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VOLUME 13 NUMBER 5 NOV/DEC 1973
AC ANALOG then our AC signal has an RMS or ef- amplified or attenuated, rectified by
fective value of 1 volt. the diode bridge and fed to the meter.
VOLTMETERS The meter then responds to this recti-
In addition to its RMS value, a wave-
by Harry Logan form also has a peak and average vol- fied average or DC value.
tage value. See Figure 1. The average value of a sine wave is
zero, so when we say average re-
AC Analog voltmeters are one of the sponding we mean the rectified aver-
most popular electronic measuring in- age or DC component after rectifica-
struments in use today. They are used tion. This DC component deflects a
ov d'Arsonval (moving coil) meter to indi-
to measure the RMS voltage of the
many waveforms commonly found in cate the RMS value of a sine wave.
electronics. See Figure 2.
This article will provide you with the ba- This sine wave has an RMS value of 1
sics of AC analog voltmeters. It will volt. Its peak value is 1.4 times its
give you a better understanding of RMS value, or 1.4 volts. Its rec-
their operation, allowing you to select tified average or DC value is .636
the right one for your particular mea- times the peak or .9 volts in the above
surement. example.
The RMS or root-mean-square vol- AC voltmeters are designed to re- Flgure 2. Average
tage is measured because this value spond to one of these three values. responding
gives us the most information about This classifies the meters into true voltmeter
the waveform. The RMS voltage is RMS responding, average re-
equivalent to a DC voltage which pro- sponding and peak responding. The The average responding meter is the
duces the same heating effect as the average and peak responding volt- most popular and economical type of
AC signal being measured. For meters are designed to measure only AC voltmeter. Its voltage scale
example, 1 volt of DC across a 1 ohm sine waves. has been made to indicatethe RMS va-
resistor will dissipate 1 watt. If we lue of a sine wave. If any other wave-
substitute any periodic waveform in Average Responding form is measured, the meter will read
place of the DC source and adjust its With an average responding volt- incorrectly. Typical average respond-
amplitude so that we again have 1 meter, a sine wave being measured is ing voltmeters are the HP 400 D/H/L,
watt of power dissipated in the load, fed through a DC blocking capacitor, 403A/B and 400E/EL.
.%
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AC ANALOG VOLTMETERS
Peak Responding DC voltage source, we can also mea- be measured with a true RMS volt-
Peak responding voltmeters are also sure current and resistance. Typical meter is crest factor. Crest factor must
peak responding voltmeters are the be considered when measuring pulse
designed to indicate the RMS value of
HP 410B and 410C. type signals-signals with a high peak
a sine wave.
RMS Responding and low RMS voltage. Crest factor is
A capacitor in the probe charges defined in terms of duty cycle or as the
through a rectifying diode to the posi- True RMS voltmeters are unique be- peak voltage divided by the RMS vol-
tive peak of the applied sine wave. cause they are the only type that accur- tage. See Figure 5.
The voltmeter then responds to the ately measure non-sinesoidal wave-
DC output from the probe. forms. They respond to the RMS or
The peak responding meter has its rec- heating value of the impressed signal.
tifier in the probe instead of inside the See Figure 4.
voltmeter, so we convert from AC to AC AMP D AMP
c
DC as close to the signal as possible.
Because the cable carries DC only,
cable capacity does not affect the
measurement. This greatly increases
the high frequency response of the
instrument. See Figure 3. TUERModOUPLE
Figure 5. Crest factor
The AC probe can be switched out of Figure 4. True RMS voltmeter
the circuit and the voltmeter can then The input signal is AC coupled, ampli-
be used to measure DC voltages. By fied or attenuated and heats a thermo-
adding shunt resistors and an internal couple. The thermocouple produces a
PROBE DC output proportional to the RMS
f--------\ value of the AC input. This DC voltage Figure 6.
is amplified and deflects the meter The pulse in Figure 6 has a crest factor
needle to the RMS value. The re- of 8. To measure it accurately, a true
sponse of the thermocouple is not de- RMS Voltmeter with a specified crest
pendent on the waveshape and thus factor of at least 8 is required. Crest
true RMS voltmeters can accurately factor limitation of a voltmeter is deter-
measure non-sinesoidal waveforms. mined by its dynamic range. For exam-
Figure 3. Peak respondlng
voltmeters A limitation on the waveforms that can ple, because the pulse in Figure 6 has
RMS VOLTAGE the square wave of Figure A? Note that the waveform
is not symmetrical around O or ground. This means the
v
RMS stands for root-mean-square.We can use this def- waveform has a DC component, +5v in this case. So
inition to calculate the RMS or heating value of any we really have two signals, +5v DC and a 1Ov p-p
waveform. Let's apply it to the 1O p-p square wave of
v square wave superimposed on it. The square wave in
Figure A. This will give us an insight into the meaning of Figure A has no DC component. Therefore the square
RMS. wave of Figure B must have a greater RMS value.
