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

A Variable Phase-Shift Frequency-

Modulated Oscillator *0. E. DE LANGEt, ASSOCIATE, IRE

Summary-The theory of operation of a phase-shift type of oscil-lator is discussed briefly. This oscillator consists of a broad-bandamplifier, the output of which is fed back to the input through anelectronic phase-shifting circuit. The instantaneous frequency iscontrolled by the phase shift through this latter circuit. True FMis obtained in that frequency deviation is directly proportional to theinstantaneous amplitude of the modulating signal and substantiallyindependent of modulation frequency.

A practical oscillator using this circuit at 65 Mc is described.

INTRODUCTION

T HE OSCILLATOR described here was developedto meet the requirements of a FM microwave re-peater system which called for operation at a mid-

band frequency of 65 Mc and linear frequency devia-tions of ± 2 Mc to ± 3 Mc at modulation frequencies upto 5 Mc with very little resultant AM. Although modu-lation is brought about by variations of a phase shift,the circuit is not the usual "phase-modulation" circuitwhich starts out with a voltage of fixed frequency andvaries its phase. In this circuit, the frequency of oscilla-tion of an oscillator is controlled by the amount of phaseshift through an electronic phase shifter. The circuitalso differs from the well-known reactance-tube modu-lator in that, for the reactance-tube circuit, the modula-tor is effectively in shunt with part or all of the oscillatortank circuit whereas, in the variable phase-shift circuit,the modulator is in series with the oscillator feedbackpath.

DESCRIPTION OF OSCILLATOR

Fig. 1 shows, in simplified block form, an oscillator ofthe phase-shift type. It is seen to consist of a broad-bandamplifier, the output of which is fed back to the inputthrough an electronic phase-shifting circuit. Switch Sshould be in position 2 for the oscillator connection. Theswitch and the voltage generator el shown in Fig. 1 arenot parts of the oscillator but are included here merelyto illustrate the operation of the circuit.The amplifier consists of a single vacuum tube with

associated input and output impedances. These imped-ances, of course, have phase characteristics. The blockZ of Fig. 1 represents an equivalent network having thesame amplitude and phase characteristics as the passivecircuits associated with the amplifier and phase shifter.Under ideal conditions, the amplitude characteristic of

* Decimal classification: R355.914.31 XR246.24. Original manu-script received by the Institute, January 13, 1949; revised manu-script received, July 19, 1949.

t Bell Telephone Laboratories, Inc., Deal, N. J.

Z would be flat and the phase characteristic would belinear over the desired frequency range.The circuits are adjusted to make Z look like a pure

resistance at midband frequency. Also, with no modula-tion voltage applied, the electronic phase shifter is ad-justed to produce a phase shift of exactly 180° at mid-band frequency. Suppose the switch S of Fig. 1 to be inposition 1 so as to apply the voltage e1 to the amplifierinput and let the frequency of el be the midband fre-quency. Then the voltage e2 appearing across the resis-tor R will be exactly in phase with el. By adjusting thegain around the loop to a value of unity, the amplitudeof the voltage e2 will be made equal to that of el. Sinceel and e2 are equal in both phase and amplitude, the cir-cuit now satisfies all of the conditions for oscillation andif the switch S is thrown to its position 2 sustained oscil-lation at midband frequency will result.

MODULATIONVOLTAGE

Fig. 1-Phase-shift oscillator, block form.

With the switch S back in position 1 consider whathappens when the phase shift through the electronicphase shifter is changed from the 180° value as happenswhen modulation is applied. If the phase shift is madeto differ from the 1800 value by an amount a then thevoltage e2 will be out of phase with the voltage e1 by theangle oa and the circuit can not oscillate at this fre-quency. If the voltage el is now changed in frequencyfrom the midband value, it will be possible to find somefrequency for which the phase shift through the imped-ance Z is equal to - a and thus compensate for thechange of phase shift produced by the active elements ofthe phase shifter and for which the voltage e2 will againbe in phase with el. If the switch S is thrown to position2, the circuit will oscillate at the last-mentioned fre-quency. Thus, the frequency at which the circuit canoscillate is determined by the phase angle introduced bythe electronic phase shifter and is hence capable of beingmodulated by this phase shifter. This can be shownmathematically as follows:

