AN200-4 Understanding Frequency Counter

AN200-4 Understanding Frequency Counter
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Understanding Frequency
Counter Specifications
Application Note 200-4
Electronic Counters Series
Input Signal to Schmitt Trigger
EON
Hysteresis
“window”
EOFF
Output
Output
of
Schmitt
Trigger
Input
EOFF
EON
RMS Sine Wave Sensitivity =
EON – EOFF
2 2
1
Table of Contents
Introduction ................................................................................................... 3
Input Characteristics .................................................................................... 5
Operating Mode Specifications ...................................................................11
Appendix A. Time Interval Averaging ........................................................29
Appendix B. RMS Specifications ...............................................................34
Appendix C. Effects of Wideband Noise ...................................................35
Appendix D. Measurement of
Counter Contributed Noise .........................................................................36
Appendix E. HP 5315A/B LSD Displayed and Resolution .......................37
2
Introduction
If you’ve ever been confused by a frequency counter data sheet or
unsure of the meaning of a particular specification, this application
note is for you. In it, we’ll define terms, work through examples, and
explain how certain parameters can be tested.
First, however, we should review the purpose of a data sheet. The
primary objective, of course, is to give you, the user, the information
you need to make a buying decision — will the instrument solve your
problem and is the performance worth the price? The instrument’s
performance is set forth in the specification section of the data sheet.
Specifications describe the instrument’s warranted performance over
the operating temperature range (usually 0°C to 50°C). Specifications should be:
1. Technically accurate
2. Useable in a practical way
3. Testable
It goes without saying that a specification must be technically accurate. However, it may be that a technically accurate description of a
parameter is so complex as to make the specification unuseable. In
this case, a conservative simplified specification will be given. In
addition to accuracy, specifications should be useable. For example,
all the error terms in an accuracy specification should have identical
units (i.e., Hz, or seconds). Finally, specifications should be testable.
The user must be able to verify that the instrument is operating according to its warranted performance.
Performance parameters which are not warranted are indicated by
giving TYPICAL or NOMINAL values. These supplemental characteristics are intended to provide useful application information. This is
usually done for parameters which are of secondary importance and
where verification on each and every instrument may be difficult and
time consuming (which would add substantially to the manufacturing
cost and therefore selling price).
Specifications for electronic frequency counters are usually divided
into three sections: Input Characteristics, Operating Mode Characteristics, and General. The Input Characteristics section describes the
3
counter’s input signal conditioning: input amplifier performance and
conditioning circuitry such as coupling selection, trigger level control,
and impedance selection. The Operating Mode Characteristics section
specifies how the counter performs in each of its operating modes or
functions such as Frequency, Period, Time Interval, and Totalize.
Range, Least Significant Digit Displayed (LSD Displayed), Resolution,
and Accuracy are usually specified. The General section specifies the
performance of the timebase and instrument features such as auxiliary
inputs and outputs (e.g., markers, trigger level lights, arming inputs,
timebase inputs and outputs), Check mode, sample rates and gate time
selection.
The next sections cover Input Characteristics specifications and
Operating Mode specifications. Well known specifications such as
coupling and input impedance are not covered. Refer to application
note 200 “Fundamentals of Electronic Frequency Counters” for a
discussion of these parameters. The examples in the next sections are
drawn mainly from the HP 5315A/B 100 MHz/100 ns Universal Counter,
the HP 5314A 100 MHz/100 ns Universal Counter, and the HP 5370A
Universal Time Interval Counter.
4
Input Characteristics
Specification
Range
Definition
Range of frequency over which input amplifier sensitivity is specified.
If input coupling is selectable, then ac and dc must be specified separately.
Example
dc COUPLED dc to 100 MHz
ac COUPLED 30 Hz to 100 MHz
Although the specification states that the input amplifier has a range
from dc to 100 MHz, it does not mean that measurements in all
operating modes can be made over this range. Consult the individual
RANGE specifications under the appropriate OPERATING MODE
specification. For example, with the HP 5315A/B, the minimum
frequency which can be measured in Frequency mode is 0.1 Hz.
Input Signal to Schmitt Trigger
EON
Hysteresis
“window”
EOFF
Output
Output
of
Schmitt
Trigger
Input
EOFF
EON
RMS Sine Wave Sensitivity =
EON – EOFF
2 2
Figure 1. Counter
sensitivity and
hysteresis.
5
Specification
Sensitivity
Definition
Lowest amplitude signal at a particular frequency which the counter
will count. Assumes that the trigger level (if available) has been
optimally set for a value equal to the midpoint of the input signal.
Sensitivity is actually a measure of the amount of hysteresis in the
input comparator and may vary with frequency. Because of this, the
sensitivity specification may be split into two or more frequency
ranges.
Hysteresis is used to describe the dead zone of a Schmitt Trigger (or
voltage comparator). Referring to Figure 1, you see that when the
input is above EON, the output goes high. When the input voltage
falls below EOFF, the output drops low. If you graph the input-output
function, it resembles the familiar hysteresis loop between magnetizing
force and magnetic flux in a magnetic material.
In order for the counter to count, the input must pass through both
limits. The p-p minimum countable signal, defined as the counter’s
input amplifier sensitivity, is equal to EON – EOFF. The rms sine wave
sensitivity =
E ON − E OFF
2 2
The input waveform must cross both hysteresis limits to generate a
count. This imposes a limit on the “useful” sensitivity of counter
inputs. In the upper waveforms of Figure 2, the noise is not of
sufficient amplitude to cross both limits. No extra counts are
Hysteresis
Window
Schmitt
Output
Hysteresis
Window
Schmitt
Output
6
Figure 2. Noise
induced counting.
generated and the frequency measurement is made without error (not
the case, however, for reciprocal counters measuring frequency —
trigger error causes measurement inaccuracies). The lower waveforms show a more sensitive counter input. In this case, the noise
does cross both hysteresis limits and erroneous counts are generated.
Since the counter input does not respond to the rms value of the
waveform but only the peak-to-peak value, the sensitivity
specification should be volts peak-to-peak with a minimum pulse
width. Since many applications involve measuring the frequency of a
sinewave signal, the specification is also given in terms of volts rms
sine wave. (Note, however, that a different waveform with the same
rms voltage may not trigger the counter — the counter responds only
to peak-to-peak.)
Example (HP 5315A/B)
10 mV rms sine wave to 10 MHz
(By looking at the RANGE specification, you see that in dc coupling
the counter will count a 10 mV rms sine wave at any frequency
between dc and 10 MHz and in ac coupling, it will count a 10 mV rms
sine wave at any frequency between 30 Hz and 10 MHz).
25 mV rms sine wave to 100 MHz
(For frequencies between 10 MHz and 100 MHz, regardless of ac or
dc coupling, the counter will count a 25 mV rms sine wave).