Again applying the definition of RMS we get:
Figure A.
ERMS = .\k10)21/2+0321/2 = 6= 7.07~
Most true RMS voltmeters are AC coupled and would
Applying the definition of RMS, we take the square root block the +5v DC component, thus measuring only the
of the average value squared. RMS value of the square wave. So when mea-
suring any non-symmetrical waveform (one with a DC
component), we must measure both the AC and DC com-
ponents separately and use this formula:
+'O
0 m v
Figure 8.
Now suppose our 1O p-p square wave looked like the
one in Figure B. Does it have the same RMS value as
For the waveform of Figure B we would get:
ERMS= .\152+52 6 ~ 7 . 0 7
=
This is the same value as was obtained applying the def-
inition of RMS.
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an RMS value of 1 volt, we should mea-
sure it on the l volt range. But the volt-
meter's amplifier must also be able to
handle the 8 volt level without satura-
tion even though we're on the one volt
range.
Of course, true RMS voltmeters can al-
so measure sine waves since their
crest factor is only 1.4. See Figure 7.
Table 1. Measurement errors from harmonic voltages.
and "b", depending upon the phase of or +1 volt. If the input signal were 10
the harmonic. The range of ampli- volts, it would be measured with +1
tudes that would be shown by the aver- volt, an accuracy of + l o % of our read-
age responding meter is more difficult ing. However, by downranging to the
Figure 7.
to diagnose, but note that in the left dia- 10 volt range, the measurement can
Typical true RMS voltmeters are the gram two half-cycles of the third har- be made to k 1YOof reading. For grea-
HP 3400A, 3403C, 3480/3484A and monic add to the fundamental while test accuracy, we should make our
3450NB. one half-cycle subtracts whereas in measurements as close as possible to
the right diagram, only one half-cycle full scale.
Distortion Effects adds while two half-cycles subtract. There are other items that contribute
All three types of meters will read cor- The waveform in the right diagram to total error. Refer to the operating
rectly with a sine wave. With a dis- therefore has a lower average value manual for your voltmeter's accuracy
c torted sine wave, only the true RMS
meter will read correctly. The average
responding and peak responding
meters will be in error.
than the left waveform.
Thus, the desired accuracy in the
measurement determines the amount
specifications.
AC Measurements with a DC
Component
of distortion, (meaning departure from
Table 1 lists the inaccuracies resulting true sine wave), that can be tolerated Another accuracy consideration when
from distortion. The table shows that a in the measured waveform. The RMS using AC voltmeters is whether the sig-
given amount of harmonic distortion voltmeter is unaffected by waveform nal contains a DC component. For ex-
may result in a wide range of possible shapes excepting, of course, those ample, if we wanted to measure the
inaccuracies, a consequence of the cases when harmonic components lie power dissipation in the load resistor
fact that the phase as well as the ampli- outside the passband of the voltmeter in Figure 9, we must consider both the
tude of a harmonic component affects circuits or beyond the crest factor. AC and DC voltage components.
the readings. This is illustrated by Fi-
The RMS responding meter is espe-
gure 8, which shows two waveforms
cially useful, for example, in the moni-
both with identical amounts of funda- toring of the line power fed to a resis-
mental frequency and added 3rd har- tive load where the line regulator dis-
monic. In the diagram at left, the funda-
torts the waveform; another applica-
mental crosses the zero baseline in
tion is measurement of the frequency
phase with the harmonic waveform
response of a communication system,
and in the diagram at right they are out
where modulation and demodulation
of phase.
processes may be non-linear to an un-
The peak responding meter would
show a range of readings between "a"
known degree. Again, the average re-
sponding meter tolerates relatively
-
Figure 9.
