096/127 = 32.25196850394, showing a relatively random noise spectrum,
where the SFDR is now about 92 dBc. In both cases, the rms value of all the noise
components is approximately q/√12, but in the first case, the noise is concentrated at
harmonics of the fundamental.
fs / fa = 32
M = 4096
fs / fa = 4096 / 127
Figure 6.122: Effect of Ratio of Sampling Clock to Input Frequency
on SFDR for Ideal 12-bit ADC
6.129
BASIC LINEAR DESIGN
Note that this variation in the apparent harmonic distortion of the ADC is an artifact of
the sampling process and the correlation of the quantization error with the input
frequency. In a practical ADC application, the quantization error generally appears as
random noise because of the random nature of the wideband input signal and the
additional fact that there is a usually a small amount of system noise which acts as a
dither signal to further randomize the quantization error spectrum.
It is important to understand the above point, because single-tone sine wave FFT testing
of ADCs is a universally accepted method of performance evaluation. In order to
accurately measure the harmonic distortion of an ADC, steps must be taken to ensure that
the test setup truly measures the ADC distortion, not the artifacts due to quantization
noise correlation. This is done by properly choosing the frequency ratio and sometimes
by injecting a small amount of noise (dither) with the input signal. The exact same
precautions apply to measuring DAC distortion with an analog spectrum analyzer.
Figure 6.123 shows the FFT output for an ideal 12-bit ADC. Note that the average value
of the noise floor of the FFT is approximately 100 dB below full-scale, but the theoretical
SNR of a 12-bit ADC is 74 dB. The FFT noise floor is not the SNR of the ADC, because
the FFT acts like an analog spectrum analyzer with a bandwidth of fs/M, where M is the
number of points in the FFT. The theoretical FFT noise floor is therefore
10log10(M/2) dB below the quantization noise floor due to the processing gain of the
FFT. In the case of an ideal 12-bit ADC with an SNR of 74 dB, a 4096-point FFT would
result in a processing gain of 10log10(4096/2) = 33 dB, thereby resulting in an overall
FFT noise floor of 74 + 33 = 107 dBc. In fact, the FFT noise floor can be reduced even
further by going to larger and larger FFTs; just as an analog spectrum analyzer’s noise
floor can be reduced by narrowing the bandwidth. When testing ADCs using FFTs, it is
important to ensure that the FFT size is large enough so that the distortion products can
be distinguished from the FFT noise floor itself.
(dB)
0
ADC FULLSCALE
N = 12-BITS
M = 4096
20
40
74dB = 6.02N + 1.76dB
60
RMS QUANTIZATION NOISE LEVEL
80
74dB
(M)
33dB = 10log10 2
100
FFT NOISE FLOOR
120
BIN SPACING =
fs
4096
107dB
fs
2
Figure 6.123: Noise Floor for an Ideal 12-bit ADC Using 4096-point FFT
6.130
CONVERTERS
DATA CONVERTER AC ERRORS
Noise in Practical ADCs
A practical sampling ADC (one that has an integral sample-and-hold), regardless of
architecture, has a number of noise and distortion sources as shown in Figure 6.124. The
wideband analog front-end buffer has wideband noise, nonlinearity, and also finite
bandwidth. The SHA introduces further nonlinearity, bandlimiting, and aperture jitter.
The actual quantizer portion of the ADC introduces quantization noise, and both integral
and differential nonlinearity. In this discussion, assume that sequential outputs of the
ADC are loaded into a buffer memory of length M and that the FFT processor provides
the spectral output. Also assume that the FFT arithmetic operations themselves introduce
no significant errors relative to the ADC. However, when examining the output noise
floor, the FFT processing gain (dependent on M) must be considered.
fs
ANALOG
INPUT
ADC
TO MEMORY
SAMPLE
AND
HOLD
BUFFER
NOISE
DISTORTION
BAND LIMITING
ENCODER
N-BITS
NOISE
DISTORTION
BAND LIMITING
APERTURE JITTER
N
TEST
SYS TEM
BUFFER
MEMORY
M- WORDS
M-POINT
FFT
PROCESSOR
QUANTIZATION NOISE
DIFFERENTIAL NON-LINEARITY
INTEGRAL NON-LINEARITY
M
POINT
2
SPECTRAL
OUTPUT
PROCESS ING GAIN = 10log10
( M2 )
ROUND OFF ERROR (NEGLIGIBLE)
Figure 6.124: ADC Model Showing Noise and Distortion Sources
Equivalent Input Referred Noise
Wideband ADC internal circuits produce a certain amount of rms noise due to resistor
and kT/C noise. This noise is present even for dc-input signals, and accounts for the fact
that the output of most wideband (or high resolution) ADCs is a distribution of codes,
centered around the nominal value of a dc input (see Figure 6.125). To measure its value,
the input of the ADC is either grounded or connected to a heavily decoupled voltage
source, and a large number of output samples are collected and plotted as a histogram
(sometimes referred to as a grounded-input histogram). Since the noise is approximately
Gaussian, the standard deviation of the histogram is easily calculated (see Reference 6),
corresponding to the effective input rms noise. It is common practice to express this rms
noise in terms of LSBs rms, although it can be expressed as an rms voltage referenced to
the ADC full-scale input range.
6.131
BASIC LINEAR DESIGN
NUMBER OF
OCCURANCES
P-P INPUT NOISE
≈
6.6 × RMS NOISE
RMS NOISE (LSBs)
n–4
n–3
n–2
n–1
n
n+1
n+2
n+3
n+4
OUTPUT CODE
Figure 6.125: Effect of Input-Referred Noise on ADC "Grounded Input"
Histogram
Noise-Free (Flicker-Free) Code Resolution
The noise-free code resolution of an ADC is the number of bits beyond which it is
impossible to distinctly resolve individual codes. The cause is the effective input noise
(or input-referred noise) associated with all ADCs and described above. This noise can be
expressed as an rms quantity, usually having the units of LSBs rms. Multiplying by a
factor of 6.6 converts the rms noise into peak-to-peak noise (expressed in LSBs peak-topeak). The total range of an N-bit ADC is 2N LSBs. The noise-free (or flicker-free)
resolution can be calculated using the equation:
Noise-Free Code Resolution = log2 (2N/Peak-to-Peak Noise).
Eq. 6.17
The specification is generally associated with high-resolution sigma-delta measurement
ADCs, but is applicable to all ADCs.
The ratio of the FS range to the rms input noise is sometimes used to calculate resolution.
In this case, the term effective resolution is used. Note that under identical conditions,
effective resolution is larger than noise-free code resolution by log2(6.6), or
approximately 2.7 bits.
Effective Resolution = log2 (2N/RMS Input Noise)
Effective Resolution = Noise-Free Code Resolution + 2.7 bits.
The calculations are summarized in Figure 6.126.
6.132
Eq. 6.18
Eq. 6.19
CONVERTERS
DATA CONVERTER AC ERRORS
Effective Input Noise
= en rms
Peak-to-Peak Input Noise = 6.6 en rms
Noise-Free Code Resolution = log2 Peak-to-Peak Input Range
Peak-to-Peak Input Noise
= log2
"Effective Resolution" = log2
= log2
2N
Peak-to-Peak Input Noise (LSBs)
Peak-to-Peak Input Range
RMS Input Noise
2N
RMS Input Noise (LSBs)
= Noise-Free Code Resolution + 2.7 bits
Figure 6.126: Calculating Noise-Free (Flicker-Free) Code Resolution
from Input-Referred Noise
Dynamic Performance of Data Converters
There are various ways to characterize the ac performance of ADCs. In the early years of
ADC technology (over 30 years ago) there was little standardization with respect to ac
specifications, and measurement equipment and techniques were not well understood or
available. Over nearly a 30 year period, manufacturers and customers have learned more
about measuring the dynamic performance of converters, and the specifications shown in
Figure 6.127 represent the most popular ones used today. Practically all the specifications
represent the converter’s performance in the frequency domain. The FFT is the heart of
practically all these measurements and is discussed in more detail in a latter section.
Integral and Differential Nonlinearity Distortion Effects
One of the first things to realize when examining the nonlinearities of data converters is
that the transfer function of a data converter has artifacts which do not occur in
conventional linear devices such as op amps or gain blocks. The overall integral
nonlinearity of an ADC is due to the integral nonlinearity of the front-end and SHA as
well as the overall integral nonlinearity in the ADC transfer function. However,
differential nonlinearity is due exclusively to the encoding process and may vary
considerably dependent on the ADC encoding architecture. Overall integral nonlinearity
produces distortion products whose amplitude varies as a function of the input signal
amplitude. For instance, second-order intermodulation products increase 2 dB for every
6.133
BASIC LINEAR DESIGN
1-dB increase in signal level, and third-order products increase 3 dB for every 1-dB
increase in signal level.
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‹
‹
‹
‹
‹
‹
‹
‹
‹
‹
‹
‹
‹
‹
Harmonic Distortion
Worst Harmonic
Total Harmonic Distortion (THD)
Total Harmonic Distortion Plus Noise (THD + N)
Signal-to-Noise-and-Distortion Ratio (SINAD, or S/N +D)
Effective Number of Bits (ENOB)
Signal-to-Noise Ratio (SNR)
Analog Bandwidth (Full-Power, Small-Signal)
Spurious Free Dynamic Range (SFDR)
Two-Tone Intermodulation Distortion
Multi-tone Intermodulation Distortion
Noise Power Ratio (NPR)
Adjacent Channel Leakage Ratio (ACLR)
Noise Figure
Settling Time, Overvoltage Recovery Time
Figure 6.127: Quantifying Data Converter Dynamic Performance
OUT
OUT
IN
IN
MIDSCALE DNL
(A)
1/4FS, 3/4FS DNL
(B)
Figure 6.128: Typical ADC/ DAC DNL Errors (Exaggerated)
The differential nonlinearity in the ADC transfer function produces distortion products
which not only depend on the amplitude of the signal but the positioning of the
differential nonlinearity errors along the ADC transfer function. Figure 6.128 shows two
6.134
CONVERTERS
DATA CONVERTER AC ERRORS
ADC transfer functions having differential nonlinearity. The left-hand diagram shows an
error which occurs at mid-scale. Therefore, for both large and small signals, the signal
crosses through this point producing a distortion product which is relatively independent
of the signal amplitude. The right-hand diagram shows another ADC transfer function
which has differential nonlinearity errors at 1/4 full-scale and 3/4 full-scale. Signals
which are above 1/2 scale peak-to-peak will exercise these codes and produce distortion,
while those less than 1/2 scale peak-to-peak will not.
Most high-speed ADCs are designed so that differential nonlinearity is spread across the
entire ADC range. Therefore, for signals which are within a few dB of full-scale, the
overall integral nonlinearity of the transfer function determines the distortion products.
For lower level signals, however, the harmonic content becomes dominated by the
differential nonlinearities and does not generally decrease proportionally with decreases
in signal amplitude.
Harmonic Distortion, Worst Harmonic, Total Harmonic Distortion
(THD), Total Harmonic Distortion Plus Noise (THD + N)
There are a number of ways to quantify the distortion of an ADC. An FFT analysis can be
used to measure the amplitude of the various harmonics of a signal. The harmonics of the
input signal can be distinguished from other distortion products by their location in the
frequency spectrum. Figure 6.129 shows a 7 MHz input signal sampled at 20 MSPS and
the location of the first 9 harmonics. Aliased harmonics of fa fall at frequencies equal to
|±Kfs ± nfa|, where n is the order of the harmonic, and K = 0, 1, 2, 3, ... The second and
third harmonics are generally the only ones specified on a data sheet because they tend to
be the largest, although some data sheets may specify the value of the worst harmonic.
RELATIVE
AMPLITUDE
fa = 7MHz
fs = 20MSPS
HARMONICS AT: |±Kfs±nfa|
n = ORDER OF HARMONIC, K = 0, 1, 2, 3, . . .
3
2
6
1
2
9
8
5
3
4
5
4
6
7
8
7
9
10
FREQUENCY (MHz)
Figure 6.129: Location of Distortion Products:
Input Signal = 7 MHz, Sampling Rate = 20 MSPS
6.135
BASIC LINEAR DESIGN
Harmonic distortion is normally specified in dBc (decibels below carrier), although at
audio frequencies it may be specified as a percentage. Harmonic distortion is generally
specified with an input signal near full-scale (generally 0.5 dB to 1 dB below full-scale to
prevent clipping), but it can be specified at any level. For signals much lower than fullscale, other distortion products due to the DNL of the converter (not direct harmonics)
may limit performance.
Total harmonic distortion (THD) is the ratio of the rms value of the fundamental signal to
the mean value of the root-sum-square of its harmonics (generally, only the first five are
significant). THD of an ADC is also generally specified with the input signal close to
full-scale, although it can be specified at any level.
Total harmonic distortion plus noise (THD + N) is the ratio of the rms value of the
fundamental signal to the mean value of the root-sum-square of its harmonics plus all
noise components (excluding dc). The bandwidth over which the noise is measured must
be specified. In the case of an FFT, the bandwidth is dc to fs/2. (If the bandwidth of the
measurement is dc to fs/2, THD + N is equal to SINAD—see below).
