HEWLETT PACKARD APPLICATION NOTE 6O

WHICH AC VOLTMETER?

Hewlett-Packord AC voltmeters are manufactured in each of the three basic kinds, rms-responding, peak-responding, and average-responding. Illustrated is one example of each: Model 3400A rms-responding(left), Model 410C peak-responding (center), and Model 403B average-responding (right).

Page 2 Appl. Note 60

Electronic ac voltmeters are classified into three broadcategories: rms-responding, peak-responding, and average-responding. The majority of ac voltmeters, however, are eitherthe average-responding or peak-responding types with the meterscale calibrated to read the rms value of a sine wave. Only asmall minority of instruments in actual use are true rms-responding instruments. This is in spite of the fact that mostmeasurements are concerned with rms values. The discussionwhich follows considers the reasons for the existence of thethree types, all three being manufactured by Hewlett-Packard,and reviews the advantages and limitations of each.

BASIC CONSIDERATIONS

Electronic ac voltmeters are ac-to-dc converters whichderive a dc current proportional to the ac input being measuredand use this current for meter deflection. Conversion to dceliminates the serious errors which otherwise would resultfrom a meter movement's sensitivity to frequency. Thedifferences among the three types of electronic meters liein their interpretation of the value of the input signal.

RMS INDICATIONS

The rms (root-mean-square) value of a waveform usuallyis the quantity of interest in ac voltage measurements. Therms value long ago was established as equivalent to a dcvoltage which generates the same amount of heat in a re-sistive load that the ac does. Eor this reason, rms voltageis synonymous with effective voltage.

The rms voltage is defined, rather imposingly, as the squareroot of the average of the squares of the quantities beingmeasured (this concept is explored more fully in Appendix I).Theoretically, this can be done by measuring the voltage pointby point along the waveform for one cycle, squaring the numeri-cal value of the voltage at each point, finding the average valueof all the squared terms, and then taking the square root of theaverage value. Regardless of the shape of the waveform, thisprocedure leads to the rms or effective value. As is well known,the rms value of a sine wave is 0.707 times the peak or maxi-mum value of the voltage waveform.

The use of average-responding rather than rms-respondingvoltmeters is a consequence of the wide use of sine waves inelectronic measurements. In calibrating an average-respond ingmeter, a pure sine wave with an rms amplitude of 1 volt can beapplied to the meter and the resulting pointer deflection markedon the scale as 1 volt. Actually, the average value of this sinewave is 0.91 volts but since pointer deflection is l inearlyproportional to the input voltage, an average-re spending metercalibrated in rms volts provides reliable indications of rmsvoltage as if the input is a sine wave. As a matter of fact,this indication is not affected more than 3'^ by as much asin harmonic content in the input waveform and useful indica-tions are obtained on waveforms with even more distortion.For this reason, average-reading voltmeters are widelyaccepted as low-cost substitutes for true rms-respondingvoltmeters.

PEAK-RESPONDING INDICATIONS

There are situations where the peak amplitude of an acsignal is significant, such as the monitoring of a transmittermodulating signal, or in studies of vibration components, orin other situations where peak energy must be known. Thedominant reason for the use of peak-responding ac voltmeters,however, lies in the nature of their circuitry. Peak-respondingcircuits allow a voltmeter to serve as a multi-function meterand, what is more important, enables it to be used at muchhigher frequencies. For example, the Hewlett-Packard 410series of peak-responding instruments retain accuracy tohundreds of megacycles.

Here again, since the majority of measurement situationsinvolve sine waves, peak-responding meters usually arecalibrated in rms volts. A calibrating sine wave of 1 voltrms amplitude actually causes a pointer deflection equivalentto 1.414 volts, but this point can be marked as 1 volt rms onthe scale. As long as the input waveform is a sine wave, thepeak-re spending indication is proportional to the rms value.The peak-responding meter, though, is much more sensitive todistortion in the waveform than the average-responding meteris. This factor will be discussed in more detail later on.

AVERAGE VALUES

The average value of an ac voltage is simply the average ofthe voltage values measured point by point along the waveform.This procedure, by omitting the squaring and root extractionneeded to obtain the rms value, results in a different numericalvalue.

The average value of a sine wave really is zero because thewaveform has equal positive and negative values when averagedfor one whole cycle. Since the equivalent dc or energy contentin the waveform usually is the quantity of interest, the averagevalue of a sine wave is taken to mean the average rectifiedvalue. The average value of one half cycle of a sine wave is0.636 times the peak value.

Actually, there are not many measurement situations wherethe average value of a waveform is the desired quantity. Anaver age-responding ac voltmeter, however, can be constructedmore simply and at less cost than a true rms-respondingvol tmeter , as shall be described later. For this reason,average-respond ing voltmeters are widely-used, although thefact that they are average-responding often receives littleconsideration.

PRINCIPLES OF OPERATION

AVERAGE-RESPONDING METERS

A simplified version of the circuit used in the -hp- 400 seriesaverage-responding ac voltmeters is shown in Fig. 1. Circuitoperation is as follows.

The test signal is applied to the attenuator through a cathode-follower, insuring a high-impedance input unaffected by rangeswitching in the attenuator. The ac amplifier has a largeamount of negative feedback thus assuring gain-stability formeasurement accuracy, as well as broadening the frequencyrange of the instrument. Inclusion of the meter circuit in thefeedback path minimizes the effects of diode non-linearitiesand meter coil inductance on circuit performance.

A large feedback factor (typically 60 dbl suppresses theeffects of variations in tube or transistor parameters sothat accuracy depends primarily on the passive components.Accuracy is readily obtained with high quality resistors.Despite the large feedback factor, the amplifiers have suffi-cient gain to obtain high sensitivity also.

Appl. Note 60 Page 3

FIG. J — Basic circuit arrangement of typical average-respondingvoltmeter. (~hp-4QQD).

It should be noted that the capacitors in the meter circuitdo not serve as storage or filter capacitors for the rectifierdiodes. Rather, they are coupling capacitors for the feedbacksignal, functioning as two capacitors in parallel. The diodesact as switches to maintain a unidirectional meter currentdespite changes in the instantaneous polarity of the inputvoltage (Fig. 2).

FIG. 2—Arrows show current flow during positive portion ofinput waveform (a) and during negative portion (b). Currentthrough meter fs o train of unidirectional half-sinusoids.

The mechanical inertia of the meter movement preventsthe pointer from responding to the individual current pulses.As a result, the pointer deflection corresponds to the averagevalue of the current pulses, rather than to the peak value.

THE PEAK-RESPONDING METER

The fundamental difference between the peak-respondingvoltmeter and the aver age-responding voltmeter concerns theuse of a storage capacitor with the rectifying diode. Thecapacitor charges through the diode to the peak value of theapplied voltage, and the meter circuit then responds to thecapacitor voltage.

Practically speaking, there are other differences. Thediode and capacitor can be placed ahead of the amplifier, asshown in Fig. 3. The capacitor can discharge but slowlythrough the high-impedance input of the amplifier so that anegligibly small amount of current supplied by the circuitunder test keeps the capacitor charged to the ac peak voltage.

