Function Generation WithUse of high-gain d-c amplifiers and voltage feedback to design accurate

electronic switches is applied to precision limiters, gates, comparators, multi-

vibrators, timers and integrator resetting circuits .. Present and future applica-

tions make the technique an important design tool

By H. KOERNER and G. A. KORN,

Dept. of Electrical Engineering, University of Arizona. Tucson. Arizona

(e)FIG. I-Conventional series limiter (A) andprecision feedback limiter (8) character-istics are compared (C)

proved limiter characteristic. Forpositive input voltages, D, conducts,and the circuit acts like any phase-inverting operational amplifier ofgain -R"jR,. Diode forward resist-ance and contact potentials are ef-fectively divided by the high loopgain of the feedback circuit.

As the input voltage becomes neg-ative, D, begins to cut off. Thisopens the feedback loop through R",so that the high amplifier gain cutsD, off sharply by increasing itscathode voltage. Diode D, limitsthe amplifier output voltage tosome positive value; and feedbackthrough D, keeps the summing-point voltage, and hence the limiteroutput voltage, accurately at zero.

Figure Ie compares the actualO.OI-cps transfer characteristics ofa precision limiter with those ofconventional series limiters.

Figure 2 shows two modifiedprecision limiters that do not re-

MODERN ELECTRONIC ANALOGcomputers can add, subtract

and integrate d-c voltages withcomponent accuracies considerablybetter than 0.05 v. Such perform-ance is obtainable at relatively lowcost with the aid of chopper-sta-bilized doc amplifiers and precisionnetwork components. In addition,modern time-division multiplierspermit multiplication of doc volt-ages with comparable accuracy.

This accuracy is not matched bythe diode series, shunt and feedbacklimiters commonly used to imple-ment various nonlinear systemcharacteristics in electronic analogcomputers." '. 3 Finite forward andback resistance of diodes and biascircuits as well as breakpoint-volt-age variations can produce errorsas large as I v.

The precision limiter circuitshown in Fig. IE employs voltagefeedback to realize a vastly im-

-300V

0.5 INPUT VOLTAGE IN VOLTS

SERIES LIMITER WITHIN302A JUNCTION DIODE

PRECISIONFEEDBACKLIMITER

(S)

OUTPUT VOLTAGE IN VOLTS

0.5

FIG. 2-Madified preCIsIon limiters (A) llnd ('ill do not require abias supply. The SO-k resistor limits Zener current

FIG. 3-Diodes and bias voltage, of new precision limiter can bereversed to obtain a lower limit

66 NOVEMBER 6, 1959 • ELECTRONICS

Operational Amplifiers150K v,

-300V ftl

- VI

£2112 6AL5

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RO'L+RO '2 +'L'2 E2

+300V

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150K0, 50K P TIME

-300V ~MIN I-X;YI MEANS THE SMALLER. OF THE 1/2 6AL5 50Kno VOLTAGES -x ANO -v VoMAX l-X,-Vl MEANS THE LARGER OF THE

D2 TIMETWO VOLTAGES -x AND -Y150K

f(:X 1,00,0 -300V

(Al (qFIG. 4-Reversal of diodes and bias pro-vides output of max (-X, -V)

FIG. 6-Dual precision limiter (A) ha·s a sharply defined characteristic (8), Applicationof push-pull gate pulses results in precision switch action (e)

quire a bias supply. In Fig. 2A,D2 of Fig. lB and its bias circuithave been replaced by a Zener diode.

In Fig. 2B the built-in O.2-v biasof the silicon-junction diodes yieldstwo different limiter characteristicsfrom the same circuit. The smallbias for the second diode is suffi-cient for precision-limiter actionand the built-in bias is not evidentin the limiter output, since there itis effectively divided by the loopgain.

Instead of limiting at zero, thenew limiter circuit of Fig. 3 limitsat a precisely adjustable level E,. =RoT/EI(R"r + Tr. + R"Tr,) , VoltageE can be positive or negative and

FIG. 5-Diode-bridge defines upper andlower limits

may, indeed, be a variable voltage.The output voltage will always bethe smaller of the two voltages-RoVtlR, and Ec (amplitude-selec-tor circuit). Note that Eo dependson the load resistance 1"r,.

As with all precision limiters, theoutput impedance is low only in thelinear part of the characteristic.If 1'r. and R" are sufficiently large,l' may be replaced by a diode to re-duce the output impedance whenlimiting.

The accurate amplitude-compar-ison circuit of Fig. 4 combines twoprecision limiters to yield Vo = min(~X, -Y) at very low output im-pedance. The circuit is related toHowe's amplitude-comparison cir-cuit' which depends on the satura-tion limiting of d-c amplifiers with-out chopper stabilization, This newcircuit permits chopper stabiliza-tion and thus substantially betteraccuracy. It may be used as a gateto turn either input voltage offand on. Reversing the diodes andbias voltages in Fig. 1 to 4 reversesthe limiter characteristics.