Signal-to-Noise-and-Distortion Ratio (SINAD), Signal-to-Noise Ratio
(SNR), and Effective Number of Bits (ENOB)
SINAD and SNR deserve careful attention, because there is still some variation between
ADC manufacturers as to their precise meaning. Signal-to-noise-and Distortion (SINAD,
or S/(N + D) is the ratio of the rms signal amplitude to the mean value of the root-sumsquare (rss) of all other spectral components, including harmonics, but excluding dc (see
Figure 6.130). SINAD is a good indication of the overall dynamic performance of an
ADC as a function of input frequency because it includes all components which make up
noise (including thermal noise) and distortion. It is often plotted for various input
amplitudes. SINAD is equal to THD + N if the bandwidth for the noise measurement is
the same. A typical plot for the AD9226 12-bit, 65-MSPS ADC is shown in Figure 6.131.
‹ SINAD (Signal-to-Noise-and-Distortion Ratio):
z The ratio of therms signal amplitude to the meanvalue of the
root-sum-squares (RSS) of all other spectral components,
including harmonics, but excluding DC.
‹ ENOB (Effective Number ofBits):
ENOB =
SINAD – 1.76dB
6.02
‹ SNR (Signal-to-Noise Ratio, or Signal-to-Noise Ratio Without
Harmonics:
z The ratio of therms signal amplitude to the meanvalue of the
root-sum-squares (RSS) of all other spectral components,
excluding the first 5 harmonics and DC
Figure 6.130: SINAD, ENOB, and SNR
6.136
CONVERTERS
DATA CONVERTER AC ERRORS
12.2
75
2V SPAN, DIFFERENTIAL
11.4
1V SPAN,
DIFFERENTIAL
SINAD (dBc)
65
10.6
9.8
60
1V SPAN,
SINGLE-ENDED
55
8.9
50
8.1
ENOB (Bits)
70
2V SPAN, SINGLE-ENDE D
45
1
10
100
7.3
1000
FREQUENCY (MHz)
Figure 6.131: AD9226 12-bit, 65-MSPS ADC SINAD and ENOB
for Various Input Full-Scale Spans (Range)
The SINAD plot shows where the ac performance of the ADC degrades due to high
frequency distortion and is usually plotted for frequencies well above the Nyquist
frequency so that performance in undersampling applications can be evaluated. SINAD is
often converted to effective-number-of-bits (ENOB) using the relationship for the
theoretical SNR of an ideal N-bit ADC: SNR = 6.02N + 1.76 dB. The equation is solved
for N, and the value of SINAD is substituted for SNR:
ENOB =
SINAD − 1.76dB
.
6.02
Eq. 6.20
Signal-to-noise ratio (SNR, or SNR-without-harmonics) is calculated the same as SINAD
except that the signal harmonics are excluded from the calculation, leaving only the noise
terms. In practice, it is only necessary to exclude the first five harmonics since they
dominate. The SNR plot will degrade at high frequencies, but not as rapidly as SINAD
because of the exclusion of the harmonic terms.
Many current ADC data sheets somewhat loosely refer to SINAD as SNR, so the
engineer must be careful when interpreting these specifications.
Analog Bandwidth
The analog bandwidth of an ADC is that frequency at which the spectral output of the
fundamental swept frequency (as determined by the FFT analysis) is reduced by 3 dB. It
may be specified for either a small signal (SSBW—small signal bandwidth), or a full6.137
BASIC LINEAR DESIGN
scale signal (FPBW—full power bandwidth), so there can be a wide variation in
specifications between manufacturers.
The small signal bandwidth will be larger than the full power bandwidth. This issue is
one of slew rate for the analog portion of the converter. This is similar to the bandwidth
specifications of an op amp.
Like an amplifier, the analog bandwidth specification of a converter does not imply that
the ADC maintains good distortion performance up to its bandwidth frequency. In fact,
the SINAD (or ENOB) of most ADCs will begin to degrade considerably before the input
frequency approaches the actual 3 dB bandwidth frequency. Figure 6.132 shows ENOB
and full-scale frequency response of an ADC with a FPBW of 1 MHz, however, the
ENOB begins to drop rapidly above 100 kHz.
FPBW = 1MHz
GAIN (FS INPUT)
GAIN
ENOB (FS INPUT)
ENOB
ENOB (-20dB INPUT)
10
100
1k
10k
100k
1M
10M
ADC INPUT FREQUENCY (Hz)
Figure 6.132: ADC Gain (Bandwidth) and ENOB vs. Frequency Shows
Importance of ENOB Specification
In some systems, notably video applications the bandwidth is specified to the level at
which the level is reduced by 0.1 dB.
Spurious-Free Dynamic Range (SFDR)
Probably the most significant specification for an ADC used in a communications
application is its spurious-free dynamic range (SFDR). The SFDR specification is to
ADCs what the third order intercept specification is to mixers and LNAs. SFDR of an
ADC is defined as the ratio of the rms signal amplitude to the rms value of the peak
spurious spectral content measured over the bandwidth of interest. Unless otherwise
stated, the bandwidth is assumed to be the Nyquist bandwidth dc to fs/2.
6.138
CONVERTERS
DATA CONVERTER AC ERRORS
Occasionally the frequency spectrum is divided into an in-band region (containing the
signals of interest) and an out-of-band region (signals here are filtered out digitally). In
this case there may be an in-band SFDR specification and an out-of-band SFDR
specification, respectively.
SFDR is generally plotted as a function of signal amplitude and may be expressed
relative to the signal amplitude (dBc) or the ADC full-scale (dBFS) as shown in
Figure 6.133.
FULL SCALE (FS)
INPUT SIGNAL LEVEL (CARRIER)
SFDR (dBFS)
dB
SFDR (dBc)
WORST SPUR LEVEL
FREQUENCY
fs
2
Figure 6.133: Spurious-Free Dynamic Range (SFDR)
FREQUENCY (MHz)
Figure 6.134: AD6645 14-bit, 80-MSPS ADC SFDR for 69.1 MHz Input
6.139
BASIC LINEAR DESIGN
For a signal near full-scale, the peak spectral spur is generally determined by one of the
first few harmonics of the fundamental. However, as the signal falls several dB below
full-scale, other spurs generally occur which are not direct harmonics of the input signal.
This is because of the differential nonlinearity of the ADC transfer function as discussed
earlier. Therefore, SFDR considers all sources of distortion, regardless of their origin.
The AD6645 is a 14-bit, 80-MSPS wideband ADC designed for communications
applications where high SFDR is important. The single-tone SFDR for a 69.1-MHz input
and a sampling frequency of 80 MSPS is shown in Figure 6.134. Note that a minimum of
89 dBc SFDR is obtained over the entire first Nyquist zone (dc to 40 MHz).
SFDR as a function of signal amplitude is shown in Figure 6.135 for the AD6645. Notice
that over the entire range of signal amplitudes, the SFDR is greater than 90 dBFS. The
abrupt changes in the SFDR plot are due to the differential nonlinearities in the ADC
transfer function. The nonlinearities correspond to those shown in Figure 6.128B, and are
offset from mid-scale such that input signals less than about 65 dBFS do not exercise any
of the points of increased DNL. It should be noted that the SFDR can be improved by
injecting a small out-of-band dither signal—at the expense of a slight degradation in
SNR.
Figure 6.135: AD6645 14-bit, 80 MSPS ADC SFDR vs.
Input Power Level for 69.1 MHz Input
SFDR is generally much greater than the ADCs theoretical N-bit SNR (6.02N + 1.76 dB).
For example, the AD6645 is a 14-bit ADC with an SFDR of 90 dBc and a typical SNR of
73.5 dB (the theoretical SNR for 14-bits is 86 dB). This is because there is a fundamental
distinction between noise and distortion measurements. The process gain of the FFT
(33 dB for a 4096-point FFT) allows frequency spurs well below the noise floor to be
observed. Adding extra resolution to an ADC may serve to increase its SNR but may or
may not increase its SFDR.
6.140
CONVERTERS
DATA CONVERTER AC ERRORS
Two Tone Intermodulation Distortion (IMD)
Two tone IMD is measured by applying two spectrally pure sine waves to the ADC at
frequencies f1 and f2, usually relatively close together. The amplitude of each tone is set
slightly more than 6 dB below full-scale so that the ADC does not clip when the two
tones add in-phase. The locations of the second and third-order products are shown in
Figure 6.136. Notice that the second-order products fall at frequencies which can be
removed by digital filters. However, the third-order products 2f2 – f1 and 2f1 – f2 are close
to the original signals and are more difficult to filter. Unless otherwise specified, twotone IMD refers to these third-order products. The value of the IMD product is expressed
in dBc relative to the value of either of the two original tones, and not to their sum.
2 = SECOND ORDER IMD PRODUCTS
f1
3
f2
= THIRD ORDER IMD PRODUCTS
NOTE: f1 = 5MHz, f2 = 6MHz
2
2
f2 - f1
f2 + f 1
2f 2
2f 1
3
3
2f1 - f2
1
4
5
2f2 - f1
6 7
10 11 12
3
3f 1
3
2f2 + f1
2f1 + f2
3f 2
15 16 17 18
FREQUENCY: MHz
Figure 6.136: Second and Third-Order Intermodulation Products
for f1 = 5 MHz, f2 = 6 MHz
Note, however, that if the two tones are close to fs/4, then the aliased third harmonics of
the fundamentals can make the identification of the actual 2f2 – f1 and 2f1 – f2 products
difficult. This is because the third harmonic of fs/4 is 3fs/4, and the alias occurs at
fs – 3fs/4 = fs/4. Similarly, if the two tones are close to fs/3, the aliased second harmonics
may interfere with the measurement. The same reasoning applies here; the second
harmonic of fs/3 is 2fs/3, and its alias occurs at fs – 2fs/3 = fs/3.
6.141
BASIC LINEAR DESIGN
Multitone Spurious-Free Dynamic Range
Two-tone and multitone SFDR is often measured in communications applications. The
larger number of tones more closely simulates the wideband frequency spectrum of
cellular telephone systems such as AMPS or GSM. Figure 6.137 shows the 2-tone
intermodulation performance of the AD6645 14-bit, 80 MSPS ADC. The input tones are
at 55.25 MHz and 56.25 MHz and are located in the second Nyquist Zone.
The aliased tones therefore occur at 23.75 MHz and 24.75 MHz in the first Nyquist Zone.
High SFDR increases the receiver's ability to capture small signals in the presence of
large ones, and prevents the small signals from being masked by the intermodulation
products of the larger ones. Figure 6.138 shows the AD6645 two-tone SFDR as a
function of input signal amplitude for the same input frequencies.
Figure 6.137: Two-Tone SFDR for AD6645 14-bit, 80-MSPS ADC,
Input Tones: 55.25 MHz and 56.25 MHz
Figure 6.138: Two-Tone SFDR vs. Input Amplitude
for AD6645 14-bit, 80-MSPS ADC
6.142
CONVERTERS
DATA CONVERTER AC ERRORS
Second- and Third-Order Intercept Points, 1 dB Compression Point
Third-order IMD products are especially troublesome in multichannel communications
systems where the channel separation is constant across the frequency band. Third-order
IMD products can mask out small signals in the presence of larger ones.
In amplifiers, it is common practice to specify the third-order IMD products in terms of
the third-order intercept point, as is shown by Figure 6.139. Two spectrally pure tones
are applied to the system. The output signal power in a single tone (in dBm) as well as
the relative amplitude of the third-order products (referenced to a single tone) is plotted
as a function of input signal power. The fundamental is shown by the slope = 1 curve in
the diagram. If the system nonlinearity is approximated by a power series expansion, it
can be shown that second-order IMD amplitudes increase 2 dB for every 1-dB of signal
increase, as represented by slope = 2 curve in the diagram.
Similarly, the third-order IMD amplitudes increase 3 dB for every 1-dB of signal
increase, as indicated by the slope = 3 plotted line. With a low level two-tone input
signal, and two data points, one can draw the second and third order IMD lines as they
are shown in Figure 6.139 (using the principle that a point and a slope define a straight
line).
SECOND ORDER
INTERCEPT
IP2
OUTPUT
POWER
(PER TONE)
dBm
THIRD ORDER
INTERCEPT
IP3
1dB
1 dB COMPRESSION
POINT
FUNDAMENTAL
(SLOPE = 1)
SECOND
ORDER IMD
(SLOPE = 2)
THIRD ORDER IMD
(SLOPE = 3)
INPUT POWER (PER TONE), dBm
Figure 6.139: Definition of Intercept Points and
1 dB Compression Points for Amplifiers
Once the input reaches a certain level however, the output signal begins to soft-limit, or
compress. A parameter of interest here is the 1 dB compression point. This is the point
where the output signal is compressed 1 dB from an ideal input/output transfer function.
6.143
BASIC LINEAR DESIGN
This is shown in Figure 6.139 within the region where the ideal slope = 1 line becomes
dotted, and the actual response exhibits compression (solid).
Nevertheless, both the second- and third-order intercept lines may be extended, to
intersect the (dotted) extension of the ideal output signal line. These intersections are
called the second and third-order intercept points, respectively, or IP2 and IP3. These
power level values are usually referenced to the output power of the device delivered to a
matched load (usually, but not necessarily 50 Ω) expressed in dBm.
