HP 8751A application note
Measuring Frequency Response
with the Agilent E5061B LF-RF
Network Analyzer
Application Note
Introduction
Evaluating frequency responses of components and circuits is essential for
ensuring the performance of electronic equipment. Especially in the case of the
high-reliability electronic equipment used in automotive, medical, and aerospace
and defense industries, it is necessary to evaluate a wide variety of components
and circuits in the low- to high-frequency ranges. Among these applications,
the low-frequency network analyzer plays an important role in ensuring the
stable and reliable operation of low-frequency analog circuits such as sensor
systems and power supplies. You need a better understanding of low-frequency
network analysis (gain-phase measurements) as well as RF network analysis
(S-parameter measurements).
This application note describes fundamentals of low-frequency network analysis
using the E5061B LF-RF network analyzer. Here we mainly discuss simple
low-frequency 2-port device measurements and associated topics such as highimpedance probing techniques and high-attenuation measurements.
Table of Contents
E5061B-3L5 LF-RF Network Analyzer.................................................... 3
Basic Measurement Configurations ...................................................... 4
50 Ω DUTs ........................................................................................... 5
Non-50 Ω DUTs, example 1 .............................................................. 5
Non-50 Ω DUTs, example 2 .............................................................. 7
In-circuit probing measurements .................................................... 8
IFBW Setting for Low-Frequency Measurement .............................. 10
High-Impedance Probing Methods ...................................................... 11
Signal Separation for Ratio Measurement ......................................... 13
High-Attenuation Measurement at Low Frequencies ...................... 15
OP Amp Measurement Example .......................................................... 20
Closed-loop gain............................................................................... 20
Open-loop gain, phase margin ....................................................... 22
CMRR ................................................................................................. 27
PSRR................................................................................................... 29
Output impedance............................................................................ 31
References ............................................................................................... 33
Table 1. Guideline for selecting test ports
Test ports
Situation
S-parameter test port Transmission and reflection
measurements in the 50 Ω
system impedance
Gain-phase test port
2
Application
Passive filters, antennas,
cables, RF amplifiers, etc.
Transmission measurements
with high-impedance probing
over 30 MHz using the
41800A active probe
High-frequency op amps
Transmission measurements
with high-impedance probing
in the low frequency range
OP amp circuits
Feedback loop measurements
DC-DC converter loop gain
High-attenuation measurements
in the low-frequency range
CMRR and PSRR of OP amps
E5061B-3L5 LF-RF Network Analyzer
The E5061B with the Option 3L5 vector network analyzer covers a broad test
frequency range from 5 Hz to 3 GHz in a single instrument. The E5061B-3L5
includes an S-parameter test port (5 Hz to 3 GHz, Zin = 50 Ω) and a gain-phase
test port (5 Hz to 30 MHz, Zin = 1 MΩ/50 Ω). Both test ports can be used for
low-frequency applications, depending on your measurement needs. Table 1
shows an example of selecting the test ports.
E5061B-3L5
Gain-phase
test port block
ATT: 20 dB/0 dB
Zin: 1 MΩ/50Ω
T
R
ATT
ATT
Zin
Zin
T
R
S-parameter
test port block
DC bias
source
LF OUT
Gain-phase test port
(5 Hz to 30 MHz)
R2
T1
T2
Port-1
S-param. test port
(5 Hz to 3 GHz)
Figure 1. E5061B-3L5 simplified block diagram
3
R1
Port-2
Basic Measurement Configurations 50 Ω DUTs
First let’s summarize how to connect DUTs in typical low-frequency network measurement applications. Here the focus is on configurations for 2-port transmission measurements. The first case is a transmission measurement for 50 Ω devices, such as filters and
cables. Figure 2 shows a configuration using the gain-phase test port. The R-ch receiver
VR monitors the source output voltage applied to the 50 Ω system impedance (incident
voltage to the 50 Ω transmission line), and the T-ch receiver VT monitors the transmitted
voltage. Then the analyzer measures the voltage ratio VT/VR which indicates the transmission coefficient S21.
Figure 2 shows a configuration using the S-parameter test port. The S-parameter test set
has built-in directional bridges, and an external power splitter is not required. In most
cases, the S-parameter test port for 50 Ω transmission measurements is used.
Most 50 Ω transmission measurement can be covered with the S-parameter test port. For
high-attenuation devices such as, mΩ impedance measurement for DC-DC converters and
large bypass capacitors using the shunt-thru method, the 50 Ω transmission measurement should be performed using the gain-phase test port rather than the S-parameter
test port. In this case, the semi-floating receiver architecture of the gain-phase receiver
ports eliminate the measurement error in the low-frequency range, which is caused by
the test cable ground loop between the source and receiver (discussed later).
E5061B-3L5
VT
50
VR
T-ch
(Zin = 50 Ω)
50
50
R-ch
(Zin = 50 Ω)
50
50
DUT
Zout
Zin
Power
splitter
Figure 2. Configuration for measuring transmission coefficient of 50 Ω DUTs with the
gain-phase test port
E5061B-3L5
50
R1
R2
A
B
Port 1
(50 Ω)
DUT
Zout
Zin
Port 2
(50 Ω)
Figure 3. Configuration for measuring transmission coefficient of 50 Ω DUTs with the
S-parameter test port
4
Basic Measurement Configurations
Non-50 Ω DUTs, example 1
Low-frequency 2-port devices often have non-50 Ω impedances. The most
typical examples are low-frequency amplifier circuits. Figure 4 shows a configuration example of measuring the frequency response of amplifiers with the
gain-phase test port. The DUT has high input impedance and the output port is
terminated with a non-50 Ω load ZL. The load impedance ZL depends on requirements of the targeted application. The load ZL can be either a resistive load or a
reactive load.
The parameter to be measured is the voltage transfer function from the DUT’s
input port to the output port, Vout/Vin. The difference from the 50 Ω transmission
coefficient measurements which were shown in Figures 2 and 3 is that the R-ch
receiver VR directly monitors the AC voltage across the DUT’s input impedance
Zin with high-impedance probing, instead of monitoring the voltage across the
50 Ω system impedance. The output voltage Vout can be monitored using the
high-impedance probing, without affecting the DUT’s load condition.