Since the capacitor charges to the total peak voltage aboveground reference, the meter reading will be affected by thepresence of dc with the ac voltage, unlike the average-respond-ing meter which has ac-coupled circuits. Furthermore, if themeasured waveform is unsymmetrical, a different reading maybe obtained if the voltmeter leads are reversed, therebycharging the storage capacitor to the negative peak (the so-called turn-over effect).

w—

Input 1D-C amplifier

FIG. 3~Peak-rcspondir)g meter circuit,

A dc amplif ier is used in the peak-responding meter todevelop the necessary meter current. The amplifier andmeter may then also be used for making dc voltage measure-ments. For this reason, most peak-responding ac voltmetersalso serve as dc voltmeters and, by the addition of shuntresistors and dc voltage sources, as mill iammeters andohmmeters. The majority of the inexpensive, multi-purposeinstruments so widely used in repair shops and laboratoriesuse this circuit arrangement.

The primary advantage of the peak-re spending voltmeter,however, is that the rectifying diode and storage capacitormay be taken out of the instrument and placed in the probe, asin the -hp- series 410 voltmeters (Fig. 4). The measured acsignal then travels no further than the diode. Rectifier diodesdesigned especially for the -hp- 410 voltmeters (Fig. 5t reducethis distance to a practical minimum so that the series induct-ance of the signal path is as short as possible and so that thecapacitance added to the test circuit by the probe is as low as1.5 pf.

Inilrumgnl

Prob» 1

^J c!(/*v C2i[vv > — • i t »•— < ' —J i i

n ' '11

D-Camplifier

FIG. 4-Another form of peak-responding voltmeter. Cl ischarged to peak voltage through diode while C2 is merelypart of low-pass filter.

FIG. 5-Diode especially designed for -bp-410 series UHF-voltmeter probe has small, plane surfaces in diode gap for minimumcapacitance. Gap is only 0.01 inch to shorten transit time.

The peak-responding voltmeter, with rectifying diode in theprobe, therefore is able to measure frequencies up to hundredsof megacycles with a minimum of circuit loading. Average-responding meters, on the other hand, must pass the ac signal

Page 4 Appl. Note 60

through test leads into the instrument and then through anamplifier before rectification. The attenuator limits frequencyresponse and the capacitance of the test leads and input circuitloads the test circuit.

The question then comes to mind: Why not use a peak-responding meter for all measurements? One reason is thesusceptibility of the peak-reading meter to errors caused byharmonic distortion in the input waveform. Another reasonconcerns the maximum sensitivity of the instrument, which islimited by diode characteristics. Diodes, whether semiconductoror thermionic, have highly non-linear ampere/volt characteris-tics below 1 volt. This non-linearity sometimes is compensatedfor by a separate non-linear meter scale on the most sensitiverange, but accuracy is difficult to achieve since similar diodesdo not necessarily have similar ampere/volt characteristics.For this reason, careful design is required to achieve even 1/2volt FSD sensitivity on the lowest range of a peak-respondingvoltmeter.

THE RF MILLIVOLTMETER

Diode non-linearities as a limit on sensitivity have beeneliminated in the -hp- Model 411A RF Millivoltmeter. Thisinstrument uses a balanced circuit, as shown in Fig. 6, withone input receiving the peak value of the voltage being measured.The balanced differential amplifier, acting as a null detector,controls the amplitude of an internally-generated ac signalwhich is fed to a second diode in the probe. The peak voltage(dc) from this diode serves as the other amplifier input. Thenull circuitry insures that the signal at the second diode hasthe same amplitude as the input signal.

The internally-generated ac has a constant frequency (100 kc)and is easily measured. It serves as the indication of the un-known input. All that is required is that the two signals beidentical in amplitude, so that diode non-linearities do notenter into the measurement. The most sensitive range on thisinstrument is 0.010 volt (10 millivolts).

FIG. 6-RF Millivoltmeter.

THE RMS VOLTMETER

In past years, rms-responding electronic voltmeters have notbeen used widely because of the difficulties in designing arugged, easily-operated instrument of reasonable cost. Re-cently, however, these difficulties have largely been overcome.A prime example is the Hewlett-Packard 3400A. It providesan attractive alternative now, wherever measurements are tobe made in the range from 10 cycles to 10 megacycles of volt-ages whose waveform is, or may be, substantially non-sinusoi-dal.

The rms-responding voltmeter presents special circuitdesign problems compared to the straightforward techniquesused in the average- and peak -re spending voltmeters. Thisis because the input voltage must be squared, and then thesquare root of the average of the squared quantity taken.

One approach has been to take advantage of the non-linearcharacteristics of diodes which, in the region below 1 volt,have an ampere/volt characteristic which approximates thecurve y = x2. The square-law detector widely used for RFpower measurements is an example of this approach. Bycalibrating the meter scale so that it indicates the squareroot of the driving voltage, the meter indicates the rms value.Precise calibration is difficult , however, because the diodecharacteristics do not always conform precisely to a square-law curve and, furthermore, this characteristic is not uniformfrom diode to diode. This problem is reduced by amplifyingthe signal, and using the much larger voltage to drive themeter through a more predictable non-linear network madeup of several diodes and resistors.

Another approach is to use a thermocouple. The signal tobe measured is applied to a fine heater wire, and a thermocoupleattached to the heater wire generates a dc proportional tothe temperature of the wire. This measurement is based onthe original concept of the rms value as the equivalent of theheating power in a waveform.

The accuracy of this arrangement has been difficult tocontrol because of the non-linear behavior of thermocouples,which complicates meter calibration, and also because of thethermal problems involved. Thermal effects are reduced byinstalling the heater and thermocouple in an evacuated glassbulb and by using fine wires of low thermal conductivity.Other problems with thermocouples have been concernedwith sluggish response and susceptibility to burn-out.

These difficulties have been overcome in the -hp- Model3400A RMS Voltmeter by application of the null balance tech-nique used in the -hp- 411A RF Millivoltmeter. Here, twothermocouples are mounted in the same thermal environment.Non-linear effects in the measuring thermocouple are can-celled by similar non-linear operation of the second thermo-couple.

As shown in the block diagram of Fig. 7, the amplified inputsignal is applied to the measuring thermocouple while a dcfeedback current is fed to the heater of the balancing thermo-couple. The dc current is derived from the voltage outputdifference between the thermocouples. The circuitry may beregarded as a feedback control system which matches theheating power of the dc feedback voltage to the input waveform'sheating power. Meter deflection is proportional to the feed-back dc, which in turn is equivalent to the rms value of theinput signal. The meter indication, therefore, is linear andnot subject to the non-linearities of the thermocouples.

hog*/

M»lur,n0 -•"

thermae nip

la lane mp ttl« rmetoupl*

*

£fc +

rO1-̂ ;

ISocanpliliir

<

FIG, 7—Block diagram of — hp—3400A rms voltmeter usingthermocouples in null-balance configuration.