It should be noted that IP2, IP3, and the 1 dB compression point are all a function of
frequency, and as one would expect, the distortion is worse at higher frequencies.
For a given frequency, knowing the third order intercept point allows calculation of the
approximate level of the third-order IMD products as a function of output signal level.
The concept of second and third-order intercept points is not valid for an ADC, because
the distortion products do not vary in a predictable manner (as a function of signal
amplitude). The ADC does not gradually begin to compress signals approaching fullscale (there is no 1 dB compression point); it acts as a hard limiter as soon as the signal
exceeds the ADC input range, thereby suddenly producing extreme amounts of distortion
because of clipping. On the other hand, for signals much below full-scale, the distortion
floor remains relatively constant and is independent of signal level. This is shown
graphically in Figure 6.140.
OUTPUT
POWER*
(PER TONE)
dBm
ADC HARD LIMITS
IN THIS REGION,
LARGE IMD
PRODUCTS RESULT
*ANALOG EQUIVALENT
OF DIGITAL SIGNAL LEVEL
MEASURED BY ADC
INTERSECTION
HAS NO PRACTICAL
SIGNIFICANCE
FUNDAMENTAL
(SLOPE = 1)
IMD PRODUCTS
CONSTANT
IN THIS REGION
(SLOPE = 1)
IMD PRODUCTS MAY
START TO INCREASE
IN THIS REGION
INPUT POWER (PER TONE), dBm
Figure 6.140: Intercept Points for Data Converters Have No Practical
Significance
The IMD curve in Figure 6.140 is divided into three regions. For low level input signals,
the IMD products remain relatively constant regardless of signal level. This implies that
as the input signal increases 1 dB, the ratio of the signal to the IMD level will increase
6.144
CONVERTERS
DATA CONVERTER AC ERRORS
1 dB also. When the input signal is within a few dB of the ADC full-scale range, the IMD
may start to increase (but it might not in a very well-designed ADC). The exact level at
which this occurs is dependent on the particular ADC under consideration—some ADCs
may not exhibit significant increases in the IMD products over their full input range,
however most will. As the input signal continues to increase beyond full-scale, the ADC
should as an ideal limiter, and the IMD products become very large.
For these reasons, the 2nd and 3rd order IMD intercept points are not specified for ADCs.
It should be noted that essentially the same arguments apply to DACs. In either case, the
single- or multi-tone SFDR specification is the most accepted way to measure data
converter distortion.
Wideband CDMA (W-CDMA) Adjacent Channel Power Ratio (ACPR)
and Adjacent Channel Leakage Ratio (ADLR)
A wideband CDMA channel has a bandwidth of approximately 3.84 MHz, and channel
spacing is 5 MHz. The ratio in dBc between the measured power within a channel
relative to its adjacent channel is defined as the adjacent channel power ratio (ACPR).
The ratio in dBc between the measured power within the channel bandwidth relative to
the noise level in an adjacent empty carrier channel is defined as adjacent channel
leakage ratio (ACLR).
ACLR
= 70dB
Figure 6.141: Wideband CDMA (W-CDMA)
Adjacent Channel Leakage Ratio (ACLR)
Figure 6.141 shows a single wideband CDMA channel centered at 140 MHz sampled at a
frequency of 76.8 MSPS using the AD6645. This is a good example of undersampling
(direct IF-to-digital conversion).The signal lies within the third Nyquist zone: 3fs/2 to 2fs
6.145
BASIC LINEAR DESIGN
(115.2 MHz to 153.6 MHz). The aliased signal within the first Nyquist zone is therefore
centered at 2fs – fa = 153.6 – 140 = 13.6 MHz. The diagram also shows the location of the
aliased harmonics. For example, the second harmonic of the input signal occurs at
2 × 140 = 280 MHz, and the aliased component occurs at
4fs – 2fa = 4 × 76.8 – 280 = 307.2 – 280 = 27.2 MHz.
Noise Power Ratio (NPR)
Noise power ratio has been used extensively to measure the transmission characteristics
of Frequency Division Multiple Access (FDMA) communications links (see Reference
7). In a typical FDMA system, 4-kHz wide voice channels are “stacked” in frequency
bins for transmission over coaxial, microwave, or satellite equipment. At the receiving
end, the FDMA data is demultiplexed and returned to 4-kHz individual baseband
channels. In an FDMA system having more than approximately 100 channels, the FDMA
signal can be approximated by Gaussian noise with the appropriate bandwidth. An
individual 4-kHz channel can be measured for “quietness” using a narrow-band notch
(band-stop) filter and a specially tuned receiver which measures the noise power inside
the 4-kHz notch (see Figure 6.142).
Noise Power Ratio (NPR) measurements are straightforward. With the notch filter out,
the rms noise power of the signal inside the notch is measured by the narrowband
receiver. The notch filter is then switched in, and the residual noise inside the slot is
measured. The ratio of these two readings expressed in dB is the NPR. Several slot
frequencies across the noise bandwidth (low, midband, and high) are tested to
characterize the system adequately. NPR measurements on ADCs are made in a similar
manner except the analog receiver is replaced by a buffer memory and an FFT processor.
GAUSSIAN
NOISE
SOURCE
GAUSSIAN
NOISE
SOURCE
LPF
NOTCH
FILTER
LPF
NOTCH
FILTER
TRANSMISSION
SYSTEM
NARROWBAND
RECEIVER
N
ADC
BUFFER
MEMORY
AND FFT
PROCESSOR
fs
RMS
NOISE
LEVEL
(dB)
NPR
FREQUENCY
0.5f s
Figure 6.142: Noise Power Ratio (NPR) Measurements
6.146
CONVERTERS
DATA CONVERTER AC ERRORS
The NPR is plotted as a function of rms noise level referred to the peak range of the
system. For very low noise loading level, the undesired noise (in nondigital systems) is
primarily thermal noise and is independent of the input noise level. Over this region of
the curve, a 1 dB increase in noise loading level causes a 1 dB increase in NPR. As the
noise loading level is increased, the amplifiers in the system begin to overload, creating
intermodulation products which cause the noise floor of the system to increase. As the
input noise increases further, the effects of "overload" noise predominate, and the NPR is
reduced dramatically. FDMA systems are usually operated at a noise loading level a few
dB below the point of maximum NPR.
In a digital system containing an ADC, the noise within the slot is primarily quantization
noise when low levels of noise input are applied. The NPR curve is linear in this region.
As the noise level increases, there is a one-for-one correspondence between the noise
level and the NPR. At some level, however, “clipping” noise caused by the hard-limiting
action of the ADC begins to dominate. A theoretical curve for 10, 11, and 12-bit ADCs is
shown in Figure 6.143 (see Reference 8).
ADC RANGE = ±VO
NPR
(dB)
62.7dB
VO
k=
σ
60
σ = RMS NOISE LEVEL
IT
S
57.1dB
11
-B
IT
S
12
-B
55
51.6dB
10
-B
IT
S
50
45
–30
–25
–20
–15
–10
RMS NOISE LOADING LEVEL = –20log10(k) dB
Figure 6.143: Theoretical NPR for 10, 11, 12-bit ADCs
Figure 6.144 shows the maximum theoretical NPR and the noise loading level at which
the maximum value occurs for 8 bit to 16 bit ADCs. The ADC input range is 2 VO peakto-peak. The rms noise level is σ, and the noise-loading factor k (crest factor) is defined
as VO/σ , the peak-to-rms ratio (k is expressed either as numerical ratio or in dB).
In multi-channel high frequency communication systems where there is little or no phase
correlation between channels, NPR can also be used to simulate the distortion caused by
a large number of individual channels, similar to an FDMA system. A notch filter is
placed between the noise source and the ADC, and an FFT output is used in place of the
analog receiver. The width of the notch filter is set for several MHz as shown in Figure
6.147
BASIC LINEAR DESIGN
2.65 for the AD9430 12-bit 170-MSPS ADC. The notch is centered at 19 MHz, and the
NPR is the “depth” of the notch. An ideal ADC will only generate quantization noise
inside the notch; however a practical one has additional noise components due to
additional noise and intermodulation distortion caused by ADC imperfections. Notice
that the NPR is about 57 dB compared to 62.7 dB theoretical.
BITS
k OPTIMUM
k(dB)
MAX NPR (dB)
8
3.92
11.87
40.60
9
4.22
12.50
46.05
10
4.50
13.06
51.56
11
4.76
13.55
57.12
12
5.01
14.00
62.71
13
5.26
14.41
68.35
14
5.49
14.79
74.01
15
5.72
15.15
79.70
16
5.94
15.47
85.40
ADC Range = ±Vo
k = Vo / σ
σ = RMS Noise Level
Figure 6.144: Theoretical Maximum NPR for 8 bit to 16 bit ADCs
NPR =
57dB
INPUT FREQUENCY
Figure 6.145: AD9430 12-bit, 170 MSPS ADC NPR
Measures 57 dB (62.7 dB Theoretical)
6.148
CONVERTERS
DATA CONVERTER AC ERRORS
Noise Factor (F) and Noise Figure (NF)
Noise figure (NF) is a popular specification among RF system designers. It is used to
characterize RF amplifiers, mixers, etc., and widely used as a tool in radio receiver
design. Many excellent textbooks on communications and receiver design treat noise
figure extensively (see Reference 9, for example)—it is not the purpose of this discussion
to discuss the topic in much detail, but only how it applies to data converters.
Since many wideband operational amplifiers and ADCs are now being used in RF
applications, the inevitable day has come where the noise figure of these devices becomes
important. As discussed in Reference 10, in order to determine the noise figure of an op
amp correctly, one must not only know op amp voltage and current noise, but the exact
circuit conditions—closed-loop gain, gain-setting resistor values, source resistance,
bandwidth, etc. Calculating the noise figure for an ADC is even more of a challenge as
will be seen.
Figure 6.146 shows the basic model for defining the noise figure of an ADC. The noise
factor, F, is simply defined as the ratio of the total effective input noise power of the
ADC to the amount of that noise power caused by the source resistance alone. Because
the impedance is matched, the square of the voltage noise can be used instead of noise
power. The noise figure, NF, is simply the noise factor expressed in dB, NF = 10log10F.
SOURCE
fs
B = Filter
Noise Bandwidth
ADC
R
FILTER
B
PFS(dBm)
R*
N
*May be external
(TOTAL EFFECTIVE INPUT NOISE) 2
NOISE FACTOR (F) =
NOISE FIGURE (NF) = 10log10
(TOTAL INPUT NOISE DUE TO SOURCE R) 2
(TOTAL EFFECTIVE INPUT NOISE) 2
(TOTAL INPUT NOISE DUE TO SOURCE R) 2
Note: Noise Must be Measured Over the Filter Noise Bandwidth, B
Figure 6.146: Noise Figure for ADCs: Use with Caution!
This model assumes the input to the ADC comes from a source having a resistance, R,
and that the input is band-limited to fs/2 with a filter having a noise bandwidth equal to
fs/2. It is also possible to further band-limit the input signal resulting in oversampling and
process gain, and this condition will be discussed shortly.
6.149
BASIC LINEAR DESIGN
It is also assumed that the input impedance to the ADC is equal to the source resistance.
Many ADCs have a high input impedance, so this termination resistance may be external
to the ADC or used in parallel with the internal resistance to produce an equivalent
termination resistance equal to R. The full-scale input power is the power of a sine wave
whose peak-to-peak amplitude fills the entire ADC input range. The full-scale input sine
wave given by the following equation has a peak-to-peak amplitude of 2 VO
corresponding to the peak-to-peak input range of the ADC:
v(t) = VO sin 2πft
Eq. 6.21
The full-scale power in this sine wave is given by:
PFS =
( VO / 2 ) 2 VO 2
=
R
2R
Eq. 6.22
It is customary to express this power in dBm (referenced to 1 mW) as follows:
⎡P ⎤
PFS( dBm) = 10 log10 ⎢ FS ⎥ .
⎣1mW ⎦
Eq. 6.23
The noise bandwidth of a nonideal brick wall filter is defined as the bandwidth of an ideal
brick wall filter which will pass the same noise power as the nonideal filter. Therefore,
the noise bandwidth of a filter is always greater than the 3 dB bandwidth of the filter by a
factor which depends upon the sharpness of the cutoff region of the filter. Figure 2.68
shows the relationship between the noise bandwidth and the 3 dB bandwidth for
Butterworth filters up to 5 poles. Note that for two poles, the noise bandwidth and 3 dB
bandwidth are within 11% of each other, and beyond that the two quantities are
essentially equal.
NUMBER OF POLES
NOISE BW / 3dB BW
1
1.57
2
1.11
3
1.05
4
1.03
5
1.02
Figure 6.147: Relationship Between Noise Bandwidth
and 3 dB Bandwidth for Butterworth Filter
6.150
CONVERTERS
DATA CONVERTER AC ERRORS
The first step in the NF calculation is to calculate the effective input noise of the ADC
from its SNR. The SNR of the ADC is given for a variety of input frequencies, so be sure
to use the value corresponding to the input frequency of interest. Also, make sure that the
harmonics are not included in the SNR number—some ADC data sheets may confuse
SINAD with SNR. Once the SNR is known, the equivalent input rms voltage noise can
be calculated starting from the equation:
⎡ VFS RMS ⎤
SNR = 20 log10 ⎢
⎥
⎢⎣ VNOISE RMS ⎥⎦
Eq. 6.24
Solving for VNOISE RMS:
VNOISE RMS = VFS RMS ⋅ 10 −SNR / 20
Eq. 6.25
This is the total effective input rms noise voltage at the carrier frequency measured over
the Nyquist bandwidth, dc to fs/2. Note that this noise includes the source resistance
noise. These results are summarized in Figure 6.148.
