saturation flux cPsat (webers) by Emax. =1/v3 wN2epsat for Of= 137 degrees.

Weare discussing these "overlap phenom­ena and their prevention at length becausethe matter of simultaneous saturation ofreactors is of concern not only in the designof frequency multipliers but also in thebroader field of polyphase magnetic am pli­fier applications. (In fact, similar problemsoccur also in polyphase switching circuits,thyratrons etc.)

The au thors have recognized the useful­ness of less sensitive cores as a means to re­press overlap short circuits. But the analy­sis and design theory becomes much more in­volved when clean-cut concepts of firing areabandoned. This makes the practical in­formation given in the paper even moreinteresting.

REFERENCE

1. F. Spinelli. Italian Patent Office Patent No.12-1825, 1912.

L. J. Johnson and S. E. Rauch. The authorswish to thank the discussers for their worth­while addition to the paper. For the theo­retical case in which remanence flux is equalto the saturation flux, they are correct intheir analysis of the short-circuit conditionswhich would exist for a tripler between theangles of 120 to 137 degrees.

Rectangular core materials which arecommercially available today have a rema­nence flux ranging from 5 to 10 per cent lessthan saturation flux measured at one oer­sted, as quoted by Arnold Engineering Com­pany for their Deltamax material. Theaverage remanence flux is approximately 7per cent below the saturation flux measuredat one oersted. In the practical applicationof the best rectangular core materials tomagnetic frequency multiplication, the fluxchange above remanence is sufficient tolimit the cross-fire currents to magnitudesconsiderably less than rated load currents.For this reason the firing angle defined as

Of= [(n-l)/n]7I'" is a realistic evaluation.For magnetic frequency multiplication of

the type discussed in the paper, the cross­firing effects due to sharp saturation aremost pronounced for the tripler. As isstated in the third paragraph of the section"Core Materials," rectangular flux char­acteristics become increasingly desirablewith increasing multiplication factor n,As a consequence, the allowable limit of fluxchange above remanence can be reduced asthe multiplication factor increases.

The authors agree with Mr. Finzi and Mr.Feth that cross-firing is very important inmultiphase magnetic .amplifiers. The firingangle is controlled and varied in such casesby resetting the core while rectifiers blockthe current flow in the load circuit. Cross­firing limits the available reset time; there­fore it reduces the effectiveness of the ap­plied control voltage. In contrast, the mag­netic frequency multiplier has no similarcontrol reset function.

Accurate Tachometry Methodswith Electronic Counters

believed to be an approach to satisfyingall of them.

Tachometry by Time IntervalMeasurement

J. M. SHULMANASSOCIATE MEMBER AlEE

Synopsis: High-speed electronic countershave become commercially available withinthe past few years which indicate by meansof a display of neon-lighted figures, andcan count from 20 to 100,000 events persecond or more with an inherent accuracyof ± 1 count in the measuring interval.By relatively simple modifications of thebasic counting circuits in these instrumentsthey can also be used for measuring shortintervals of time to an accuracy of ± 10microseconds, The measured time intervalis displayed directly in figures indicatingthe decimal fraction of a second to thenearest hundred-thousandth. Tachornetryis a fruitful application of these instruments.Three methods of using the counters intachometry are described here, and thead vantages and limi tations of each methodare discussed.

AP ERSIST ENT problem of makingrapid, accurate speed measurements

on a large motor test floor led to the in­vestigation of the commercially availableelectronic counter as a tachometer. Indeveloping a form of tachometer suitablefor the particular test floor conditions in­volved, three tachometry methods wereinvestigated. Since each of the three sys­tems has advantages and disadvantagesfor any given application, all three willbe discussed with the aim of pointingthese out and indicating thereby the par­ticular applications in which each mightbe most useful. The importance of this

problem is attested by the considerableliterature on electronic tachometry.v'"However, prior to the use of the decimalelectronic counter7 most of the arrange­ments were too complicated and cumber­some for general use.

Eight criteria were set up as a basisfor determining the relative merit of dif­ferent tachometry methods:1. Can measurements be obtained at anyspeed within the required range to therequired accuracy?2. Can measurements be obtained withoutmechanical coupling to the shaft?3. Is human error minimized?4. Can measurements be taken by oneperson instead of two?