The analyzer’s high-impedance receivers and the DUT should be connected with
coaxial test cables or 10:1 passive probes, depending on the requirements of the
maximum test frequency, the probing input impedance, the probing input capacitance, and so on (discussed later). When you use the coaxial test cables, a
T-connector can be used at the R-ch probing point. To compensate the frequency
response and phase errors between two probes/test cables, the response thru
calibration should be performed. For example, by contacting the T-ch probe to
the point TP1.
E5061B-3L5
VT
T-ch
(Zin = 1 MΩ)
VR
Coaxial test cables,
or 10:1 passive probes
TP2
DUT
Zout
Zin
Low-Z High-Z
TP1
50
R-ch
(Zin = 1 MΩ)
Calibration:
Response thru cal.
by contacting T-ch
probe to TP1
ZL
Vout
Vin
Figure 4. Configuration for measuring amplifiers with the gain-phase port (up to 30 MHz)
5
Basic Measurement Configurations
Non-50 Ω DUTs, example 1 (continued)
If you need to measure the frequency response of an amplifier up to more than
30 MHz, or if you need to probe the amplifier with a very small probing capacitance, the solution is to use the active probe at the S-parameter test port.
Figure 5 shows a configuration example. Unlike the configuration that was
shown in Figure 4, the ratio measurement is referenced to the 50 Ω impedance
of the built-in R1 receiver, and the response thru calibration must be performed
by probing TP1 in order to correctly measure the voltage transfer function Vout/
Vin. If the response thru calibration is not performed (and if a feed thru is not
connected), the measured gain will be about 6 dB higher than the correct value
because the AC voltage measured at the internal 50 Ω reference receiver will be
about half of Vin.
For measurements in high frequencies over tens of MHz, connecting the 50 Ω
feed thru to the DUT’s input port can prevent the standing wave that may be
caused by the impedance mismatch between the analyzer’s 50 Ω source and
the DUT’s high input impedance. However, it must be noted that connecting
the feed through will form a shunt signal path from the center conductor to the
ground of the test cable, and this may cause measurement errors associated
with the ground loop in the high-attenuation measurements such as CMRR and
PSRR. If this is of concern, it is better not to connect the feed thu.
E5061B-3L5
50
R1
R2
A
B
Port 1
(50 Ω)
TP1
Port 2 with active probe
(High-Z)
DUT
TP2
Zin
Zout
High-Z Low-Z
Feed thru
(optional)
50
Vin
ZL
Vout
Calibration:
Response thru cal.
by contacting active
probe to TP1
Figure 5. Configuration for measuring amplifiers with the S-parameter test port and
active probe (up to 30 MHz)
6
Basic Measurement Configurations
Non-50 Ω DUTs, example 2
Figure 6 and 7 shows configuration examples for measuring 2-port devices whose
input and output impedances are several hundreds of Ωs to 1 or 2 kΩ. Typical applications are low-frequency passive filters, such as ceramic filters and LC filters. In these
examples, impedance matching is implemented by simply connecting a series resistor.
The configuration of Figure 6 uses the gain-phase test port. The ratio VT/VR indicates
the transmission coefficient for the 1 kΩ system impedance.
Some types of filters need to be tested by connecting a load capacitor CL in parallel
with the load resistor. The input capacitance of the high-impedance probe must be
small enough not to affect the filter’s characteristics. So the high-impedance T-ch
receiver should be connected with the 10:1 passive probe which has the input capacitance around 10 pF. Or, if the DUT is very sensitive to the capacitive loading, use the
S-parameter test port with the active probe, see amplifier measurement configuration
shown in Figure 5.
The equivalent measurement can be achieved by using the 50 Ω input instead of using
high-impedance probing at the T-channel and connecting another matching resistor as
shown in Figure 7. This configuration is simpler and has an advantage that no probe
capacitance is applied at the T-ch. However, it is not suitable for testing high-rejection
filters because the measurement dynamic range is degraded by the series matching
resistor. The degradation is 20*Log (50/1000) = 26 dB, in this case.
E5061B-3L5
VT
10:1 passive
probe
CL
VR
T-ch
(Zin = 1 MΩ)
1 kΩ
DUT
Zout
1 kΩ
Zin
1 kΩ
950
50
50
R-ch
(Zin = 50 Ω)
50
50
Power
splitter
Calibration:
Response thru cal.
by connecting thru
device in place of DUT
Figure 6. Configuration for measuring passive IF filters with high-impedance probing
(for DUTs not extremely sensitive to capacitive loading)
E5061B-3L5
50
R1
R2
A
B
Port 1 (50 Ω)
950
Zin
1 kΩ
Zout
1 kΩ
950
Port 2 (50 Ω)
CL
Figure 7. Configuration for measuring passive IF filters with 50 Ω input
7
Basic Measurement Configurations
In-circuit probing measurements
The next application example is an in-circuit probing measurement, in which we
measure the frequency response between two test points in the circuit under
test. Figure 8 shows how to measure the frequency response of block-2 with
the gain-phase test port. The frequency response of the circuit block-2 can be
directly measured by probing TP1 and TP2 with dual high-impedance probing.
Similarly to the amplifier measurement configuration shown in Figure 4, connection between the analyzer’s high-impedance receivers and the DUT should be
appropriately selected from either the coaxial test cables or 10:1 passive probes,
depending on the requirements on maximum test frequency, probing input
impedance, probing input capacitance, and so on.
E5061B-3L5
VT
VR
T-ch
(Zin = 1 MΩ)
50
R-ch
(Zin = 1 MΩ)
Coaxial test
cables, or
10:1 passive
probe
Block-2
TP2
TP1
Block-1
T/R = TP2/TP1
Figure 8. In-circuit measurement using dual high-impedance probing with the gain-phase
test port (up to 30 MHz)
8
Basic Measurement Configurations
In-circuit probing measurements (continued)
The maximum test frequency range of the E5061B’s gain-phase test port is 30 MHz.