‹ Start with the SNR of the ADC measured at the carrier frequency
(Note: this SNR value does not include the harmonics of the
fundamental and is measuredover the Nyquist bandwidth, dc to fs/2)
SNR = 20 log10
VFS-RMS
VNOISE-RMS
VNOISE-RMS = VFS-RMS 10 –SNR / 20
‹ This is the total ADC effective input noise at the carrier frequency
measured over the Nyquist bandwidth, dc to fs/2
Figure 6.148: Calculating ADC Total Effective Input Noise from SNR
The next step is to actually calculate the noise figure. In Figure 2.70 notice that the
amount of the input voltage noise due to the source resistance is the voltage noise of the
source resistance √(4kTBR) divided by two, or √(kTBR) because of the 2:1 attenuator
formed by the ADC input termination resistor.
The expression for the noise factor F can be written:
F=
VNOISE RMS2
kTRB
[
]
⎡ VFS RMS2 ⎤ 1
1
⎥ ⎡ ⎤ 10 −SNR / 10 ⎡ ⎤
=⎢
⎢
⎥
⎢
R
⎢
⎥ ⎣ kT ⎦
⎣ B ⎥⎦
⎣
⎦
Eq. 6.24
6.151
BASIC LINEAR DESIGN
The noise figure is obtained by converting F into dB and simplifying:
NF = 1010logF = PFS(dBm) + 174 dBm – SNR – 1010logB,
Eq. 6.25
Where SNR is in dB, B in Hz, T = 300 K, k = 1.38 × 10–23 J/K.
Oversampling and filtering can be used to decrease the noise figure as a result of the
process gain as has been previously discussed. In this case, the signal bandwidth B is less
than fs/2. Figure 6.149 shows the correction factor which results in the following
equation:
NF = 1010logF = PFS(dBm) + 174 dBm – SNR – 10 log10[fs/2B] – 10 log10B. Eq. 6.26
÷2
fs
4kTBR
kTBR
~
FILTER
R
f
B= s
2
VNOISE-RMS
kTRB
2
=
B = Filter
Noise Bandwidth
R
PFS(dBm)
= VFS-RMS 10
VNOISE-RMS
F=
ADC
VFS-RMS 2
1
R
kT
–SNR / 20
10
–SNR / 10
1
B
NF = 10 log10F = PFS(dBm) + 174dBm – SNR – 10 log10B ,
where SNR is in dB, B in Hz,
T = 300K, k = 1.38× 10–23 J/K
Figure 6.149: ADC Noise Figure in Terms of SNR,
Sampling Rate and Input Power
Figure 6.151 shows an example NF calculation for the AD6645 14-bit, 80-MSPS ADC.
A 52.3 Ω resistor is added in parallel with the AD6645 input impedance of 1 kΩ to make
the net input impedance 50 Ω. The ADC is operating under Nyquist conditions, and the
SNR of 74 dB is the starting point for the calculations using Eq. 6.26. A noise figure of
34.8 dB is obtained.
Figure 6.152 shows how using an RF transformer with voltage gain can improve the
noise figure. Figure 6.152A shows a 1:1 turns ratio, and the noise figure (from
Figure 6.151) is 34.8. Figure 6.152B shows a transformer with a 1:2 turns ratio. The
249 Ω resistor in parallel with the AD6645 internal resistance results in a net input
6.152
CONVERTERS
DATA CONVERTER AC ERRORS
impedance of 200 Ω. The noise figure is improved by 6 dB because of the noise-free
voltage gain of the transformer. Figure 6.152C shows a transformer with a 1:4 turns ratio.
The AD6645 input is paralleled with a 4.02 kΩ resistor to make the net input impedance
800 Ω. The noise figure is improved by another 6 dB. Transformers with higher turns
ratios are not generally practical because of bandwidth and distortion limitations.
fs
ADC
FILTER
R
NF =
f
B< s
2
R
PFS(dBm)
PFS(dBm) + 174dBm – SNR – 10 log10
Measured
DC to fs / 2
where SNR is in dB, B in Hz,
B = Filter
Noise Bandwidth
fs / 2
– 10 log10B,
B
Process
Gain
T = 300K, k = 1.38 × 10–23 J/K
Figure 6.150: Effect of Oversampling and Process Gain on ADC Noise Figure
1:1
TURN S RATIO
50Ω
AD6645
50Ω
FILTER
B = 40MHz
52.3Ω
z
z
z
z
V FS P-P = 2.2V
fs = 80MSPS
SNR = 74dB
Inpu t 3dB BW = 250MHz
1kΩ
VFS P-P = 2.2V
fs = 80MSPS
VFS-RMS = 0.778V
PFS =
(0.778) 2
50
= 12.1mW
PFS(dBm) = +10.8dBm
NF = PFS(dBm) + 174dBm – SNR – 10 log10B
= +10.8dBm + 174dBm – 74dB – 10 log10(40 × 106)
= 34.8dB
Figure 6.151: Example Calculation of Noise Figure
Under Nyquist Conditions for AD6645
6.153
BASIC LINEAR DESIGN
Even with the 1:4 turns ratio transformer, the overall noise figure for the AD6645 was
still 22.8 dB, still relatively high by RF standards. The solution is to provide low noise
high gain stages ahead of the ADC. Figure 6.153 shows how the Friis equation is used to
calculate the noise factor for cascaded gain stages. Notice that high gain in the first stage
reduces the contribution of the noise factor of the second stage—the noise factor of the
first stage dominates the overall noise factor.
1:1 TURNS RATIO
(A)
50Ω
AD6645
50Ω
B=
40MHz
52.3Ω
1kΩ
z VFS P-P = 2.2V
z fs = 80MSPS
z SNR = 74dB
z Input 3dB BW = 250MHz
NF = 34.8dB
PFS(dBm) = +10.8dBm
1:2 TURNS RATIO
(B)
50Ω
AD6645
200Ω
B=
40MHz
249Ω
NF = 28.8dB
1kΩ
PFS(dBm) = +4.8dBm
(C)
50Ω
1:4 TURNS RATIO
AD6645
800Ω
B=
40MHz
4.02kΩ
NF = 22.8dB
1kΩ
PFS(dBm) = –1.2dBm
Figure 6.152: Using RF Transformers to Improve Overall ADC Noise Figure
RS
G1
F1
FT = F1 +
G2
F2
F2 – 1 +
G1
G3
F3
F3 – 1
G1•G2
+
G4
F4
RL
F4 – 1
+...
G1•G2•G3
High gain in the first stage reduces the
contribution of the NF of the second stage
NF of the first stage dominates the total NF
NFT = 10 log10FT
Figure 6.153: Cascaded Noise Figure Using the Friis Equation
6.154
CONVERTERS
DATA CONVERTER AC ERRORS
Figure 6.154 shows the effects of a high gain (25 dB), low noise (NF = 4 dB) stage
placed in front of a relatively high NF stage (30 dB)—the noise figure of the second stage
is typical of high performance ADCs. The overall noise figure is 7.53 dB, only 3.53 dB
higher than the first stage noise figure of 4 dB.
RS
G1 dB = 25dB
G2 dB = 0dB
NF1 = 4dB
NF2 = 30dB
RL
G1 = 10 25/10 = 10 2.5 = 316, F1 = 10 4/10 = 10 0.4 = 2.51
F2 = 10 30/10 = 10 3 = 1000
G2 = 1,
FT = F1 +
F2 – 1
G1
= 2.51 +
1000 – 1
= 2.51 + 3.16 = 5.67
316
NF T = 10 log 105.67 = 7.53dB
‹ The first stage dominates the overall NF
‹ It should h ave the highest gain possible with the l owest NF possible
Figure 6.154: Example of Two-Stage Cascaded Network
In summary, applying the noise figure concept to characterize wideband ADCs must be
done with extreme caution to prevent misleading results. Simply trying to minimize the
noise figure using the equations can actually increase circuit noise.
For instance, NF decreases with increasing source resistance according to the
calculations, but increased source resistance increases circuit noise. Also, NF decreases
with increasing ADC input bandwidth if there is no input filtering. This is also
contradictory, because widening the bandwidth increases noise. In both these cases, the
circuit noise increases, and the NF decreases. The reason NF decreases is that the source
noise makes up a larger component of the total noise (which remains relatively constant
because the ADC noise is much greater than the source noise); therefore according to the
calculation, NF decreases, but actual circuit noise increases.
It is true that on a stand-alone basis ADCs have relatively high noise figures compared to
other RF parts such as LNAs or mixers. In the system the ADC should be preceded with
low-noise gain blocks as shown in the example of Figure 6.154.
6.155
BASIC LINEAR DESIGN
Aperture Time, Aperture Delay Time and Aperture Jitter
Perhaps the most misunderstood and misused ADC and sample-and-hold (or track-andhold) specifications are those that include the word aperture. The most essential dynamic
property of a SHA is its ability to disconnect quickly the hold capacitor from the input
buffer amplifier as shown in Figure 6.155. The short (but non-zero) interval required for
this action is called aperture time (or sampling aperture), ta. The actual value of the
voltage that is held at the end of this interval is a function of both the input signal slew
rate and the errors introduced by the switching operation itself. Figure 6.155 shows what
happens when the hold command is applied with an input signal of two arbitrary slopes
labeled as 1 and 2. For clarity, the sample-to-hold pedestal and switching transients are
ignored. The value that is finally held is a delayed version of the input signal, averaged
over the aperture time of the switch as shown in Figure 6.155. The first-order model
assumes that the final value of the voltage on the hold capacitor is approximately equal to
the average value of the signal applied to the switch over the interval during which the
switch changes from a low to high impedance (ta).
The model shows that the finite time required for the switch to open (ta) is equivalent to
introducing a small delay te in the sampling clock driving the SHA. This delay is constant
and may either be positive or negative. The diagram shows that the same value of te
works for the two signals, even though the slopes are different. This delay is called
effective aperture delay time, aperture delay time, or simply aperture delay, te. In an
ADC, the aperture delay time is referenced to the input of the converter, and the effects of
the analog propagation delay through the input buffer, tda and the digital delay through
the switch driver, tdd, must be considered. Referenced to the ADC inputs, aperture time,
te', is defined as the time difference between the analog propagation delay of the front-end
buffer, tda, and the switch driver digital delay, tdd, plus one-half the aperture time, ta/2.
ANALOG
DELAY, tda
INPUT
SIGNAL
INPUT
SAMPLING
CLOCK
APERTURE
TIME, ta
ta = APERTURE TIME
tda = ANALOG DELAY
tdd = DIGITAL DELAY
te = ta / 2 = APERTURE DELAY
TIME FOR tda = tdd
te
2
CHOLD
SWITCH
DRIVER
VOLTAGE ON
HOLD CAPACITOR
SWITCH
INPUT SIGNALS
1
DIGITAL
DELAY, tdd
1
2
SWITCH
DRIVER OUTPUT
ta
te' = APERTURE DELAY
TIME REFERENCED TO INPUTS
t
te' = tdd – tda + a
2
HOLD
SAMPLE
Figure 6.155: Sample-and-Hold Waveforms and Definitions
6.156
CONVERTERS
DATA CONVERTER AC ERRORS
The effective aperture delay time is usually positive, but may be negative if the sum of
one-half the aperture time, ta/2, and the switch driver digital delay, tdd, is less than the
propagation delay through the input buffer, tda. The aperture delay specification thus
establishes when the input signal is actually sampled with respect to the sampling clock
edge.
Aperture delay time can be measured by applying a bipolar sine wave signal to the ADC
and adjusting the synchronous sampling clock delay such that the output of the ADC is
mid-scale (corresponding to the zero-crossing of the sine wave). The relative delay
between the input sampling clock edge and the actual zero-crossing of the input sine
wave is the aperture delay time (see Figure 6.156).
Aperture delay produces no errors (assuming it is relatively short with respect to the hold
time), but acts as a fixed delay in either the sampling clock input or the analog input
(depending on its sign). However, in simultaneous sampling applications or in direct I/Q
demodulation where two or more ADCs must be well matched, variations in the aperture
delay between converters can produce errors on fast slewing signals. In these
applications, the aperture delay mismatches must be removed by properly adjusting the
phases of the individual sampling clocks to the various ADCs.
If, however, there is sample-to-sample variation in aperture delay (aperture jitter), then a
corresponding voltage error is produced as shown in Figure 6.157. This sample-to-sample
variation in the instant the switch opens is called aperture uncertainty, or aperture jitter
and is usually measured in rms picoseconds. The amplitude of the associated output error
is related to the rate-of-change of the analog input. For any given value of aperture jitter,
the aperture jitter error increases as the input dv/dt increases. The effects of phase jitter
on the external sampling clock (or the analog input for that matter) produce exactly the
same type or error.
