1960 IRE TRANSACTIONS ON INSTRUMENTATION 509

Switching Levels in Transistor Schmitt Circuits*T. J. GALVINt, R. A. GREINERI, MEMBER, IRE, AND W. B. SWIFTt, MEMBER, IRE

T11 MHE widely used Schmitt trigger circuit' has been e eEanalyzed in considerable detail as a tube circuit.2-4 161R, i7i'R, CCThe circuit is obviously one which can be built to * i

work in essentially the same way with transistors inplace of the tubes. The purpose of this paper is to report I, R4an analysis of the transistor Schmitt circuit in which TI T2primary attention was given to switching levels, RR.hysteresis, and ways of readily adjusting both. 12 4 e4 l eThe transistor Schmitt circuit, shown in Fig. 1, has 6B+6| 2 Z41 R7 e3

two stable states, characterized by high and low outputeo. The circuit abruptly changes from one state to the -1 _I___'_l__other under the control of the input voltage ei. The criti-cal values of input voltage which cause such changes arecommonly known as the switching or triggering levels.In this paper, E+ will be defined as the triggering levelwhen the input is increasing; E- when it is decreasing. E+

The hysteresis voltage or backlash is defined as (a - - L(a) or _ _

Eh = E+-E-. (1)Thus, in Fig. 2(b) the output corresponding to the input ' Timof Fig. 2(a) is shown. Time

OPERATION0 I l lIThe essential requirement for obtaining an accurate E c c

analysis of the Schmitt trigger is to notice that switching -depends upon having both transistors unsaturated. (b) >That is, if the input is low with T, cut off and T2 sat- ' ccE1-IcRLurated, an increase in es to pull T, out of cutoff will not o0cause switching. The circuit will switch only after ei has Timebeen further increased so that (e3-e2) is reduced to tin- Fig. 2-(a) Typical input to Schmitt trigger circuit.saturate T2. Even then, a minute further increase in ei (b) Output of circuit for input shown in (a).is required to pull T2 far enough out of saturation sothat the over-all loop gain exceeds uniity before the CALCULATION OF SWITCHING LEVELSswitching takes place.An analytical solution to the problem of calculating Tce folloFing data are used in conjunction with the

switching levels E+ and E- wNould, therefore, be very circut of Fig 1involved. Furthermore, one wvould have to use a graphi- R,=R2=2.2 Kcal representation of the tratisistor. Hence, one might R3= 10 Kas well use a method wfhich is entirely graphical. A R4=22 Kmethod is presented here whlich turns out to be quite R5=6.9 Ksimple. The only assulnplioii required is that the loop R6=0.68 Kgain increases so rapily, -,is ci is increased beyond the R7= 18 Kvalue which unsaturate-s T,2, that E+ is practically equal EC= -12 volts.to the- value( of e- wh;-,)li} 1lsluae T_totevaue f e wih atuteT. Transistors P', and T, are 2N135. To find the upward

* Received by the PGI, Atwnlst 6, 1959. trig-ger level E+, we assume that switching will occurt Space Technology Lalb<.~ Inc., Los Angeles, Calif.whn7icdutsfiielyofreT2utfsar-$ UJniversity of Wisconlsin, Mladison, WVis.whnI cnutsficelyofreT2utfsar-0. H1. Schmitt, "A therrnion1ic trigger," J. Sci;. Insir., vol. 15, tion. Therefore, the value of collector current in T,, ci,l2 D. F. Fitzgerald, "Analysis and Synthwesis of the Schmritt Trigger which will force T2 out of saturation, must be found. ToCirculit," M.S.E.E. thesis, U]niversity of Wisconsin, Mladisonl; 1956. do this, the point of operation of "2 as it leaves satura-J. Millman and H. Taub, "Pulse and Digital Circuits," MVc- tio mutb stbihd

Graw-Hill Book Co., Inc., New York, N. Y., 1956. onmsbestlshd4R. J. Parent, "tGraphical analysis for circulits containing over-driven vacuum tubes," Proc. NEC, vol. 7, pp. 263-274; 1952. EC=i7R2 + ecei ± (eic + eie ± ii)R6. (2)

510 IRE TRANSACTIONS ON INSTRUMENTATION December

Neglecting the small base current and i2, we obtain eb2 -2.98 voltsi4= ~~~0.1655 maEc- icIR6 ece2 R7 18 KR2 R6 R2± *R6 =5 = 14 + ib2 -0.1655 ma + (-0.12 ma)