Appl. Note 60 Page 5

One note of caution about rms voltmeters concerns thecrest factor. The maximum crest factor is defined as themaximum ratio of the waveform peak-to-rms value that canbe accommodated. The crest factor is limited primarily bythe amplifiers, and the maximum represents the level beyondwhich the input waveform drives the amplifiers into non-linearoperation. The -hp- 3400A RMS Voltmeter maintains full scaleaccuracy with crest factors as high as 10:1. At 10'} of fullscale deflection, waveforms with crest factors as high as100:1 are accommodated. The meaning of a crest factor ofthis magnitude is perhaps not immediately apparent. Whendealing with pulse waveforms there is a natural tendency toconsider that crest factor is about the same as peak-to-average ratio, or the inverse of the duty factor. Actually,the crest factor is nearly equivalent to the inverse of thesquare root of the duty factor. Thus a pulse waveform of1% duty cycle, or 100:1 peak-to-average power, turns outto require of the rms-responding voltmeter a crest factoraround 10. An rms voltmeter which meets this specificationmust first have an amplifier dynamic range sufficiently wideto pass pulses ten times the amplitude of the full-scale rmsvalue, and, furthermore to anticipate the measurement ofpulse trains with both positive and negative pulses, must havedouble that dynamic range. In the design, however, widedynamic range is not the only consideration. To preventthermocouple burnout, the amplifier design must have some

sort of power limiting. Straightforward amplitude limiting,as can be seen, is not the answer, since this would limit thecrest factor. The amplifier therefore must be designed wi tha limit on the voltage-time pjrgduct, to prevent thermocoupleburnout , while yet allowing a wide dynamic range. Crestfactor may then be taken as a figure of merit for rms-re-sponding voltmeters.

WHICH VOLTMETER TO PICK?

The basic facts about ac voltmeters discussed so far can besummarized as follows:(1) For measurements involving sine waves with only modest

amounts of distortion (<10r;}, the average-respondingvoltmeter provides the best accuracy and most sensitivityper dollar.

(2) For high-frequency measurements (»1 Me), the peak-responding voltmeter with diode-probe input is the mosteconomical choice. Peak-responding circuits are accept-able as part of an AC-DC voltohmmeter if the inaccuraciescaused by distortion in the input waveform can be tolerated.

(3) For measurements where it is important to determinethe effective power of waveforms that depart significantlyfrom a true sinusoidal form, the true rms-respondingvoltmeter is the appropriate choice.

Instrument Primary Uses Frequency Rang* Voltage or Current Range I n p u t Impedance

AC M e a s u r e m e n t s

400D*

40 OH"

400L*

403A*

403B*

3400A*

411A«"

Wide range ac measurements,high sensitivity

High accuracy wide range acmeasurements

Log voltages, linear dbmeasurements

Battery-operated portable; fast,accurate, hum-free ac measure-ments

AC voltage measurements in lab orfield; ac line or battery operation

True rms readings of complex acwaveforms

Millivolt, db readings to gigacyclerange

10 cps to 4 me

10 cps to 4 me

10 cps to 4 me

1 cps to 1 me

5 cps to 2 me

10 cps to 10 me

500 kc to 1 gc

0.001 to 300 v full scale,12 ranges

0.001 to 300 v full scale,12 ranges

0.001 to 300 v full scale,12 ranges

0.001 to 300 v full scale,12 ranges

1 mv to 300 v full scale

0.001 to 300 v full scale

10 mv to 10 v full scale,7 ranges

10 meg, 15, 25 pf shunt

10 meg, 15, 25 pf shunt

10 meg, 15, 25 pf shunt

2 megohms, 40, 20 pf shunt

2 megohms

10 megohms, 25 pf shunt

Typically 200 K at 1 me, Iv

AC -DC -OHMS

410B**

410C**

Audio, rf, vhf measurements; dcvoltages; resistances

DC voltage; resistance, current;audio, rf, vhf measurements, withac probe

dc; ac— 20 cpsto 700 me

dc; ac— 20 cpsto 700 me

dc, 1 to 1000 v full scaleac, 1 to 300 v full scale

dc v, 14 mv to 1500 vfull scale; dc amps,1.5 ^a to 150 ma fullscale; ac v, 0.5 to 300 vfull scale

dc, 122 megohmsac, 10 megohms/1.5 pf

dc v 100 megohmsac, 10 megohms/1.5 pf

* Average-res ponding *'Peak-responding * RMS-responding

Data subject to change without notice

TABLE 1-Hewlett-Packard AC VoJfmefers.

Page 6 Appl. Note 60

DISTORTION EFFECTS

How much distortion in the measured signal can be toleratedby average- or peak-responding meters? No firm answer canbe given to this question since so many factors are involved.

Table 2 lists the inaccuracies resulting from distortion. Thetable shows that a given amount of harmonic distortion mayresult in a wide range of possible inaccuracies, a consequenceof the fact that the phase as well as the amplitude of a harmoniccomponent affects the readings. This is illustrated by Fig. 8,which shows two waveforms both with identical amounts offundamental frequency and added 3rd harmonic. In the diagramat left, the fundamental crosses the zero baseline in phase withthe harmonic waveform and in the diagram at right they are outof phase.

Id phot* rhird h

FIG. B— Phase of harmonics in waveform affect shape and thuspeak value of complex wave.

The peak responding meter would show a range of readingsbetween "a" and "b", depending upon the phase of the harmonic.The range of amplitudes that would be shown by the averageresponding meter is more difficult to diagnose, but note thatin the left diagram, two half-cycles of the third harmonic addto the fundamental while one half-cycle subtracts whereas inthe right diagram, only one-half cycle adds while two half-cycles subtract. The waveform in the right diagram there-fore has a lower average value than the left waveform. Adetailed analysis of the effects of waveform on voltmeterreadings is presented in Appendix II.

To repeat, the desired accuracy in the measurement deter-mines the amount of distortion (meaning departure from truesine wave) that can be tolerated in the measured waveform,The rms voltmeter is unaffected by waveform shapes excepting,of course, those cases when harmonic components lie outsidethe passband of the voltmeter circuits. The rms-respondingmeter is especially useful, for example, in the monitoring ofthe line power fed to a resistive load, where the line regulatordistorts the waveform; another case in point is measurementof the frequency response of a communication system, wheremodulation and demodulation processes may be non-linear to anunknown degree. Again, the average-responding meter toleratesrelatively large amounts of distortion, while the peak-respondingmeter is most sensitive to waveform.

HarmonicContent

0

10 percent 2nd

20 percent 2nd

50 percent 2nd

10 percent 3rd

20 percent 3rd

50 percent 3rd

True rmiva lue

no100. 5

102

112

IOC. 5

102

112

Average -responding meter

100

100

tOO- 102

100.110

96-104

94 108

90-116

Peak-responding meter

100

90 to 1 10

80 to 120

75 to ISO

90 to 1 10

88 to 120

108 to ISO

VOLTMETERS AND NOISE

An oscillogram showing typical circuit noise is shown inFig. 9. A peak-responding meter responds to the highestpeak of such a waveform during the period of measurement,but the meter indication seldom reaches this peak value becauseof several complicating factors. These include the charging anddischarging time constants of the voltmeter input circuit andthe impedance of the test circuit at the point of measurement.In general, the peak-responding meter reads noise 3 to 5 timeshigher than the actual rms value. Although peak-respond ingvoltmeters can be used for noise measurements, extreme careis required when interpreting the readings.

TABLE 2-Measurement errors from harmonic voltages.

FIG. 9—Oscillogram of noise voltage illustrates variable peak

values.

The average-responding meter does much better with noisevoltages since it does read the average value, which ordinarilyis constant. Probability analysis shows that the average valueof noise (rectified) is 0.8862 times the rms value (the rmsvalue of random or gaussian noise is the same as cr, the standarddeviation). This correction factor should be applied with care,however, since any alteration of the character of the noise, whichis most likely to happen in electronic circuits because of non-linearities, alters the correction factor. The average-respond-ing meter is well-suited, though, for relative measurements ofnoise levels.