+FS
ZERO CROSSING
ANALOG INPUT
SINEWAVE
0V
-FS
–t e '
+te '
SAMPLING
CLOCK
t e'
Figure 6.156: Effective Aperture Delay Time
Measured with Respect to ADC Input
6.157
BASIC LINEAR DESIGN
dv
Δv =
dt
ANALOG
INPUT
dv
= SLOPE
dt
Δt
Δ v RMS = APERTURE JITTER ERROR
NOMINAL
HELD
OUTPUT
Δ t RMS = APERTURE JITTER
HOLD
TRACK
Figure 6.157: Effects of Aperture Jitter and Sampling Clock Jitter
The effects of aperture and sampling clock jitter on an ideal ADCs SNR can be predicted
by the following simple analysis. Assume an input signal given by
v(t) = VO sin 2πft
Eq. 6.27
The rate of change of this signal is given by:
dv/dt = 2πfVO cos 2πft.
Eq. 6.28
The rms value of dv/dt can be obtained by dividing the amplitude, 2πfVO, by √2:
dv/dt| rms = 2πfVO / √2.
Eq. 6.29
Now let Δvrms = the rms voltage error and Δt = the rms aperture jitter tj, and substitute:
Δvrms / tj = 2πfVO / √2.
Eq. 6.30
Δvrms = 2πfVO tj/ √2.
Eq. 6.31
Solving for Δvrms :
The rms value of the full-scale input sinewave is VO/√2, therefore the rms signal to rms
noise ratio is given by
⎡ V / 2 ⎤
⎡ 1 ⎤
⎡V / 2 ⎤
O
SNR = 20 log10 ⎢ O
⎥ = 20 log10 ⎢
⎥.
⎥ = 20 log10 ⎢
Δ
v
2
f
t
π
2
fV
t
/
2
π
rms
j
⎢
⎥
⎢
⎥⎦
O j
⎣
⎦
⎣
⎣
⎦
6.158
Eq. 6.32
CONVERTERS
DATA CONVERTER AC ERRORS
This equation assumes an infinite resolution ADC where aperture jitter is the only factor
in determining the SNR. This equation is plotted in Figure 6.158 and shows the serious
effects of aperture and sampling clock jitter on SNR, especially at higher input/output
frequencies. Therefore, extreme care must be taken to minimize phase noise in the
sampling/reconstruction clock of any sampled data system.
tj = 1ps
100
SNR = 20log 10
16
1
2 π ft j
14
tj = 10ps
80
SNR
(dB)
12
10
tj = 100ps
60
ENOB
8
tj = 1ns
40
6
4
20
0
1
3
10
30
100
FULLSCALE SINEWAVE INPUT FREQUENCY (MHz)
Figure 6.158: SNR Due to Aperture Jitter and Sampling Clock Jitter
This care must extend to all aspects of the clock signal: the oscillator itself (for example,
a 555 timer is absolutely inadequate, but even a quartz crystal oscillator can give
problems if it uses an active device which shares a chip with noisy logic); the
transmission path (these clocks are very vulnerable to interference of all sorts), and phase
noise introduced in the ADC or DAC. As discussed, a very common source of phase
noise in converter circuitry is aperture jitter in the integral sample-and-hold (SHA)
circuitry, however the total rms jitter will be composed of a number of components—the
actual SHA aperture jitter often being the least of them.
6.159
BASIC LINEAR DESIGN
A Simple Equation for the Total SNR of an ADC
A relatively simple equation for the ADC SNR in terms of sampling clock and aperture
jitter, DNL, effective input noise, and the number of bits of resolution is shown in
Figure 6.159. The equation combines the various error terms on an rms basis. The
average DNL error, ε, is computed from histogram data. This equation is used in
Figure 6.160 to predict the SNR performance of the AD6645 14-bit, 80-MSPS ADC as a
function of sampling clock and aperture jitter.
SAMPLING
CLOCK JITTER
SNR = – 20log10 (2π × fa × tj rms) 2 +
fa
tj rms
QUANTIZATION
NOISE, DNL
2 1+ε
3
2
2N
+
EFFECTIVE
INPUT NOISE
2 × √2 × VNOISErms
2
1
2
2N
= Analog input frequency of fullscale input sinewave
= Combined rms jitter of internal ADC and external clock
ε
= Average DNL of the ADC (typically 0.41 LSB for AD6645)
N
= Number of bits in the ADC
VNOISErms = Effective input noise of ADC (typically 0.9LSB rms for AD6645)
If tj = 0, ε = 0, and VNOISErms = 0, the above equation reduces to the familiar:
SNR = 6.02 N + 1.76dB
Figure 6.159: Relationship Between SNR, Sampling Clock Jitter,
Quantization Noise, DNL, and Input Noise
Figure 6.160: AD6645 SNR vs. Aperture Jitter
6.160
CONVERTERS
DATA CONVERTER AC ERRORS
Two decades or so ago, sampling ADCs were built up from a separate SHA and ADC.
Interface design was difficult, and a key parameter was aperture jitter in the SHA. Today,
most sampled data systems use sampling ADCs which contain an integral SHA. The
aperture jitter of the SHA may not be specified as such, but this is not a cause of concern
if the SNR or ENOB is clearly specified, since a guarantee of a specific SNR is an
implicit guarantee of an adequate aperture jitter specification. However, the use of an
additional high-performance SHA will sometimes improve the high-frequency ENOB of
a even the best sampling ADC by presenting “dc” to the ADC, and may be more costeffective than replacing the ADC with a more expensive one.
ADC Transient Response and Overvoltage Recovery
Most high speed ADCs designed for communications applications are specified primarily
in the frequency domain. However, in general purpose data acquisition applications the
transient response (or settling time) of the ADC is important. The transient response of
an ADC is the time required for the ADC to settle to rated accuracy (usually 1 LSB) after
the application of a full-scale step input. The typical response of a general-purpose 12 bit,
10-MSPS ADC is shown in Figure 6.161, showing a 1 LSB settling time of less than
40 ns. The settling time specification is critical in the typical data acquisition system
application where the ADC is being driven by an analog multiplexer as shown in
Figure 6.162. The multiplexer output can deliver a full-scale sample-to-sample change to
the ADC input. If both the multiplexer and the ADC have not both settled to the required
accuracy, channel-to-channel crosstalk will result, even though only dc or low frequency
signals are present on the multiplexer inputs.
Figure 6.161: ADC Transient Response (Settling Time)
6.161
BASIC LINEAR DESIGN
Most ADCs have settling times which are less than 1/fs max, even if not specified.
However sigma-delta ADCs have a built in digital filter which can take several output
sample intervals to settle. This should be kept in mind when using sigma-delta ADCs in
multiplexed applications.
The importance of settling time in multiplexed systems can be seen in Figure 6.163,
where the ADC input is modeled as a single-pole filter having a corresponding time
constant, τ = RC. The required number of time constants to settle to a given accuracy
(1 LSB) is shown. A simple example will illustrate the point.
Figure 6.162: Settling Time is Critical in Multiplexed Applications
RESOLUTION,
# OF BITS
LSB (%FS)
# OF TIME
CONSTANTS
6
1.563
4.16
8
0.391
5.55
10
0.0977
6.93
12
0.0244
8.32
14
0.0061
9.70
16
0.00153
11.09
18
0.00038
12.48
20
0.000095
13.86
22
0.000024
15.25
Figure 6.163: Settling Time as a Function of Time Constant
for Various Resolutions
Assume a multiplexed 16-bit data acquisition system uses an ADC with a sampling
frequency fs = 100 kSPS. The ADC must settle to 16-bit accuracy for a full-scale step
function input in less than 1/fs = 10µs. The chart shows that 11.09 time constants are
6.162
CONVERTERS
DATA CONVERTER AC ERRORS
required to settle to 16-bit accuracy. The input filter time constant must therefore be less
than τ = 10 µs/11.09 = 900 ns. The corresponding, risetime tr = 2.2τ = 1.98 µs. The
required ADC full power input bandwidth can now be calculated from BW = 0.35/tr =
177 kHz. This neglects the settling time of the multiplexer and second-order settling time
effects in the ADC.
Overvoltage recovery time is defined as that amount of time required for an ADC to
achieve a specified accuracy, measured from the time the overvoltage signal re-enters the
converter's range, as shown in Figure 6.164. This specification is usually given for a
signal which is 50% outside the ADC's input range. Needless to say, the ADC should act
as an ideal limiter for out-of-range signals and should produce either the positive fullscale code or the negative full-scale code during the overvoltage condition. Some
converters provide over- and under-range flags to allow gain-adjustment circuits to be
activated. Care should always be taken to avoid overvoltage signals which will damage
an ADC input.
ADC SHOULD
READ FS CODE
Figure 6.164: Overvoltage Recovery Time
ADC Sparkle Codes, Metastable States, and Bit Error Rate (BER)
A primary concern in the design of many digital communications systems using ADCs is
the bit error rate (BER). Unfortunately, ADCs contribute to the BER in ways that are not
predictable by simple analysis. This section describes the mechanisms within the ADCs
that can contribute to the error rate, ways to minimize the problem, and methods for
measuring the BER.
Random noise, regardless of the source, creates a finite probability of errors (deviations
from the expected output). Before describing the error code sources, however, it is
important to define what constitutes an ADC error code. Noise generated prior to, or
inside the ADC can be analyzed in the traditional manner. Therefore, an ADC error code
is any deviation from the expected output that is not attributable to the equivalent input
noise of the ADC. Figure 6.165 illustrates an exaggerated output of a low amplitude sine
6.163
BASIC LINEAR DESIGN
wave applied to an ADC that has error codes. Note that the noise of the ADC creates
some uncertainty in the output. These anomalies are not considered error codes, but are
simply the result of ordinary noise and quantization. The large errors are more significant
and are not expected. These errors are random and so infrequent that an SNR test of the
ADC will rarely detect them. These types of errors plagued a few of the early ADCs for
video applications, and were given the name sparkle codes because of their appearance
on a TV screen as small white dots or “sparkles” under certain test conditions. These
errors have also been called rabbits or flyers. In digital communications applications, this
type of error increases the overall system bit error rate (BER).
(SPARKLE CODES,
FLYERS, RABBITS)
LOW-AMPLITUDE
DIGITIZED SINEWAVE
Figure 6.165: Exaggerated Output of ADC Showing Error Codes
In order to understand the causes of the error codes, we will first consider the case of a
simple flash converter. The comparators in a flash converter are latched comparators
usually arranged in a master-slave configuration. If the input signal is in the center of the
threshold of a particular comparator, that comparator will balance, and its output will take
a longer period of time to reach a valid logic level after the application of the latch strobe
than the outputs of its neighboring comparators which are being overdriven. This
phenomenon is known as metastability and occurs when a balanced comparator cannot
reach a valid logic level in the time allowed for decoding. If simple binary decoding logic
is used to decode the thermometer code, a metastable comparator output may result in a
large output code error. Consider the case of a simple 3 bit flash converter shown in
Figure 6.167. Assume that the input signal is exactly at the threshold of Comparator 4
and random noise is causing the comparator to toggle between a 1 and a 0 output each
time a latch strobe is applied. The corresponding binary output should be interpreted as
either 011 or 100. If, however, the comparator output is in a metastable state, the simple
binary decoding logic shown may produce binary codes 000, 011, 100, or 111. The codes
000 and 111 represent a one-half scale departure from the expected codes.
The probability of errors due to metastability increases as the sampling rate increases
because less time is available for a metastable comparator to settle.
6.164
CONVERTERS
DATA CONVERTER AC ERRORS
Various measures have been taken in flash converter designs to minimize the metastable
state problem. Decoding schemes described in References 12 to 15 minimize the
magnitude of these errors. Optimizing comparator designs for regenerative gain and small
time constants is another way to reduce these problems.
Figure 6.166: Metastable Comparator Output States
May Cause Error Codes in Data Converters
Metastable state errors may also appear in successive approximation and subranging
ADCs which make use of comparators as building blocks. The same concepts apply,
although the magnitudes and locations of the errors may be different.
Establishing the BER of a well-behaved ADC is a difficult, time-consuming task; a single
unit can sometimes be tested for days without an error. For example, tests on a typical 8bit flash converter operating at a sampling rate of 75 MSPS yield a BER of
approximately 3.7 × 10–12 (1 error per hour) with an error limit of 4 LSBs. Meaningful
tests for longer periods of time require special attention to EMI/RFI effects (possibly
requiring a shielded screen room), isolated power supplies, etc. Figure 6.167 shows the
average time between errors as a function of BER for a sampling frequency of 75 MSPS.
6.165
BASIC LINEAR DESIGN
This illustrates the difficulty in measuring low BER because the long measurement times
increase the probability of power supply transients, noise, etc. causing an error.
Figure 6.167: Average Time Between Errors vs. BER
When Sampling at 75 MSPS
6.166
CONVERTERS
DATA CONVERTER AC ERRORS
DAC Dynamic Performance
The ac specifications which are most likely to be important with DACs are settling time,
glitch impulse area, distortion, and Spurious-Free Dynamic Range (SFDR).