large amounts of distortion, while the
peak responding meter is most sensi- Since the AC signal is a square wave,
tive to distortion. we have to use a true RMS voltmeter
to measure its RMS value. However,
most meters are AC coupled so the
Voltmeter Accuracy DC component is blocked. We
The accuracy of AC voltmeters is often must include this DC portion of our sig-
specified as a percentage of full scale. nal to get the total power dissipation. A
For example, if our voltmeter is speci- DC voltmeter must be used to mea-
Figure 8. Phase of harmonics in sure the DC component. The RMS val-
waveform affect shape
fied as 1% of full scale and we are on
and thus the peak value the 100 volt range, any measurement ue of the waveform can then be calcu-
of a complex wave. would be in error by +1% of 100 volts lated using both meter readings and
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A C ANALOG VOLTMETERS
the formula: ERMs =
7
(DC)2 + (AC)
The trend in voltmeters is toward digi-
RMS meters are unaffected
by distortion.
crest factor limitation of your volt-
meter.
tal readouts. Some digital voltmeters 2. RMS voltage is measured 6. Any time you measure a signal
can be direct coupled when measur- because it gives us the most informa- that is non-symmetrical, you must
ing an AC signal with a DC compon- tion about the waveform; it is equiva- measure both the AC and DC compon-
ent. This allows you to make the lent to a DC voltage which produces ents and compute the RMS value from
above measurement without any cal- the same heating effect as the AC be- this formula:
culations. ing measured.
3. For a quick workbench check of
ERMs =-4
SUMMARY AND HINTS your AC voltmeter, you can use your 7. For maximum accuracy, use your
scope's square wave calibrator out- voltmeter as close as possible to full-
1. Peak and average responding AC put. For a lv peak to peak signal, the scale deflection.
voltmeters accurately measure pure true RMS meter will read 0.51; the
sine waves only. The more we deviate average responding 0 . 5 5 ~and the
from a pure sine wave, the greater the peak responding 0.35~. Reference material for the article included
error. Peak responding are affected HP Application Note 60 "Which AC Volt-
the most by distortion. As a rule of 4. Peak responding voltmeters can meter;" HP Application Note 124 "True
thumb, average responding meters measure the highest frequencies, typi- RMS Measurements;" and HP Videotape
can tolerate up to 10% harmonic distor- cally up to 0.5 to 1 GHz. No. 900308 Opt. 605, "Choosingthe Right
tion and peak responding 5%. True 5. If you measure pulses, know the AC Voltmeter."
SCALE FACTORS will respond to the 9 v rectified average value and mul-
The reason peak and average responding volt- tiply by its scale factor of l .1 l to read 10 volts. There-
meters are accurate only on sine waves is because of fore all three meters read 1 O for this sine wave, which
v
the scale factors designed into them. Consider the is correct.
waveform in Figure A. An RMS responding voltmeter
will measure the true RMS value of 10 V and it will de- Consider now the waveform in Figure B. An RMS re-
flect the meter to 10 v (that is, its scale factor is exactly sponding meter will measure and display 10 v, which is
1 .O). A peak responding meter will respond to the 14 v the correct RMS voltage for this waveform. A peak re-
peak but will apply a scale factor of 0.707, and therefore sponding meter will respond to the 10 v peak but wi//
it will also deflect its meter to the desired 10 volts read- still apply the correction factor for a sine wave of 0.707
ing, (14 x 0.707 = 1 ) An average responding meter
0. and thus display 7.07 v. An average responding volt-
meter will respond to the rectified average of 10 v but it
will also apply its scale factor for a sine wave of 1.1 1, dis-
playing 11.1 v.
Since peak and average responding voltmeters are
w----tr designed to measure sine waves, each has a scale fac-
tor for sine waves. Measuring any other wave shape re-
quires a different scale factor and therefore these
Figure A. 1OV RYS Sine wave Figure B.1OV Square wave meters read incorrectly.
Harry Logan is currently
working in HP Corporate Tele-
vision producing several new
video tapes. He joined the Com-
pany eight years ago and has
NQEL
spent most of that time in the
Training Department teaching
customers and HP personnel on
low frequency instrumentation.
Harry is an avid photogra-
phy enthusiast; he enjoys wood-
working and gardening, in addition
to playing the accordion and
organ.