75 mV peak-to-peak pulse at minimum pulse width of 5 ns.
Specification
Signal Operating Range
Definition
If the signal peaks extend beyond the specified signal operating
range, one or more operating modes may give incorrect results; for
example, frequency miscounting or time interval inaccuracies.
Example (HP 5370A)
–2.5 V to +1 V
Specification
Dynamic Range
Definition
The minimum to maximum allowable peak-to-peak signal range,
centered on the middle of the trigger level range. If the input signal
exceeds this range, then the input amplifier may saturate, causing
7
transitions of the input to be missed. The dynamic range is limited by
the range over which the differential input of the amplifier can swing
without saturation.
For some input amplifiers, the dynamic range puts a further restriction
on the allowable signal peaks as specified by the signal operating
range. The signal peaks must always stay within the signal operating
range specification and the peak-peak value must stay within the
maximum dynamic range specification.
Example (HP 5370A)
50 × 1: 100 mV to 1 V p-p pulse
50 × 10: 1 V to 7 V p-p pulse
1 M × 1: 100 mV to 1 V p-p pulse
1 M × 10: 1 V to 10 V p-p pulse
The following condition is allowable for the HP 5370A.
OK:
1V
Maximum
Peak-to-Peak
of Dynamic
Range
Trigger
Level
Signal
Operating
Range
–2.5 V
Figure 3. Valid
input signal for the
HP 5370A.
Neither of the following conditions is allowable for the HP 5370A.
Not OK:
1V
Signal
Exceeds
Dynamic
Range
Signal
Operating
Range
–2.5 V
Signal
Exceeds
Signal
Operating
Range
Not OK:
1V
Signal
Operating
Range
–2.5 V
8
Figure 4. Invalid
input signals for
the HP 5370A.
Specification
Trigger Level
Definition
For instruments with a trigger level control, the range over which
trigger level may be varied should be indicated. Trigger level is usually
the voltage at the center of the hysteresis band and physically is the dc
voltage applied to one input of the input comparator.
For instruments with a readout of trigger level (a dc signal or voltmeter
reading), the settability of the trigger level should be indicated as well
as the accuracy. The settability specification indicates to what tolerance trigger level may be set and the accuracy specification indicates
the worst case difference between the indicated trigger level and the
actual trigger point.
Specification
Damage Level
Input Signal
+V
To
Trigger Level
Indicator
Comparator
(Schmitt
Trigger)
Trigger Level
Control
Actual Trigger Point
(+ Slope)
Trigger
Level
Hysteresis
Window
Actual Trigger Point
(– Slope)
Figure 5. Trigger
level and actual
trigger point.
Definition
Maximum input the counter can withstand without input failure. The
value may vary with attenuator setting and coupling selected.
Example (HP 5315A/B)
ac and dc × 1:
dc to 2.4 kHz
2.4 kHz to 100 kHz
>100 kHz
250 V (dc + ac rms)
(6 × 105 V rms Hz)/FREQ
6 V rms
ac and dc × 2:
dc to 28 kHz
28 kHz to 100 kHz
>100 kHz
500 V (dc + ac peak)
(1 × 107 V rms Hz)/FREQ
100 V rms
9
For signals less than 2.4 kHz, the dc + ac rms voltage peak may not
exceed the value 250. For example, a 100 V rms 1 kHz signal could be
accompanied by a dc level as high as 150 volts without damage.

280 = 500 V 
 360 +



2
For signals in the range of 2.4 kHz to 100 kHz, the rms voltage times
the frequency must be less than 6 × 105 V rms × Hz. A 10 kHz signal,
therefore, could be at a level as high as 60 V rms:
 6 × 10 5 rmsV × Hz

= 60 Vrms 



10 4 Hz
To find the maximum rms voltage which can be applied to the counter
input without damage, divide the specified volt rms × Hz product by
the frequency; i.e., in the case of the HP 5315A/B in the × 1 attenuator
position:
6 × 10 5 Vrms × Hz
Freq ( Hz )
For each operating mode of the counter, Range, LSD Displayed,
Resolution, and Accuracy are specified. Each of these terms will be
defined in detail with examples.
10
Operating Mode Specifications
Specification
Range
Definition
The minimum value of the input which can be measured and displayed
by the counter up to the maximum value of the input.
Examples (HP 5315A/B)
Frequency Range: 0.1 Hz to 100 MHz
Time Interval Range: 100 ns to 105 s
Since the HP 5315A counts a 10 MHz clock (100 ns period), the smallest
single shot time interval which will permit the counter to accumulate at
least one count during the time interval is 100 ns. The maximum time
interval is what can be measured before the counter overflows.
Time Interval Average Range: 0 ns to 105 s
Since the time interval average operating mode accumulates counts
during a large number of successive time intervals, it is not required
that at least one count be accumulated during each time interval. If only
one count were accumulated during 200 time intervals, the time interval
average would be computed as
100 ns = 0.5 ns .
200
Specification
LSD Displayed
Definition
The LSD Displayed is the value of the rightmost or least significant digit
in the counter’s display. The LSD Displayed may vary with gate time
and magnitude of the measured quantity. (For example, the LSD
Displayed by a reciprocal counter varies with gate time and frequency.)
For a digital instrument like a counter, output readings are discrete
(quantized) even though the inputs are continuous. Even for the case
where the input quantity is perfectly stable, the counter’s readings may
fluctuate. This fluctuation is due to quantization error (±1 count error).
11
The value of the LSD Displayed often is the same as the quantization
error which represents the smallest non-zero change which may be
observed on the display. Because of this, resolution and accuracy
statements often specify quantization error as ± LSD Displayed.
Main Gate
DCA
2.5 Hz Signal
Case 1: 1 Second
Case 2:
1 Second
Display
Main Gate
Flip-Flop
TB
Decade
Dividers
2 Hz
3 Hz
Figure 6. ±1 count error.
Quantization error arises because the counter can’t count a fraction of a
pulse — a pulse is either present during the gate time or it isn’t. The
counter can’t detect that a pulse was present just after the gate closed.
Additionally, since the opening of the counter’s main gate is not synchronized to the input signal, the quantization error may be in either
direction. Consider a 2.5 Hz signal as shown in the figure. In case 1,
the counter’s gate is open for 1 second and accumulates 2 counts —
the display will show 2 Hz. In case 2, the same length gate accumulates
3 counts for a display of 3 Hz.
Although we say ±1 count, we do not mean that a particular measurement can vary by both + and – one count. The measurement can vary
by one count at most. The reason that you have to say ±1 count is that
from a single measurement, you don’t know a priori which way the next
measurement will jump or if it will jump at all. So the specification has
to include both possibilities.