If you want to perform incircuit measurements up to more than 30 MHz, the solution
is to connect a single active probe to the S-parameter test port, and perform the two
step measurement sequence as illustrated in Figure 9.
First we measure the response of the block-1 by connecting the active probe to TP1
and save the measured data into the memory trace. And then we measure the entire
response of the block-1 plus block-2 by probing TP2. The measured data is stored
into the data trace. Then we can obtain the frequency response of the block-2 using
the data/memory trace math function of the analyzer.
The equivalent measurement is possible if we performing the response thru calibration by probing TP1 and then performing the measurement by probing TP2. This will
directly give the response of the block-2 referenced to TP1 without using the trace
math function.
If the DUT’s output characteristic at TP2 is sensitive to the capacitance at TP1, the
DUT’s condition in the step 2 will slightly differ from that of the step 1, and the measurement result obtained by combining these two measurement results may contain
errors. To minimize errors, connect a dummy capacitor C2 whose capacitance is
about the same as the input capacitance of the active probe only when making
the measurement of step 2 as shown in Figure 9. For example, this capacitance
compensation method is required for measuring the phase margin of high-speed OP
amps using this dual-step measurement technique. (A measurement example will be
shown later.)
E5061B-3L5
50
R1
R2
A
B
Port 1
(50 Ω)
Port 2 with active
probe (High-Z)
Step 1
(B/R1)
Block-1
Step 2
(B’/R1)
Block-2
TP1
(B’/R1)/(B/R1)
= TP2/TP1
TP2
C2
Figure 9. In-circuit measurement with a single high-impedance probe (up to 30 MHz)
9
IFBW Setting in Low-Frequency Measurements
The IFBW (IF bandwidth) setting is one of the most common questions that many LF network analyzer users may first encounter. In high-frequency measurements, it is possible to
use a wide IFBW for faster sweep speed, but for low-frequency measurements we need to
set the IFBW to a narrow value to avoid measurement errors mainly caused by the LO feed
through. For example, let’s assume the case of measuring a high-attenuation device where
start frequency = 1 kHz and IFBW = 3 kHz. The small signal attenuated by the DUT is upconverted to an intermediate frequency (IF) and passes through the IF filter of the receiver.
Here the problem is that the leakage signal from the local oscillator (LO feed through)
also passes through the IF filter because its frequency is very close to the IF frequency as
shown in Figure 10, and this causes unwanted large measurement response.
Figure 11 shows an example of measuring a 60 dB attenuator with the E5061B’s gain-phase
test port under the conditions of source level = –10 dBm, start frequency = 1 kHz, and
IFBW = 3 kHz, the attenuator setting of T and R ports is 20 dB. As you can see, incorrect
measurement response appears around the start frequency due to the LO feed through. A
similar problem also occurs even when the measured RF signal level is high (e.g. in a
low-pass filter measurement).
In this case, the measured trace around the start frequency will be unstable due to the
interference caused by the LO feed through that exists in the very close frequency to the
RF signal. To avoid these problems, set the IFBW to a sufficiently narrower value than the
start frequency (e.g. 5 times smaller), or use the IFBW AUTO mode in which the analyzer
automatically selects narrow to wide IFBW settings depending on the frequency decade in
the logarithmic sweep, so that the total sweep time won’t be very long. The E5061B’s IFBW
AUTO mode sets the IFBW to one fifth of the start frequency of each decade.
IFBW = 3 kHz
IF = LO-RF
RF signal to be measured
= 1 kHz
From DUT
1 kHz
LO-RF
IF + 1kHz
(LO feed thru)
LO =
IF + 1kHz
Receiver
Figure 10. Measurement error caused by LO feed through
IFBW= 3 kHz
–60 dB
IFBW= AUTO
Figure 11. Example of 60 dB attenuator measurement (Start = 1 kHz, IFBW = 3 kHz and AUTO)
10
High-Impedance Probing Methods
Using an appropriate probing method is important for making accurate highimpedance probing measurements. Special attention needs to be made to the
probe input capacitance. The large input capacitance reduces the probe input
impedance at high frequencies. For example, if the input capacitance at the
probe end (= Cin) is 100 pF, the input impedance (= 1/(2*pi*f*Cin)) is 15.9 kΩ at
100 kHz, which is still high impedance. If the frequency goes up to 10 MHz, the
input impedance is 159 Ω, which is not high enough for many applications. Also,
the large input capacitance affects measurements which are sensitive to capacitive loading, such as passive IF filters, resonant circuits, and some amplifier
parameters which depend on the capacitance condition (e.g. phase margin measurement). For these applications, it is necessary to use probing methods which
provide small input capacitances if the network analyzer has a high-impedance
input port like the E5061B. The easiest way for accessing the DUT is to use a
coaxial test cable, such as a BNC to test clip lead, or a 1:1 passive probe to the
high-impedance input port as shown in Figure 12.
If the measurement frequency range is lower than 1 MHz and if the probing
capacitance of capacitive loading is not a problem for the DUT, this method is
a good solution. Unlike a 10:1 passive probe, the measurement dynamic range
is not degraded by the probe and small signals can be measured with a good
signal-to-noise ratio. The drawback of this method is that the input capacitance
of the probe will be large, because the test cable capacitance is added to the
capacitance of the high-impedance input port. The input capacitance at the
cable end will be more than several tens of picofarads even if using a short
cable. Therefore, this method is not suitable for measurements in the highfrequency range of over 1 MHz. Also, it is not suitable for the measurements
which are sensitive to capacitive loading.