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REPLACEMENT PART CROSS REFERENCE
When selecting replacement parts for pacitance, etc. There may also be substitute part will work in the circuit.
your HP products, you may notice that slight mechanical differences, such as Perhaps an HP part could be ordered
many manuals list only an HP part the shaping or length of leads. In some and installed at some later date.
number for the part, even though it ap- cases special quality checks are em- To help you in these situations, here's
pears that this part is manufactured by ployed to ensure that high reliability a cross-reference of HP part numbers
one of the large semiconductor manu- parts are used at the factory and at HP to JEDEC numbers for transistors and
facturers. Service personnel often ask field offices. diodes, plus a listing of manufacturer
why only HP part numbers are listed. and manufacturers' part numbers for
It is recommended that HP replace- Therefore, we suggest obtaining re- ICs. While every attempt was made to
ment parts be used to ensure that the placement parts from HP to maintain ensure the accuracy of the list, it is ad-
original performance of the product the quality that you have paid for in visable to compare the description of
will be obtained. While some parts your instrument. There may be situa- the device being replaced with the de-
used in HP instruments are identical to tions however where HP replacement scription of the substituted part. For ex-
that which can be purchased at a local parts are not in stock and substituting ample, if the service manual describes
electronics distributor, many times parts will allow you to return the pro- the device being replaced as a "dual
parts will be selected for certain charac- duct to service immediately. In these J-K flip-flop", check this against the
teristics, such as gain, bandwidth, ca- cases it may be worthwhile to see if a description of the replacement part.
HP P/N JEDFC NO. 1050-0096 --
-- 2N2189 1P51-0025 --
-- 7N1706 1853-0310 --
-- 2N4398 1854-0214 -- `ZN3904
-- 2N1482
0122-0004 --
-- IN4809
1850-0099
1850-0103 --
--
7N9h4
7N2190
1851-0031
1061-0034 --
--
2Nlh05
2NlF.056
1853-0311
1853-0314 --
--
2N3792
2N2905A
1854-0215
1854-0216 -- 2 h 3 4 4 1
-- 2N344,L
0122-0005
0122-0017 --
--
1Y4010
1N4804
1050-0107
1850-0108 --
--
7N798A
7N277
2N2374
19q1-0039
1851-0041 --
--
2N1121
2N2430
1853-0320
1853-0322 --
--
2N4032
2N2946A
1854-0217
1854-0218 -- 2N3393
--
0122-0025
0122-0062 --
--
1N4811A
1N5468A
1850-0109
1850-0110 --
-- 7N604
iec;3-0006
1R53-0007 --
--
2N7174
2N7251
1853-0323
1853-0327 --
--
2N4900
2N2944A
1854-0219
1854-0220 --
--
7N3663
2N395Y
0122-0070
0122-0245 --
--
1N5456A
1N513Q
1850-0111
1R50-0112 --
--
7N404A
7N2001
1853-000R
1P53-0012 --
--
2N7750
ZN2904A
1853-0328
1853-0340 --
--
2Nb211
2N5884
1854-0226
1854-0231 --
--
2N4314
-2N3688
0122-0246
0122-0247 --
--
1N5139A
1N5140
1950-0113
1P50-0114 --
--
7N1997
2N1905
1853-0013
1PS3-0014 --
--
2N2004
EN7304
1853-0342
-- *ZN595b 1854-0233
-- 7N3866
0122-0248
0122-0249 -- lN5140A
IN5141
1850-0119
1850-0124 -- ?N963
7N466
1R53-0015
-- *ZNW*O
1853-0344
1853-0349 --
--
2N5876
2N533J
1854-0234
