modulation.5 The falling transition is recorded in thesame manner as the rising transition except that thereadings are made on the inverted scale beginning atthe top. The measuring apparatus can be calibrated orchecked by recording the output of the square-wavegenerator directly.

It is believed that portable square-wave measuringequipment of the type described will be found useful

6R. D. Kell and G. L. Fredendall, "Selective side-band trans-mission in television," RCA Rev., vol. 28, pp. 425-444; April, 1940.

in experimental work, in routine checking, and indetermining specifications of television apparatus. Therecorded data are permanent and can be filed forfuture reference and comparison with similar square-wave records. Reconstruction of the square-waveresponse on paper is obtained readily by plotting theinstantaneous recorded values. The form of the datais also directly suitable for analysis by the chartmethod described in a companion paper.'

A New Direct Crystal-Controlled Oscillatorfor Ultra-Short-Wave Frequencies *

W. P. MASONt, FELLOW, I.R.E., AND I. E. FAIRt, ASSOCIATE, I.R.E.

Summary-An ultra-high-frequency crystal oscillator isdescribedwhich utilizes a mechanical harmonic of an AT or BT crystal. Withthe oscillator freqvencies as high as 197 megacycles, harmonics ashigh as the 23rd have been excited. Taking the second electrical har-monic of the oscillator, frequencies as high as 300 megacycles, or 1meter have been obtained. Since a mechanical harmonic is used, thecrystal can be of a practical size to handle and adjust. The harmonicvibration of theA Tand BT crystals have as low a temperature coefficientas the fundamental mode, and temperature coefficients of less than twoparts per million per degree centigrade are easily obtained. Stabilitycurves for this type of oscillator are shown and the results indicate thatat 120 megacycles stabilities in the same order of magnitude as forordinary crystal oscillators can be obtained. Without temperature orvoltage control it appears likely that the frequency should remain con-stant to ± 0.0025 per cent.

Some measurements have been made of the properties of harmoniccrystals at high frequencies. It wasfound that the Q of a crystal is inde-pendent of the frequency but in general increases with harmonic order.The ratio of capacitances r of a crystal increases as the square of theharmonic order. It is shown that in order to obfain a positive reactancein the crystal Q >2r. This relation will only be satisfied for harmonicsofA T crystals less than the 7th. As a result oscillator circuits such as thePierce circuit cannot be used to drive crystals at high harmonic fre-quencies. A discussion of oscillator circuits is given and it is shownthat a capacitance-bridge oscillator circuit with the crystal in one armis the best type to use for high-frequency harmonic crystals.

I. INTRODUCTION

D URING the last several years high-frequencyJg} vacuum tubes of moderate power output' have

been developed which extend the commerciallyusable frequency spectrum into the ultra-short-waveregion. Point-to-point station transmitters working at120 megacycles and 150-megacycle aircraft trans-mitters are examples of such moderate power equip-ment. These applications require high-frequency oscil-lators with stabilities of the high order of magnitudeswhich are attainable with crystal oscillators. This sta-

* Decimal classification: R355.65. Original manuscript receivedby the Institute, December 3, 1941; revised manuscript received,March 18, 1942.

t Bell Telephone Laboratories, Inc., New York, N. Y.I A. L. Samuel and N. E. Sowers, "A power amplifier for ultra-

high frequencies," PROC. I.R.E., vol. 24, pp. 1464-1483; Novem-ber, 1936; Bell Sys. Tech. Jour., vol. 6, pp. 10-34; January, 1937.

bility has been obtained in the past by using crystaloscillators working under 20 megacycles with a numberof stages of harmonic generation.

It is the purpose of this paper to describe a crystaloscillator which is controlled directly by a crystal reso-nance as high in frequency as 197 megacycles. Thisresonance is a mechanical harmonic of a low-coefficientAT-cut crystal. The mechanical harmonic has the sametemperature coefficient as the fundamental AT crystalwhich can be made under two parts per million perdegree centigrade. Since a mechanical harmonic is usedthe crystal is considerably thicker than it would be ifit had to vibrate as its fundamental in the ultra-short-wave region, and hence it can be ground and adjustedmuch more easily than a very thin crystal. The par-ticular oscillator whose properties are described hereuses the 15th mechanical harmonic of an AT-cutcrystal and produces a frequency of 120 megacycles.