E5061B
High-Z input port
Zin = 1 MΩ//30 pF)
Coax cable or 1:1 passive probe
Rr
Cp
Cr = 30 pF
Figure 12. Coaxial test cable or 1:1 passive probe
11
Cin = Cp + Cr
(e.g. 100 pF,
depends on
cable length)
High-Impedance Probing Methods (continued)
The probe input capacitance can be reduced using a 10:1 passive probe for
oscilloscopes, which is designed for use with the high-impedance input port, as
shown in Figure 13. The 10:1 passive probe generally gives small input capacitance around 10 pF at the probe end, which enables high-impedance probing up
to higher frequencies. Similarly to general oscilloscope applications, using the
10:1 passive probe is an orthodox way for high-impedance probing if the analyzer has built-in high-impedance inputs. The drawback is that the measurement
dynamic range is degraded by 20 dB due to the 10:1 attenuation of the probe. So
this method is not suitable for applications where very small signals need to be
measured.
The active probe provides a high input resistance and a very small input capacitance without attenuating measured signals due to the active circuit integrated
in the probe end, as shown in Figure 14. For example, the input resistance//
capacitance of the 41800A active probe (DC to 500 MHz) is 100 kΩ//3 pF.
Moreover, by adding the 10:1 adapter at the probe end, we can achieve 1
MΩ//1.5 pF, although the dynamic range is degraded by 20 dB in this case. If
you need to measure over 30 MHz, or if the DUT is very sensitive to the capacitive loading, it is recommended to use active probe.
E5061B
High-Z input port
Zin = 1 MΩ//30 pF)
1:1 passive probe
Cs
Rr
Cp
Rs
Cr
(Cr + Cp):Cs = 9:1, Rr:Rs = 1:9
Cin = 1/(1/(Cr + Cp) + 1/Cs)
= (Cr + Cp)/10
= 10 pF or so
Figure 13. 10:1 passive probe
E5061B
50 Ω S-parameter
test port
Active probe
Rr
Figure 14. Active probe
12
Cr
Cin = Cr
= 3 pF or less
Signal Separation for Ratio Measurements
To measure the transmission coefficient for 50 Ω devices such as passive filters
in the system impedance Z0 = 50 Ω (or for devices with other Z0 values by converting the system impedance with matching circuits), the source output signal
must be separated into the 50 Ω R-ch receiver and the DUT’s input port. If using
a source output port which does not have a built-in signal separation device,
such as a built-in power splitter or a built-in directional bridge, it is necessary to
separate the signal externally using an appropriate separation device.
The E5061B-3L5 has a S-parameter test port and most of 50 Ω transmission
measurements can be covered without using the external signal separation
device. But in some transmission coefficient measurements that should be
covered by the gain-phase test port, such as output impedance measurements
of DC-DC converters with the shunt-thru technique, you need the external signal
separation device.
In general network analysis targeting linear devices, the most important
requirement for the separation device is that it provides the 50 Ω source output
impedance (source matching) when making the ratio measurement. The most
common and recommended separation device is a two-resistor type power
splitter which covers a broad frequency range from DC to GHz and provides an
excellent source output impedance for the ratio measurement.
The ratio measurement using the power splitter shown in Figure 15-a is
equivalent to making two measurements shown in Figure 15-b by considering
the AC voltage Vo at the branch point as a virtual source voltage. As shown in
this figure, the equivalent source output impedance in both R-ch and T-ch measurements will be precisely 50 Ω, which is generally an ideal source matching
condition for 50 Ω network measurements.
Note that the two-resistor type power splitter is just applicable to ratio measurements and not suitable for absolute voltage measurements in the 50 Ω system
impedance because the splitter’s physical output impedance seen from the DUT
is not 50 Ω but 83.3 Ω.
R-ch
VR
50
R-ch
50
VR
50
Vo
Power
splitter
50
T-ch
VT
50
T-ch
DUT
50
50
50
VT
Vo
(a)
DUT
50
Vo
(b)
Figure 15. 50 Ω ratio measurement with a power splitter
13
Signal Separation for Ratio Measurements (continued)
Alternative separation devices to the power splitter are low-frequency directional couplers, or reactive power dividers (AC-coupled with a transformer)
that have a high isolation between the two output ports (more than 25 or 30
dB). Examples are mini-circuits (www.minicircuits.com) ZFDC-15-6 directional
coupler (0.03 to 35 MHz, BNC) or ZFSC power divider (0.002 to 60 MHz, BNC).
Although their frequency range is just three or four decades and the lower
frequency coverage is just down to several kHz or several tens of kHz, they are
reasonable solutions if their frequency ranges meet the application needs. Due
to the high isolation between two output ports, the reflected signal at the DUT’s
input will not directly go to the R-ch receiver and the R-ch measurement will not
be affected.
Since the equivalent source matching for ratio measurements is not as good as
that of two-resistor type power splitters, an attenuator pad (6 dB or so) should
be connected between the output port and the DUT to improve the source
matching, if necessary. The superiority of these separation devices over the
power splitter is that the absolute source output impedance (port matching) is
50 Ω. This enables you to perform the absolute voltage measurements in the 50
Ω environment, although this may not be so significant in general low-frequency
applications in contrast to RF applications.
A three-resistor type resistive power divider which has resistors of Z0/3 in its
three arms is not applicable to the ratio measurement. Its equivalent source
output impedance is not 50 Ω but 50/3 = 16.7 Ω if we consider its branch point
as a virtual signal source (similar to the two-resistor type power splitter), and
the isolation between output ports is small (= 6 dB). Using the three resistor
type power divider in the ratio measurement will give significant measurement
errors unless the DUT’s input impedance is exactly 50 Ω.
To 50 Ω
R-ch input
From 50 Ω
source
To DUT
Figure 16. Directional coupler/bridge
16.7
16.7
16.7
Figure 17. Resistive power divider (Not applicable for ratio measurements)
14
High-Attenuation Measurement at Low Frequencies
Measurement error
Measuring high attenuation with conventional low-frequency network analyzers
is likely to be affected by the errors associated with the test cable ground loop
in the low frequency below 100 kHz. These errors are critical in applications
such as CMRR and PSRR measurements of low-frequency amplifiers. The most
significant problem is the error caused by the cable shield resistance (braid
resistance), which is not negligible in the low-frequency range below 100 kHz.