Examples (HP 5314A)
Frequency LSD Displayed:
Direct Count 0.1 Hz, 1 Hz, 10 Hz Switch Selectable
Prescaled 10 Hz, 100 Hz, 1 kHz Switch Selectable
For direct count, the number of cycles of the input are totalized during
the gate time. For a 1 second gate time, each count represents 1 Hz
(the LSD Displayed). For a 10 second gate time, each count represents
0.1 Hz.
12
For a prescaled input, the number of counts accumulated during the
gate time is reduced by the prescale factor over what would be accumulated by a direct count counter. Consequently, for a 1 second gate, each
count represents N Hz where N is the prescale division factor. In the
HP 5314A, the counter prescales by 10.
(HP 5315A/B)
Frequency LSD Displayed
10 Hz to 1 nHz depending upon gate time and input signal. At
least 7 digits displayed per second of gate time.
In the definition section of the HP 5315A/B data sheet, you read:
–7
LSD = 2.5 × 10
× Freq
Gate Time
LSD =
2.5
Gate Time
If Freq <10 MHz
If Freq ≥ 10 MHz
All above calculations should be rounded to the nearest decade.
For the HP 5315A/B there are no decade steps of gate time since the
gate time is continuously variable. Additionally, since it is a reciprocal
counter for frequencies below 10 MHz, the LSD Displayed depends
upon the input frequency. Simply stated, you can be assured of at least
7 digits per second of gate time which means that for a 1 second gate
time and a 10 kHz input frequency, the LSD displayed will be at least
0.01 Hz:
7th digit
↓
10000.00
(In actual fact, the HP 5315A/B will display 0.001 Hz for this example.)
For 0.1 seconds, you’ll get at least 6 digits. For fractional gate times,
round off to the nearest decade (e.g., 0.5 seconds and below rounds to
0.1 seconds and above 0.5 seconds rounds to 1 second).
As an example, let’s compute the LSD Displayed for a 300 kHz input
measured with a 0.5 second gate time:
2.5 × 10 −7 × 300 × 10 3 = 0.15 Hz.
0.5
Rounding to the nearest decade gives LSD = 0.1 Hz. This will be the
value of the least significant digit in the counter’s display. Of course,
the user doesn’t have to figure this out in practice — all he has to do is
look at the counter’s display.
13
The reason for the unusual LSD Displayed specification is that the
HP 5315A/B is a reciprocal counter with a continuously variable gate
time for frequencies below 10 MHz and a conventional counter with a
continuously variable gate time for frequencies above 10 MHz.
For frequencies below 10 MHz, the counter synchronizes on the input
signal which means that the counting begins synchronously with the
input. Two internal counters then begin accumulating counts. One
counter counts 10 MHz clock pulses from the internal timebase and a
second counter accumulates input events. This counting continues
during the selected gate time. The microprocessor then computes
frequency by computing
EVENTS
TIME
(or computes period by dividing
TIME
.)
EVENTS
Unlike a conventional counter which simply displays the contents of
the decade counting assemblies, the HP 5315A must compute the
number of significant digits in the resultant of the division EVENTS/
TIME. In the microprocessor algorithm, it was decided to truncate
digits such that
LSD Displayed
FREQ
will always be less than 5 × 10–8. Rounding the quantity
 2.5 × 10 −7

 Gate Time × Freq 


to the nearest decade meets this requirement.
Period LSD Displayed:
100 ns to 1 fs (femptosecond: 10–15 second) depending upon
gate time and input signal.
In the definition section of the HP 5315A/B data sheet, the following
explanation is given:
–7
× Per
LSD = 2.5 × 10
Gate Time
LSD =
2.5
× Per 2
Gate Time
for Per > 100 ns
for Per ≤ 100 ns
All above calculations should be rounded to the nearest decade.
14
As an example, a 50 ns period measured with a 50 millisecond gate time
would have an LSD equal to:
2.5
50 × 10
−3
 50 × 10 −9 


2
= 1.25 × 10 −3
Rounding to the nearest decade gives 0.1 ps as the LSD Displayed.
Time Interval Average LSD Displayed
100 ns to 10 ps depending upon gate time and input signal.
In the definition section of the HP 5315A/B data sheet, the following is
given:
1 to 25 intervals
25 to 2500 intervals
2500 to 250,000 intervals
250,000 to 25,000,000 intervals
> 25,000,000 intervals
LSD
100 ns
10 ns
1 ns
100 ps
10 ps
To compute the number of time intervals averaged, N, multiply the gate
time by the frequency (time interval repetition rate). For example, if a
time interval average measurement is made on a 1 µs time interval at a
200 kHz repetition rate and you select a 2 second gate time,
N = 2 × 200 × 10 3 = 400 × 10 3 .
In this case, the LSD Displayed by the counter would be
100 picoseconds.
The measurement time required to make the measurement is simply
the gate time which is 2 seconds.
Prior to the microprocessor controlled HP 5315A/B, time interval
averaging counters displayed more digits than you could believe when
in time interval average function. This is because ±1 count error is
improved only by N but the displayed number of digits increases by
N. The microprocessor of the HP 5315A/B solves the problem by only
displaying the digits you can believe. The HP 5315A/B decides to
display the LSD which results, in the worst case, in a one sigma confidence level, meaning that for a stable input time interval, approximately 68% of the readings will vary by less than the LSD displayed. In
most cases, however, the confidence level is much higher and may be
as high as 10 σ.
15
Time interval averaging is a statistical process. Consequently, the
counter performs an average and displays the result which is an
estimate of the actual time interval. The more time intervals averaged,
the better the estimate. Even if the input time interval is perfectly
stable, time interval average measurements made on the time interval
will vary from measurement to measurement. As the number of
averages in each time interval average measurement is increased, the
variation between measurements is decreased. A measure of the
variation is σ, the standard deviation.
σ
σ
σ
Actual Value
Actual Value
Actual Value
N Increasing
Figure 7.
Histogram plot
of time interval
average
measurements.
σ decreases as N,
the number of
time intervals in
each average
reading, is
increased.
For time interval averaging, in the worst case,
2σ =
Tclock
N
where Tclock = period of counted clock and N = number of independent time intervals averaged. For a normal distribution, ±2 σ includes
95% of all the readings. The HP 5315A/B decides to display the LSD
which results, in the worst case, in a one sigma confidence level.
σ=
Tclock
2 N
= 100 ns
2 N
100 ns = 10 ns .
When N = 25 , σ =
2×5
100 ns = 1 ns .
When N = 2500, σ =
2 × 50
So in each range, the LSD Displayed is the worst case σ. Over most of
the range, the LSD is significantly better than ±1 σ. For example, in the
25 to 2500 interval range, 10 ns is the LSD Displayed.
For N = 25, 10 ns = 1 σ
but for N = 100, 10 ns = 2 σ
and for N = 2500, 10 ns = 10 σ
(68% confidence)
(95% confidence)
(∼100% confidence)
See appendix A for more on time interval averaging.