The diode-bridge limiter shownin Fig. 5 is used in some commer-cial analog computers to establish

upper and lower limits in a singleoperation. Thus, if the input volt-age V, exceeds the upper limitinglevel T/.E,/(Tr, + 1',), diodes D., andD, are off while D2 and U, are on.This action is reversed if V, <Tr.Ej (1'1, + TJ, Series pairs ofdiodes conduct in the linear portionof the characteristic. Since thediode-bridge limiter is a series lim-iter, its limiting action is muchbetter than that of the more fa-miliar dual-shunt and feedback lim-iters," By applying positive andnegative gate pulses, this circuitcan be used as an electronic switch(bridge modulator)."

The dual precision limiter ofFig. 6 combines a diode bridge andprecision-limiter action. In thelinear portion of the characteristic,the circuit acts like an accuratephase-inverting feedback amplifieressentially unaffected by the bridgecircuit. As soon as the bridge be-gins to limit, the feedback loopopens. The high-gain amplifierdrives the bridge decisively into itslimits, and a sharply-defined limitercharacteristic is obtained. DiodesD, and D2 constitute a conventionalshunt limiter to keep the summing

ElECTRONICS • NOVEMBER 6, 1959 67

FIG. 7-0utput of comparator is used for accurate computations FIG. a-Bistable (A) and free-running (B) multivibrators

point at zero. The shunt limitercan be replaced by a pair of back-to-back Zener diodes in low-fre-quency applications.

The upper and lower limitingvoltages need not be equal and op-posite and may be variable. Sinceall four bridge diodes cease to con-duct if E, < E", application of push-pull gate pulses yields a precisionswitch with negligible forward re-sistance as illustrated in Fig. 6C.

Comparators and MultivibratorsIn doc analog-computer usage, a

comparator is an output-limitedhigh-gain doc amplifier; its outputvoltage changes abruptly from onelimiting level to the other when-ever the algebraic sum of the inputvoltages changes sign." 3 In Fig. 7,a conventional feedback-diode lim-ited comparator' drives a diode-bridge limiter decisively into eitherlimit to. produce an accuratelylimited comparator characteristic.Whereas the conventional com-parator serves mainly for switchingor relay-driving purposes, the out-put voltage of the precision com-parator can be used in accuratecomputations.

Combining a compa.rator and aphase-inverting doc amplifier in aregenerative loop produces a bi-

stable multi vibrator' with the trans-fer characteristics indicated in Fig.SA. The improved circuit shownproduces push-pull output voltagessuitable for driving diode-bridgegates (Fig. 5 and 6) without anadditional phase inverter.

Addition of the integrator loopshown in Fig. SB gives a free-run-ning multi vibrator.' When a pre-cision comparator is used, a remark-ably useful l-f signal generator(0.01 to 2,000 cps) for accurate tri-angular waveforms and pulses per-mitting precise amplitude andpulse-width modulation are ob-tained.

Each of the timer circuits of Fig.9 combines a precision limiter witha doc integrator and may be re-garded as an analog of the familiarphantastron circuit.

Each circuit produces a sharprise in the amplifier output voltageas the latter reaches the limitinglevel set by a precision limiter. Ineach case one can reverse diodesand voltages to produce outputs ofopposite polarity.

Integrator Reset CircuitsBefore a computer run, each in-

tegrator of an electronic differentialanalyzer must be reset to a giveninitial condition by charging the

integrating capacitor to the initial-condition voltage." Alternatively,one may discharge the integratingcapacitor to zero and add the initial-condition voltage E in a succeedingamplifier.

Figure lOA shows an electronicresetting circuit of the latter type;such a circuit can reset the inte-grators of a repetitive analog com-puter to zero twenty times per sec-ond.· The resetting circuit of Fig.lOB is a considerable improvement,since it permits one to set initial-condition voltages different fromzero without an external summingamplifier. The modifications shownjust about double the capacity of thecomputer in question. The triodeswitches in Fig. lOA and lOB canbe replaced with diode-bridgeswitches with excellent results: Ifthe resistance appearing in serieswith the switch of Fig. lOB is ob-jectionable, the switch must bedrawn through a simple cathodefollower.

Figure 11 shows an accurate re-setting circuit which would replacethe usual relay resetting circuit ofa slow doc analog computer." Thecircuit operates essentially like thecircuit for resetting the timer ofFig. 9B. The double diode-limitercircuit operates in the reset condi-

TIME

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FIG. 9-Precision timing circuits can be reset by push button or relay (A) and by electronic switch (B)

68 NOVEMBER 6, 1959 • ELECTRONICS

FIG. IO-Reselling circuit (A) is modified(B) to double copocity of computer

ADJUST.•...BIASSDK

K:X 1,000 -300V

FIG. 12-For h.f operation of precisionlimiter, capacitors are adjusted to obtainbest frequency response without ringing

and a novel amplitude-distributionanalyzer for estimation of prob-ability densities." Related switch-ing techniques can be applied toanalog computers with automatic-programming features such as auto-matic scale-factor changes, analogstorage or memory circuits andsample-hold circuits. Higher fre-quency versions of these circuits

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will make possible new applicationsin storage and sampling devices.

