Current Stabilizers*

J. N. VAN SCOYOCt, ASSOCIATE I.R.E. AND E. H. SCHULZt, ASSOCIATE, I.R.E.

Summary-The degree of regulation to be expected from severaltypes of current stabilizers is considered. Regulation equations arederived and a graphical-design method is presented.

The regulation produced by a single pentode is much better thanthat of a single triode. Two cascode-connected pentodes give a betterregulation but the tube drop is greater and the circuit is more com-plex. The regulation may be improved by using nonlinear resistorsin the control circuit.

INTRODUCTION

C^ URRENT stabilizers are used in various applica-tions to regulate against current changes pro-duced by line-voltage fluctuation or load-resist-

ance variation. These circuits are used in photometry,measurement work, magnetron oscillators, etc. A cur-rent stabilizer may be used advantageously as a cou-pling device in direct-current amplifier work where avoltage divider is required to satisfy quiescent condi-tions, but no division of voltage change is desired.

It is the purpose of this paper to show the degree ofregulation to be expected from several-circuits and topresent a design procedure. Several practical regulatorcircuits are described.

DERIVATIONSThe circuit diagram and equivalent circuit of a simple

degenerative current stabilizer-are shown in Fig. 1. Asolution of the equivalent circuit for a change in the

, Loadh0R

a. Circuit Diagram

b. Equivalent CircuitFig. 1-Cascode-connected current stabilizer.

power-supply voltage yields the following expressionfor the change in load current:

nEAl = - (for E)

RL+ rp + (1 + l)RK(1)

* Decimal classification: 621.375.1. Original manuscript receivedby the Institute, December 20, 1943; revised manuscript received,February 19, 1944.

t Illinois Institute of Technology, Chicago, Illinois.

where AI is the current change in amperesE is the power-supply voltagen =AE/E is the per unit change of voltage.

The current will beI= EL/RL (2)

where EL is the voltage drop across the load. The perunit change of current is thenAl /S RL E \

) )n (for AE). (3)I \RL + rP+ (1 + A)RK EL I

The derivation of the regulation expression for changesin load resistance is simplified by assuming the tube-characteristic curves to be straight lines. Then,

EI= -- E (4)

RL + rp + (1 + /)RKTaking the derivative with respect to RL and expressingthe results in terms of current and resistance increments,

-mRLE

Al=[RL+ rp + (1 + M)RKI2 (for ARL) (5)where m is the per unit change in RL (i.e., ARL=mRL)If (5) is divided by (2) and the results are simplified,the per unit change in current may be expressed as

AI / ~~RL \2/ E+l( RL(1F+ A)RK ) EL )m (for RL) (6)

I RL+rp+(1+,u)RK 1kELI

MILLIAMPERES

Fig. 2-Volt-ampere characteristics of tungsten lamps suitable for uscin current stabilizer.

USE OF NONLINEAR ELEMENT FOR RKAn examination of (3) and (6) indicates that RK

should be as large as possible for good regulation. How-ever, increasing RK increases the grid bias and hencethe tube drop. As a result the ratio E/EL is increased,

Proceedings of the I.R.E. 415July, 1944

Proceedings of the I. R. E.

thus limiting the advantage which may be secured in'this way. Also the plate dissipation of the tube is in-creased by the increase in voltage, and the requiredpower-supply voltage is increased.The use of a nonlinear resistor (such as a tungsten-

filament lamp) for RK will result in some improvementbecause the tube drop is dependent on the actual valueof the cathode resistor, while, as far as changes in cur-rent are concerned, RK is equal to the slope of the volt-ampere curve of the resistor. The :slope of this curvemay be from two to three times as large as the actualresistance at the operating point (see Fig. 2) and hence anappreciable improvement in regulation may be obtained.

Because lamps and similar thermal devices have adefinite time lag the improvement in regulation does notapply to sudden surges or residual hum voltages. Theadvantage to be gained from their use is, therefore, some-what limited.