16
Specification
Resolution
Definition
In optics and in many other fields, resolution of a measuring device is
determined by the minimum distance between two lines which are
brought closer and closer together until two lines can no longer be
observed in the output as shown in Figure 8. Resolution is defined at
the point where the two lines are just close enough to cause the output
to look like one line.
For a frequency counter, resolution can be defined similarly. If two
stable frequencies are alternately measured by the counter and slowly
brought closer together in frequency as shown in Figure 9, there will
come a point at which two distinct frequencies cannot be distinguished
due to randomness in the readings. Random readings are due to
quantization error and trigger error (for reciprocal counters).
Input
Output
Input to
Counter
f1
f2
f1
f2
Histogram
of Counter
Readings
Resolution
Figure 8. Resolution — optical system.
Figure 9. Resolution — frequency
measurements.
Resolution is the maximum deviation (or may be expressed as rms
deviation if random noise is resolution limiting) between successive
measurements under constant environmental and constant input
conditions and over periods of time short enough that the time base
aging is insignificant. Practically speaking, it represents the smallest
change in the input quantity which can be observed in the measurement result.
Of course, resolution can never be better than the LSD Displayed.
Sometimes, the resolution is equal to the LSD Displayed. Often, the
resolution is not as good as the LSD Displayed because of jitter and
trigger error which are random noise induced errors.
17
Since resolution is often limited by noise (noise on the input signal or
noise from the counter), resolution is sometimes specified as rms (1 σ)
deviation about the average value or will have rms terms as part of the
specification. See appendix B for a discussion of how to interpret an
rms resolution or accuracy specification.
Examples (HP 5314A)
Frequency Resolution: ±LSD
±LSD is the ±1 count quantization error of a traditional frequency
counter. If the LSD is 1 Hz, then changes in the input frequency greater
than 1 Hz will be observable in the measurements.
Period Resolution
± LSD ± 1.4 ×
Trigger Error
N
For the HP 5314A, the PERIOD LSD is selectable from 10 ns to 0.1 ns
(100 ns/N for N = 1 to 1000 where N equals the number of periods in
the period average measurement).
For period measurements, the input signal controls the opening and
closing of the main gate. Since the input signal is controlling the
opening and closing of the gate, even a small amount of noise on the
input can cause the gate to open and close either too early or too late,
causing the counter to accumulate either too few or too many counts.
Consider an input signal passing through the hysteresis window of a
counter (Figure 10). In the absence of noise, the counter’s gate would
open at point A. Consider a noise spike with sufficient amplitude to
cross the upper hysteresis limit at point B, thus causing the counter to
start gating too soon. The rms trigger error associated with a single
trigger is equal to:
X 2 + e 2n
input slew rate at trigger point
where X = effective rms noise of the counter’s input channel
(= 80 µV rms for the HP 5314A and HP 5315A/B.)
en = rms noise voltage of input signal measured over a bandwidth
equal to the counter’s bandwidth. (See appendix C for a discussion of
how noise can affect wide band counter inputs.)
18
Trigger Error
Noise Spike
Hysteresis
Window
( 2 × 2 × RMS
Sensitivity Spec)
B
A
Figure 10. Trigger
error.
RMS Noise on Signal = 1 mV RMS
1 µs
1V
Trigger
Trigger
Figure 11. Trigger
error example.
Period
Since for period measurements, trigger error occurs at the beginning
and end of the measurement and the noise adds on an rms basis, the
rms trigger error for period measurements (and frequency measurements made by a reciprocal counter) is:
1.4 × X 2 + e 2n
input slew rate at trigger point
seconds rms
The effective rms noise contributed to the total noise by the counter’s
input circuitry has never before been specified and in many instances
has been negligible. However, as sophisticated applications for
counters increase, it is apparent that this noise contribution should be
specified. Not all counter inputs are equally quiet and for some applications, this is important. In appendix D, how the effective counter input
noise is measured is presented.
If the HP 5314A were used to measure the period of the waveforms in
figures 10 and 11, the rms trigger error would be
80 µV 2 + 1 mV 2
input slew rate at trigger point
= 1 mV = 1 ns rms.
1 V/µs
Since there is trigger error associated with both the start and stop input,
the total trigger error for the measurement equals 1.4 × 1 ns (trigger
errors add on an rms basis) = 1.4 ns rms. If the LSD were 0.1 ns, then
19
the quantization is negligible and the resolution for the measurement
would be ±1.4 ns rms. This means if M period average measurements
were made under the above conditions, there would be a variation of
results. If the standard deviation of the M measurements were computed, it would be around 1.4 ns rms, meaning that approximately 68%
of the M measurements were within ±1.4 ns of the actual period.
As a second example, let’s compute the HP 5314A’s resolution for a
period measurement on a 1 V rms sine wave at a frequency around
10 kHz. The noise on the signal is approximately 10 mV rms.
If A = the rms amplitude of the sine wave, then the signal may be
described by the equation
S = A 2 sin 2 π ft
dS = A 2 2 π f COS2 π ft
dt
Assuming triggering at the midpoint of the sine wave where the slope
is maximum,
dS
dt
MAX
=2 2Aπf
Figure 12 is a plot of slew rate versus frequency for various values of
sine wave signal amplitude in volts rms. For our example, 1 V rms at
10 kHz has a slew rate of 90 × 103 V/S (assuming triggering at the
midpoint — if the counter is set to trigger closer to the peaks of the
sine wave, the slope is decreased greatly and trigger error will be much
greater).
Figure 13 plots trigger error versus slew rate for various values of rms
noise on the input signal. The lowest curve is for no noise on the input
signal and is due only to the 80 µV rms noise contributed by the
counter’s input. According to Figure 13, for a slew rate of 90 × 103
and noise equal 10 mV rms, the trigger error is approximately 1 × 10–7
seconds or 100 ns rms. Total trigger error is 100 ns rms × 1.4 =
140 ns rms.
For an LSD of 10 ns, the quantization error is negligible so the rms
resolution is ±140 ns rms. In general, the resolution specification will
consist of some errors expressed in peak-to-peak (p-p) and other
errors expressed in rms. Usually, either the (p-p) errors or the (rms)
errors will predominate, allowing the smaller error to be neglected.
For those cases where the (p-p) errors and rms errors are nearly equal,
multiply the (rms) error by three to approximate a peak-to-peak value.
This will allow the errors to be added on a linear basis without the
difficulty of interpreting an addition of rms and peak-to-peak terms.