Figure 18 illustrates a high-attenuation measurement with the network analyzer.
As the DUT’s attenuation is very high, the DUT’s output voltage Vo will be very
small. Ideally, the measured AC voltage at the receiver VT should be also Vo.
However, in the low-frequency range, external common mode noise is likely to
flow into the test cable ground loop between the source and receiver as shown
in Figure 18, and voltage Vc2 appears across the resistance of the cable outer
shield, Rc2. The voltage Vc2 will cause a voltage measurement error at the
receiver VT, because the voltage to be measured, Vo, is very small. As a result,
the measured attenuation will be erroneous.
Depending on the phase relationship between Vo and Vc2, the measured
attenuation can be higher, or lower than the DUT’s true attenuation value. Or,
sometimes the error appears as a dip in the trace.
Shield (braid) resistance of coax cable
Ideally, VT =Vo,
but actually
VT = Vo + Vc2
Rc2
Vo
VT
V = Vc2
(= Va)
Rc1
High-Attn
DUT
Va
(= GND fluctuation due to noise)
Error
Rc2 = 10 mΩ or several –10 mΩ
DUT’s attn: < –80 dB
Common-mode noise
Figure 18. Measurement error due to cable shield resistance (1)
15
VR
High-Attenuation Measurement at Low Frequencies
Measurement error (continued)
The test cable ground loop cause another measurement error in the lowfrequency range. You can assume the DUT has a shunt signal path with a small
impedance Zsh. Typical examples are mΩ impedance measurements for the
low-frequency PDN components such as DC-DC converters and large bypass
capacitors using the shunt-thru technique.
Ideally, the source signal flowing through the DUT should return to the source
side through the outer shield of the cable.
However, the source current also flows into the test cable shield of the T-ch
receiver-side in the low-frequency range. Similarly to the case of the commonmode noise, the source current flowing into the T-ch cable shield will cause the
voltage Vc2 across cable outer shield resistance Rc2, and this will cause the
error in the measurement at the receiver VT. In this case, the measured attenuation will be larger than the DUT’s true attenuation value.
Note that these measurement errors associated with the test cable ground loop
occurs only in the low frequency below 100 kHz. In the higher frequency range,
the coaxial test cable’s inductance act like a common-mode choke (balun)
described in the next section, and the error current does not flow through the
shield of the VT receiver side.
Source current
Ideally, VT =Vo,
but actually
VT = Vo + Vc2
Rc1
Rc2
Vo
VT
Zsh
V = Vc2
(= Va)
Ideal source
return path
Error
Source current also flows
into T-ch shield
Va
(= GND fluctuation due to
source current)
Figure 19. Measurement error due to cable shield resistance (2)
16
VR
High-Attenuation Measurement at Low Frequencies
Conventional solution
There are several techniques to minimize these measurement errors. The most
common approach is to clamp magnetic cores to the test cables or wrap the
test cables several times around magnetic cores. The equivalent circuit of using
magnetic cores is shown in Figure 20. The magnetic core increases the shield
impedance and suppresses the current from flowing through the cable shield,
while not affecting the signal that flows in the center conductor and returns in
the cable shield.
The shield impedance caused by the core’s self inductance reduces the common
mode noise current flowing through the ground loop and the source current
flowing into the shield of the VT receiver side. Also, the core attached at the
source side forces the source current to return through the shield, back to the
source side.
However, it is not easy to implement this solution, because we need to find a
good magnetic core that has very large inductance (high permeability) to fully
eliminate the errors down to the low-frequency range. Also, sometimes it is
difficult to judge whether the core is sufficiently working or not, especially if the
DUT’s attenuation characteristic is not flat.
An example toroidal core recommended for this application is Metglas Finemet
F7555G (Φ 79 mm) www.metglas.com.
Coax cable
Core
Core
Rc1
Rc2
Vo
Zsh
VT
VR
Common-mode noise
Figure 20. Solution with magnetic cores
17
High-Attenuation Measurement at Low Frequencies
Solution with E5061B-3L5
The gain-phase test port (5 Hz to 30 MHz) of the E5061B-3L5 has a unique
hardware architecture that enables you to eliminate the measurement error
associated with the source-to-receiver test cable ground loop. Figure 21 shows
a simplified block diagram when using the gain-phase test port. The receivers
are semi-floated with the impedance |Zg|, which is about 30 Ω in the lowfrequency range below 100 kHz. Similarly to the case of using the magnetic
core, we can intuitively understand that the shield current is blocked with the
impedance |Zg|. Or, if you assume that the voltage swing at the DUT’s ground
side is Va as shown in Figure 21, since Rshield is much smaller than the receiver
input impedance 50 Ω, VT is approximately derived as follows,
VT = Vc2 + Vo
= Va x Rc2/(Rc2+Zg) + Vo
Since Rc2 << |Zg|, the first term of the above equation is negligible. So VT
will be almost Vo that we want to measure. Thus the DUT’s high attenuation or
mΩ shunt impedance can be correctly measured by minimizing the effect of the
shield resistance. The E5061B’s gain-phase test port enables easy and accurate
high-attenuation measurements in the low-frequency range.
On the other hand, the S-parameter test port of the E5061B-3L5 has a normal
grounded receiver architecture, like most of other existing low-frequency
network analyzers. If you want to measure the low-frequency high-attenuation
devices with the S-parameter test port (for example, if you want to measure
them up to more than 30 MHz, that cannot be covered with the gain-phase test
port), it is necessary to use the magnetic cores to eliminate the errors caused by
the test cable ground loop.