Theoretically the electromechanical coupling of aharmonic crystal varies inversely as the order of themechanical harmonic and the ratio of capacitances inthe equivalent circuit varies proportionally to thesquare of the order of the mechanical harmonic. It be-comes increasingly difficult to excite a harmonic vibra-tion with the ordinary oscillator circuits and in factharmonics higher than the 5th cannot usually be ex-cited with the Pierce circuit for example. The reasonfor this is that the Pierce circuit requires the crystal tohave a positive reactance in order that oscillation shalltake place. It is shown below that in order for a positivereactance to occur in the crystal it is necessary thatk2/2 > 1/Q or Q > 2r where Q is the ratio of reactance ofthe coil in the electrical representation of the crystal toits resistance, k the electromechanical coupling factor,and r the ratio of the shunt static capacitance Co of the

Proceedings of the I.R.E.464 October, 1942

Mason and Fair: Crystal Control for Ultra-Short Waves

crystal to the series capacitance C1. The ratio of ca-pacitances of a fundamental AT crystal as usuallymounted is in the order of 1000 to 1 and hence 2r forthe 5th harmonic would be 50,000. The Q of a crystalis usually not much larger than this so the 5th har-monic is about the highest harmonic that can be drivenby the usual oscillator circuits.

For this application the circuit used consists of ahigh-frequency pentode with a tuned grid and plate

L, R1 C

Co

Fig. 1-Equivalent electrical circuit for piezo-electric crystal.

coupled back through a capacitance bridge of whichthe crystal forms one arm. For this circuit the crystalimpedance does not have to have a positive reactanceand it has been found possible to control the frequencyof an oscillator with harmonics up to the 23rd orhigher.The stability obtainable with this oscillator is about

the same as can be obtained with ordinary circuits atlower frequency. The stability with plate-voltagechange is in the order of 0.05 cycle per megacycle pervolt. The temperature coefficients of the crystal areunder two parts per million per degree centigrade.Without regulation of voltage or temperature the fre-quency should be stable to + 0.0025 per cent or better.With regulation the stability can be increased.

II. PROPERTIES OF HIGH-FREQUENCY CRYSTALSIn order that a crystal shall be useful in an ultra-

high-frequency oscillator it is necessary that its Q shallremain high in the high-frequency range. Since nomeasurements have been published on how the Q's ofcrystals vary with frequency it was thought worthwhile to measure the Q's of AT-cut crystals over a

COMPARISON RESISTANCE

Fig. 2-Resistance method for measuringQ of crystal.

wide frequency range. For this purpose 9 crystals wereobtained whose fundamentals varied in frequency from800 kilocycles to 20 megacycles. The Q of a crystal isdefined with respect to the equivalent circuit of thecrystal shown in Fig. 1. Here the static capacitance ofthe crystal is designated by C0, while the effect of themotional impedance of the crystal is represented by theseries-resonant circuit L1, C1, and R1. The Q of thecrystal is defined as the ratio (27rfRLl)/Rl where fRis the resonant frequency.Three independent methods were used to measure

the Q of the crystals. At the lower frequencies the

method used was the one described in a former paper2and shown in Fig. 2. It consists in measuring the reso-nant frequency fR, the antiresonant frequency fA, theresistance at resonance R, and the static capacitanceC0 of the crystal. From these the Q of the crystal canbe calculated from the formula

Q= /(fAf _ where A=fA-R. (1)2IrfRCoR 4irRCOA

At higher frequencies, the measurement of resistancebecomes less reliable. At these frequencies, however,the reading of vacuum-tube voltmeters is satisfactory,so the circuit of Fig. 2 was modified to that of Fig. 3,

VERY LOW ~~VACUUMOSCILLATOR VREYISANC TUBERESISTANCE ~~~~VOLTME TERB

Fig. 3-Voltmeter method for measuringQ of crystal.

and the resonant and antiresonant frequencies weremeasured as well as the voltage across the low terminalresistance at resonance and antiresonance. It is readilyshown that the Q of the crystal will be given by theformula

fR / VR= - where A =fA -fR2A VV

(2)

and VR and VA are the voltages across the terminatingresistance at the resonant and antiresonant fre-quencies, respectively. A third method used was tomeasure the voltage across the terminating resistanceat antiresonance and a few cycles from antiresonance.For this case the Q of the crystal is given by

fA[Qc) 2

Q= V (3)where A is the difference in frequency between theantiresonance and the frequency for which the voltageVc is measured. All three methods were compared onseveral crystals and checked within a few per cent.

9000(0

70000~-

0 50000-94ooo-4,Am

20000

10000

0 2 3 4 5 6 7 8 9 10 11 12 13 14 IS 16 17 18 19 20FREQUENCY IN MEGACYCLES PER SECOND

Fig. 4-Measurements of the Q of fundamental AT-cut crystalsover a frequency range.

The measurement of the fundamental frequencies ofthe 9 crystals are shown in Fig. 4. Although the Qvaries over a considerable range from crystal to crystal,

2 W. P. Mason, "Electric wave filters employing crystals aselements," Bell Sys. Tech. Jour., vol. 13; pp. 405-452; July, 1934.