20
Slew Rate (V/S)
1M
500K
200K
100K
50K
20K
10K
5K
A
MS
1V R
0
= 70
A
MS
R
mV RMS
200
V
A = 100 m V RMS
A = = 50 m RMS
A 20 mV RMS
A = 10 mV
A=
A=
2K
1K
500
200
100
50
20
10
5
2
1
0.5
0.2
0.1
1
2
5
8 10
20
50 80 100 200
500 800 1K
mV
S
RM
2K
MS
VR
0m
= 50
5K 8K 10K 20K
50K 80K 100K 200K 500K800K 1M 2M
5M 8M 10M
Frequency (Hz)
Figure 12. Slew rate vs frequency
10–1
5
2
10–2
5
Trigger Error (seconds)
2
10–3
5
2
10–4
5
2
10–5
5
Best case performance
2
10–6
5
N=
1
N = 0 mV R
5m
V R MS
MS
N=
1
N = mV R
M
N = 500 µV S N
=3
200
RM
mV
S
N=
µ
RM
0 V V RMS
S
RM
S (o
nly
80µ
VR
MS
nois
e of
2
10–7
5
HP
531
5A/
B)
2
10–8
0.1
0.2
0.5 0.8 1
2
5
8 10
20
50 80 100 200
500 800 1K
2K
5K 8K 10K 20K
50K 80K 100K 200K
500K
1M
Slew Rate (V/S)
Figure 13. Trigger error vs slew rate
21
Example (HP 5315A/B)
Frequency Resolution:
± LSD1
1
±1.4 × trigger error
× Freq
Gate Time
due to arithmetic truncation, quantization error will be ± 1 or
± 2 counts of the LSD as follows :
±2 counts of LSD if LSD < 1 × 10 −7 for Freq < 10 MHz
FREQ
1
±2 counts of LSD if LSD <
for Freq ≥ 10 MHz
FREQ Gate Time × Freq
±1 count of LSD for all other cases
In the definition section, trigger error is defined as:
(80 µV) 2 + e 2n
input slew rate at trigger point
and en = rms noise on input signal for a 100 MHz bandwidth.
The quantization error will be either ±1 or ±2 counts of the LSD. This is
a direct result of the decision in the microprocessor algorithm to
truncate digits whenever
LSD Displayed
FREQ
is less than 5 × 10–8. Since the HP 5315A/B counts a 10 MHz timebase
for frequencies less than 10 MHz, the quantization error can never be
less than
±1 = ±1 × 10 −7 .
10 MHz
So, whenever
LSD Displayed
FREQ
is less than 1 × 10–7 (but greater than ±5 × 10–8), the quantization error
is specified as ±2 counts of the LSD Displayed.
Refer to appendix E for more discussion of HP 5315A/B operation with
respect to LSD Displayed and Resolution.
22
Let’s compute the resolution achievable when measuring a 100 mV rms
20 kHz sine wave with a 2 second gate time. The LSD Displayed will be
0.001 Hz (just look at the counter). The quantization error will be
±0.002 Hz since
LSD = 0.001 = 0.5 × 10 −7
FREQ 2 × 10 4
which is less than 1 × 10–7. For a rms noise level on the signal of 1 mV
rms, and referring to Figure 12 and Figure 13, the trigger error is seen
to be ~4 × 10–8 s.
Re solution = ±0.002 Hz ±
1.4 ( 4 × 10 −8 )
× 2 × 10 4 ≅ ±0.002 Hz.
2
HP 5315A/B
Best Case Resolution for 1 Second Gate
100 Hz
1 kHz
50 mV rms
±260 µHz
±350 µHz
±0.0012 Hz
±0.01 Hz
±0.1 Hz
±1 Hz
±1 Hz
100 mV rms
±135 µHz ±225 µHz
±0.0011 Hz
±0.01 Hz
±0.1 Hz
±1 Hz
±1 Hz
500 mV rms
± 35 µHz ±125 µHz
±0.001 Hz
±0.01 Hz
±0.1 Hz
±1 Hz
±1 Hz
1 mV rms
±23 µHz
±0.001 Hz
±0.01 Hz
±0.1 Hz
±1 Hz
±1 Hz
±113 µHz
10 kHz
100 kHz
1 MHz
10 MHz
100 MHz
The above chart gives frequency resolution versus input sine wave rms
amplitude, i.e.,
1.4 × trigger error
× Freq.
gate time
It is best case since the trigger noise is assumed to only come from the
counter (i.e., 80 µV) and not from the input signal source.
Resolution = ±0.002 Hz ±
Example (HP 5315A/B)
Time Interval Average Resolution:
± LSD ±
Start Trigger Error
N
±
Stop Trigger Error
N
Where N = Gate Time × Freq
To be technically accurate, the start and stop trigger error could be
added on a root mean square basis. For simplicity, they’re added
linearly which understates the actual resolution by 2 .
23
As an example, we’ll compute the resolution for a time interval measurement on the following:
200 ns
1 µs
Frequency of
Waveform = 500 kHz
1V
T.I.?
Figure 14. Trigger
error example.
If you select a gate time of 1 second, then N = 1 s × 500 × 103 = 500 × 103.
So the LSD = 100 ps.
Start trigger error =
80 µV
= 80 × 10 −12 s rms
1 V/1 µs
Stop trigger error =
80 µV
= 16 × 10 −12 s rms
1 V/200 ns
Resolution = ±100 ps ±
80 ps
50 × 10
4
±
16 ps
50 × 10 4
≅ ±100 ps
Specification
Accuracy
Definition
Accuracy may be defined as the closeness of a measurement to the true
value as fixed by a universally accepted standard. The measure of
accuracy, however, is in terms of its complementary notion, that is,
deviation from true value, or limit of error, so that high accuracy has a
low deviation and low accuracy a high deviation.
The plot in Figure 15 shows successive measurement readings for two
cases. In case 1, the readings are fairly consistent and repeatable. In
case 2, the readings are more spread out. This could be due to noise or
Actual Value
Measurement
Reading
Case 1
Case 2
Time
24
Figure 15.
Accuracy
the operator’s inability to consistently read an analog dial. Intuitively,
you feel that case 1 is better than case 2. If it’s not more accurate, at
least it’s more repeatable and this is useful if you’re concerned with
measuring differences between devices.
Notice that both cases are offset from the actual value. The important
thing is that this offset is a systematic error which can be removed by
calibration. The random errors of case 2 cannot be calibrated out.
Differential channel delay (T.I.)
Bias
Trigger level timing error (T.I.)
Aging
(systematic errors)
Timebase error
Accuracy
Temperature
Quantization error (and jitter)
Resolution
Trigger error
(random errors)
Timebase short term stability
The above chart shows universal counter accuracy as having two
components: bias and resolution. Resolution may be limited by quantization error (or jitter as in the case of the HP 5370A Universal Time
Interval Counter), trigger error (period, TI and frequency for reciprocal
counters) and sometimes the short term stability of the timebase. Bias
is the sum of all systematic errors and may be reduced or entirely
removed by calibration. In many operating modes, timebase error is the
dominant systematic error. For time interval measurements, differential
channel delay and trigger level timing error are often the dominant
systematic errors.