PENTODE STABILIZER CIRCUITSEquations (3) and (6) indicate that for the best regu-

lation rp and ,x should be large. Both requirements are

Rd

VR150|RL

VR 150

- :lt5Y 3Wl_=P6F6

Fig. 3-Pentode current stabilizer.

satisfied by the use of a pentode. Fig. 3 shows the cir-cuit of a stabilizer using a pentode. The screen voltage issupplied by means of VR gas tubes connected in serieswith a dropping resistor Rd across the line. A portion ofthe voltage existing across the VR tubes is applied- tothe control grid so as to reduce the tube drop. However,the change in grid voltage due to a change in I is equalto the change in voltage drop across RK. This schememakes it possible to use a large value of RK without anunduly high tube drop.An increase in load current reduces the screen voltage

because the drop across RK is included in the screen-cathode voltage. This decrease in screen voltage tendsto reduce the current and thus aids the regulation. Atreatment similar to that used aboveC indicates that

+ = ( RL+_ Rp+(+.L+j-)R-C)(E)> (for AE) (7)I I=RL+rP+(jI+l+/.2)RK EL2AI=/ ~RL \2/ E

VRL+rp(l+8l+2,Rg Jt EDm)(for ARL) (8)where,ul is the control-grid-plate-amplification factorand /u2 is the screen-plate-amplification factor. This

derivationt n,eglects the effects of screen current throughRK and of changes in screen current which will actuallyreduce the regulation somewhat; however, if the screencurrent is not too large, the results will be reasonablyaccurate.

CASCODE-CONNECTED STABILIZERFig. 4 shows a regulator with two tubes connected in

cascode' and its equivalent circuit. The various grid

a;Circuit Diagram

'. rc

,b. Equiwolent CircuitFig. 4-Cascode-connected stabilizer.

potentials are obtained from a voltage divider connectedacross two (or more) VR tubes in series. Since each ofthe grid voltages consists of a constant voltage plus thedrop across RK, the change in each grid voltage is equalto the change in drop across R2. The following equationsmay be written:

EAl = - AIRKEA2 = - AIRK -AIrp + pE0 (9)

AI(R,r + RK + 2rp) AEI = EL/RL.

The solution of these equations yields

Ai=(R++ +) (E)n (forAE) (10)RL+ (2+A),rp+ (1 /t)2RX E;

A process similar to that used in the derivation of equa-tion (6) gives

( ~~RL IE\E( )m (for ARL) ( 1)

RL+(2+,)rP+ (1+I)2RK EL

1 The term 'cascode" as distinguished from "cascade" applies toan amplifier in which the tubes are connected in series to obtain directcoupling.

416 Juily

Van Scoyoc and Schulz: Current Stabilizers

The effect of change in screen voltage was ignored in thisderivation, but it may be taken into account by substi-tuting A+4,u2 for,u. However, the effect of change inscreen current will tend to reduce the effect of screen-

voltage changes and hence the results of (10) and (11)are well within design accuracy.

CURRENT-STABILIZER DESIGN

The design procedure consists of the choice of a tube,a value of RK, and the power-supply voltage E requiredto give a certain maximum current variation for givenranges of line voltage and of load resistance.

For small changes in voltage and load resistance theequations given above may be used to calculate the de-gree of regulation to b'e expected; however, for largechanges it is necessary to use a graphical solution.

Fig. 5 shows a graphical solution of a current stabilizer.For a given value of RK the grid voltage for any assumedplate current is known and hence a plate-current-plate-voltage curve may be constructed for this value ofRK as follows: Assume a value of ib, calculate the gridvoltage, and plot the intersection of the tube curve forthis value of grid voltage and the ordinate for the as-

sumed current. Repeat the process for various assumedcurrents until sufficient points are obtained to plot a

curve. If a lamp is used for RK, the grid voltage must betaken from the lamp volt-ampere curve.

After the curve for the assumed RK is obtained, thecurrent to be expected for any E and RL may be foundby drawing a load line of slope -tan-1[1/(1L+RK)]'through the point eb= E, ib =0.'The intersection of thisload line and the characteristic curve gives the currentto be expected. In Fig. Sa a solution is obtained' for a

constant load resistance and variable impressed voltageby sliding the load line along the axis over the range ofvoltages to be expected and reading the values of' cur-

rent. In Fig. 5b a solution is'obtained for a constantvoltage and variable load resistance by drawing thevarious load lines through the point ib=O, eb=E andnoting the values of current to be obtained.

It should be noted that this solution ignores the effectof screen-voltage changes and hence gives a pessimisticanswer. It may be necessary to plot special curves ap-plying to the particular value of screen voltage to beused.A tube with high values of jt and rp should be chosen.