1854-0235 --
--
PN3440
ZN1484
0122-0250 --
-- 1N514 1A 1R50-0126 --
--
ZNZA69
lR53-0016
1853-0019 --
--
*?N7678
2N1131
1853-0351
1853-0360 --
--
2N6OS3
2N379YA
1854-0237
1854-0238 --
--
2N373d
2N3933
0122-0251
niz-0252 --
--
1N5142
1N5142A
1850-0127
1850-0128 --
--
2N519A
2N3988
1853-0023
1953-0029 --
--
*?N3703
2N7614
1053-0362
1854-0004 --
--
2Nb053
EN743
1854-0242
1854-0246 --
--
2N3262
*2N3643
0122-0253
0122-0254 --
--
1N5143
1N5147A
1850-0129
1850-0132 --
--
3N1541
7N1540
1053-0029
1853-0031 --
--
*2N7702
?N77P9
1~54-0005
--
--
2~701 iaslr-0248
-- ?N4044
0122-0255
-- 1N5144 1850-0137
-- 7N976 1053-0033
-- 2N3318
1854-0006
1854-0009
--
2N706
2N709
1854-0252
1854-0255 --
--
2N3713
*2N3642
0122-0256
0122-0257 --
--
lN5144A
1N5145
1850-0139
--
--
2N1379 1853-0034
--
--
*2NW06 1854-0010
-- 2N834 1854-0259
-- 2~3766
0122-0258
--
1N5145A
1850-0140
1850-0145
--
7N1533
7N1926
1953-0039
1953-0045
--
*2N7678A
2N4076
1854-0011
1854-0013 --
--
2N835
2N2211A
1854-0260
1854-0263 --
--
2N3227
2N3019
0122-0259
0122-0260 --
--
1N5146
1N5146A
1850-0146
lR50-0150 --
--
7N1501
7N1358
1953-004b
1853-0051 --
--
2N7250
2N4037
1854-0017
1854-0021 --
--
2~706a
2NY18
1854-0264
1854-0270 -- 2N3715
*?N4?65
0122-0261
-- 1N5147 1850-0151
-- 7N1309 lRc3-0052
-- 2N7740 1854-0027
-- Q2N2714 1A54-0278 --
-- 2N7702
0122-0262
0122-0263 --
--
1N5147A
1N5148
1850-0154
1850-0158 --
--
7N508A
7N2635
1R53-0057
18`;3-0058 --
--
3N91
rZNlf.44
1854-0029
-- 2N271L 1854-0291
-- 2N7194
0122-0264
-- 1N5 14RA 1850-0160
-- 2N2147
7N2 188
1853-0059
-- 2N7791
1854-0032
1854-0033 --
--
2N2221
2N3391
1R54-0282
lR54-0286 --
--
EN7583
ZN5217
1850-0003
1850-0017 --
--
ZN1516
2N525
1850-0166
1850-0170 --
-- >N1377
1953-0062
1953-0066 --
--
*2N7645
Q2N4250
1854-0036
1R54-0039 --
--
ZN2958
2N305J
lA54-02A7
1054-0289 -- 2Nd15
2N730
1850-0019
1850-0020 -- 2N599
2N1143
1050-0172
1850-0173 --
7N2996
7N1307
1853-0069
1453-0071 -- *2N4122
2N7494
1854-0048
--
2N2857 1R54-0301 --
-- 2N776l
--
-- 2N44 1 -- -- 1854-0050
-- 7N916 1054-0302
-- `2N7405
1850-0021
1850-0027
-- 2N1516
1850-0178
1850-01PO --
--
ZN1038
2N1374
1P53-0072
1053-0076 --
--
i'Nb074
`2N4062
1P54-0053
1854-0056 --
--
7N2218
7N7119
1854-0304
1854-0300 --
--
2N24R3
2N7553
1850-0031
1850-0032 --
--
2N526
2N404
1950-0181
1050-ole2 --
--
?N2552
7N1378
1953-0077
1Rq3-0080 --
--
*?N4749
*?Ll4RA8
1854-0057
-- 7N3855A 1854-0311
-- 244240
1850-0037
-- 2N274 1850-01P5
-- 7N1545 lR53-0081
-- *2N4?58
1854-0060
1854-0062 --
--
2N3565
?N1701
1854-0313
1854-0315 --
--
2N7771
2N363J
1R50-0041
1850-0047 --
--
2N384
2N582
1R50-0190
1R50-0192 --
--
3NP13R
?N7614
1953-0084
lR53-0086 --
--
7N4018
*2N5087
1854-0063
-- 7N7055 1854-032.3
--
--
2N2HS'r
1850-0048
-- 2N650 1P50-0194
-- 2N1523 1853-0089
-- 2N4917
1854-0064
lR54-0066 --
--
2N7710
2N2925
1854-0324
1854-0325
--
2N3739
2N3478
1050-0049
1850-6051
1P50-0052
--
--
2N100AR
2N1500
2N598
1850-0195
1850-0198 --
--
3N1970
ZNZ 156
1853-0098
1853-0100 --
--
*2N50R6
`2N4355
1854-0067
1854-0072 --
--
7N2102
7N3054
1854-0.327
1854-0345 --
--
*2N3&16
2N5179
1850-0054 --
-- 2N652A
1950-0199
1850-0200 --
--
2N3325
7N1414
1853-0204
1853-0205 -- 2N4Q20
EN2907
1854-0076
1054-0079 -- 7N1973
7N3439
1824-0347