If iai is zero, the equation reduces to the well-known = - 0.286 maequation for a load line. As ici increases, the effect is the ec1 = eb2 + i5R4same as if ECC had decreased. Unfortunately, i,j is not Ecc- ecknown. One may approximate the solution by assuming =cR=ici equals zero and, on this basis, drawing a load line asshown in Fig. 3. The operating point of T2 can then be -12 - (-9.28 volts)found. This operating point implies a value for the cur- 2.2 Krent i,,. The value, ia, of current so obtained can then -0.954 ma.be used to obtain a better approximation to the operat-ing point. This is donie by using a source voltage which e) Construct a new load line usingis now Ec j-aR6, and drawing a new load line. A few Ecc - ic1R6 = (-12) - (-0.954 ma)(0.68 K)cycles of this process will lead to a very close approxima-tion to the correct operating poinlt. -= 11.35 volts

2 N 135 as the effective value of E, The preceding-5 steps can then be repeated until i,j equals the

assumed value.-o Approximations In this example, the following operating conditions for

4 fir<_second--- =T2 when"it is leaving saturation are foundfinal

-3 4~~~~~~~~~~~~~~~~~2=- 0.115 maE.0 ece g= - 0.2 volt

E2 -.0 ~~~~~~~~~~~~~~~~i2= 3.95 ma

.ii = - 0.782 maN t\>-.02 e., = - 9.64 volts.

00 -2 N X This concludes step 1) of the procedure.O -2 -4 -6 -8 -10 2) With these results in hand, we may calculateece (Volts) ee = -ece2

Fig. 3-Construction for graphical calculation =(12) - (2.95 ma)(2.2 K) - (0.2 volt)of triggering levels.-3.1 volts

The steps to the procedure are as follows:ecei = C- ee

1) Find the operating point of the output transistor.a) Using the characteristics of a 2N135 in Fig. 3, 9.64 volts) - (3.1 volts) 6.54 volts.

construct a static load line for a 12-volt source Knowing ecei and icl, the operating point of Ti, the fol-and a 2.88 K load resistance, which is the total lowing information is obtained from the characteristicof 2.2 K collector resistance and 0.68 K emitter curves:resistance.

b) From this load line, at the point of saturation, =- 0.023 maebel = 0.1 volt.1b2 = - 0.12 ma

ece2 = - 0.2 volt 3) E+ can be calculated,

ic2 = - 4.1 ma. ebel -0.1 voltZ2 ~ -= 0.0145ma

c) Using this information, calculate R5 6.9 Kil= i2 +1~ ibi = (-0.023 ma) + (-0.0145 ma) = 0.037 maeC2 - eC-sc

= - 12- (-4.1 ma)(2.2 K) = -2.98volts. E l3+ee+e= - (0.037 ma) (10 K + 0.1 volt + 3.1 volts)

d) It can be assumed that eC2=e62 at this point, =3.57 volts.since T72is at the edge of the saturation region.This assumption allows jic to be calculated as To calculate E-, it will be assumed that the circuitfollows: wTill switch when eb0ei equals zero, which is when T2

1960 Galvin, et al.: Switching Levels in Transistor Schmitt Circuits 311

E_cc., region. The calculations are much simpler than those inthe previous section, and often yield qualitatively cor-

iR4 $ rect results despite the assumptions involved. SwitchingR4___________________level changes will be discussed resulting from variation

of several circuit elements in turn.R /R I VARIATION OF R1

I i - e The effect of varying R1 experimentally is shown inRiI; BE2 R Fig. 5. With T1 cut off, an increase of R1 decreases theR6R base voltage of T2 and hence reduces E+. When T1 is con-

ducting, the emitter voltage is approximatelyEcc R6

Fig. 4-Approximate equivalent circuit used for ee =calculating the value of E-. R6+ R1

leaves cutoff. This assumption errs very slightly by pre- Since e, is important in considering the conduction ofdicting a high value of E-. With T2 cut off, the circuit T1, R, has considerable effect on E-.can be redrawn as in Fig. 4.