The rms-responding meter, of course, provides the mostreliable measurements of noise or signals with noise. Indeed,the widest present use of rms-responding meters is found inmeasurements involving noise. In this service, the readingsof both aver age-re spending and peak-res ponding meters mustbe interpreted with care and often with questionable assumptions.Correction factors for peak-reading instruments, for example,rely on the assumption that energy distribution is gaussian outto the tips of the distribution (See Appendix II). So long as itscrest factor and frequency range are adequate to the purpose,the rms-responding instrument may be taken as giving accuraterepresentations of effective power even where the signal mayhave been subjected to unknown variations due to non-linearitiesor frequency discrimination in the circuitry under investigation.

SIGNALS PLUS NOISEMany measurements are concerned with sine wave signals

corrupted by noise. To find the true value of the sine wave,the usual procedure is to measure the noise voltage withoutthe signal present, and then measure signal and noise together.Subtraction of the noise voltage from the total yields the signalvoltage.

Appl. Note 60 Patic 7

As discussed previously, the rms-responding meter providesthe most reliable indication while the peak-responding meteris unsatisfactory to a degree which depends on the amplitudeof the noise. The average-responding meter handles signalsplus noise fairly reliably. The response of rectifier diodes tonoise is not linear, however, so care should l>e exercised. Asa practical matter, though, if the signal-to-noise ratio isgreater than 5, the error in the readings is no greater thanother voltmeter errors.

A NOTE ON METER SCALES

Most ac voltmeters have three scales printed on the meterface, as shown in Fig. 10. Two voltage scales are providedto accommodate the 1-3-10 range switching sequence commonlyused. This allows the lowest one-third portion of one rangeto be expanded to full scale by switching to the next lowestrange. Meter readings therefore may always be taken in theupper two-thirds of the scale for highest accuracy. The -hp-Model 410C uses a 5-15-50 range sequence so that the com-monly found 115 volts will lie in the upper portion of the scale(150 volt range).

The ratio between the two voltage scales was chosen tocorrespond to a 10-db difference between scales so that onlyone decibel scale is necessary. The decibel scale, however,corresponds to power and it provides a valid reading only

when the meter reads the voltage across the appropriateimpedance. For the convenience of comnuini eat ions personnel,where db readings are widely used, the 0 db mark commonlyis set to 0 dbm, equivalent to the voltage developed across a600 ohm resistor when dissipating 1 mill iwatt (0.77,") v ) . The-hp- 411A RF Voltmeter, on the other hand, establishes the0 db level at 1 milliwatt across 50 ohms for convenience inworking with HF systems.

Logarithmic scales commonly are achieved with a metermovement having pole pieces shaped so that deflection sensitivitybecomes progressively less as deflection increases. The lowerparts of the voltage scales are thus expanded so that percentageaccuracy is constant across the whole scale, rather than being afixed percentage of full scale deflection. At the same time, thedecibel scale becomes linear. Since this type of meter is mostwidely used in communications, the db scale is placed on theoutermost circumference.

The attainable accuracy of a high-quality electronic voltmeteris determined primarily by the accuracy of the meter calibra-tion. High accuracy meters, such as the Hewlett-PackardModel 400H, use individually-calibrated meters. To i m p r i n treading resolution when this accuracy is available, a larji i ' rmeter face is used and a mirror-scale is included to minimi/eparallax errors in reading,

Based on material appearing in EDN- -November 1963 Test

Instrument Issue, "Which AC Voltmeter?" by Howard L. Roberts

FIG. 10-Meter face of typical average-responding meter with 1 - 3 - 10 range sequence (lefl). Meter at right has

logarithmic response with scales expanded towards low end of range.

Page 1A-1 Appl. Note 60

APPENDIX I

If there were "n" discrete values in a seriesof measurements, the rms value is found bysquaring the value of each measurement, add-ing the squared values, dividing by thenumber of discrete values to find the averageand taking the square root of the average.Mathematically, this is expressed as:

If the quantity being measured were a con-tinuous function, such as a voltage waveform,the summation process is replaced by inte-gration. Then the rms value is expressed as:

2 d t

where the measurement is carried outthrough the interval 0 to t.From this, the rms value of one half-cycleof a sine wave is found:

E = / J -™» ./ ff

The average value of a quantity is simplythe algebraic average of values taken through-out the period of interest. If there were "n"discrete values within this period, this wouldbe described simply as:

= — t11 /' = !

If the quantity varies continuously, theaverage value is defined mathematically as:

- | fyd.t }'

Note that the inertia of the meter movementof an average-reading voltmeter performsthis integration.

The average value of one half-cycle of asine wave then is:

E B W = -: r^""**1*TT Jfi

9= — E

TT max

= 0.636 E_,

= 0.707 K

Appl. Note 60 Page 2A-1

APPENDIX II

Keprint of material appearing in H-P Journals -• Vol 6 No's 8, 9 & 10 Apr, May & June 1955,

"Some Effects of Waveform on VTVM Readings" by B.M. Oliver

Some Effects of Waveform on VTVM Readings

WHEN using a vacuum-tubevoltmeter calibrated in rms

values, how is the peak-to-peakvalue of a square wave obtainedfrom the voltmeter reading? Orwhat is the effect on the reading ofthe presence of 10% third harmonic?In practice, numerous questions suchas these occur as to how waveformsother than pure sine waves influencethe voltmeter reading. Before ques-tions of this nature can be answered,however, it is necessary to know theopsrating principle of the voltmeterbeing used.

•hp- voltmeters are of two types:those in which the meter deflectionis proportional to the average valueof a rectified cycle of the appliedwaveform and those in which thedeflection is proportional to thepositive peak value. Equivalent cir-cuits of these types are shown in Fig.1. In the -hp- average-reading typethe applied waveform is amplified

HIGH Z •*

AVERAGE READING

( A )

PEAK READING

( 8 )

Fig. 1. (a) Average-reading type circuitused in -hp- 400 series voltmeters to ob-tain relative freedom from u'aveformeffects as discussed in accompanying arti-cle, (b) Peak-reading type circuit used in-hp- 410 voltmeters. Although this circuithas greater sensitivity to u-aveform effects,it is possible, through suitable design tooperate the circuit up to hundreds ofmegacycles as in the -hp- 410B 700-mega-

cycle voltmeter.

to a convenient high level. It is thenrectified and the resultant currentpulses applied to a d-c milliammetercalibrated in terms of the input volt-age. The ballistic characteristics ofthe meter integrate the moments offorce in the meter movement to pro-duce a steady deflection of the meterpointer. Any d-c component in theapplied voltage is excluded from themeasurement because of the inputblocking capacitor.

In the -hp- peak-reading type cir-cuit (Fig. l[b}) the positive peak ofthe applied waveform charges acapacitor through a diode. The re-sulting d-c voltage, or a knownfraction of it, is then applied to astabilized d-c amplifier. A voltage-calibrated meter monitors the ampli-fier output. Again, any d-c compon-ent is excluded.