Also the tube must have sufficient current capacityand its plate dissipation capacity must be greater thanthe maximum plate dissipation to be expected.2 A suffi-cient number of VR tubes should be used to obtain a

reasonable screen voltage. If it is necessary to operatewith a low screen voltage (to economize on VR tubes or

because E is not sufficient to keep the glow currentwithin the normal range for variations of E) it may bedesirable to operate the control grid with a positive

2 Maximum plate dissipation is obtained when E is a maximumand RL a minimum. The plate dissipation is EbI where Eb is the dis-tance oa in Fig. 5b.

potential to reduce the tube drop. The resistor Rdshould be of such a size as to keep the VR tube currentwithin the normal range.

COMPARISON OF STABILIZERS AND CONCLUSIONSTable I indicates the degree of regulation to be ex-

pected from different circuits supplying the same load.The values in this table were calculated and are accurate

'a. Variable Impressed Voltage

240 3201e b

b.Variable- Load ResistanceFig. 5-Graphical solution for a current stabilizer.

for small changes only. However, in most cases thechanges to be regulated against are less than 10 to 20per cent and these results are reasonably accurate. Fig.

TABLE ICALCULATED CHARACTERISTICS OF SEVERAL CURRENT STABILIZERS USED TO

SUPPLY 15 MILLIAMPERES TO A 3000-OHM LOAD

Circuit Al/I forAE=nE Al/I forARL=mRL

1. 6F6 triode (Fig. 1)RK=3-watt lamp, E=550 volts 0.9 n -0.06 m

2. 6F6 triode (Fig. 1)RK =6-watt lamp, E =245 volts 0. 93 n -0o.16 mz

3. 6F6 pentode (Fig. 3)RK =3-watt lamp, E =270 voltsE = -25 volts, E0 =250 volts(2-VRl50 tubes) 0.023 n -6 X10-6m

4. 6F6 cascode (Fig. 4)RK =3-watt lamp, E =550 voltsE = -17.5 volts, En0 =220 volts(3-VRl5O tubes) 1.87 X10-4 n 2.86 XI09 m

1944 417

Proceedings of the I.R.E.

6 shows experimetal curves taken in the laboratory onregulators similar to those in Table I with the exceptionthat the screens were operated at a lower voltage andthe control grids were operated with a small negative or

.I

-J

-j

lRL=0

1 L 86000uwliiiiz1--1-----0 200 400 600 800 10C

E IN voLTS

Circu'it of Figure 4

o0 L2 4000 80-0_0 200 400_ 600 800 io1E IN VOLTS

Circuit of Figure 1 C6F6 Tube RK=3W Lamp)

lator will make it possible to maintain the VR tube cur-rent within the normal range over a much wider range ofvoltage variation.

Fig. 7 shows a current stabilizer used as an element inthe voltage divider feeding the grid of the direct-currentamplifier in a degenerative voltage stabilizer. This di-vider is necessary to keep the grid at a negative potentialbut a resistance divider is undesirable because it alsodivides the changes of output voltage. Since the currentin the divider remains constant and hence the dropacross the resistor is held constant, any change in out-

, 20 R - = = -

41 %ttt ____I L

a~ 204R.~00 60n pr IT ___I~v0 200 4CE 60N

. N..1;E IN V.OLlt

800

Fig. 7-Current stabilizer used as voltage divider in adegenerative-type voltage regulator.

1000

Circuit of Figure 3

Fig. 6-Experimental results on three current-stabilizer circuits.

perhaps a positive grid voltage. It is evident from theseresults as well as from the equations that much betterregulation may be obtained for load-resistance variationthan for line-voltage variation'.Many applications of these circuits suggest them-

selves. For example, the use of a current stabilizer as a

dropping resistor in series with a VR tube-voltage regu-

put voltage must appear across the regulator tube andhence upon the grid of the direct-current amplifier.

It has been shown that the stabilizers in the order oftheir regulating capability are: (1) cascode-connectedcircuit, (2) pentode circuit, and (3) triode circuit. If thestabilizers were listed in the order of their relative sim-

plicity, the order would be reversed. The triode circuitgives the poorest regulation and has the largest tubedrop. The cascode connection gives the best regulationbut the tube drop is high. The pentode is a good com-

proimise between good regulation and simplicity and itgives the smallest tube drop.

Reference(1) F. W. Hunt and R. W. Hickman, "On electric voltage stabiliz-

ers," Rev. Sci. Instr., vol. 10, pp. 6-11; January, 1939.

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