Since the base current ibi and i2 are small, the circuit VARIATION OF R2can be considered to contain a balanced bridge when From the experimental results shown in Fig. 6, it canebe2 is zero. If the transistor T1 is considered to be an be seen that R2 can be varied considerably withoutequivalent resistor RT, then the bridge in Fig. 4 is bal- changing E+ or E-.anced when When T2 is conducting, the base voltage of T2 is

R4R6 22 K(0.88 K) somewhat fixed. If R2 is increased, ee and ebe2 will de-RT - = 832 ohms. crease. However, to force T2 out of saturation, T1 must

R7 18 K be driven further so that ebe2, at this point, has about the

Therefore, same value. E+ will, therefore, remain relatively con-stant.

E -12= - - = - 3.28 ma If R2 is decreased, ee increases and a larger value of ei

Rtotai 3.66 K is needed to turn on T1.

-3.28 ma(R4 + R7) When T2 is cut off, R2 has no effect on the circuit;1C1 = = 3.16 ma hence it will not change E-.

RT + R6 + R4 + R7 Inasmuch as T2 operates as a linear amplifier whenand conducting, variation in the collector load is expected to

ecc ~icRT = (-3.16 ma) (832 ohms) =-2.64 volts, vary the collector voltage and the output.

Using the characteristic curves, VARIATION OF R3R3 is the resistance of the input source or a resistor1b1 = - 0.072 ma added to obtain the desired operation of the circuit.

and Since R3 forms a voltage divider to the input, it isebel = 0.2 volt, easy to predict that if R3 is decreased, E+ and E- have

E- is then calculated lower values. The base current is much larger when T1is completely conducting; therefore: R3 effects E- more

i2 = - = - 0.029 ma than E+. The results are shown in Fig. 7.R5

VARIATION OF R4 AND R7il = ibl + i2 = (-0.029 ma + (-0.072) = 0.101 ma

VRAINO 4ADR

E= ib3± ebe2= (-0.029 ma + (-0.072) =-0.101ma R4 and R7 form an attentuator from the collector ofE-= ~iR3 + ebel ± lclI6 T1 to the base of T2; therefore, they will be discussed to-= 0.101 ma (10 K) + 0.2 volt + (-3.16 ma)(0.68 K) gether. When R4 is decreased or R7 increased, the attenu-= 3.36 volts. ation is reduced; hence, the base to emitter voltage of T2is increased. T1 must, therefore, conduct more to drive

It should be noted here that, allowing for graphical ap- T2 out of saturation. A larger value of E+ will result.proximations, the results of this section have been con- Also, if the attenuation is reduced, 77. turns on with afirmed by experiment. larger voltage on the base of T1. As the attenuation to

VARIATIONSOF SWITCHNG LEVELSthe base of the output transistor is reduced, both E± andE- increase. Results are shown in Figs. 8 and 9.

Some insight can be gained into switching level varia- E- will not increase as rapidly as E± since the largertions by supposing that the Schmitt circuit is switched value of es results in a lower value of e4, which is passedby the entry of T1 into the unsaturated but conducting on to the base of T2.

512 IRE TRANSACTIONS ON INSTRUMENTATION December

Voriotion of Trigger Levelsos R, is Varied

4

\3- Voriotion of Trigger Levels

2 os R7 is Varied

>i 2

0 ~ ~ ~ ~~ ~ ~ ~ ~ ~~~~~~~~)

0 2 4 6 8 10 12 14 16 Is 20 0

R, (KQ) 16 16 20 22 24 26 28 30R7 (Kf)

Fig. 5-Variation of trigger levels as R1 is varied.Fig. 9-Variation of trigger levels as R7is varied.

4

4 E +

33 Variation of Trigger Levels

E- as R5 is Voried

Voriation of Trigger Levels 22 as R3 is Varied >

_ ___, 2 4 6 8 10 1'2 14 16 180 2 3 4 5 6 7 8 R5 (KR)

R2 i(()

Fig. 6-Variation of trigger levels as is varied. Fig. 10-Variation of trigger levels as R5 is varied.

5'

4.

4I

En~~~~~~~~~~~~~~~~~~~~~~~~~~~~E3

3Voriotion of Trigger Levels Variation of Trigger Levelsas R. is VariedasR

0 400 800 1200 1600 2000

0 2 4 6 8 10 12 14 16

R3 (KQa) Fig. 11-Variation of trigger levels as R6 is varied.

Fig. 7-Variation of trigger levels as R3 is varied.