Both of these circuits are calibrat-ed so that they indicate the rmsvalue of an applied pure sine wave.That is, the average-read ing typereads 1.11 times the average value ofa rectified cycle of any applied wave;the peak-reading type reads 0.707times the positive peak. The rmscalibration of (or scale used with)both meters applies as long as theinput is a pure sine wave. But whenthe meters are used to measure com-plex waves, the readings must becorrectly interpreted because theratios of rms to average and rms topeak are usually not the same in acomplex wave as in a sine wave. Ingeneral the average-read ing metergives readings on complex waveswhich are closer to the true rmsvalues than does the peak readingmeter.

EXTREMES OF ERROR, AVERAGE-READINGMETERS

In a square wave the unique re-lation exists that the average, rms,and peak values are all the same.

-hp- Model 400D 10 cps - 4 megacyclevoltmeter uses average-reading type

circuit.

(b)-hp- Model 41 OB 700-megacycle volt-meter uses peak-reading type circuit.

Fig. 2

Since an average-read ing meter in-dicates 1.11 times the average value,it will indicate 11% high far the rmsvalue of a square wave. Further, asquare wave has the lowest ratio ofrms value to absolute average valueof any wave. It follows, then, that anaver age-read ing meter will neverread more than 11% high.

At the other extreme consider aseries of short duty cycle pulses hav-ing a given rms value. As the dutycycle approaches zero, the pulseamplitude need only increase as

Page 2A-2 Appl. Note 60

I/A/duty cycle to keep the rms valueconstant. Thus, the absolute averagevalue of the wave approaches zero.It Is conceivable, then, that an aver-age-reading meter would indicateas much as 100% low. Excludingshort duty cycle pulse waveforms,however, an average-read ing meterseldom reads more than 20% low oncomplex waves.

SECOND HARMONIC WITHAVERAGE-READING METERS

The accuracy with which an aver-age-reading meter will indicate therms value of a wave with harmoniccontent depends not only on theamplitude of the harmonic but onits phase and order as well. In thecase of a wave with second harmoniccontent, the difference between thetrue rms value of the wave and thereading indicated by an average-reading voltmeter will be small formost waves encountered in practice.

Fig. 3 shows the calculated rangeof absolute average values of a waveconsisting of a fundamental withvarious amounts of second har-monic. The upper and lower limitsof the shaded area are determined bythe phase of the harmonic withrespect to the fundamental. Con-sider, for example, a wave consistingof a fundamental combined with an"in-phase" second harmonic, i.e., asecond harmonic whose zero-axisintercepts coincide with the corres-ponding fundamental intercepts asshown in Fig. 4(a). In each half cycleof the fundamental, the second har-monic contributes a positive compo-nent and a negative componentwhich are equal in area and so donot alter the average value of therectified wave. An in-phase secondharmonic will thus cause no changein the meter reading until the har-monic reaches a value such that itsinitial slope (slope at 0, 2-rr, 4ir, etc.,radians) exceeds the slope of thefundamental. For such higher slopes

the complex wave acquires addi-tional crossings of the zero axis.When this happens, the harmonicadds area to the rectified wave andthe average value begins to increase.Since the initial slope of a secondharmonic does not exceed the slopeof the fundamental until the har-monic reaches a value of 50%, theaverage value of the wave will re-main constant until an in-phase sec-ond harmonic reaches this value.The lower boundary of the shadedarea in Fig. 3 shows this case.

The condition for which a secondharmonic will cause the averagevalue of the complex wave to followmost closely the rms sum of the com-ponents is where the harmonic has a"quadrature" relation to the funda-mental, i.e., the peaks of the har-monic occur at thet ime the f u n d a -mental interceptsthe zero axis, asillustrated in Fig.4(b). This is alsothe condition usu-ally encountered inpractice. A squarelaw term in a trans-fer characteristic,for example, pro-duces a quadraturerelation for the sec-ond harmonic.

The calculatedaverage values fora wave consistingof a fundamental

RESULTANT WAVE

IN PHASE HARMONIC(A)

QUADRATURE HARMONIC(B)

Fig. 4. (a) In-phase harmonic causes low-est readings on average-reading volt'meter, (b) Quadrature harmonic causesaverage-reading voltmeter to follow rmsvalue most closely. Quadrature relationis case usually encountered in practice.

1.3

10

EFFECT

AVFftAf,

OF 2ND HARMONICON

E READING METER

raw /?«s sun

f~RHS

S~~*

1>^£^^-' .-•'

-f\

RE)

*

S

OIHG

/'

^

mmtmi MS

i 10 20 30 40 50 60 TO 00 90 10

PERCENT 2 N D H A R M O N I CFig. 3. Calculated limits (shaded area) of absolute averagevalue of wave consisting of fundamental and various amountsof second harmonic. Small circles show experimental verifi-cation of calculated data. Dashed line shows true rms value.

with various amounts of a quadra-ture second harmonic are plotted inFig. 3 as the upper boundary for theshaded area.

The calculated data in Fig. 3 wereverified experimentally by establish-ing a "fundamental" and a "secondharmonic" and adjusting these sothat they caused a slow beat on an-hp- 400D average-reading typemeter. The limits of the beat werethen observed. The data obtained inthis manner are plotted as small

circles on the curve. The close agree-ment is apparent.

In examining Fig. 3 it will be seenthat for second harmonics of typicalmagnitudes the average-readingtype meter will give readings quiteclose to the true rms sum. For a sec-ond harmonic of 25% magnitude,for example, the error of the average-reading meter is but 3% and thisapplies in the case of an in-phaseharmonic. With a 10% second har-monic, the error is less than 1%.

Appl. Note 60 Page 2A-3

THIRD HARMONIC WITHAVERAGE-READING METERS

A wave consisting of a fundamen-tal and the third harmonic causesconsiderably greater variations inthe reading of an average-readingtype voltmeter than does a wavewith second harmonic content. Thisis shown in Fig. 5. Whereas thereading of the meter on a wave con-taining second harmonic is alwayslower than the rms value, the read-ing with a wave containing thirdharmonic can be either high or lowfor harmonic contents up to amounts

as high as 75%.In the case of a wave having third

harmonic, the maximum area underthe complex envelope and thus themaximum meter reading occur whenthe harmonic contributes the areaof an extra half-cycle (Fig. 6{a]) of

1 i

1.2

EFFECT OF 3RD HARMONICON

AVERAGE READING METER

20 30 40

PERCENT

60 70

H A R M O N I C

Fig. 5. Calculated limits of absolute average values of u'afeconsisting of fundamental with various amounts of thirdharmonic. Small circles show experimental verification of

calculated data.

the harmonic to the total waveform.This situation determines the valuesof the upper boundary of the shadedarea in Fig. 5. The minimum aver-age area occurs when the harmonicsubtracts the area of one-half cycleof its waveform from the funda-mental. This determines the lower

boundary for the shaded area for

harmonic content up to 33i%.For more than 33i% third har-

monic slope reversals occur as beforeand the extra added area causes the

lower limit to begin to rise.

The calculated data in Fig. 5 wereverified experimentally in a mannersimilar to the verification for Fig. 3-The results are plotted in Fig. 5.

Not only does the third harmoniccause greater variations in the meterreading than the second harmonic,but, it will cause greater variationsthan any other harmonic. The ex-tremes of error with "small amounts"of odd harmonics are given by thepercentage of the harmonic dividedby the order of the harmonic. "Smallamounts" of harmonic in this casecan be defined as percentages lessthan 100 n where n is the order ofthe odd harmonic.