Except for time interval measurements, accuracy is specified as
resolution plus timebase error. Timebase error is the maximum fractional frequency change in the timebase frequency due to all error
sources (e.g., aging, temperature, line voltage). The actual error in a
particular measurement may be found by multiplying the total ∆f/f of
the timebase (or ∆t/t which equals ∆f/f) by the measured quantity.
Example
Aging Rate: <3 × 10–7/month
Temperature <5 × 10–6, 0 to 50°C
Line Voltage: <1 × 10–7, ±10% variation
The total fractional frequency change in oscillator frequency is the sum
of all effects. If the counter has not been calibrated for a year, the total
∆f/f due to aging is 3 × 10–7/month × 12 month = 3.6 × 10–6. For worst
case temperature variations, ∆f/f due to temperature is 5 × 10–6.
25
Including worst case line voltage variation, the total ∆f/f due to all
sources is 8.7 × 10–6. The worst case frequency change in the 10 MHz
oscillator would be 8.7 × 10–6 × 10–7 = 87 Hz.
If measuring a 2 MHz frequency, the timebase error would cause an
error of ±8.7 × 10–6 × 106 = ±17 Hz.
If measuring a 100 µs time interval, the timebase error would cause an
error of ±8.7 × 10–6 × 10–4= ±0.87 ns ≅ ±1 ns.
Example (HP 5370A) Opt 001
Aging Rate: <5 × 10–10/day
Short Term: <1 × 10–11 for 1 s average
Temperature: <7 × 10–9, 0°C to 50°C
Line Voltage: <1 × 10–10, ±10% change
What is the timebase error in the measurement of a 5 MHz signal using
the HP 5370A Opt. 001? The HP 5370A hasn’t been calibrated for
1 month and the temperature change from when it was calibrated to
now is 5°C at most.
∆f
f
aging
∆f
f
temperature
= ±5 × 10 −10 / day × 30 days = ±1.5 × 10 –8
= ±7 × 10 −9 × 5° = ±7 × 10 −10
50°
(For oven oscillators only, the temperature specification may be taken
as essentially linear so that if the actual temperature change is only a
tenth of the specification temperature change, then the ∆f/f variation
will be a tenth of the specified ∆ f/f. However, RTXO’s and TCXO’s are
definitely nonlinear.)
∆f
f
line voltage
∆f
f
total
= ±1 × 10 −10
= ±1.5 × 10 −8 ± 7 × 10 −10 ± 1 × 10 −10 = ±1.6 × 10 −8
∆f error = f × 1.6 × 10 −8 = ±5 × 10 6 × 1.6 × 10 −8 = ±0.08 Hz
For time interval measurements, two additional errors are present:
differential channel delay and trigger level timing error. Differential
channel delay is the difference in delay between the start channel and
the stop channel. For example, in the HP 5315A/B, this delay difference is specified as ±4 ns maximum.
26
Trigger level timing error is the time error (in seconds) due to error in
the trigger level readout (see Figures 16 and 17). If there is no readout
of trigger level, then this error cannot be specified.
Unlike trigger error, trigger level timing error is a systematic error. The
major component of the trigger level error comes from the fact that the
actual trigger level is not a measurable level. The only dc level which
can be measured is the output generated by the trigger level control
which sets the level on one side of the comparator.
This voltage represents the center of the hysteresis band.
In the absence of a specification, the trigger level error may be estimated at ±1/2 hysteresis band. The hysteresis band is equal to the
peak-to-peak pulse sensitivity.
Trigger Level
Indicated
Actual
Trigger Point
Trigger Level Error
Hysteresis
Band
Trigger Level
Timing Error (TLTE)
TLTE =
Trigger Level Error
Signal Slew Rate at Trigger Point
Figure 16. Trigger
level timing error.
TLTE
Upper
Hysteresis
Limit
Measured
Trigger
Level
Lower
Hysteresis
Limit
TLTE
Figure 17. Trigger
level timing error.
27
Specification
Time Interval Average Minimum Dead Time
Definition
Minimum time between a previous time interval’s STOP and the current
time interval’s START.
Start
Start
Stop
Stop
In order to measure X,
this pulse width must be
≥ 200 ns for the HP 5315A/B.
Dead Time
T. I.
X
Figure 18. Dead time.
Figure 19. Dead time example.
Example (HP 5315A/B)
Minimum Dead Time: 200 ns
This puts an upper limit of 5 MHz on the highest time interval repetition
rate in time interval averaging for the HP 5315A/B.
28
Appendix A. Time Interval Averaging
Time interval averaging reduces the ±1 count quantization error as well
as a trigger error.
Since time interval averaging is a statistical process and is based on
laws of probability, the precision and accuracy of a time interval
average measurement are best discerned by examining the statistics of
the quantization error. In Figure A-1, consider the time interval, τ, to be
made up of an integer number of clock pulses, Q, plus a fraction of a
clock pulse, F. Any time interval may be thus represented. The quantization error can only take on two values. It can be F · Tclock, which it
takes on with a probability of (1 – F) or it can be (F – 1) Tclock which it
takes on with a probability of F. If you work through the algebra, you’ll
find that the mean or expected value of the quantization error is 0 and
the standard deviation is equal to Tclock
F (1 – F)
Derivation:
τ
F
Q
Figure A-1. T = Q (integer clock periods) + F (Fractional clock period).
Time Interval = Tclock (Q + F)
Q = Integer
F = Fraction
Error can only take two values:
E = F Tclock with probability (1 – F)
= (F – 1) Τclock with probability F
µ E = F Tclock (1 – F) + (F – 1) Tclock F
= F Tclock – F 2 Tclock + Tclock F 2 – Tclock F = 0
σ E = E (x 2 ) – E (x 2 )
= F2 T
= F2 T
=FT
clock 2
clock 2
clock 2
σ E = Tclock
(1 – F) + (F – 1) 2 T
– F3 T
clock 2
+
F
clock 2
F3 T
clock 2
– 2 F2 T
clock 2
+ FT
clock 2
(1 – F)
F (1 – F)
29
If we average N independent measurements, then by using the law of
averages and identically distributed random variables, we get the
following results.
µE =
∑ µE
=0
N
2
T2
σ
F (1 – F)
σ E = E = clock
N
N
2
σE =
Tclock
F (1 – F)
N
The mean of the average quantization error is 0 (this means that the
expected value of the average is the true time interval) and the variance of the average quantization error is just the variance of the
original distribution divided by N. Thus, the standard deviation is
divided by N and the expression for the standard deviation of the
average quantization error becomes
Tclock
F (1 − F )
N
If we consider σ E to be a measure of the resolution, then this says that
the resolution depends not only on the period of the clock and the
number of time intervals averaged, but also the time interval itself
(i.e., F).