Source current
T port
Vo
VT
LF OUT
Rc1
Rc2
Zsh
V = Vc2
VT = Vo
R port
VR
Va
Zg
Zg
Common-mode noise
VT = Vo + Vc2
= Vo + Va x Rc2/(Zg + Rc2)
= Vo
|Zg| = about 30 Ω at low-frequency range
Rc2 = 10 mΩ or several –10 mΩ
Figure 21. Solution with E5061B-3L5 gain-phase test ports
18
High-Attenuation Measurement at Low Frequencies
Effectiveness of gain-phase test port
Figure 22 shows the transmission measurement results of a 90 dB coaxial
attenuator with E5061B’s Sparameter test port and the gain-phase test port. The
test frequency range is 100 Hz to 10 MHz. The traces in the channel-1 (left side)
are the measurement results with the S-parameter test port. As you can see, the
measurement result without a magnetic core indicates incorrectly higher values
in the low-frequency range, which is the error caused by the test cable ground
loop between the source and receiver. Another trace in the same graph is the
measurement result by attaching a clamp-on type magnetic core to the test
cable. The measurement in the low-frequency range is slightly improved, but is
still not accurate in the very low-frequency range.
On the other hand, the trace in the channel-2 (right side) is the measurement
result using the gain-phase test port. As you can see, –90 dB attenuation is correctly measured down to 100 Hz, without being affected by the test cable
ground loop.
S-parameter test port
without magnetic core
Gain-phase test port
without magnetic core
–90 dB
S-parameter test port
with magnetic core
Figure 22. Comparison of the measurement results among 3 different configurations
19
OP Amp Measurement Example
Closed-loop gain
The following sections show measurement examples of various frequency
response characteristics of operational amplifiers.
Figure 23 shows a configuration example of measuring the closed-loop gain of a
simple inverting amplifier (Av = –1) using the gain-phase test port
(up to 30 MHz).
To minimize the influence of the probing capacitance to the amplifier’s loading
condition, it is recommended to use the 10:1 probes, which give relatively small
input capacitances.
To accurately measure the gain and phase characteristics, the response thru
calibration should be performed by connecting the T-ch probe to the point TP1,
so that the gain and phase errors between two probes are eliminated.
T
R
LF OUT
10:1 passive
probes
Coax
cable
+Vcc
R2
RL
R1
–
+
TP2
–Vee
TP1 T: Zin = 1 MΩ
R: Zin = 1 MΩ
R1 = R2 = 1 kΩ
RL = 1 kΩ
Figure 23. Configuration example of closed-loop gain measurement with the gain-phase test port
20
OP Amp Measurement Example
Closed-loop gain (continued)
If you want to measure the amplifier’s frequency response up to more than 30 MHz, the
solution is to use the S-parameter test port and the active probe. Figure 24 shows a configuration example. The response thru calibration by probing the point TP1 is necessary,
because the R-ch receiver has 50 Ω input and we need to set the reference to TP1 so that
the voltage transfer function from the DUT’s intput and output ports can be measured.
Figure 25 shows a closed-loop gain measurement example of a high-speed operational
amplifier by using the E5061B’s S-parameter test port and the 41800A active probe. The
marker is put on the –3 dB cutoff frequency, which indicates the bandwidth of this amplifier circuit is approximately 20 MHz.
Port 2 with active
probe (High-Z)
Port 1
(50 Ω)
+Vcc
TP1
R1
–
R2
+
–Vee
TP2
RL
R1 = R2 = 1 kΩ
RL = 1 kΩ
Figure 24. Configuration example of closed-loop gain measurement with the S-parameter test port
Closed-loop gain
1 dB/div
0 dB
45 deg/div
Phase
180 deg
Frequency = 100 Hz to 100 MHz
Source level = 0 dBm
IFBW = AUTO (Upperlimit = 1kHz)
Figure 25. Closed-loop gain measurement example
21
OP Amp Measurement Example
Open-loop gain
There are several methods for measuring the open-loop gain of OP amps. The
most common method is to measure the voltage ratio VT/VR in the circuit,
Figure 26. Assuming that the open-loop gain of the OP amp is A, if we look at
the current Ir2, the following equation can be derived:
(VT-VR)/R2 = {VT-(-A x VR)}/Zout
If Zout << R2, the voltage ratio VT/VR can be calculated as follows:
VT/VR = (-A-Zout/R2)/(1-(Zout/R2))
= -A
In the case of high-gain OP amps, if the closed-loop gain Av is small (e.g. Av
= –R2/R1 = –1), the voltage VR will be too small to be accurately measured,
especially in the low-frequency range where the open-loop gain is very high.
In the linear operating region, if the closed-loop gain Av is increased, the voltage
VR will also be increased proportionally and the measurement will be easier for
the analyzers. For example, if |Av| = R2/R1 = 10, VR will be 10 times (= 20 dB)
higher than the case of |Av| = 1. Here it should be noted that VT will also be 20
dB higher and you’ll need to avoid the receiver from overloading when measuring VT. Also the measurement in the higher frequency range will be inaccurate,
because the linear region of the amplifier circuit is narrower if Av is high. The
open-loop gain measurement can be implemented by using either the dual probing method, or single probing method.
Ir2
R2
R1
–
Zout
+ A
VR
–A x VR
VT
Av = –R2/R1
Figure 26. Configuration example of open-loop gain measurement
22
OP Amp Measurement Example
Open-loop gain (continued)
Figure 27 shows a measurement configuration with the gain-phase port. The
ratio measurement T/R will directly indicate the open-loop gain A. To accurately
measure the phase response without affecting the loading condition due to
the large probing capacitance, 10:1 passive probes should be used, rather than
coaxial test cables.
T
R
LF OUT
10:1 passive
probes
R-ch
(High-Z)
+Vcc
R2
R1
–
+
RL
R1 = R2 = 1 kΩ
RL = 1 kΩ
TP2
TP3
–Vee
TP1 T: Zin = 1 MΩ, ATT=0 dB
R: Zin = 1 MΩ, ATT=0 dB
Figure 27. Configuration example of open-loop gain measurement with the gain-phase test port
23
OP Amp Measurement Example
Open-loop gain (continued)
Figure 28 shows a open-loop gain measurement example of an OP amp in the
unity gain condition (R1 = R2 = 1 kΩ) using the gain-phase configuration shown
in Figure 27. The test frequency range is from 10 Hz to 30 MHz. The phase margin can be derived from these measurements. By simply calculating the transfer
function of the feedback path as β = R1/(R1 + R2) = ½ = –6 dB (assuming no
phase shift), crossover point where the loop gain |–A x β|=0 dB can be found
by placing the marker at the +6 dB point. And the phase margin can be directly
given by the marker on the phase trace, as we are looking at the loop transfer
function –A x β which includes the 180 degree inversion at the OP amp input
port.