1328 November

De Lange: A Variable Phase-Shift Frequency-Modulated Oscillator

Let b be the phase shift around the loop in Fig. 1, theswitch being in position 1 and 4D being the shift frompoint 1 to point 2. Then 1> is a function of the modulat-ing voltage v and of the frequency w.That is, 1=1 (v, w)Differentiating,

d4 = - dv + -Idcav OW

where

= the rate of change (at constant frequency) ofav phase through the phase-shifter circuit with

voltage

=the slope of the phase characteristic of the totalaw circuit including the amplifier and the passive

elements of the phase shifter

=also the group delay around the loop.

For oscillation cJ = 3600 at all times and ddb= 0

do,

dv Ov O9W

Modulation linearity and sensitivity are seen to de-pend essentially upon the phase characteristics of theelectronic phase shifter and of the impedances repre-sented by the Z of Fig. 1. If the phase-shift versus modu-lation-voltage characteristic of the phase shifter is linearand if the phase versus frequency characteristic of Z islinear or if the nonlinearities of these two characteristicscancel each other; i.e., if (0J./cv)/(Q9J/do) is independ-ent of frequency, the resultant modulation will be lin-ear. For maximum modulation sensitivity and linearity,the amplifier band should, in general, be made as broadas practicable.

6 A K 5PHASE SHIFTER

MOOULATIONINPUT

Fig. 2-Simplified schematic of oscillator.

The electronic phase shifter as used in this ocillatoris shown at the left-hand side of the simplified schematicof Fig. 2. The inductances L2 and L3 serve merely totune out the input capacitances of tubes Vi and V2 re-spectively. The phase-shift circuit consists of L1 in serieswith R1 and this series combination shunted by anotherconsisting of C1 in series with R2. If the elements are sochosen that R, = R2 = V\L/C1, the impedance lookinginto the phase shifter is purely resistive and has thevalue R1 at all frequencies. When w = (1/VL,C,), thegrid voltages of tubes V1 and V2 are equal in magnitudeand have their phases shifted by equal amounts but inopposite directions with respect to the input voltage.The plates of the phase-shifter tubes are directly in

parallel with the result that the current output of thephase shifter is the sum of the plate currents of tubes V1and V2.

In Fig. 3 is shown, in vector form, the action of thephase shifter when co= i/VZLC. The vectors OA1 andOA2 represent the plate currents of tubes V1 and V2 re-spectively when these tubes are adjusted to have equalvalues of transconductance. The resultant current I isin phase with the applied voltage.

A'2

A2,'-- '"l

X ___~~~~~~~"I, 1/A11

S~_: _- II

"I

_,.

"7-A1

Fig. 3-Phase-shifter currents, vector diagram.

If now the transconductance of tube V2 is increasedfrom its former value and that of Vi decreased by anequal amount, the current vectors become as shown byOA2' and OA1' and the resultant current I' leads thecurrent I.

In order for the circuit to satisfy conditions for oscil-lation, it is necessary for the voltage e2 of Fig. 1 to beequal in magnitude as well as in phase to the voltage el;i.e., there must be unity gain around the loop. Further-more, for linear modulation, it is desirable to keep thetotal voltage on the grids of the modulator tubes belowthe overload value. To keep the amplitude of oscillationat a fairly low and constant level, a crystal limiter wasadded to the circuit. This limiter consists of a pair of1N28 silicon crystals oppositely poled and shuntedacross one of the oscillator tuned circuits. Because of itsextremely small time constant, this limiter performssatisfactorily for modulation frequencies well above SMc.

PERFORMANCEIn order to determine the modulation capabilities of

the oscillator, different amounts of 1 ,000-cps modulatingvoltage were applied and the amount of distortion re-

(4- - l-9 -r

1949 1329

i 1-

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