300001 4 1. 1ii if ii ii ii

i~~0. Il

465

Proceedings of the I.R.E.

there is no significant trend with frequency. The ratioof capacitances for the fundamental AT crystals wasaround 1000 to 1.The harmonic vibrations of three of the crystals were

also measured and the resulting Q's are shown inFig. 5. The crystal having a fundamental at 1 mega-cycle has a fundamental Q of 98,000 and progressively

400 000

350000

300000

250000

0

0 2 4 6 8 10 12 14 16 18 20 22 24 26FREQUENCY IN MEGACYCLES PER SECOND

Fig. 5-Measurements of the Q of harmonicAT-cut crystals.

higher Q's at the higher-order harmonics. The othercrystals have lower initial Q's but all show an increas-ing Q with harmonic order. The crystal having a funda-mental of 8 megacycles is one of the crystals used inthe oscillator described in this paper.

It is thought that the variation in Q of shear-vibrat-ing crystals is due to very minute cracks on the surfacewhich cause a small amount of rubbing when the crys-tal vibrates. This is borne out by the fact that etchedor polished crystals usually have a higher Q than non-treated crystals. This is probably also the explanationof the higher Q in the harmonic crystals for a harmoniccrystal is similar to a number of crystals in series witha number of vibrating surfaces as shown in Fig. 6. Allthe internal surfaces will be whole and free from cracks.If most of the resistance is associated with the outsidefaces it follows that a harmonic crystal with a largenumber of internal faces should have less dissipationthan a fundamental crystal. At the high-order har-monic the Q seems to approach an asymptote of400,000 to 500,000, which is probably the Q associatedwith the internal dissipation.

These data indicate that as far as internal dissipa-tion is concerned, the Q of a crystal is independent ofthe frequency. If, however, one goes from a conditionfor which the Q is controlled by the surface dissipationto a condition where the Q is controlled by the internaldissipation, the Q will increase.A measurement of the ratio of capacitances of the

higher-order harmonics indicated that the ratio of ca-pacitances increases about as the square of the har-monic order. This is in agreement with theory for in anodd-harmonic crystal of order n, only 1/nth of thepiezoelectric effect is engaged in driving the crystal at

its harmonic frequency and the other (n - 1)/n partsannul each other. The electromechanical couplingfactor is3

k = d26n4C

(4)

where d26n, the piezoelectric constant is d26/n, C66 isthe shear elastic constant, and K the dielectric con-stant of the crystal. It follows that the coupling variesinversely as the harmonic order. The ratio of capaci-tances r being3

r 8-( k2)ir k2

(5)

is approximately proportional to n2.It is a matter of interest to find how the impedance

of a harmonic crystal varies with the harmonic. It hasbeen shown previously3 that the impedance of a piezo-electric crystal is given by the expression

-zj(l - k2) L1 -f2/fi2+ 1Q(- k2)](,JCo - 1 -f2/f22 + j/Q

(6)

where Co is the static capacitance of the crystal, f1 theresonant frequency, andf2 the antiresonant frequency.Also, fi2 =f22(1 - k2). Inserting this value and express-ing the equation in the form of a resistance and re-actance we find

zc =

k22 f2 f4 I -

Q- i - k2 - -L (2 -k2) +4 +Q2Q [(2122 + Q2_

wcoQ 12)21]-(7)

Fig. 6-Harmonic mode of motion.

The reactance term will have a maximum whenf2=f22(1-1/Q). At that frequency the impedance ofthe crystal will be

2 2_O *(8)wcoC

W. P. Mason, "An electromechanical representation of a piezo-electric crystal used as a transducer," PROC. I.R.E., vol. 23, pp.1252-1264; October, 1935.

466 October

Mason and Fair: Crystal Control for Ultra-Short Waves

Hence, in order that the crystal shall exhibit a positivereactance

k2Q 2>1 or k2>

2 Q(9)

But the ratio of capacitance is given by (5). Hence, thecondition4 for the crystal to exhibit a positive reactance

Q > 2(1 + r) -2r. (10)

zero gain and zero phase shift are given by

R, -XA+XB+XRg -XA + XD] L XC]

and

XAXBXCXA + XB + XC

If we assume that Q is in the order of 75,000 or less,which is certainly higher than can be obtained in mostuntreated crystals, and a ratio r of 1000 for a funda-

Fig. 7-Equivalent circuit of Pierce-type oscillator.

mental AT crystal, the highest-order harmonic thatwill show a positive reactance is the 5th harmonic foran AT-cut crystal.