DAC Settling Time
The settling time of a DAC is the time from a change of digital code to when the output
comes within and remains within some error band as shown in Figure 6.168. With
amplifiers, it is hard to make comparisons of settling time, since their error bands may
differ from amplifier to amplifier, but with DACs the error band will almost invariably be
±1 or ±½ LSB.
The settling time of a DAC is made up of four different periods: the switching time or
dead time (during which the digital switching, but not the output, is changing), the
slewing time (during which the rate of change of output is limited by the slew rate of the
DAC output), the recovery time (when the DAC is recovering from its fast slew and may
overshoot), and the linear settling time (when the DAC output approaches its final value
in an exponential or near-exponential manner). If the slew time is short compared to the
other three (as is usually the case with current output DACs), then the settling time will
be largely independent of the output step size. On the other hand, if the slew time is a
significant part of the total, then the larger the step, the longer the settling time.
ERROR BAND
T=0
DEAD
TIME
SLEW
TIME
RECOVERY
TIME
LINEAR
SETTLING
Figure 6.168: DAC Settling Time
Settling time is especially important in video display applications. For example
a standard 1024 × 768 display updated at a 60 Hz refresh rate must have a pixel rate
of 1024 × 768 × 60 Hz = 47.2 MHz with no overhead. Allowing 35% overhead
time increases the pixel frequency to 64 MHz corresponding to a pixel duration of
6.167
BASIC LINEAR DESIGN
1/(64 × 106) = 15.6 ns. In order to accurately reproduce a single fully-white pixel located
between two black pixels, the DAC settling time should be less than the pixel duration
time of 15.6 ns.
Higher resolution displays require even faster pixel rates. For example, a 2048 × 2048
display requires a pixel rate of approximately 330 MHz at a 60 Hz refresh rate.
Glitch Impulse Area
Ideally, when a DAC output changes it should move from one value to its new one
monotonically. In practice, the output is likely to overshoot, undershoot, or both (see
Figure 6.169). This uncontrolled movement of the DAC output during a transition is
known as a glitch. It can arise from two mechanisms: capacitive coupling of digital
transitions to the analog output, and the effects of some switches in the DAC operating
more quickly than others and producing temporary spurious outputs.
IDEAL TRANSITION
TRANSITION WITH
DOUBLET GLITCH
t
t
TRANSITION WITH
UNIPOLAR (SKEW)
GLITCH
t
Figure 6.169: DAC Transitions (Showing Glitch)
Capacitive coupling frequently produces roughly equal positive and negative spikes
(sometimes called a doublet glitch) which more or less cancel in the longer term. The
glitch produced by switch timing differences is generally unipolar, much larger and of
greater concern.
Glitches can be characterized by measuring the glitch impulse area, sometimes
inaccurately called glitch energy. The term glitch energy is a misnomer, since the unit for
glitch impulse area is Volt-seconds (or more probably µV-sec or pV-sec. The peak glitch
area is the area of the largest of the positive or negative glitch areas. The glitch impulse
area is the net area under the voltage-versus-time curve and can be estimated by
approximating the waveforms by triangles, computing the areas, and subtracting the
negative area from the positive area as shown in Figure 6.170.
The mid-scale glitch produced by the transition between the codes 0111...111 and
1000...000 is usually the worst glitch. Glitches at other code transition points (such as 1/4
and 3/4 full-scale) are generally less. Figure 6.171 shows the mid-scale glitch for a fast
low-glitch DAC. The peak and net glitch areas are estimated using triangles as described
6.168
CONVERTERS
DATA CONVERTER AC ERRORS
above. Settling time is measured from the time the waveform leaves the initial 1 LSB
error band until it enters and remains within the final 1LSB error band. The step size
between the transition regions is also 1 LSB.
+V1
A1
t
A2
t1
–V2
t2
PEAK GLITCH IMPULSE AREA = A1 ≈
NET GLITCH IMPULSE AREA
Figure 6.170:
V1· t1
2
= A1 – A2 ≈
V1· t1
2
–
V2· t2
2
Calculating Net Glitch Impulse Area
SETTLING TIME
= 4.5ns
NET GLITCH AREA = 1.34 pV-s
PEAK GLITCH AREA = 1.36 pV-s
2 mV/DIVISION
1 LSB
1 LSB
1 LSB
5 ns/DIVISION
≈ 4.5ns
Figure 6.171: DAC Mid-scale Glitch Shows 1.34 pV-s
Net Impulse Area and Settling Time of 4.5 ns
6.169
BASIC LINEAR DESIGN
DAC SFDR and SNR
DAC settling time is important in applications such as RGB raster scan video display
drivers, but frequency-domain specifications such as SFDR are generally more important
in communications.
If we consider the spectrum of a waveform reconstructed by a DAC from digital data, we
find that in addition to the expected spectrum (which will contain one or more
frequencies, depending on the nature of the reconstructed waveform), there will also be
noise and distortion products. Distortion may be specified in terms of harmonic
distortion, Spurious Free Dynamic Range (SFDR), intermodulation distortion, or all of
the above. Harmonic distortion is defined as the ratio of harmonics to fundamental when
a (theoretically) pure sine wave is reconstructed, and is the most common specification.
Spurious free dynamic range is the ratio of the worst spur (usually, but not necessarily
always a harmonic of the fundamental) to the fundamental.
Code-dependent glitches will produce both out-of-band and in-band harmonics when the
DAC is reconstructing a digitally generated sine wave as in a Direct Digital Synthesis
(DDS) system. The mid-scale glitch occurs twice during a single cycle of a reconstructed
sine wave (at each mid-scale crossing), and will therefore produce a second harmonic of
the sine wave, as shown in Figure 6.172. Note that the higher order harmonics of the sine
wave, which alias back into the Nyquist bandwidth (dc to fs/2), cannot be filtered.
+ FULL SCALE
fO = 3MHz
MIDSCALE
fS = 10MSPS
– FULL SCALE
AMPLITUDE
CANNOT
BE FILTERED
fO
fS – 2fO
0
1
2
3
4
fS
fS – f O
2fO
5
6
7
8
FREQUENCY (MHz)
9
10
fS
2
Figure 6.172: Effect of Code-Dependent Glitches on Spectral Output
It is difficult to predict the harmonic distortion or SFDR from the glitch area specification
alone. Other factors, such as the overall linearity of the DAC, also contribute to
distortion. In addition, certain ratios between the DAC output frequency and the sampling
6.170
CONVERTERS
DATA CONVERTER AC ERRORS
clock cause the quantization noise to concentrate at harmonics of the fundamental thereby
increasing the distortion at these points.
It is therefore customary to test reconstruction DACs in the frequency domain (using a
spectrum analyzer) at various clock rates and output frequencies as shown in
Figure 6.173. Typical SFDR for the 16-bit AD9777 Transmit TxDAC™ is shown in
Figure 6.174. The clock rate is 160 MSPS, and the output frequency is swept to 50 MHz.
As in the case of ADCs, quantization noise will appear as increased harmonic distortion
if the ratio between the clock frequency and the DAC output frequency is an integer
number. These ratios should be avoided when making the SFDR measurements.
PARALLEL OR
SERIAL PORT
PC
DDS
SYSTEM
N
N
DAC
LATCH
fo
STABLE
FREQUENCY
REFERENCE
fc
SPECTRUM
ANALYZER
Figure 6.173: Test Setup for Measuring DAC SFDR
DAC OUTPUT FREQUENCY (MHz)
Figure 6.174: AD9777 16-bit TxDAC SFDR, Data Update Rate = 160 MSPS
6.171
BASIC LINEAR DESIGN
There are nearly an infinite combination of possible clock and output frequencies for a
low distortion DAC, and SFDR is generally specified for a limited number of selected
combinations. For this reason, Analog Devices offers fast turnaround on customerspecified test vectors for the Transmit TxDAC family. A test vector is a combination of
amplitudes, output frequencies, and update rates specified directly by the customer for
SFDR data on a particular DAC.
Measuring DAC SNR with an Analog Spectrum Analyzer
Analog spectrum analyzers are used to measure the distortion and SFDR of high
performance DACs. Care must be taken such that the front end of the analyzer is not
overdriven by the fundamental signal. If overdrive is a problem, a band-stop filter can be
used to filter out the fundamental signal such that the spurious components can be
observed.
Spectrum analyzers can also be used to measure the SNR of a DAC provided attention is
given to bandwidth considerations. SNR of an ADC is normally defined as the signal-tonoise ratio measured over the Nyquist bandwidth dc to fs/2. However, spectrum analyzers
have a resolution bandwidth which is less than fs/2—this therefore lowers the analyzer
noise floor by the process gain equal to 10 log10(fs/2·BW), where BW is the resolution
noise bandwidth of the analyzer (see Figure 6.175).
dB
NOISE FLOOR
BW
(NOISE BANDWIDTH)
SWEEP
fs
f
2
BW = ANALYZER RESOLUTION NOISE BANDWIDTH
SNR = NOISE FLOOR – 10 log10
fs/2
BW
Figure 6.175: Measuring DAC SNR with an Analog Spectrum Analyzer
It is important that the noise bandwidth (not the 3-dB bandwidth) be used in the
calculation; however from Figure 6.147 the error is small assuming that the analyzer
narrowband filter is at least two poles. The ratio of the noise bandwidth to the 3-dB
bandwidth of a one-pole Butterworth filter is 1.57 (causing an error of 1.96 dB in the
process gain calculation). For a two-pole Butterworth filter, the ratio is 1.11 (causing an
error of 0.45 dB in the process gain calculation).
6.172
CONVERTERS
DATA CONVERTER AC ERRORS
Other AC Specifications
Again, there are some specifications that may be encountered that are less common and
are listed below.
Acquisition Time: The acquisition time of a sample-and-hold circuit for a step change is
the time required by the output to reach its final value, within a specified error band, after
the track command has been given. Included are switch delay time, the slewing interval,
and settling time for a specified output voltage change. This spec is less common now
that the sample and hold function has largely been integrated into the ADC.
Automatic Zero: To achieve zero stability in many integrating-type converters, a time
interval is provided during each conversion cycle to allow the circuitry to compensate for
drift errors. The drift error in such converters is substantially zero.
Channel-to-Channel Isolation: In multiple DACs, the proportion of analog input signal
from one DAC’s reference input that appears at the output of the other DAC, expressed
logarithmically in dB. See also crosstalk.
Charge Transfer (or Offset Step): the principal component of sample-to-hold offset (or
pedestal), is the small charge transferred to the storage capacitor via interelectrode
capacitance of the switch and stray capacitance when switching to the hold mode. The
offset step is directly proportional to this charge, viz.,
Offset error = Incremental Charge/Capacitance = ∆Q/C.
It can be reduced somewhat by lightly coupling an appropriate polarity version of the
hold signal to the capacitor for first-order cancellation. The error can also be reduced by
increasing the capacitance, but this increases acquisition time. Again a spec that has
become less common since the sample and hold function has largely been integrated into
the ADC.
Crosstalk: Leakage of signals, usually via capacitance between circuits or channels of a
multichannel system or device, such as a multiplexer, multiple op amp, or multiple DAC.
Crosstalk is usually determined by the impedance parameters of the physical circuit, and
actual values are frequency-dependent. See also channel-to-channel isolation.
Multiple DACs have a digital crosstalk specification: the spike (sometimes called a
glitch) impulse appearing at the output of one converter due to a change in the digital
input code of another of the converters. It is specified in nanovolt- or picovolt-seconds
and measured at VREF = 0 V.
Differential Gain (ΔG): A video specification which measures the variation in the
amplitude (in percent) of a small amplitude color subcarrier signal as it is swept across
the video range from black to white.
Differential Phase (Δϕ): A video specification which measures the phase variation (in
degrees) of a small amplitude color subcarrier signal as it is swept across the video range
from black to white.
6.173
BASIC LINEAR DESIGN
Feedthrough: Undesirable signal-coupling around switches or other devices that are
supposed to be turned off or provide isolation, e.g., feedthrough error in a sample-andhold, multiplexer, or multiplying DAC. Feedthrough is variously specified in percent, dB,
parts per million, fractions of 1 LSB, or fractions of 1 volt, with a given set of inputs, at a
specified frequency.
In a multiplying DAC, feedthrough error is caused by capacitive coupling from an ac
VREF to the output, with all switches off. In a sample-and-hold, feedthrough is the
fraction of the input signal variation or ac input waveform that appears at the output in
hold. It is caused by stray capacitive coupling from the input to the storage capacitor,
principally across the open switch.
Settling Time—ADC: The time required, following an analog input step change (usually
full-scale), for the digital output of the ADC to reach and remain within a given fraction
(usually ± ½LSB).
6.174
CONVERTERS
CONVERTER AC SPECIFICATIONS
REFERENCES:
DATA CONVERTER AC ERRORS
1.
W. R. Bennett, “Spectra of Quantized Signals,” Bell System Technical Journal, Vol. 27, July 1948,
pp. 446-471.
2.
B. M. Oliver, J. R. Pierce, and C. E. Shannon, “The Philosophy of PCM,” Proceedings IRE, Vol. 36,
November 1948, pp. 1324-1331.
3.
W. R. Bennett, “Noise in PCM Systems,” Bell Labs Record, Vol. 26, December 1948, pp. 495-499.
4.