Figure A-2 shows a normalized plot of the standard deviation of the
error versus fractional clock pulse portion of the time interval and
shows that the maximum sigma occurs when F = 1/2 (i.e., when the
time interval is equal to n + 1/2 clock periods).
For this worst case, the quantization error of the time interval average
measurement is equal to 1/2 the period of the clock divided by the
square root of N, the number of time intervals averaged.
This means that, in the worst case, out of a number of time interval
average measurements, 95% (if N large) of the measurements will fall
within
T
± clock ( = ±2σ E )
N
of the actual time interval (in the absence of other errors).
30
0.5
0.4
σE
N
Tclock
0.3
0.2
0.1
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
σE N
= 0.5 for F =1/2
Tclock
σE =
Tclock
Worst Case
2 N
Worst Case : F =1/2
Figure A-2. σE
versus fractional
clock period.
The typical data sheet specifies that the error in a time interval average
measurement is ±1 count (clock) divided by the square root of N, the
number of time intervals in the average. You see immediately that this
specification is precisely twice the standard deviation of the worst case
quantization error.
What does this all mean? It means that the specification of ±1 count
error for a time interval average measurement is not really the maximum possible value of the error. For a normal distribution, it does
mean, however, that 95% of the readings on a given time interval will
fall within ±Tclock divided by N . However, there is also the 5% of the
readings which fall outside the two sigma worst case limits. You can
see in Figure A-3 that as you increase the number of time intervals
averaged, the spread of the distribution shrinks.
2σ
–Tclock
+Tclock
N
N
Increasing N
Figure A-3.
Decreasing σ with
increasing N.
For N small, the distribution of the counter’s reading is not normal — it
has a beta probability distribution. However, for large N, the distribution of the time interval average reading may be approximated by the
normal distribution.
31
Figure A-4 shows some histogram plots on some time interval average
measurements using the HP 5345A counter. The HP 5345A was
connected to a desktop calculator which was also equipped with a
plotter. The counter took a number of time interval average measurements. The resulting histogram plots show the probability distribution
of the time interval average readings. The calculator program also
computed the mean and standard deviation of the readings and plotted
the mean and one sigma tick marks on the graph.
This first graph shows the histogram for 200 time intervals in the
average measurement. The sigma was found to be 0.52 nanoseconds.
You’ll notice that this distribution is not normal but looks like a beta
probability distribution. (In each case, the counter took a total of 100
time interval average measurements.)
The second graph is for a 100 fold increase in the number of time
intervals in the average measurement. (The scale on the x axis has
been expanded to 0.1 ns/division.) For a 100 fold increase, you’d
expect the 100 or a 10 time decrease in the standard deviation.
Notice that the sigma is now 0.056 nanoseconds. This distribution,
with N = 20,000 appears approximately normal.
The third graph is for another 100 fold increase in the number of
samples. The sigma has decreased to 0.0077 nanoseconds, a factor of
8 (not quite 10).
32
Histogram
Mean = 50.732 ns
Sigma = 0.525 ns
N = 2 × 102
1 ns
Histogram
Mean = 50.777 ns
Sigma = 0.057 ns
N = 2 × 104
0.1 ns
Histogram
Mean = 50.7784 ns
Sigma = 0.0077 ns
N = 2 × 106
.01 ns
Figure A-4.
Histogram plots
with increasing N.
33
Appendix B. RMS Specifications
In the specification for resolution and accuracy, random errors are
specified in terms of their rms value. Although one generally thinks of
an accuracy statement as being a statement of the maximum possible
error in the measurement, random noise errors are best specified on
an rms basis instead of a peak basis. This is most easily demonstrated
by examining the graph in Figure B-1 which is a plot of the expected
maximum (peak) value in a sample (expressed in standard deviations
away from the mean) as a function of sample size. As can be seen, the
most probable peak value which will be observed in a sample depends
on sample size and σ. For a sample size of 10, one would expect the
peak value to equal 1.5 σ or one and a half times the rms value. But,
for a sample size of 1000, you will probably observe a peak value
which is over 3 σ or over three times the rms value. One cannot
specify a peak value, then, unless a sample size is also specified.
As an example, consider making time interval average measurements
on a stable 10 µs input time interval and the counter is set up such that
the resolution is 125 ns rms. According to Figure B-1, if you take 10
time interval average measurements, the most probable maximum time
interval observed would be 10.188 µs and the minimum 9.812 µs (10 µs
± 1.5 σ). However, if you take 1000 samples, the maximum time
interval observed is likely to be 10.388 µs and the minimum 9.612 ps
(10 µs ± 3.1 σ). However, the rms specification means that for any
number of samples, you have a 68% confidence level that the actual
time interval is somewhere between 9.875 µs and 10.125 µs (10 µs ± σ).
For higher confidence, use 2 σ so that for our example, you could say
with 95% confidence that the actual time interval is between 9.75 µs to
10.25 µs (10 µs ± 2 σ).
6
Standard Deviation
5
4
3
2
1
0
1
34
10
100
1k
10k
Sample Size
100k
1M
10M
Figure B-1. The
most probable
maximum value
within a Gaussian
zero-mean sample.
Appendix C. Effects of Wideband Noise
–10 dBm
–60 dB
0
500 MHz
Spectrum Analyzer Representation
Figure C-1.
Spectrum analyzer
representation of
signal plus
wideband noise.
How do you determine the noise contributed by the signal source over
the counter’s bandwidth? One possible approach is to measure the
signal of interest plus noise on a spectrum analyzer with a certain IF
bandwidth and then calculate the noise over the counter’s bandwidth.
Consider measuring a 10 MHz signal with a counter having a 500 MHz
bandwidth. Let’s say that you look at your 10 MHz signal on a spectrum
analyzer with a IF bandwidth of 10 kHz and it shows the noise from the
10 MHz source to be flat and 60 dB below the fundamental, or at –70
dBm. –70 dBm into 50 is approximately 70 µV rms. Obviously, you
say, noise is no problem. You hook up the 10 MHz source to your
counter and the counter display gives random readings. Why? Since
the frequency counter is a time domain measuring instrument while the
spectrum analyzer is frequency domain, the counter input sees the
integral of all the spectral components over its bandwidth.
If the spectrum analyzer’s 3 dB IF BW is 10 kHz, the equivalent random
noise bandwidth is 12 kHz (1.2 × 10 kHz). Correcting the –70 dBm by
2.5 dB because of detector characteristic and logarithmic scaling, we
can say that we have –67.5 dBm/12 kHz. To find the noise in a 500 MHz
bandwidth, add
10 log 500 MHz = 46.2 dB.
12 kHz
So, the noise in 500 MHz is –67.5 + 46.2 = –21.3 dBm which is equivalent
to 19 mV rms. This causes a high level of trigger error and is responsible for the random readings. For high sensitivity counters, this level
of noise could cause erratic counting.