5. Can the equipment be used by relativelyunskilled personnel?

6. Can the equipment, particularly thepickup device, withstand mechanical abuse?

7. Can a change in measurements fromone shaft to another be made easily andquickly?

8. Is the reading obtained directly inrevolutions per minute (rpm)?

All the tachometry methods used priorto the electronic counter failed to meet oneor more of these requirements. Thefirst two electronic counter methods to bedescribed, while not meeting all the re­quirements, filled some of them out­standingly well. The third method is

In this method of determining shaftspeed, the time interval for 1 revolution ofthe shaft is measured and displayed inhundred-thousandths of a second by thecounter. Fig. 1 shows the block diagramof the system for doing this. The outputof a lOO-kc oscillator is fed through anelectronic gate to the counter input. Amagnetic pickup placed near the keywayon the shaft produces a signal whichstarts and stops the electronic gate on suc­cessive signal pulses produced as the key­way passes the pickup. The number ofcycles of the lOO-kcoscillator output per­mitted to pass through to the counterwithin the period of 1 revolution T R isthus numerically equal to T R in hundred­thousandths of a second. This number isdisplayed by the counter and repeated atany preset interval. The shaft speed inrevolutions per second is the reciprocalof the counter reading times 10.5

The time interval method has an in­herent accuracy inversely proportional tothe measured speed, as shown in Fig. 2.

Paper 54-290, recommended by the AlEE Instru­ments and Measurements Committee and ap­proved by the AlEE Committee on TechnicalOperations for presentation at the AlEE Summerand Pacific General Meeting, Los Angeles, Calif.,June 21-25, 1954. Manuscript submitted August21, 1953; made available for printing April 27,1954.

J. M. SHULMAN is with the Westinghouse ElectricCorporation, Sunnyvale, Calif.

Acknowledgment is made to Dr. W. A. Edson ofthe Stanford University Electronics ResearchLaboratory for helpful suggestions regardingmultiplier circuitry and for assistance in editingthe text.