H. S. Black and J. O. Edson, “Pulse Code Modulation,” AIEE Transactions, Vol. 66, 1947, pp. 895899.
5.
H. S. Black, “Pulse Code Modulation,” Bell Labs Record, Vol. 25, July 1947, pp. 265-269.
6.
Steve Ruscak and Larry Singer, Using Histogram Techniques to Measure A/D Converter Noise,
Analog Dialogue, Vol. 29-2, 1995.
7.
M.J. Tant, The White Noise Book, Marconi Instruments, July 1974.
8.
G.A. Gray and G.W. Zeoli, Quantization and Saturation Noise due to A/D Conversion, IEEE Trans.
Aerospace and Electronic Systems, Jan. 1971, pp. 222-223.
9.
Kevin McClaning and Tom Vito, Radio Receiver Design, Noble Publishing, 2000,
ISBN 1-88-4932-07-X.
10. Walter G. Jung, editor, Op Amp Applications, Analog Devices, Inc., 2002, ISBN 0-916550-26-5,
pp. 6.144-6.152.
11. Brad Brannon, Aperture Uncertainty and ADC System Performance, Application Note AN-501,
Analog Devices, Inc., January 1998. (available for download at http://www.analog.com)
12. Christopher W. Mangelsdorf, A 400-MHz Input Flash Converter with Error Correction, IEEE
Journal of Solid-State Circuits, Vol. 25, No. 1, February 1990, pp. 184-191.
13. Charles E. Woodward, A Monolithic Voltage-Comparator Array for A/D Converters, IEEE Journal of
Solid State Circuits, Vol. SC-10, No. 6, December 1975, pp. 392-399.
14. Yukio Akazawa et. al., A 400MSPS 8 Bit Flash A/D Converter, 1987 ISSCC Digest of Technical
Papers, pp. 98-99.
15. A. Matsuzawa et al., An 8b 600 MHz Flash A/D Converter with Multi-stage Duplex-gray Coding,
Symposium VLSI Circuits, Digest of Technical Papers, May 1991, pp. 113-114.
16. Ron Waltman and David Duff, Reducing Error Rates in Systems Using ADCs, Electronics Engineer,
April 1993, pp. 98-104.
17. K. W. Cattermole, Principles of Pulse Code Modulation, American Elsevier Publishing Company,
Inc., 1969, New York NY, ISBN 444-19747-8. (An excellent tutorial and historical discussion of data
conversion theory and practice, oriented towards PCM, but covers practically all aspects. This one is
a must for anyone serious about data conversion! Try internet secondhand bookshops such as
http://www.abebooks.com for starters).
18. Robert A. Witte, Distortion Measurements Using a Spectrum Analyzer, RF Design, September, 1992,
pp. 75-84.
6.175
BASIC LINEAR DESIGN
19. Walt Kester, Confused About Amplifier Distortion Specs? Analog Dialogue, 27-1, 1993, pp. 27-29.
20. Dan Sheingold, Editor, Analog-to-Digital Conversion Handbook, Third Edition, Prentice-Hall,
1986.
6.176
CONVERTERS
TIMING SPECIFICATIONS
SECTION 6.7: TIMING SPECIFICATIONS
In most cases, the digital signals of a converter are designed to operate at standard levels
with standard interface specifications. Common interfaces are parallel or serial (most
commonly SPI® or I2C® compatible, but, at the high speed, LVDS is making inroads).
The fact that we are compatible with defined standards means that the timing and voltage
levels defined in these specifications are met.
The digital signals of a converter generally divided into one of three groups: address,
data, and control.
Common timing specifications include:
Logic low level: the voltage level at which the signal is guaranteed to be seen as a logic
0. This level is generally specified at whatever power supply the converter is guaranteed
to run at. This means that you will generally see different specification table for 3 V and
5 V supplies.
Logic high level: the voltage level at which the signal is guaranteed to be seen as a logic
1. Again, this will be given at the various power supply voltages.
Rise time: for a step function, the time required for a signal to change from a specified
low value to a specified high value. Typically, these values are 10% and 90% of the step
height (see Figure 6.176).
Fall time: for a step function, the time required for a signal to change from a specified
high value to a specified low value. Typically, these values are 10% and 90% of the step
height (see Figure 6.177).
90%
90%
10%
10%
Rise time
Fall time
Figure 6.176: Rise Time and Fall Time
Setup Time: the time that the data input must be valid before the output latch samples.
Hold Time: the time that data input must be maintained valid after the output samples.
6.177
BASIC LINEAR DESIGN
Propagation Delay: the time that takes to the sampled data input to propagate to the
output.
Pulsewidth High: the minimum time a pulse must be at the logic high level
Pulsewidth Low: the minimum time a pulse must be at the logic low level
Other timing specifications are typically from one signal transition to another. These
signals will be defined in the specifications. As an example see Figure 6.178.
Often the output current available is also specified. This will help determine fan out, the
number of standard loads that the output can drive. But we will discuss in the circuit
board considerations section why it is probably not wise to have the converter drive
significant current.
Occasionally a high speed converter has a clock input that is not a standard logic signal
level. This is often to make the signal easier to generate and propagate on the printed
circuit board. For example, for optimum performance, the AD6645 must be clocked
differentially. The encode signal is usually ac-coupled into the ENC and ENC pins via a
transformer or capacitors. These pins are biased internally and require no additional bias.
The input impedance of the input and the signal level will be specified. See Figure 6.176.
Figure 6.177: Encode Command Specifications for the AD6645
6.178
CONVERTERS
TIMING SPECIFICATIONS
Figure 6.178: Sample Timing Specifications for the AD6645
6.179
BASIC LINEAR DESIGN
Notes:
6.180
CONVERTERS
HOW TO READ A DATA SHEET
SECTION 6.8: HOW TO READ A DATA SHEET
While there is not an industry standard concerning data sheets (what they cover, what
information is included, and where that information is located) for the most part, data
sheets from various manufacturers generally are similar in construction. In this section
we will take a look at several data sheets and try to give a feel for where to find certain
information and how to interpret what is found.
As a demonstration we will look at 5 data sheets:
AD6645
High speed ADC
AD9777
High speed DAC (TxDAC, Interpolating DAC)
AD7678
General-Purpose ADC
AD5570
General-Purpose DAC
AD7730
Σ-Δ ADC
The part numbers chosen are arbitrarily, they were chosen only to give a range of parts.
The Front Page
This page is designed to give you the basic information you might need to choose the
part. Referring to Figure 6.178. We can break this up into 3 sections.
Section 1 is the features. These bullet points are what are considered by the manufacturer
to be the more important parameters of the product for its intended application. The
targeted applications are typically listed as well.
The 2nd section is the product description. This typically covers some of what the
manufacturer considers to be the salient features of the op amp.
The 3rd section is the functional block diagram. Many times you can get information from
the block diagram. In this instance we can see that the ADC has a pipeline architecture, in
this case 3 stage.
The Specification Tables
There are an unlimited number of conditions possible to measure any given specification.
Obviously it is not possible to test all possible conditions. So a representative set of
conditions are chosen. The test conditions are specified (1 in Figure 6.178). Occasionally
if further clarification or modification of the conditions are required, they are handled as
footnotes (2 in Figure 6.179).
On many converters some individual specifications may have multiple entries. This is for
different performance levels. It an also be for different temperature ranges (usually
commercial, industrial, or military). In this case it is for different speed grades. This can
be seen in Figure 6.179 (3).
6.181
BASIC LINEAR DESIGN
2
1
3
Figure 6.179: Example Data Sheet Front Page
6.182
CONVERTERS
HOW TO READ A DATA SHEET
1
3
2
1
2
Figure 6.180: Example Data Sheet Specification Page
6.183
BASIC LINEAR DESIGN
Figure 6.181: Typical AC Specifications
6.184
CONVERTERS
HOW TO READ A DATA SHEET
Figure 6.182: Typical Timing Specification page
6.185
BASIC LINEAR DESIGN
Figure 6.183: Typical Timing Specification page 2
6.186
CONVERTERS
HOW TO READ A DATA SHEET
Figure 6.184: Typical Timing Specifications page 3
6.187
BASIC LINEAR DESIGN
Note that there are typically 3 possibilities for the specifications, Min, Typ, and Max. See
Figure 6.180 (3). At Analog Devices any specification in the min (minimum) and max
(maximum) columns will be guaranteed by test. This can be a direct test, or, in some
instances, testing one parameter will guarantee another. A typ (typical) specification is
just that, typical. Depending on the particular specification, the deviation from the typical
can be substantial. And you have no way of knowing what the range of variation on the
typ specification is. Sometimes you will find a typ and a min (or max) for the same
specification. This tells you that although the test limits are at a particular level (min or
max) the typicals tend to run much better than the test limits. For example, in the data
sheet example in Figure 6.180, the gain error is guaranteed to be ±10% (full-scale), but
the error is typically 0 % (FS). When designing, using typs is risky. You are much better
off using mins or maxes for error budget analysis.
Testing is one of the most expensive steps in the manufacturing of integrated circuits.
Therefore a more highly specified part will typically cost more than a less completely
specified part. But, in your system, the higher specified part may be required to guarantee
the circuit performance.
As can be seen from the examples in Figures 6.179 to 6.182, the example used (in this
case the AD6645) is specified for both dc and ac, as explain in the earlier section on
converter specifications. Note that the dc specifications are in terms of absolute levels
(volts, amps, etc.) while the ac specifications tend to be in terms of dB.
Also note in Figure 6.181 that the digital signal levels are also specified in terms of
voltage levels. They are also specified in terms of time. These are the “switching
specifications” of Figure 6.182. These specifications are for individual signals (rise and
fall times, pulse width high, etc.) as well as between signals (setup and hold times, etc.).
The Absolute Maximums
There is always a section (usually just after the specification tables) with the absolute
maximum ratings. These are typically voltage and temperature related.
The process used to fabricate the op amp will typically determine the maximum supply
voltage. Maximum input voltages typically are limited to the supply voltages. It should
be pointed out that the supply voltage is the instantaneous value, not the average, or
ultimate value. So if a converter has voltages on its input but the supply voltage is not
present, which could occur during power up when one section of the system is powered
but others aren’t, the converter is overvoltaged, even if when the converter power is
applied, everything is within operational limits.
The overriding concern for semiconductor reliability is to keep the junction temperature
below 150°C. There will be a θja given for the various package options. This is the
thermal resistance from the junction to free air. The units are °C/Watt. To use this
information simply determine the dissipation of the package. This would be the quiescent
current times the supply voltage. Then take the maximum dissipation generated by the
6.188
CONVERTERS
HOW TO READ A DATA SHEET
output stages (output current times the difference between the output voltage and the
supply voltage). Add these together and you will have the total package dissipation, in
watts. Multiply the thermal resistance by the dissipation and you have the temperature
rise. You start with the ambient temperature (in °C, typically taken to be 25°C), take the
rise calculated above and that will give you the junction temperature. Remember that the
ambient temperature should be in operation. Circuits packaged in an enclosure, which is
in turn placed in a rack with other equipment will have an internal ambient temperature
that could be significantly above the air temperature in the room that it is located in. This
must be considered.
The thermal resistance has two components θjc and θca. θjc is the thermal resistance from
the junction to the case. There is not much you can to about that. θca is the thermal
resistance from the case to the air. This we can effect relatively easily by adding a heat
sink. The thermal resistance add linearly. Also note that these values are in free air.
Moving air allows more cooling, especially with a heat sink.
Figure 6.185: Typical Absolute Maximum Ratings
The Ordering Guide
Many converters are available in multiple packages and/or multiple temperature ranges.
Each of the various combinations of package and temperature range requires a unique
part number. This is spelled out in the ordering guide. See Figures 6.186 to 6.187.
6.189
BASIC LINEAR DESIGN
Just as a note, in the case of general purpose ADCs and DACs, the commercial (0°C to
70°C) temperature range has mainly become obsolete. The reason for this is that most
circuits yield to the industrial temperature range. It is less expensive to support less part
types. Each discrete part number requires a separate test program, separate inventorying
and other supporting documentation. The exception to this rule is for parts designed for a
specific application which is, by definition, commercial. An example of this is consumer
applications, such as audio. Wider temperature range for these parts offer no advantage.
The industrial temperature range can also mean different things. The standard industrial
temperature range is −40°C to 85°C. A common variant on this is what is commonly
called the automotive temperature range −55°C to 85°C. 0°C to 100°C is also common.
The military temperature range is −55°C to 125°C.
Figure 6.186: Ordering Guide Example 1 (for the AD7684)
Figure 6.187: Ordering Guides Example 2 (for the AD5570)
The “brand” column of the ordering guide is the package marking for small packages.
The markings that are customary on the DIP package will not physically fit on the much
smaller surface mount packages. For instance, DIP packages would typically include the
part number, date code (when the IC was “made,” typically when it passes final test) and
occasionally some other information. Obviously, the space available for marking on
surface mount packages is very much limited. So the 3 character code is used instead.
6.190
CONVERTERS
HOW TO READ A DATA SHEET
Pin Description
In the pin description, information on the pin function, including optional functionality
for multipurpose pins are described. Often the descriptions are expanded upon in the
main body of the data sheet.