The trace fluctuation in the high gain area is due to the dynamic range degradation caused by the 20 dB loss of the passive probe. Since we are measuring the
open-loop gain with the amplifier of unity gain, the measured AC voltage at the
R-ch receiver will be extremely small in the high gain area and this causes the
trace fluctuation. The trace fluctuation in the high gain area is not a problem for
evaluating the phase margin from the measurement data in the lower gain area.
But, if you also want to measure the very high gain in the low-frequency range,
separately perform another open-loop gain measurement using coaxial test
cables instead of 10:1 passive probes. The receiver attenuator setting should
be 0 dB at the R-port, and 20 dB at the T-port, so that the very small voltage at
the R-ch receiver can be measured with good SNR. Note that this measurement
configuration is applicable only in the low to middle frequency range where the
open-loop gain is high and the voltage appearing at the R-ch receiver
will not exceed the receiver’s maximum input level with the attenuator setting
of 0 dB.
100 dB
80 dB
Open-loop gain
=|T/R|
60 dB
Phase
40 dB
6 dB (= β = R1/(R2 + R1)
Phase margin
0 deg
Frequency = 100 Hz to 100 MHz
Source level = 0 dBm
IFBW = AUTO (100 Hz limit)
OP amp open-loop gain measurement example
(with 10:1 passive probes)
Figure 28. Open-loop gain and phase measurement example with the gain-phase test port
24
OP Amp Measurement Example
Open-loop gain (continued)
If the OP amp’s open-loop gain must be measured up to more than 30 MHz,
the solution is the S-parameter test port with the active probe. Since the
S-parameter test port allows us to use just a single active probe, you’ll need to
use a two step measurement technique. The procedure is as follows:
1. Perform the response through calibration by probing TP1.
2. Measure S21 by probing TP2 and memorize the trace data with
DATA -> MEM function (Step 1).
3. Connect a dummy capacitor to TP2, and measure S21 by probing TP3
(Step 2).
4. Calculate Data/Memory with the data math function to obtain the open-loop
gain.
The dummy capacitor connected in step 2 duplicates the probing capacitance of
step 1 which affects the open-loop phase measurement in the high-frequency
range. Its capacitance should be about the same capacitance as the active
probe’s input capacitance.
If you need to measure a very high open-loop gain, it might be better to attach
magnetic cores to the test cable to eliminate the measurement errors associated with the ground loop, which may affect the small signal measurement of
the step 1.
Coax cable
Port 2 with active
probe (High-Z)
Port 1
(50 Ω)
S21 (Step 1)
Data- > Mem
Open-loop gain
= Data/Mem
R1 = R2 = 1 kΩ
RL = 1 kΩ
TP1
S21 (Step 2)
+Vcc
TP2
R1
–
R2
+
TP3
RL
–Vee
Figure 29. Configuration example of open-loop gain measurement with a single active probe
25
OP Amp Measurement Example
Open-loop gain (continued)
Figure 30 shows a measurement example of the open-loop gain and phase with
the configuration of Figure 29. Trace 1 is the measured response by probing TP2,
which indicate the ratio of the input voltage and the attenuated voltage at TP2.
Trace 2 is the measured response by probing TP3, which is the closed-loop gain
and phase. And, trace 3 is the open-loop gain and phase calculated from these
measurement results. The results are calculated by using the trace math function (data/memory).
As previously described, the phase margin is indicated by the phase measurement value at the 6 dB open-loop gain point, where the loop gain is 0 dB. In this
example, the phase margin is about 86 degrees.
Trace 3: Open-loop gain (data/memory)
70 dB
0 dB
Trace 2: Step 2 phase (data)
Trace 3: Open-loop phase
(data/memory)
Trace 2: Step 2 magnitude
(data)
Trace 1: Step 1 phase
(memory)
-70 dB
Frequency = 100 Hz to 100 MHz
Source level = 0 dBm
IFBW = AUTO (100 Hz limit)
Trace 1: Step 1 magnitude
(memory)
Figure 30. Open-loop gain and phase measurement example with a single active probe
26
OP Amp Measurement Example
CMRR
The CMRR (Common-mode Rejection Ratio) of OP amps and other lowfrequency differential amplifiers is generally difficult to measure, because you
need to measure very high-attenuation for the common-mode input. The CMRR
is defined as CMRR = Ad/Ac, where Ad is the differential-mode gain and Ac is
the common-mode gain. Figure 31 shows the configuration using the gain-phase
test port. To measure high attenuation, the coaxial test cables are used for
connecting the receivers to the DUT, instead of 10:1 passive probes which have
20 dB loss.
The common-mode gain (attenuation) Ac is measured by turning SW1 to the
A-position. The differential gain Ad is measured by turning the switch SW1 to
the B-position. Then the CMRR is calculated as Ad/Ac (= 20 x Log (Ad/Ac) in
dB). The differential gain of this circuit is |Ad| = R2/R1 = 10. Accordingly, the
common-mode gain Ac is 10 times (20 dB) larger than the case of |Ad|=1. This
allows the analyzer to measure high CMRR over 100 dB.
Due to the semi-floating receiver architecture of the gain-phase test port, you
can accurately measure high CMRR by eliminating the error associated with the
test cable ground loop.