It should be noted that, for typi-cal amounts of this worst harmonic,the third, the accuracy of an average-reading meter is still good. Third

harmonics up to10%, for example,can cause errors ofup to only 3.3%.

COMBINED HAR-MONICS WITHAVERAGE METERS

When more thanone h a r m o n i c ispresent in the ap-p l i e d wave, them a t h e m a t i c s ofeach case becomesmore complicatedand the number ofcases is increasedtremendously. As aresult no analyticstudy of the situa-

tion has been made.Some experimental data have been

compiled, however, for the case of

combined second and third harmon-ics with various amounts of funda-mental. This case is of interest indistortion measurements made bythe fundamental rejection method.

The data are shown in the second,third, and fourth curves of Fig. 7 forwaves containing second and thirdharmonics in variousratiosof funda-mental from infinite fundamental(i.e., zero harmonics) to zero funda-mental (i.e., infinite harmonics).

R E S U L T A N T *AVE

M A X I M U M A R E A( A )

RESULTANT WAVE

MINIMUM AREA

( B )

Fig. 6. In-phase (a) and out-of'phase (b)third harmonic. In phase relation gives

more accurate readings.

The shaded areas represent the ex-tremes of readings (as per cent oftrue total rms) obtained as the phaseof the fundamental varied with re-spect to the harmonics. For thesecurves the second and third "har-monics" were adjusted to be offfrequency with a slow beat of ap-proximately 1 cps. Then the funda-mental frequency was adjusted tobeat at 0.1 cps with respect to thiscombination. The extremes of de-flection were then noted during thecourse of many complete cycles ofthe lowest beat frequency. The dataobtained are plotted as the limits ofthe shaded areas. The shaded areasthus give the extreme errors for allrelative phases of the fundamentaland second and third harmonics.

These curves show the tendencyof an average-reading meter to readlow on complex waves. When theinput consists of many inharmoni-cally related sinusoids, the error ap-proaches that for gaussian noise,which is about 11% low as will beshown later.

EXTREMES OF ERROR,P E A K - R E A D I N G METERS

With peak-reading type meters,the limits of error can theoreticallyrange from 100% low to infinitelyhigh. Consider, for example, thepulse waveform shown in Fig. 8.

Page 2A-4 Appl. Note 60

20 30 40 50 60 70 90 100 100 90 80 TO 60 50 40 30 20 10

P E R C E N T = H U R H O H I C S ( H H S )

F U N D A M E N T A L ( R M S )P E R C E N T -

F U H D H H E m i ( R M S )

H A R M O N I C S ( R M S )

Fig. 1. Data showing effects of harmonics in various amounts and combinations on average-reading type voltmeter. Curves for 2nd only and 3rd only on both halves of figure are calculatedand experimentally confirmed as explained in text. Note change of scale in right half of figure.

This waveform can be shown cohave an mis value

where 8 is the duty cycle '/>. Sincethe actual meter deflection is pro-portional to the peak value of thewaveform, the ratio of E,,eak to EM11B

will show the operation of the meter

'8(1-8)

Thus, if the waveform has a lowvalue for 8, the duty cycle, the meterreading will, in the limit, be infi-nitely high. If the duty cycle has arelatively large value approachingunity (i.e., the pulses will become

h

Fig. 8. Pulse u-aveform defining valuesused in text.

Appl. Note 60 Page 2A-5

what are usually considered to benegative pulses), the meter readingwill approach zero or be 100% low.

HARMONICS WITHPEAK-READING METERS

Since the deflection of a peak-reading meter is proportional to thepeak of the applied waveform, themaximum reading will be obtainedon such a meter when the relativephases of the wave components aresuch that a peak of the harmoniccoincides with the peak of the fun-damental. The maximum readingfor a given magnitude of harmonicwill thus be the same regardless ofthe order of the harmonic. The ratioof this maximum to the fundamentalis plotted as the upper curve in Fig. 9.

The minimum val-ue that the peak canhave will be obtainedwhen a peak of theharmonic is in phaseopposition to thepeak of the funda-mental. The lowestminimum peak val-ues will be obtainedwith low order har-monics. As the orderof the harmonic isincreased, the mini-mum peak value willincrease until it ap-proaches as a limitthe maximum peak value, i.e., whenthe fundamental and harmonic peakscoincide. The reason that the mini-mum reading finally increases as theamount of the harmonic is increasedis that the harmonic ultimatelycauses neighboring peaks to beformed (see Fig. 6{a}). These arewhat the meter then responds to, andtheir amplitude increases with in-creased harmonic. The higher thisorder, n,of the harmonic, the smaller

mum possible reading of the meter.Higher harmonics will give mini-mum reading curves that progres-sively approach the curve for themaximum possible reading.

If the error in Fig. 9 for a peak-reading meter is compared with thatin Figs. 3 and 5 for an average-read-ing meter, the superiority of theaver age-read ing meter in approxi-mating the true rms value of thewaveform will at once be apparent.

AVERAGE AND PEAK METERSWITH A-M WAVES

If an average meter is being usedto measure an amplitude-modulatedwave, the meter will, if the modula-tion is linear, read the rms of theaverage or unmodulated carrier.

30 40P E R C E N T

50 60 TO

H A R M O N I C

Fig. 9. Curves shou-ing maximum and minimum readingspossible on peak-reading meter u-hen applied uave consistsof fundamental it-ith various amounts of harmonic content.

A peak meter will read the rmsvalue of the peak r-f amplitude.

The two meters can thus be com-bined to make readings of the per-centage modulation of the modulat-ed wave, because percent modulationis equal to 100 \.(El,,.ak/Ea^.,HK,.)—l}.

AVERAGE AND PEAKMETERS WITH HUM

It often happens that a smallamount of hum is combined with thevoltage to be measured. When the

/100\ frequency to be measured is rela-is the percentage I , ) at which • , . . , - , ,v n2 ' tively high with respect to the humthese peaks first form.

The two lower curves in Fig. 9show the error possible when thephases of the second or third har-monics are such as to cause the mini-

frequency, a small amount of humsuch as 10% will increase the read-ing of an average type meter byabout one-half as much as it wouldincrease the reading of a true rms

meter. (Thus, 10% hum will givea reading which is 1.0025 times thereading without hum, i.e., an in-crease of only i%.)

A peak-reading meter, on theother hand, will add the hum volt-age linearly to the desired voltage.The meter reading will thus be highby an amount approximately equalto the hum amplitude (10% hum willresult in a meter reading of 110%).

AVERAGE METERS WITHGAUSSIAN NOISE

The voltage of thermal noise ischaracterized by a probability dis-tribution which is of gaussian shape.Shot noise will also have a gaussianprobability distribution if the aver-age number of shots per second ismuch greater than the bandwidth incycles per second. Impulse noise be-haves as shot noise only if the im-pulses are totally independent andoccur at random times. Rectifiedgaussian noise as obtained from anenvelope detector does not have agaussian distribution.

The indication of an average-read-ing meter on noise can be calculatedas follows. The rectified d-c voltageV,, from noise will be

V0 = vp(v)dv = vp{v)dv

where the second integral followsfrom the first if p(V) is symmetricalabout zero.