Figure 6.188A: Typical Pin Description
6.191
BASIC LINEAR DESIGN
Figure 6.188B: Typical Pin Description (cont.)
Defining the Specifications
This section contains a brief description of the specifications. It is, in effect, a subset of
the earlier section where we defined the converter specifications. The definitions will be
more compact and only those specifications that apply to the particular converter will be
defined.
Also in this area specialized specifications will be defined. An example of this might be
differential gain and differential phase, which are definitions specific to the video
industry.
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HOW TO READ A DATA SHEET
Equivalent Circuits
Driving the inputs of a converter, especially at high frequencies, is not a trivial task.
Loading of an output pin can also be equally as challenging. Knowing the architecture of
circuit connected to that pin may be of assistance in understanding how to interface that
pin.
Things that might be of interest for an input pin is the input impedance, so that the source
impedance can be matched, for instance, and the dc level biasing the pin. Normally this
bias is at half the supply voltage (assuming single-supply operation), but this is not
always the case.
Figure 6.189: Typical Equivalent pin circuits
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The Graphs
Many parameters vary over the operational range of the converter. An example is the
variation of spurious free dynamic range (SFDR) with frequency. See Figures 6.190 to
6.193. So to completely specify the SFDR of a part there would be a specification at
particular input frequency, which typically would appear in the specification table, and
graphs showing variation with input frequency, sampling rate, and level.
Figure 6.190: Typical performance graphs
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HOW TO READ A DATA SHEET
The information presented in the graphs is not uniform from vendor to vendor or even
from part to part from the same manufacturer. Higher performance parts tend to be more
completely specified. For the most part the graphs should be considered typical values.
Figure 6.191: Typical performance graphs page 2
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Figure 6.192: Typical performance graphs page 3
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HOW TO READ A DATA SHEET
Figure 6.193: Typical performance graphs page 4
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The Main Body
The main body of the data sheet contains detailed information on operations and
applications of the converter. Early on at Analog Devices, it was determined that just
giving someone an amplifier and letting them go off on their own to try to build whatever
it is that they want to build was not the best approach. Therefore, Analog Devices
includes application information with the data sheet.
Circuit Description
Typically the first part of the main body of the data sheet is the circuit description. Since
the topology of the converter can determine the applicability of a particular converter in a
particular design, understanding the internal operation of the converter can be very
helpful. This is especially true when an understanding of the input structure of a
converter may be helpful in designing the driver circuit.
Figure 6.194: Typical circuit diagram
Many converters, such as the AD9777 and the AD7730 that we are using as examples in
this section, are really more than just converters. They are more exactly subsystems,
containing both converters and support circuitry. The operation of all of the subsections
of these circuits is described.
As we said previously, driving an ADC input is not trivial at high speeds. Understanding
the input configuration is essential. The same is true for the data outputs. On the DAC
side the interface issues are reversed (data in/signal out), but just as important.
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HOW TO READ A DATA SHEET
Interface
To use a converter we have to get the data into or out of it. There are basically two
different ways to accomplish this, parallel and serial.
The parallel interface is relatively straightforward. The only timing issues that may have
to be considered are set up and hold times. Obviously, with the advent of low supply
voltages, signal levels of the digital interface need to be observed.
Figure 6.195: Typical parallel interface timing diagram
In the case of the AD7678, which is an 18-bit converter, there may be an issue interfacing
with a 16 bit (or 8 bit) microprocessor bus. The output register logic is flexible enough to
allow the 18-bit word to interface to these narrower data busses. See Figure 6.196.
Figure 6.196: Data bus interface example
The case of serial interface is typically a bit more complicated. Many times the serial
interface conforms to a certain interface standard. You will see that many of the serial
interface converters conform to the SPI, QSPI®, MICROWIRE, or I2C standards.
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For the serial interface the converter could act as a master or a slave. The differentiation
is determined by who generates the timing clock. The master typically generates the
clock.
The width of the serial clock is variable. The data can be MSB first or LSB first. The time
slots that line up with the data bits must be defined. Since there are multiple possibilities,
each must be defined.
Figure 6.197: Typical DAC serial timing diagram
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HOW TO READ A DATA SHEET
Register Description
Many converters have multiple operational modes. Some have on board circuitry, such as
a multiplexer or programmable amplifier (PGA) that must be configured. This requires
writing to control registers. Each bit in each word must be defined.
Figure 6.198: Typical register description (partial)
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Application Circuits
Often some typical application circuits are provided to assist in applying the converters.
Figure 6.199: AD6645 Typical Application Circuit
Figure 6.200: AD7730 Typical Application Circuit
When looking at the applications circuits, note that the recommended support part
numbers, while still valid, may no longer be the best choices. This is because newer parts
may have been released since the data sheet was written. Always look to see if a newer
part may be better.
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HOW TO READ A DATA SHEET
Evaluation Boards
The only way to be sure that your design works is to actually build it. But as has been
mentioned several times, the layout of a printed circuit board is as critical as any other
part of the design. To that end, manufacturers often make evaluation boards available.
This is an advantage for the design engineer, since it relieves him of the responsibility of
developing and manufacturing an evaluation board. It also allows him to test a portion of
the design before committing to the prototype run.
But the evaluation board serves the manufacturer as well. Since the manufacturer controls
the design of the board, he can insure that the evaluation system shows off the part in it
best light. The manufacturer will ensure that the performance of the board will not limit
the performance of the part. This means a more fair evaluation, since many variables are
removed.
The schematic and board layouts are typically presented in the data sheet. Often the
Gerber files for the evaluation board are available as well from the manufacturer. A word
of warning is in order though. Just cut and pasting the Gerber files into your design is not
enough to ensure optimum performance. Integrating the evaluation board section into the
rest of the system is important as well. For instance, what if there is more than one
converter in the system? The grounding scheme of the evaluation board, which worked in
the instance of the one converter evaluation system, may be inadequate for larger
systems.
Evaluation boards are typically part of larger systems for evaluation of a converter.
Typically software is included to interface to the part. This software typically runs on a
PC and includes a human interface. Evaluation systems are covered in more detail in the
chapter on design aids.
Summary
Not all data sheets for converters (or any other classification of part, for that matter) are
the same, not from different manufacturers or even from the same manufacturer. But
there are some features which are more or less standard. Knowing what the look for and
where to look for it can make the daunting task of part selection a bit easier and possibly
more exact.
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Notes:
6.204
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CHOOSING A DATA CONVERTER
SECTION 6.9: CHOOSING A DATA CONVERTER
Often the choice of the data converter is the cornerstone of the entire design. As we have
seen in the previous sections, a converter can have many specifications. Now that we
have gone over what those specifications mean and how to read a data sheet we are ready
to proceed to the next step. How, then, do you determine which converter best suits your
needs?
Determine the Parameters
The most obvious parameters that we may need to specify the converter are the resolution
and sample rate. Remember that the resolution of converter and the accuracy may not be
the same. Quite often it is really the accuracy that is required.
For ADCs, when we think of sample rate, we generally mean the maximum frequency.
However, when the sample rate is reduced, the hold time requirements of the hold
capacitors in the sample-and-hold section of the ADC increase proportionally. This can
lead to errors if the sample rate is slow enough for the droop rate of the sample-and-hold
to allow the sampled voltage to decay till it is out of the error band before the next sample
period. While the droop rate of ADCs with internal SHAs is typically not specified, a
minimum sample rate will be. This effect is dependant on the architecture of the ADC.
Successive approximation ADCs rarely have this problem but pipelined architectures
often do.
How the ADC is to be used may also effect the part selection. Pipelined ADCs and Σ-Δ
converters typically don’t have a control signal for starting the conversion. They are
designed to convert continuously. This makes them a bit more difficult to use in
applications in which the sample must be synchronous. This would include multiplexed
applications and those where the sample is to be triggered by an external stimulus. Flash
or successive approximation type converters are probably a better choice in these type of
applications.
We stated in the specifications section that there are two ways to specify the converter, ac
specifications and dc specifications. In general ac specifications tend to be important with
continuous sampling, higher speed. DC specifications tend to be more important with
single conversion or multiplexed applications, which tend to be lower speed.
What is the frequency range of the input signal? For high frequency applications, is the
input frequency band in the first Nyquist zone, or is undersampling to be employed?
Another point: Nyquist says that the input frequency can be up to half of the sample rate
(for baseband sampling), but the antialiasing filter complexity increases sharply as the
upper end of the input frequency band approaches the Nyquist frequency (Fs/2). By using
oversampling, moving the sample rate out so that the input frequency band is
proportionally smaller, system cost and complexity can be reduced.
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The analog considerations for interfacing DACs are typically much less involved. In
general, the decisions are whether the DAC should be current out or voltage out. If
current out, the DAC will typically dictate the use of a current to voltage (I/V) converter.
One possible exception is whether the DAC is multiplying, in which case you need to
specify the input signal.
On the digital side, the primary consideration is whether the data bus is parallel or serial.
With the proliferation of low voltage circuits, the voltage level of the interface also needs
to be defined. In many cases the data output level is the same as the power supply, but
some converters have a separate power pin which sets the voltage level of the digital
interface. While the parallel interface is fairly simple, there are some added questions
concerning the serial interface. Does it need to support a standard such as SPI, I2C, or
LVDS?
If the resolution of the converter is not the same as the data bus width (interfacing a 12 bit
converter to an 8 bit parallel bus for instance) the converter will require multiple
read/write cycles. Similarly, in a serial interface you may have to specify right or left
justified data.
In some converters control words must be written to the converter as well.
As always, what the physical environment the converter must operate in is a concern.
What is the temperature that the system must operate in? Is there a size limitation? What
power supplies are available? Also, high speed converters tend to be relatively high
power dissipation devices. Thermal considerations must also be considered.
Part of this process is determining the values for the various parameters. In doing this you
should determine an optimum value and an acceptable range. For example, you may have
a target value of full 16 bits for the accuracy, but you may be able to live with 2 LSBs of
differential nonlinearity and by loosening this spec, a better overall fit could be made.
The temperature range over which that the circuit will be required to operate will affect
this as well. The physical size of the package and the cost, as always, should be
considered. It is good practice to allow a little margin on the specs, if possible, so that
aging effects, etc., don’t cause the circuit to go out of spec.
Prioritizing the Parameters
As can be seen from the discussion above, there can be a number of considerations
involved in selecting a part. Typically, however, there are one or two that are more
important than the rest. It is always a good idea not to overspecify a part. The more
specifications that have to be met, the harder it will be to meet all of them.
Selecting the Part
The last step is to finally select the part. The “brute force” method would be to gather
data books and randomly start looking at the specs for each of the parts individually. This
would quickly get out of hand. There are several tools that make the job much easier.
6.206
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CHOOSING A DATA CONVERTER
One such tool is a selection guide. These appear frequently in magazine ads and
promotional mailers. The main difficulty with using these guides is that, in many
instances, the lists are not all inclusive, but instead are usually focused on specific sub
groups such as new products, single-supply, low power, etc. The narrow focus may cause
you to miss some otherwise acceptable options. An example of a selection guide, in this
case called a solutions bulletin is given in Figure 6.201.
ADI provides a piece of literature called “The Short Form Designers Guide” which is
much better suited to the purpose. It contains all of ADI’s current product offering, sorted
by function and performance. Two of the main parts of the short form are the product
trees and selection guides.
Using the converter section as an example, we can choose between several possibilities,
each of which are expanded further in subsequent trees. This allows the designer to drill
down to a particular converter which will be acceptable in his application. Figures 6. 202
through 6.205 shows part of the ADC selection tree.
The selection trees only give one, maybe two, specs. It is designed to be the start of the
selection process. More detailed specs are given in the selection guides, which will take a
category corresponding the one of the sections of the selection trees, and then sort the
parts by the relevant parameter. For example, for converters, they would be sorted by
resolution, lowest resolution first. The converters are then sorted by the next parameter,
in this case sampling rate.
In addition to the specs used to sort the parts, there are several other specs given. These
include package size and cost. The cost quoted is generally the 1000 piece price for the
base grade of the converter. It should be used for comparison purposes. Small quantities
will typically be priced higher, higher quantities will generally be lower.
An alternative is the parametric search engine. Here you enter the relevant parameters for
your design. The converter search is shown in Figures 6.206 through 6.207. You can also
prioritize the selection by clicking on the “priority” box. The search will then search the
database of parts and it will come up with 10 alternatives.
A particularly nice feature of the search engine is that if it can’t meet your selection
criteria exactly, it will come back with a selection of parts that come close to matching
your criteria. Where there is not a match, the parameter is presented in red. This allows
the designer the chance to evaluate how well his application lines up with available
components.
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Figure 6.201: Typical Solutions Bulletin Front Page
6.208
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CHOOSING A DATA CONVERTER
Figure 6.202:
Short Form Selection Guide Top Level
Figure 6.203: Short Form ADC Selection Table, Front Page
6.209
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Figure 6.204: Short Form Selection Guide 2nd Level
Figure 6.205: Short Form Selection Guide ADC Page
6.210
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CHOOSING A DATA CONVERTER
Figure 6.206: Parametric Search General Page
Figure 6.207: Parametric Search AC Specs Page
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6.212
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