PROCEEDINGS OF THE I.R.E.- Waves and Electrons Sechton

sulting at each level of modulation was determined. Fora typical adjustment and a frequency shift of ± 2 Mc,second-harmonic amplitude was measured to be 32 dbbelow that of the fundamental- and third-harmonicamplitude 37 db below fundamental. Somewhat betterlinearity of modulation has been obtained by more care-ful adjustment of the circuit.When operated from regulated power sources, the

6AK5 oscillator proved to be quite free of frequencydrifts. After a one-hour warm-up period, a drift of 25 kc

took place in the succeeding hour. Modulation at power-line frequency was measured and found to be ±8 kc.AM effects have not as yet been evaluated but these ef-fects are known to be small.

ACKNOWLEDGMENTThe writer wishes to acknowledge the helpfujl co-

operation of W. M. Goodall and A. F. Dietrich of theseLaboratories in the design and testing of this oscillator.

The Reactance-Tube Oscillator *HAN CHANGt AND V. C. RIDEOUTt, MEMBER, IRE

Summary-The reactance-tube oscillator is a combination reac-tance-tube circuit and oscillator circuit which uses but a single tube.It has two forms-one derived from the capacitive reactance-tubecircuit and one from the inductive reactance-tube circuit; with slightvariations the first may be made to resemble the Hartley oscillatorcircuit, and the second the Colpitts oscillator circuit. Experimentswith this oscillator have shown that linear frequency variation versusgrid voltage change with constant output amplitude may be obtainedover a range of more than five per cent in the region of 1 to 4 Mc.

I. ANALYSIS OF OPERATION

C ONSIDER the schematic circuit of the reactance-tube shown in Fig. 1. The admittance across ter-minals a-b is:

1 1 gmZ2Yab + + (1)

Zl +Z2 rp Z1+ Z2

The first term on the right side of equation (1) is theadmittance of the phase-shifting network. The remain-

Then

1 1 jYT = - + gmnA cos 0 + igmA sin 0 = --+-.

rp RT XT (3)

Here RT and XT are the effective parallel resistive andreactive components of YT. It can be seen that RT maybe negative if rp is large and cos 0 is negative. The neces-sary condition for cos 6 to be negative is that the reac-tive parts of Z, and Z2 have opposite signs. If RT can bemade negative in this manner and if a parallel resonantcircuit is connected across terminals a-b, oscillationsmay build up. Furthermore, since 1/rp and gm vary inthe same way with grid bias voltage, RT might be ex-pected to remain constant over a considerable range.

Fig. 2(a) shows such an oscillator circuit derived froma capacitive reactance-tube circuit. In this case the fre-quency of and condition for oscillation are approxi-mately given by

1 +gMCo(LpRv + LvRv) -1/2

2r/LpCp(l + -a) L + CpEp(l + a) ] (4)

g..

RpCp(Lp- Lg) + CpLp2/Corp + Cp2LpRp/Co

where

a = (Co/Cp)(1 + Lg/Lp).I --Ib

Fig. 1-Basic reactance-tube circuit.

ing terms represent the admittance added by the tube,which will be called YT. Let

Z2 = Aej0= A cos 0 + jA sin 0.ZI + Z2

(6)

Similar expressions for the oscillator circuit of Fig.2(b), which is derived from the inductive reactance-tubecircuit, are

VF1+ b Ff = 1IL2 7r \LpCp _

(2)gm >

* Decimal classification: R355.911.1. Original manuscript re-ceived by the Institute, April 4, 1949; revised manuscript received,August 1, 1949.

t University of Wisconsin, Madison, Wis.

(7)gnLpRv+ b "]

Lo(l + b)_

(Lo + Lp)(RpCO/Lp + C,,/Cprp)

(Cv + Cv) (Rg + Ro)La, (8)

November1330

Chang and Rideout: The Reactance- Tube Oscillator

where

b = (Lp/Lo)(1 + Cp/Cv). (9)

In equations (4) and (7) the circuit constants are sochosen that the second term within the brackets is small.Both may then be expanded to show that a linear changein frequency with gm is possible.

CoI

R

L

(a)

Cg

(b)Fig. 2-(a) Capacitive reactance-tube oscillator circuit.

(b) Inductive reactance-tube oscillator circuit.

From (6) it may be seen that the frequency of oscilla-tion is lower than the natural frequency of the tank cir-cuit, and that increase in gm causes the frequency to be-come still lower, with resultant operation still furtherdown on the resonance curve of the tank circuit. Thereduced output voltage which might be expected in thiscase is counter-balanced by the increased plate currentwhich results when grid bias is decreased to increasegm,,. Thus it is possible to see in a qualitative way thatreasonably constant output might be expected. By asimilar argument, constant output may be expected inthe inductive reactance-tube oscillator circuit. Here,however, operation is on the high-frequency side of tank-circuit resonance, and increasing gm further increasesfrequency.The circuits of Fig. 2 may be simplified by making Cp

equal to zero in Fig. 2(a) or making Lp infinite in Fig.2(b). It is interesting to note that the first reactance-tube oscillator circuit then resembles the Hartley oscil-lator and the second the Colpitts oscillator.

II. NOTES ON DESIGNIn both types of circuits the frequency is approxi-

mately 1/2rV/LPCP. The percentage frequency devia-tion can be determined by considering the term gmRgLp/Lo in the inductive reactance-tube circuit and gmRgCo/Cp in the capacitive reactance-tube circuit. Note thatthe latter expression is obtained from (4) by assumingLpRp>>L,R,, a condition which is necessary in practicefor good operation.The ratios Lp/Lo or Co/Cp should be very small, say

about 0.1. By fixing the gm variation range, R0 is deter-mined. The impedance of Z2 should be about one-fifthof the impedance of Z1. Under the above conditions atank circuit of effective Q of about 20 was found satis-factory in the case of a 6L6 tube. The exact value of Lpor Cp is determined, with the help of the approximatefrequency, by the condition for oscillation. This condi-tion should hold at the smallest value of gm in the rangeof operation.

III. EXPERIMENTAL RESULTSExperiments have been conducted chiefly in the 1- to

4-Mc range. Fig. 3 shows typical sets of curves of fre-quency variation and radio-frequency current in thetank capacitor Cp as grid voltage is varied. Greater fre-quency variation is possible by increasing R0 and thenmaking other compensating adjustments, or by extend-ing the grid voltage range to include positive voltages.

zw0

z0

wa

F

,4

aC-4

a:

GRID BIAS (VOLTS)

Fig. 3-Typical curves of frequency and amplitude for a capacitivereactance-tube oscillator (center frequency 1,322 kc), and an in-ductive reactance-tube oscillator (center frequency 1,553 kc).

A modified circuit resembling the Hartley oscillatorwas tested and was found to give a 7 per cent linearrange of frequency variation with the constants used.

Tests made with a number of different types of tubesshow that beam power tubes are most satisfactory, al-though power triodes have been used successfully.

13311949