452 Shulman-Accurate Tachometry Methods with Electronic Counters NOVEMBER 1954

~~~~DECIMAL

COUNTINGUNITS

r-I SECOND~

d L

-i t-I SECONDS

-lL_JlL~I SECONO-i

As shown by the block diagram in Fig.4, this is a method in which the counter

back on more convenient methods ratherthan put on and take off disks even whenadequate adapters are available. Thedesire to eliminate the disk was the mainmotivating factor which led to the de­velopment of the third method.

SHAFT SPEED- RPM

Direct-Reading Tachometer withElectronic Multiplier

TIME BASEGENERATOR

ELECTRONICGATE

~~

I.JI~

/

i//

/

/~V"

~

ILI~

/

V/

V

/V

I/./~

1/

V/

v

/~

1100 I;~OO tOpOO 50POO I()C >.:>00

MAGNETICPICKUP

.00

1.0....Zl&Joa:UJQ.I

~a::::>8cr o.....ZLLJ~LLJa::::>(/)<tLIJ:EoUJUJQ.

f/) .0

--i rMICRh~ECONOS--JV\Mtv---

-i r- &SECONDS

---JWHrffi--)........."....

60- oaTH STEEL DISK

100 KILOCYCLEOSCILLATOR

DECIMAL

~~U~UCOUNTING

UNITS

~ r- ~O SECOND

~-_-....I~--

SHAFT

60 CYCLE A-C LINE

Fig. 3. Direct-reading tachometer with mechanical multiplication to indicate 60 times therevolutions per second

disk can be attached. Also the problemof moving the disk from one shaft toanother may be a disadvantage if motorshaving many shaft sizes are to be tested.The practical importance of this particu­1ar point as i t relates to a motor produc­tion test floor is worth stressing. In thelaboratory, it is considered no trouble atall to put an attachment on a shaft fortachometry purposes. On a test floor,however, the operation is time-consum­ing ~ and test personnel will tend to fall

ELECTRONICGATE

QQ

~1iR--i ""-~TART-STOPI .. I SIGNAL INPUT

~

-i riO MICROSECONDS

1\f'v"v"vQJ'v"J\j

\100 KILOCYCLECRYSTAL ~----'--_""

OSCILLATOR

Fig. 3 shows the block diagram of anarrangement mechanically obtaining andthen counting 50 times the number ofshaft revolutions per second and thus dis­playing on the counter the exact rpm ofthe shaft. A 50-tooth steel disk mountedon the shaft is used with a magneticpickup to give a number of output pulsesper second numerically equal to rpm.These pass through an electronic gate tothe counter. The gate is opened andclosed by two successive pulses spaced atexactly 1 second from a time base gen­erator. Depending on the accuracy ofthe time base desired, the I-second timebase can be derived from either a IOO-kcoscillator or from a 50-cycle line fre­quency.

The main disadvantage of this methodis the necessity of having a portion ofshaft extension available on which the

Direct-Reading Tachometer withMechanical Multiplier

Fig. 2 (right. Theoretical maximum accuracy of speed measurement bytime interval

This is the theoretical accuracy based ona counting accuracy of ± 1 count in theinterval TR' Other errors in the systemmay raise the line slightly, but over thespeed ranges most commonly measured,between 100 and 10,000 rpm, the order ofaccuracy obtainable is higher than thatpossible with most nonlaboratory tachom­etry methods. At very high speeds itwould be possible to increase the accuracyby use of a higher frequency oscillator orby counting for more than 1 revolution.The high accuracy of this method, par­ticularly at speeds of 3,600 and lower, isits primary advantage. Its disadvan­tage is that it is not a direct-readingmethod.

KEYFJ /ET~ PICKUP

';JlrSHAfT '------------

Fig 1 (above). Block diagram of system for determining shaft speed bymeasurement of time interval for 1 revolution

NOVEMBER 1954 Shulman-Accurate Tachometry Methods with Electronic Counters 453

Locking Range,Per Cent of

Highest Frequency

5 to 1 13.54 to 1 14.83 to 1 22.62 to 1 25.2

Locking Ratio

Table I. Frequency Ranges for DifferentRatios

~~~~DECIMALCOUNTING

UNITS

ELECTRONICGATE

-l I-~ SECONDS

-JV\NVV\r- -.ll lL~I SECOND-i

\LOCKEDOSCILLATORS

--I r-TR SECONDS

Fig. 4. Direct-reading tachometer with locked oscillators controlling a count of 60 times therevolutions per second

l I L V60 SECOND

60 CYCLEO~A_-C_L_IN_E ~-AJV'v---

TIME BASEGENERATOR

Signal Pickup

A satisfactory pickup for getting sig­nals from a shaft keyway, or toothed disk,is essential to the success of any of the

with straight multipliers the accuracyis less because the in put to the counterconsists of series of pulses separated bygaps and the count is affected by thepoint in the sequence at which the meas­uring period starts.

It is convenient to use locking ratios of3, 4, and 5 to obtain a total multiplica­tion of 60. Fig. 5 shows a circuit usingphase-shift oscillatorsr"!" with circuitconstants for locking 3,600-cycle nominaloutput with 60-cycle input. In tests todetermine the frequency ranges overwhich these circuits will lock at differentratios, the results shown in Table I wereobtained:

To cover a speed-measuring rangegreater than the lowest locking range ob­tainable, it is necessary to provide meansfor changing the oscillator frequencieseither continuously or in switched steps.The latter method is convenient whenspeed measurements are to be made on a-cinduction motors only, since the slipwithin the loading range is usually lessthan 10 per cent.