Coaxial cable
R-ch
(High-Z)
+Vcc
TP1
TP2
T-ch
(High-Z)
RL
R2
R1
–
R2
R1 = 100 Ω
R2 = 1 kΩ
RL = 1 kΩ
A
+
R1 SW1
B
–Vee
Figure 31. Configuration example of CMRR measurement with the gain-phase test port
27
OP Amp Measurement Example
CMRR (continued)
CMRR measurement higher than 30 MHz can be performed by using the S-parameter test
port and the active probe. In this case, magnetic cores should be attached to the test cable
as shown in Figure 32 to eliminate the measurement error caused by the common mode
noise. One example of magnetic core is Metglas Finemet F7555G (Φ 79 mm:
www.metglas.com)
Figure 33 shows the measurement example with gain-phase test port. Trace 1 is the
common-mode gain Ac, and Trace 2 is the differential-mode gain Ad (= 20 dB). The
common-mode gain Ac of about –90 dB is accurately measured by eliminating the ground
loop effects. Trace 3 is the CMRR calculated from these measurement results. The marker
indicates that the CMRR at 100 kHz is about 80 dB. In the lower frequency range, the CMRR
is more than 100 dB.
Port 1
(50 Ω)
+Vcc
Port 2 with active
probe (High-Z)
TP1
R1
TP2
–
R2
C
+
D
SW1
R1
RL
R2
–Vee
R1 = 100 Ω
R2 = 1 kΩ
RL = 1 kΩ
Figure 32. Configuration example of CMRR measurement with the S-parameter test port
100 dB
Trace 3: CMRR (data/memory)
20 dB
Frequency = 100 Hz to 100 MHz
Source level
for Ac measurement): 0 dBm
for Ac measurement): –15 dBm
IFBW = Auto (100 Hz limit)
Receiver ATT setting
Ac measurement: 20 dB (R-ch) -80 dB
0 dB ( T-ch)
Ad measurement: 20 dB (R-ch and T-ch)
The balance of R1 and R2 is not fully optimized
in this measurement example.
Trace 2: Diff-mode gain |Ad|(data)
20 dB/div
Trace 1: Common-mode gain|Ac|(memory)
100 Hz
10 MHz
Figure 33. CMRR measurement example with the gain-phase test port
28
OP Amp Measurement Example
PSRR
The PSRR (Power Supply Rejection Ratio) of amplifiers is another difficult
parameter to measure as it requires high-attenuation measurements. Here we
consider the definition of PSRR = Av/Ap, where Av is the closed-loop gain of
the amplifier circuit and Ap is the gain from the power supply port (positive or
negative) to the output port. Similarly to the CMRR measurement, Ap is proportional to Av in the linear operating region.
Figure 34 shows a configuration example of measuring the PSRR (positive
PSRR) by using the gain-phase test port. Since |Av| = R2/R1 = 1, the measured
gain of this circuit directly indicates the inverse of the OP amp’s PSRR (= 1/Ap,
which is a negative dB value). The source signal is applied to the positive power
supply port with a DC bias voltage. The E5061B has a built-in DC bias source
which enables you to internally superimpose the DC voltage bias onto the AC
source signal.
LF OUT
(DC Bias ON)
R-ch (High-Z)
AC + DC
TP1
T-ch
(High-Z)
TP2
R2
R1
–
+
RL
–Vee
R1 = R2 = 1 kΩ
RL = 1 kΩ
Figure 34. Configuration example of PSRR measurement with the gain-phase test port
29
OP Amp Measurement Example
PSRR (continued)
PSRR measurements higher than 30 MHz can be performed by using the
S-parameter test port and the active probe. Similarly to the CMRR measurement
with the S-parameter test port, it is recommended to attached magnetic cores
to the test cable to eliminate the measurement error associated with the test
cable ground loop. Figure 36 shows a PSRR measurement example with the
gain-phase test port. The marker indicates that the PSRR at 1 kHz is –87 dB.
E5061B-3L5 has a DC monitor function, and you can check the DC voltage level
that is actually applied to the DUT.
Port 2 with active
probe (High-Z)
Port 1
(DC Bias ON)
AC + DC
R1
–
+
R2
RL
R1 = R2 = 1 kΩ
RL = 1 kΩ
–Vee
Figure 35. Configuration example of PSRR measurement with the S-parameter test port
DC monitor
-87 dB
20 dB/div
Frequency = 100 Hz to 100 MHz
Source level = –10 dBm
IFBW = Auto (20 Hz limit)
Receiver ATT setting = 20 dB (R-ch), 0 dB (T-ch)
Figure 36. PSRR measurement example with the gain-phase test port
30
OP Amp Measurement Example
Output impedance
This is not a 2-port transmission measurement, but a 1-port impedance measurement. In general, OP amps have closed-loop output impedances that range
from several tens of mΩ at low frequencies up to 100 Ω at high frequencies.
To fully cover this impedance range, the reflection measurement method is the
proper solution. Figure 37 shows a configuration example of measuring the
closed-loop output impedance of OP amps. The open/short/load 3-term calibration (1-port full calibration) must be performed.
+Vcc
R1
–
R2
+
–Vee
R1 = R2 = 1 kΩ
Figure 37. Configuration example of output impedance measurement
31
OP Amp Measurement Example
Output impedance (continued)
Figure 38 is a measurement example of the closed-loop output impedance. The
measured traces show the impedance magnitude that are plotted by using the
impedance conversion function. The trace shown on the left side indicates the
output impedance in logarithmic scale [20 x log |Z| dB]. The trace shown in the
right side indicates the output impedance in linear scale [Ω].
100 Ω
20 x log|Z|(dB)
1Ω
10 mΩ
Frequency = 100 Hz to 100 MHz
Source level = 0 dBm
IFBW = Auto (300 Hz)
Figure 38. Output impedance measurement example
32
|Z|(Ω)
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Revised: October 1, 2009
Reference
[1] Robert A. Witte, “Spectrum and Network Measurements”
Product specifications and descriptions
in this document subject to change
without notice.
[2] Willy M. Sansen, Michael Steyaert, Paul J. V. Vandeloo, “Measurement
of Operational Amplifier Characteristics in the Frequency Domain”, IEEE
Transaction on Instrumentation and Measurement, Vol. IM-34, No.1, March 1985
© Agilent Technologies, Inc. 2010
Printed in USA, April 28, 2010
5990-5578EN
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