If the noise is gaussian, the prob-ability p(V)dV that the instantane-ous voltage lies between V and V +dVis:

p(V)dV dV

where a is the rms noise voltage.Substituting this into the expressionfor V,, gives

/-oo V *

y Z

"a/2^

2<r

Ve dv

Since the meter is calibrated to readthe rms value of a sine wave, the

Page 2A-6 Appl. Note 60

indicated voltage V, :: 1.11 (i.e.,

7 r~ ) times V,,, where V., is the

average or rectified value. Thus,

For gaussian noise this becomes

= 0 866 or - I . O S d b

Average-reading meters thus read 1db low on gaussian noise providedthat no overload occurs on the peaks.

PEAK METERSWITH GAUSSIAN NOISE

The reading of a peak meter ongaussian noise depends on the effi-ciency of rectification, i.e., on theratio of the resistance through whichthe input capacitor is charged tothat through which it is discharged.If the noise is extremely wide bandcompared with the reciprocal of thecharge and discharge time constantsof the meter, the reading will besteady and found as follows:

dischorge ~ charge

where R(, — discharging resistanceRr — charging resistanceV0 = rectified d-c value of

• c .CTVr

Vfl dv

£. 2 C T *

v 0C

-°- is the ratio of rectified d-c to the(7

true rms of the noise. If the meter iscalibrated to read rms on a sinewave, then V,, = \/2 Vi where V, isthe indicated rms. Hence

Rd—RC

where K = _indicoted_ rmsTrue rms

nose

The factor K is plotted as a func-tion of R,, R, in Fig. 10. This curveallows one to estimate the correctionfactor to be applied to the readingof a peak meter to get the rms of agaussian noise input. The approxi-mate region of the curve applicableto the -hp- 410B is marked.

Although the curve is useful sinceit is quite flat in the region of inter-

est, several considerations dictatethat it should be used only for roughestimating. For one thing the charg-ing resistance is rather uncertain inmost cases since it depends on diodeperveance and current. Further, withvery high R,t R, the current drawn

•

• PEAK READING HE..GAUSSIAN NOISE 1

^X

TERPUT

rtt

«(S*-wrou

^-'

10* WJ 10* 101 »*

Fig. 10. Plot of correction factor for peak-reading meters ivhen used to measure rmsvalue of gaussian noise. Portion of curveapplicable to -hp- Model 410 is marked.Curve should be used only for rough

estimating.

by the diode is infrequent and largeso that loading on the circuit by themeter tends to suppress the highpeaks and decrease K. Finally, thecurve is predicated on the probabil-ity distribution being gaussian outto the tips of the distribution. Anyamplifier non-linearity will changethe distribution.

-B, M. Oliver

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2nd Floor, Suite 13Casablanca Buildings196 Adelaide TerracePer th . W A. 6000Tel 21-3330

CEYLONUnited Electiicili Lid.P.O. Boi 681Yahala BuildlnfStaples StreetC.l.-i*. 2Tel: 54%Cable HOIPOINT Colombo

FRANCEHewlett-Packard FranceQuartier de CourtaboeulBolte Poslile No. 691 OrsayTel: 920 88 01Cable: HEWPACK OriayTHei: 60048

Hewlett-Packard France4Quai det Etro i ts69 lyao SimeTel: 42 63 45Cable HEWPACK lyonTelei: 31617

GERMANYHewlett-Packard Vertrlebs-CmbHLie tze nbu r je r s Ir as se 30I Berlin W 30Tel: 24 60 65/66Telei: 18 34 05

Hewlett. Packard Vertrlebs GmbHHerrenbergerslrasse 110703 BMNngtn, WiirltembergTel. 07031-6671Cable: HEPAG Brjblingen

Telei: 7265 739Hewlett-Packard Vertrlebs GmbHAchenbachslrasse 154 DUiseldorl 1Teh 68 52 58/59Telei: 85 86 533

Hewlett-Packard Verlrlebi-GmbHBerliner Straise 1176 Frankfurt Nieder-EschbaehTel: 50 10 64Cablt: HEWPACKSA FrankfurtTelei: 41 32 49

AUSTRALIACYPRUSKypronlci19-190 Hommer AvenueP.O. Boi 752NlcniaTel: 6282-75628Cable: HE-l-rUMI

ETHIOPIAAf r i can Salespower & Agency

Private Ltd., Co.P. 0. Boi 71858/59 Cunningham St.Addis AbabaTeh 12285Cable: ASACO Addisababa

HONG KONGSchmidt S Co. (Hong Kong) Ltd.P.O. Box 2971S11, Prince's Building10, Chater RoadHani KoniTel: 240168, 232735Cable: SCHMIDTCO Hong Kon|

INDIAThe Scientific Instrument

Co. Ld.6, Tej Bahadur Sapru RoadAllahagad 1Tel: 2451Cable: SICO AllihbadThe Scientific Instrument

Co., Ltd.12 5 Dickenson RoadBmialore -1Cable: SICO BangaloreThe Scientific Instrument

Co , Ld.240. Dr. DadaOhai Naoroji RoadBombay 1Tel: 26-2642Cable. SICO BombayThe Scientific Instrument

Co., Ld.11, Esplanade EastCalculi) ITel: 23-4129c,M>it sico CalcuttaThe Scientific Instrument Co., Ld.30. Mount RoadMadras 2Tel: 86319Cable: SICO Madiat

Hewlett-Packard Verthebs-CmbHSeim Strahhause 262 Hamburg 1Tel: 24 05 51/52Cable HEWPACKSA HamburgTHei: 21 5312

Hewlett-Packard Verlrlebi-GmbHReglnfrleditrasse 138 Miinchtn 9Tel: 0811 69 59 71/75Cable: HEWPACKSA MiinchenTelei: 52 49 85

GREECE

IB. Ermoii Streeta them 126Tel: 230 301Cable: RAKAR AthensTelei: 21 59 62

IRELANDHewlett-Packard Ltd.224 Bath RoadSlough, Bucks. EnglandTel: Slough 753-31341Cable: HCWPIE SloughTelei. 84413

ITALYHewlett-Packard Italians S.p.A.Via Amerigo Vespucci 220124 MilanTel: 6251 (10 lines)Cable: HEWPACKIT MilanTelei 32046

The Scientific Instrument Co. Ltd.5 8-525 Mahatma Gandhi RoadHyderabad. 1 lA-PHndlaCable: SICO Hyderabad

The Scient i f ic Instrument Co., Ld.B-7. Ajmerl Cite Eiln.Hew Delhi 1Teh 27-1053Cable: SICO New Delhi

INDONESIABah Bo Ion Trading Coy, N VOjalah Merdeka 29Bandung

IRANTelecom, Ltd.P. 0. Bo> 1812240 Kh. Saba ShomallTeheranTel: 43850, 48111Cable: BASCOM Teheran

ISRAELElectronics t Engineering

Div. of Motorola Israel Ltd16, Kreroenetikl StreetT*l-AvlrTel: 35021 (4 lines)Cable: BASTEL Tel-AmTele* Bastel TV 033-569

JAPANYokogawa Hevdelt-Packard Lid,Nisei Ibaiagl Bldg.2-2-8 KasugaIbaragi-ShiQua*Teh 23-1641

Yokogawa-Hewlelt -Packard Ltd.Ito BuildingNo. 59. Koton choNakamura-ku, Nagiya CityTel: 551-0215