J-I SECOND-..J

~

sion of a time interval, in this case theperiod of 1 revolution of the shaft, intoequal parts. This is essentially the sameaction that the disk accomplishes mechan­ically when its teeth are equally spacedaround its periphery. On the other hand,electronic multiplying circuits which pro­duce a discrete number of output signalsfor each input signal cannot do this."They would correspond in the mechanicalanalogy to a disk having its teeth extend­ing over only a portion of its periphery.In terms of speed-measuring accuracythis means that the use of synchronizedoscillators can give speed readings to theinherent accuracy of the coun ter, ± 1count in the counting interval, whereas

--f riO MICROSECONDS

---'\J\J\Mr--

100 KILOCYCLE \OSCILLATOR

counts and displays the number of cyclesper second of the last of a series of sinu­soidal oscillators. Each oscillator in theseries is locked by one of lower frequency,and the first one in the serie, is locked by al-pulse-per-revolution signal from theshaft. If the total multiplication of the se­ries is 60, the frequency of the last osci1la- .tor is numerically equal to the shaft speedin rpm. The arrangement shown in Fig. 4in effect substitutes an electronic circuitfor the 60-tooth disk in Fig. 3, and thusgives a direct-reading method without thedisadvantages of the disk.

Synchronized free-running oscillatorsused for multiplication of frequency inthis way can actually accomplish the divi-

60 CYCLEOSCI

180 CYCLEOSC.

720 CYCLEOSC.

3600 CYCLEOSC.

6AC7 6AC7 6AC7 6AC7

PICKUPINPUT

Fig. 5. Locked oscillator circuit for controlling 3,600 cycles nominal from 60-cycle nominal input signal

454 Shulman-Accurate Tachometry Methods with Electronic Counters NOVEMBER 1954

.2 .3.4.5.6 .7 .8 .9 1.0DISTANCE FROM PICKUP TO SHAFT -INCHES

"'\.Kaq,

'X,,-........"4

X<, \.

'-"", '"\.\2- ''-.~- -,,,~ "p 09 ,\.N:.o

K " ~\"-, r\\

~I'"" ,\. '\. -,

"' ... '\. "'~to , '\. I'~~L \" \ -,

.~ \ l\ '"" I~ \ ",

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~~ \ "\'-' \ '\.

~ \. "", \

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[\, , -,

108

6

.2

.04.I

.10

.08

.06

Fig. 7 (right). Pickupresponse characteris-tics: Solid line,with disk; dashline, with keyway

in shaft

o!:io 2>~c(

~ 1.0~ .8~ .6c(ILlCL .4

.3

4

3

Fig. 6 (left). Mag- 40netic pickup and 3060-tooth disk signalgenerator combina- 20

tion

Summary

three tachometry methods described.Photoelectric pickups of several typeswere tried on the test floor. Becausethey could not stand abuse and were diffi­cult to adjust and susceptible to straypickup, none of these were consideredentirely satisfactory. A rugged magneticpickup was designed for use with a 60­tooth disk, as shown in Fig. 6. Thispickup has enough sensitivity to be used1/2 inch or more from either the disk ora shaft, as shown in Fig. 7. The shapeof wave forms obtained in each case isshown in Fig. 8.

Fig. 8. Signal wave forms from pickup: (left) with disk; (right) with shaft keyway

From the standpoint of operating con­venience, the electronic tachometer showsreal worth on a production test floor,where it is usually impractical to makeand use a laboratory-type setup for get­ting accurate speed measurements. Thecounter portion of the electronic tachom­eter may be mounted on or near themeter board in such a way that the testercan take speed readings along with othermeter readings. A second operator isnot required to hold or watch the pickup,which can be mounted on a tripod adja­cent to the shaft and left alone. A co­axial cable suffices to connect the pickupwith the counter system. In the firstand third methods described, the pickupcan be moved quickly from one shaft toanother. Except for phase reversal thesignalgenerated by the pickup is the samewhether the keyway is open or filled witha steel key; therefore, speed can bemeasured whether or not the motor iscoupled to a load.

References

1. ELECTRONIC TACHOMETER, W. Richter. M a­chine Design, Cleveland, Ohio, vol. 21, no. 11,Nov. 1949, pp. 133-36.

2. PRECISION SPEED MEASUREMENT OF ROTATINGEQUIPMENT, M. W. Hellar, General ElectricRefJiew, Schenectady, N. Y., vol. 52, no. 10, Oct.1949, pp. 22-26.

3. PRECISION MEASUREMENT OF ROTARY MOTION,R. J. Flnden. Electronic Engineering, London,England, vol. 22, no. 263, Jan~ 1950, pp. 2-8.