VARIATION OF R5

When R6 is reduced sufficiently, E+ and E- will in-61 crease because of the added drop through R5, as shown5 E\ in Fig. 10.

VARIATION OF R6|~~~~~~~~~~~It is expected that variation of R6 would result in

3 changes of both E+ and E- since R8 controls the emitter" ~~~~Variation of Trigger Levels voltage. Fig. 11 shows that R6 can be used to vary both> 2 ~~~~~~~~~~~triggeringlevels without greatly disturbing the hyster-

4

esis. When T2 is conducting, decreasing R6 decreases theemitter voltage; but the base voltage of T2 remains con-

C0 4 8 1'2 '6 20 24 stant. If 7'3 is conducting, the reduction of R6 decreasesR4 (Kfl) both the emitter voltage and the base voltage of T2.

Fig. 8-Variation of trigger levels as R4 is varied. Thus, E+ is more sensitive than E- to changes in R6.

1960 Bean: A Simple Comparator for the Intercornparison of Unsaturated Standard Cells 513

When T2 is cut off, the output voltage equals E, It is further assumed that the circuit returns to itsWhen T2 is saturated, the output is original state when T1 reaches cutoff, so that

EccR6 E6Ecceo E =

R6+ R2 R6+R1

Therefore, R6 is very important in designing the output The above assumption gives an approximation whichlevels and total output amplitude. is about three or four tenths of a volt low.

In designing Schmitt trigger circuits, these two equa-CALCULATION OF THE VARIATION OF TRIGGER LEVELS tions, although only approximate, can be useful since

It can be assumed that the transistors are perfect they give considerable insight into the determinationswitches; i.e., when the transistor is cut off, the current of switching levels.through it is zero, and when the transistor is conducting, CONCLUSIONSthe voltage across it is zero.When T2 is conducting, the circuit will be assumed to This paper is intended to present a study of the

switch when the base to emitter voltage of T1 reaches transistor Schmitt trigger circuit and not to present azero. Under this assumption, conduction of T1 is neg- complete design procedure.lected. The error introduced in this way is a few tenths Analytical calculations are made of switching levelsof a volt. Thus, of a more or less typical circuit to illustrate a rather

accurate method. Approximate calculations and experi-E+ EccR6(R±+ R4 + R1) mental results are included to show the effect, on switch-

R6R2 + (R6 + R2)(R4 + R1) ing levels, of variations in various circuit elements.

A Simple Comparator for the Intercomparison ofUnsaturated Standard CeIlse

RICHARD C. BEANt, MEMBER, IRE

INTRODUCTION type is necessary. A very accurate method of measure-T HE PROBLEM of devising an efficient and ac- ment consists of connecting a cell of known value in

curate method of intercomparing unsaturated series opposition with the cell of unknown value andstandard cells is becoming more important every measuring the difference voltage with the potentiome-

day. This situation is due to several factors, The ac- ter. The main problem with this method arises when thecuracy of measurement on some assembly lines is such operator becomes confused concerning the direction inthat a reference voltage requiring standard-cell ac- which he should apply the correction.curacy is quite commonplace. Individual standards lab- THE SIMPLE COMPARATORoratories throughout industry are becoming more pop-ular. Also, because of the increasing workload, the prob- The comparator to be described has been developedlem of acquiring personnel skilled in standards labora- in the Division Standards Laboratory of the Convairtory work is becoming somewhat acute. plant, Fort Worth, Tex. It consists basically of a Lin-

Several methods for the periodic recalibration have deck Potentiometer arranged in a configuration to in-been in use, but they all have their limitations. Direct dicate the difference voltage between a cell of unknownmeasurement with a precision potentiometer is not ac- value and each cell in a bank of cells of known valuecurate enough for most standard-cell applications, and directly with a conventional meter. As shown in thethe method of comparing a cell against one or more circuit of Fig. 1, the comparator has, as a power source,standards, using the potentiometer as a transfer device twTol number-six dry cells connected to a ten-turn,calls for a special setup every time a calibration of this 5000-ohm potential divider in such a manner as to sup-

ply either positive or negative voltage to the circuit.The current from this source, which is monitored by the

* Received by the PGJ, September 25, 1959.t Hewlett Packard Co., Palo Alto, Calif. Formerly Convair, Div. microammeter, causes a voltage drop across the pre-of General Dynamics Corp., Fort Worth, Tex. cision four-terminal resistor. The meter and resistor