The writers are grateful to theElectrical Engineering Departmentof the University of Arizona and toP. E. Russell, Department Head,for their continuing support of thiswork. The writers thank R. Bell,K. Hanson, W. Herndon, H. Shavetand S. Jurich, all students at theUniversity of Arizona for their help.

. REFERENCES(1) C. D. Morrill and R. V. Baum. Diode

Limiters Simulate Mechanical Phenomena,E'LECTRONICS, p 122, November, 1952.

(2) C. L . .Johnson, "Analog ComputerTechniques," McGraw-Hili, N. Y., 1956.

(3) G. A. Korn and T. M. Korn, "Elec-tronic Analog Computers," 2nd Ed, Mc-Graw-Hili, N. Y., 1%6.

(4) R. M. Howe, Representation of Non-lInear Functions By Means of OperationalAmplifiers, '['1"(/"'.s. IRE-PGEC, Dec. 1956.

(5) R. .J. Medkeff and R. .J. Parent.A Diode Bridge L.imiter For Use WithElectronic Analog Computers, P,·oc. AlEE70, Sec. T-I-170, 1951.

(6) N. D. Diamantides, A Multi!)urposeElectronic Switch for Analog ComputerSimulation and Autocorr'elation Applica-tions, '[',·ans. IRE-PGEC, Dec. 1956.

(7) J. Millman and H. Taub. "Pulseand Digital Circuits," McGraw-Hill, N. Y.,1956.

(8) G. A. Philbrick Researches, Boston,Massachusetts, Specification Sheet ForType K2-J Integrating Component, 1952.

(9) L. Lofgren, Predictors in Time-shared Analog Computers, P,·oc. Int. Anal-Of/Y COlnpntati.on Meeting, Brussels, Bel-gium, 1956.

(10) N. D. Tomlinson, FundamentalCircuits and Techniques Used With Elec-tronic Analog Computers, Report AP-77079, Goodyear Aircraft Company, Akron,Ohio, 1956.

(11) G. A. Korn, Analog-computer De-velopment Projects 1958/9, ACL Mem.oNo.2, Electrical Engineering Department,University of Arizona, Tucson, Arizona,1959.

(12) W. F. Caldwell, G. A. Korn, V. R.Latorre and G. R. Peterson, A PrecisionAmplitude-distribution Analyzer, ACLMemo No.6, Electrical Engineering De-partrnent, University of Arizona, Tucson,Arizona, 195!1.

E Vo

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150K HoOV

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ApplicationsNonlinear operational-amplifier

circuits of the type described per-mit analog-computer representa-tion of nonlinear characteristics(dead space, limit tops, backlashand hysteresis) in dynamic systemsand simulated modulation systemswith excellent accuracy. The newcircuits can frequently replace op-erational relays and thus permitfaster compl.1ter operation.

These accurate analog switchingand comparison techniques can beused in various automatic checkoutand quality-control devices. In thelaboratory the new circuits haveproved extraordinarily useful in thedesign of the following special com-puting elements: quadrant switchesfor trigonometric function gen-erators'O, electronic decommuta-tors", analog-to-digital convertersU,

simple and remarkably accuratetriangle-integration multipliers"

K oX 1.000FIG. ll-Accurate reselling circuit usesnew voltage divider to minimize effects ofIimiter.diode leakage and contact voltage

in each bridge circuit.Figure 12 shows a simple pre-

cision limiter and its transfercharacteristic at 5 kc. The separa-tion between forward and returntraces is due to phase shift, nothysteresis. Optional diode Do re-duces the output impedance whenlimiting. Using Philbrick K2-X docamplifiers, the ideal limiter charac-teristics, are approximated towithin 0.5 v at 5 kc for sinusoidalinput of 40 v peak-to-peak. Theswitching step shown in Fig. 12 isminimized by small back bias (0.2to 0.5 v) on Do.

tion; the new circuit uses four in-stead of two diodes in an attemptto shunt diode-leakage currentsfrom the bias supplies to ground.

R .

Performance

With suitable chopper-stabilizeddoc amplifiers, reference-voltagesupplies and precision network com-ponents, the limiter circuits of Fig.1 to 3 yield static accuracies betterthan 0.05 volt, as exemplified bythe limiter characteristic shown inFig. Ie.·

As in the case of electronic multi-pliers, the static accuracy of a non-linear operational-amplifier circuitmay be compromised by frequency-response requirements. The sharpbreak characteristics of precisionlimiter circuits depend on highopen-loop gain and may deterioratesomewhat above 2 cps becau.se ofwiring and patch bay capacitancesin multipurpose computers. Thesituation is much more favorablein circuits with short leads.

The high capacitance (25 JLJLF)

of most silicon-junction diodes ca-pable of standing 100 v inverse volt-age may necessitate the use ofvacuum diodes that have low ca-pacitances (5 JLJLF) but relativelylarge plate resistances (1,000ohms). In this connection, Lofgren"has suggested the use of two vac-uum diodes and two junction diodes

70 CIRCLE 71 ON READER SERVICE CARD-+-