(To learn more about noise measurements using spectrum analyzers,
get a copy of Hewlett-Packard Application Note 150-4.)
35
Appendix D. Measurement of
Counter Contributed Noise
Output of Voltage
Comparator
(Schmitt Trigger)
(Fast Transitions)
HP 3312A
Function
Generator
HP 180
Scope
Counter
Under
Test
HP 5370A
Time Interval
Counter
Figure D-1.
Measurement
setup for
measuring
counter
contribution
noise.
Set the HP 3312A for a 100 mV peak-to-peak triangle wave with a
period of 200 ms (1V/S slew rate) and apply this to the counter input.
The output of the “counter under test’s” Schmitt trigger (voltage
comparator) is fed to the HP 5370A which is measuring period. If the
counter under test has a marker output (buffered comparator output),
use the marker output. Otherwise, a scope probe can be used to pick
up the comparator output.
Put the HP 5370A in PERIOD mode displaying STD DEV with a sample
size of 1000. The equivalent single channel counter noise is equal to
STD DEV ( seconds rms ) × slew rate (VOLTS/SEC)
2
Make the test at other slew rates and check for maximum.
36
Appendix E. HP 5315A/B LSD
Displayed and Resolution
If you assume a 1 second measurement time, you can see from the
following chart what would happen if the HP 5315A/B counter were to
display a constant number of digits:
Input
Frequency
8 Digit
Display
(H z)
Least
Significant
Digit
LSD
LSD
FREQ
100 kHz
200 kHz
300 kHz
400 kHz
500 kHz
600 kHz
700 kHz
800 kHz
900 kHz
100,000.00
200,000.00
300,000.00
400,000.00
500,000.00
600,000.00
700,000.00
800,000.00
900,000.00
0.01 Hz
0.01 Hz
0.01 Hz
0.01 Hz
0.01 Hz
0.01 Hz
0.01 Hz
0.01 Hz
0.01 Hz
1 × 10–7
5 × 10–8
3 × 10–8
2.5 × 10–8
2 × 10–8
1.7 × 10–8
1.4 × 10–8
1.3 × 10–8
1.1 × 10–8
Due to the time base, the best the counter can resolve is 1 part in 107
per second (1 count in 10 MHz). From the chart above, it is apparent
that the resolution limit would be exceeded above 100 kHz with a 1
second gate. When does the microprocessor decide to cut off the last
digit as meaningless? As it turns out, the designer of the HP 5315A
programmed the processor to truncate the last digit if the displayed
resolution exceeds 5 × 10–8. This insures that the last digit is never
worse than ±2 counts and can, in fact, be much better than ±1 count.
The actual behavior of the HP 5315A/B for a 1 second gate time is
shown in the following chart:
Input
Frequency
Actual
Display
Significant
Digit
100 kHz
200 kHz
300 kHz
400 kHz
500 kHz
600 kHz
700 kHz
800 kHz
900 kHz
100,000.00
200,000.00
300,000.0
400,000.0
500,000.0
600,000.0
700,000.0
800,000.0
900,000.0
0.01 Hz
0.01 Hz
0.1 Hz
0.1 Hz
0.1 Hz
0.1 Hz
0.1 Hz
0.1 Hz
0.1 Hz
Least
LSD
FREQ
1×
5×
3×
2.5 ×
2×
1.7 ×
1.4 ×
1.3 ×
1.1 ×
10–7
10–8
10–7
10–7
10–7
10–7
10–7
10–7
10–7
Notice that at 300 kHz the displayed resolution overstates the actual
error by a factor of 3. However, for simplicity in the specifications, it
37
was decided to conservatively specify accuracy and resolution limits at
±1 count whenever the ratio of the LSD to Displayed reading is greater
than 1 × 10–7.
Above 10 MHz, the situation changes only slightly. The counter now
synchronizes on the timebase, counts the number of events during the
gate time, and calculates
EVENTS or TIME .
TIME
EVENTS
in this case, the resolution limit is identical to a conventional counter:
±
1
Gate Time
Let’s see what a similar chart would look like if you measure a 100 MHz
signal with gate times from 0.1 s to 0.9 s (remember the gate time of the
HP 5315A/B is continuously variable):
Gate
Time
Display
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
100 000 00
100 000 00
100 000 00
100 000 00
100 000 000
100 000 000
100 000 000
100 000 000
100 000 000
LSD
1
Gate Time
Specified
Quantization
Error
10 Hz
10 Hz
10 Hz
10 Hz
1 Hz
1 Hz
1 Hz
1 Hz
1 Hz
10 Hz
5.0 Hz
3.3 Hz
2.5 Hz
2.0 Hz
1.7 Hz
1.4 Hz
1.3 Hz
1.1 Hz
± 1 LSD
± 1 LSD
± 1 LSD
± 1 LSD
± 2 LSD
± 2 LSD
± 2 LSD
± 2 LSD
± 2 LSD
Again, for reasons of simplicity, the resolution and accuracy specification above 10 MHz conservatively indicates ±2 count whenever the LSD
Displayed is less than
1
.
Gate Time
38
39
H
For more information about HewlettPackard Test and Measurement products,
applications, services, and for a current
sales office listing, visit our web site,
httpL//www.hp.com/go/tmdir. You can
also contact one of the following centers
and ask for a test and measurement sales
representative.
United States:
Hewlett-Packard Company
Test and Measurement Call Center
P.O. Box 4026
Englewood, CO 80155-4026
1 800 452 4844
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Hewlett-Packard Canada Ltd.
5150 Spectrum Way
Mississauga, Ontario
L4W 5G1
(905) 206 4725
Europe:
Hewlett-Packard
European Marketing Centre
P.O. Box 999
1180 AZ Amstelveen
The Netherlands
(31 20) 547 9900
40
Japan:
Hewlett-Packard JApan Ltd.
Measurement Assistance Center
9-1, Takakura-Cho, Hachioji-Shi,
Tokyo 192, Japan
(81) 426 56 7832
(81) 426 56 7840 Fax
Latin America:
Hewlett-Packard
Latin American Region Headquarters
5200 Blue Lagoon Drive
9th Floor
Miami, Florida 33126
U.S.A.
(305) 267 4245/4220
Australia/New Zealand:
Hewlett-Packard Australia Ltd.
31-41 Joseph Street
Blackburn, Victoria 3130
Australia
1 800 629 485
Asia Pacific:
Hewlett-Packard Asia Pacific Ltd.
17-21/F Shell Tower, Time Square,
1 Matherson Street, Causeway Bay,
Hong Kong
(852) 2599 7777
(852) 2506 9285
Data Subject to Change
Hewlett-Packard Company
© Copyright 1997
Printed in U.S.A. May 1997
5965-7664E
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