•. A RECORDING TACHOMETER FOR MEASURING

INSTANTANEOUS ANGULAR SPEED VARIATIONS,S. P. Bartles. Electrical Engineering, vol. 70,Sept. 1951,PP. 816-19.

5. A NEW HIGH-ACCURACY COUNTER-TYPETACHOMETER, T. M. Berry, C. L. Beattie. ElectricalEngineering, vol. 69, July 1950, p. 605.

6. AN ELECTRONIC TACHOMETER, H. G. jerrard,S. W. Punnett. Journal of Scientific Lnstruments,London, England, vol. 21, Sept. 1950, pp. 244-45.

7. A NEW 100 KC COUNTER FOR USE IN ELEC­TRONICS AND INDUSTRY, E. A. Hilton, HewlettPackard Journal, Palo Alto, Calif., vol. 4, no. 3,Nov. 1952.

8. VACUUM TUBE OSCILLATORS (book), W. A.Edson. John Wiley & Sons, Inc., New York,

N. Y., 1953, chapters 13 and 14.

9. PHASE SHIFT OSCII.LATORS, E. L. Ginzton,L. M. Hollingsworth. Proceedings, Institute ofRadio Engineers, New York, N. Y., vol. 29, Feb.1941, pp. 43-49.

10. PHASE SHIFT OSCILLATOR DESIGN CHARTS,W. W. Kunde. Electronics, New York, N. Y.,Nov. 1943, pp. 132-33.

11. EXTENDING THE FREQUENCY RANGE OF THEPHASE SHIFT OSCILLATOR, R. W. Johnson. Pro­ceedings, Institute of Radio Engineers, New York,N. Y., vol. 33, Sept. 1945, pp. 597-603.

12. THE TAPERED PHASE SHIFT OSCILLATOR, P. G.Sulzer. Proceedings, Institute of Radio Engineers,New York, N. Y., vol. 36, Oct. 1948, pp. 1302-05.

NOVEMBER 1954 Shulman-Accurate Tachometry Methods with Electronic Counters 455

Discussion

R. M. Saunders (Dniversity of California,Berkeley, Calif.): To Mr. Shulman'sexcellent paper on tachometry methodsemploying some techniques of digitalcounting and display, I should like to adda note about the photoelectric methodwhich he dismisses as being an unsatis­factory test floor operation. While it istrue that photoelectric devices are moresusceptible to mechanical damage thaninductive devices, and that they generatespurious signals owing to ambient light,there are instances where no other type ofpickup can be used. When working withmachines whose power output is affectedby the variable magnetic reluctance effectsof the transducer or the windage of a disksimilar to that shown in Fig. 6, or whoseshaft is not equipped with a fiat-spot fora keyway '(or in some cases never broughtout), recourse to photoelectric methods isan absolute requirement. Such cases arisein dealing with actuators and transducersused in feedback control systems.

As a case in point, in our undergraduateelectrical machinery laboratory we offeran experiment on the' acceleration methodof measuring the torque of a gyrospinmotor. The terminal speed of this motoris 24,000 rpm and develops a maximumtorque of approximately 5 ounce-inches.In this case the tachometry is performedby cutting a small window in the housingof the gyro and inserting a clear plasticwindow. The rotor is then painted withsix alternate black and white segmentswhich are looked at by a photoelectriclight source and cell combination. Theou tput from the photoelectric cell is then

fed directly into the events-per-unit-timeindicator and the speed is then given intens of revolution on a 4-register counter.This motor takes 5 to 10 minutes to ac­celerate to full speed. During that timethere is an adequate period in which 100observations of the speed of the motorcan be recorded. By subtracting adjacentreadings, and knowing the moment ofinertia, the torque developed by the motorcan be obtained.

For application to larger motors, astandard strip of paper with 60 segmentshas been developed for use with our stand­ardized laboratory couplings. This stripof paper is glued on the couplings resultingin a display in rpm, thus performing thesame function of multiplication as Mr.Shulman's electronic multiplier.

Mr. Shulman has very nicely solved theproblem of the testing of large inductionmotors and other machines of fairly largesize on a test floor where, by the very natureof the equipment involved, the workmenare not sufficiently careful to use photo­electric pickups. The situations which Ihave described have been applied largelyto laboratory or testing precision equip­ment, where the care exercised is more the~aliber of instrument work, and the dangerfrom mechanical shock is greatly minimized.