Vokoi;a*a. Hewlett-Packard Ltd.Ohashi Building59 Yoyogi 1-chromeShibuya-ku, Tiki*Tel: 370-2181/7Telei: 232-2024YMPCable. YHPMAJtKET TOK 23-724

Hewlett-Packard Ital iana S.p.A.Palauo ItaliaPiana Marconi 2500144 R«me - EurTel: 591 2544Cable: HEWPACKIT DomeTelei 61514

NETHERLANDSHewlett-Packard Benelui. N.V,Weerdestein 117Amiterdam, Z 11Teh 42 77 77Cable: PALOBEN AmsterdamTelei: 13 216

NORWAYHewlett-Packard Nor ge A/SBoi 149Nesieien 13HailvnTel S3 83 60Cable: HEWPACK OsloTele. 6671

PORTUGALTelectraRua Rodrigo da Fonseci 103P 0. Boi 2531L i sbon 1Tel: 6B 60 72Cable: TELECTRA LisbonTelei: 1598

KENYAH. J. Tilbury Ltd.P. 0. Boi 2754Suite 517/518Hotel Ambaisadeur•MlTel: 25670. 26803. 68206, 58196Cable: AR1AYTEE Nairobi

KOREAAmerican Trading Co., Korea. Ltd.P.O. Bo. 1103Dae Kyung Bldg.107 Sejong RoChongro KuStemTel: 75-5841 <4 linet)Cable: AMTRACO SeoulLEBANONConstantin E. MachdiiClemenceau StreetP.O. Boi 7213BeirutTel: 220846Cable: ELECTRONUCLEAR Beirut

MALAYSIAMECOMB Malaysia Ltd.2 Loron( 13/6ASection 13Peta l in* Jaya. S( Ian torCable: MECOMB Kuala Lumpur

MOZAMBIQUEA. N. Goncalvei, LDA.4.1 Apt. 14 Av. 0. lullP.O. Boi 107Laurenc* MaiqueiCable NEGON

NEW ZEALANDHewlett-Packard (H.I i Ltd.32-34 Kent TerraceP.O. Bo. 9441Wellington. N.I.Tel: 56-409Cable HEWPACK Wellington

PAKISTAN (EAST)Mushko & Company. Ltd,31. Jmnah Avenue0»«aTel: 80058Cable: NEWDEAL Dacca

SPAINAtaio IngenieroiGanduier 76Barcelona 6Tel: 211-44-66Ata io IngenierosEnrloue Laneta 12Madrid. 16Tel: 235 41 44Cablt: TELEATAIO MadridTelei: 2 72 49

SWEDENHewlett-Packard (Sverige) ABHagakersgatan 9CS 411 04 Mtlndil 4Tel: 031 - 2 7 6! 00

Hewlett-Packard {Sverige] ABSvelsarvlgen 7S171 20 Solna 1Tel: (08) 98 12 50Cable: MEASUREMENTS

StockholmTelei: 10721

SWITZERLANDHewlett Packard (SchweH) AGZurcherilrasse 20895 2 SchlierenZirlcnTel: [0511 98 18 21/24Cable: HEWPACKAG ZurichTelei: 53931

PAKISTAN (WEST)Mujhkd & Company, Ltd.Oosman ChambersVictoria RoadKarachi 3Tel: 51027. 52927Cable: COOPER ATOR Karachi

PHILIPPINESElectronic! Inc.2129 Pasong TamoMakati. RlialP.O. BOi 4126ManilaTel 88 91 71 or 88-81-76Cable: ELEMEX Manila

SINGAPOREMechanical and Combustion

Engineering Company Ltd.9, Jalan KllaniSinfapvre, 3Tel: 642361-1Cable: MECOMB Singapore

SOUTH AFRICAHewlett Packard South Africa

(Pty.). Ltd.Hill House41 Somerset Rd.Cape TawnTel: 3 6019Cable: HEWPACK Cape TownTele1; 7018CTHewlett Packard South Africa

(Pty.). LM.P.O. Bo* 3171630 De Beer StreetBraimfontein, JohannesburgTel: 724-4172 724-4195Telei: 0226 IHCable: HEWPACK Johannesburg

TAIWANHwa Slieng Electronic Co., Ltd.P.O. Boi 1558Room 404Chia Hsin BuildingNo. 96 Chung Shan

North Road. Sec. 2TaipeiTel 555211 Eit. 532539Cable: VICTRONIX Taipei

Hewlett Packard (Schweii) A.G.Rue du Bois du-Lan 71217 Meyrin-GanevaTeh (022)41 5400Cable HEWPACKSA GenevaTelei: 2 24 86

TURKEYTelekom Engineering BureauP.O. Boi 376-GalataIstanbulTel: 49 40 40Cable: TELEMATION Istanbul

UNITED KINGDOMHewlett-Packard ltd.224 Bath RoadSlough. BucksTeh Slough 33341Cable: HEWPIE SiouthTelei: 84413

YUGOSLAVIABel ram S.A.83 avenue des MimosasBrusieli 15. BelgiumTeh 14 13 32, 34 26 19Cable: BELRAMEL BrusselsTelei: 21790

FOR AREAS NOT LISTED,CONTACT:Hewlett-Packard S.A.Rue du Bois-du Lin 71217 Meyrm-GeneiaTel: (022) 41 54 00Cable.- HEWPACKSA GenevaTelei: 2.24.86

TANZANIAR. 1. Tilbury Ltd.P.O. Boi 2754Suite 517/518Hotel AmbassadeurNairobiTel: 25670, 26801. 68206. 58196Telei: INTENCO BK 226Cable. ARMYTEE Nairobi

THAILANDThe International

Engineering Co., Ltd.P. 0. Bo* 19614 Sukhumvlt RoadBangkokTel: 910722 <7lmei)Cable: GYSOM Bangkok

UGANDAR. J. Tilbury Lid.P.O. Bo< 2754Suite 517/518Hotel AmbassadeurKairotJiTeh 25670. 26803. 68206, 58196Cable: AR1AYTEE Nairobi

VIETNAMPeninsular Trading Inc.P.O. Boi H-3216 Hlen-VuongSilflflTel: 20.805Cable PENINSULA Saigon

ZAMBIAR. J. Tilbury (Zambia) Ltd,P.O. Bo< 2792LusakaZambia. Central Africa

FOR AREAS NOT LISTED,CONTACT:Hewlett-Packard Export

Marketing1200HillvlewAve.Palo Alto. California 94304Tel: (415) 326-7000TWJt- 9lQ-3f3-l2§7Cable HEWPACK Palo Al toTelii: 034-8461

F o r m o r e i n f o r m a t i o n . c « l ! y o u r l o c a l H P Sa l« i O f f i c e o r E a s t ( 2 0 1 ) 2 6 5 - 5 0 0 0 • M i d w e s t ( 3 1 2 ) 677 -0400 • South (404 ) 4 3 6 - 6 1 8 1W e s t ( 2 1 3 ) 8 7 7 - 1 2 8 2 Or, w r i t e : H • w I • tl- Pa c k a rd , 1501 P a q t Mill R o a d . Pdlo A l t o , C a l i f o r n i a Y 4 3 0 4 . In Europ . , 1 2 1 7 M • y r i n - G * n«va

Printed in U.S.A. 5952-2136

13 APRIL 1967