]. M. Shulman: As Mr. Saunders pointsout, there are many applications where aphotoelectric pickup system might be betterthan a magnetic pickup, or where a mag­netic pickup might be ruled out entirely.The remarks about pickups were not in­tended to discourage the use of photoelectricpickups where they are applicable.

Mr. Saunders' comments on how he is

using the counter to obtain speed-torquecharacteristics on a motor having longstarting time are of interest. Accuratespeed-torque curves on large motors aredifficult to obtain by load testing, and theso-called inertia method in which angularacceleration is measured as a function oftime and plotted as a function of speedduring the starting period is potentiallya solution to this problem. The methodused by Mr. Saunders is of course muchtoo slow for most motors, which start ina few seconds or a fraction of a second.Considerable work, notably that of S. S. L.Chang of New York University, has beendone in making speed-torque curves byphotographing an oscilloscope trace, withthe use of electronic means to obtain speedas a function of time and to differentiatethe speed-time characteristic. H. W.Hansen of Westinghouse Electric Corp.,Sunnyvale, Calif. and the author havedeveloped a number of improvements inthis method and hope to present the resultsin the near future.

John Corl of Berkeley Scientific Division,Beckman Instruments Iric., Richmond,Calif., has pointed out that any system usingfree-running oscillators is not fail-safe.This is true and must be taken into accountwhen using the third method. Mr. Corlproposes that a fail-safe direct-readingtachometer could be formed by a digitalconverter which would measure the timeinterval, as described in the first method,and operate on this number by taking thereciprocal and multiplying by 6 X LG",where n is determined by the unit of timeused in the measurement. If this couldbe done at reasonable cost, it would forman ideal tachometer from the standpointof the requirements listed in the paper.

Networks For Digital-to-Analogue ShaFt­Position Transducers

s. J. a-NEILASSOCIATE MEMBER AlEE

switching components necessary. Thedirection of the magnetic field induced bythe stator voltages is compared with thedirection of the rotor coil axis. The rotorshaft turns through an angle proportionalto the digital input. Magnetic convert­ers of this type are inherently minor-arcsensing devices.

DIGITAL computers have been usedextensively in the solution of mathe­

matical problems requiring both speedand accuracy in their computation. Morerecently, digital computers are being em­ployed to control analogue equipment.The control of machine tools is one ex­ample of this application.'

In the solution of mathematical prob­lems it is often sufficient to present theoutput in the form of a table of numbers.In the control of analogue equipment,however, the digital computer outputmust first be converted to analogue formin order to vary some analogue input tothe controlled equipment.

The analogue-to-digital conversion

problem is as old as the digital computer.It is only recently that the inverse prob­lem (the digital-to-analogue conversion)has become important. This paper dealswith the networks required in a particulartype of digital-to-analogue shaft-positionconverter.

The converters (or transducers) forwhich these networks are designed havebeen described previously. 2 Alternatingor direct voltages which are approximatesine functions of the digital input are ap­plied to the stator windings of 2-phase or3-phase electromechanical machines, suchas resolvers or synchros. Approximatesine waves composed of straight-line seg­ments are used to reduce the number of

The Problem

The problem is to design networkswhich produce voltages which are ap­proximate 2-phase or 3-phase sine func­tions of a binary digital number. The

Paper 54-272, recommended by the AlEE Com­puting Devices Committee and approved by theAlEE Committee on Technical Operations forpresentation at the AlEE Summer and PacificGeneral Meeting, Los Angeles, Calif., June 21-25,1954. Manuscript submitted, March 11, 1954;made available for printing April 27, 1954.

S. J. O'NEIL is with the Parke MathematicalLaboratories, Jnc., Concord, Mass.

This work was accomplished at the Air ForceCambridge Research Center, with which theauthor was formerly associated. The author isindebted to R. P. Bigliano for the design of thebasic network for obtaining linear voltage waveforms.

456 0' Neil-Digital-to-A nalogue Shaft-Position Transducers NOVEMBER 1954