III. STANDARD OSCILLATOR CIRCUITSFOR CRYSTALS

As a consequence of the fact that high-harmoniccrystals will not show a positive reactance, it followsthat the standard oscillator circuits, such as the Piercecircuit, cannot be used to excite high-harmonic-ordercrystals. The only type of oscillator circuit which willannul the large shunt capacitance of the crystal, whichprevents the crystal from having a positive reactancenear the resonant frequency, is a bridge-type circuit,as discussed in Section IV. When this reactance isannulled, however, the resulting circuit reduces to a

circuit similar to the Pierce circuit or to one in whichthe phase is reversed by the use of a phase-reversingtransformer, depending on whether the crystal is in theseries or lattice arm of the bridge. Since the stabilityof the circuit depends on which connection is used andcan be evaluated from a consideration of the stabilityof standard oscillator circuits, it has appeared worthwhile to include a discussion of them.The Pierce-type oscillator circuit consists of a 7r-net-

work connection of reactances between the plate andgrid of the tube as shown in Fig. 7. Such a circuit isrequired to produce a 180-degree phase shift in orderto offset the 180-degree phase shift produced in thevacuum tube. The other common connection is to use

a phase-reversing transformer or two tubes in tandem,so that the network itself is required to produce a zero

phase shift.If we consider a tube as represented by the circuit

shown in Fig. 7, following Llewellyn,5 the condition for

' This condition was first derived by R. A. Sykes.6 F. B. Llewellyn, "Constant frequency oscillators," PROC.

I.R.E., vol. 19, pp. 2063-2094; December, 1931,

where ,u is the amplification factor of the tube, RP andR, are the plate and grid resistances of the tube, andXA, XB, XC the coupling reactances which incorporatethe distributed capacitances of the tubes. These for-mulas assume that the tube introduces a phase angleof 180 degrees. In case two tubes are used in tandemor the 180-degree phase shift is produced in a unity-coupled transformer, the sign of 1u in (11) will be re-

versed. For two tubes, ,u will have the significance ofthe ratio between the voltage applied in the plate cir-cuit of the last tube to the voltage applied on the gridof the first tube.

For the first type circuit, A will ordinarily be greaterthan (XB+Xc)/Xc and hence XB will have to be ofopposite sign to XA and greater in absolute magnitude;for writing,

XA (1 +m)- m wehaveXB = - XA.

XA + XB m

Introducing this value into (12), we have

XA2(1 + m)R,R, = -

XAm -

Xc

(13)

(14)

Since XA2 is positive, the right-hand side of (14) can

only be made positive if XA is the same sign as Xc and

mXc > XA. (15)

These equations show that XA and Xc must be ofthe same sign and opposite to XB while the sum of

IXB

Fig. 8-Reactance curves for Pierce-type oscillator.

XA and Xc must be larger in magnitude than XB. If(XB+XC)/Xc is of opposite sign to u and greater inmagnitude it is readily shown that the resulting con-

dition on XA will not satisfy (13) and hence the oscil-lator will not oscillate under these conditions.

Since we do not know RP and R, explicitly, the fre-quency cannot be calculated definitely from these

is

(11)

(12)

4671942

Proceedings of the I.R.E.

equations unless Rp, R5, and the distributed capaci-tances of the tubes are evaluated as functions of thevoltage and current conditions in the tube. Ways forminimizing the variation with tube and circuit con-ditions, however, are evident from (12). If, for ex-ample, the crystal is connected in the XB arm, it is

If m1 is greater than unity,

-mni( + ml)<in2 <0.o

ml1-1This type of circuit will have great stability when

the crystal is worked near its resonance frequency forwhich case XB is a small quantity A. Then, for thiscase,

RP, 1 XAXC-_=-1; RR =A 'A (18)

CG =

(B)

Fig. 9-Oscillator using phase-reversing transformer.

readily shown that the maximum voltage and tuningstability will occur when the XA arm, which usuallyconsists of a tuned circuit, is tuned for a frequencyconsiderably lower than the crystal resonance. Underthese conditions, as shown by Fig. 8, XA is muchsmaller than XB or Xc, the value of R, is large, and thefrequency is determined nearly by the condition thatXA+XB+XC=O. A change in RpR, caused by achange in voltage will produce only a small frequencychange on account of the large value already existingfor the product RpR. The maximum stability for thistype of oscillator circuit occurs for a minimum output.On the other han'd, if we employ a circuit with two

tubes or a phase-reversing transformer, the point ofgreatest voltage stability can be made to come at thehighest power output. One such circuit is shown inFig. 9(A). For a finite coupling between the two trans-former windings, the equivalent network of the circuitis shown in Fig. 9(B). The leakage reactance can becombined with the crystal reactance if desired, inwhich case it will lower the resonant point slightly orif desired a series capacitance can be inserted to annulthe leakage reactance.The condition for oscillation for this type of circuit

can be obtained from (11) and (12) by reversing thesign of u in (11). If we let

XAA=iml or XB = XA(1 -m1)/ml (16)

XA + XB

then, in order to oscillate, ml must be positive. If mlis between zero and unity then

ml(- iml)XA = (M2 -Ml)Xc where 0 < M2 < . (17)1-rml

If we let XA and Xc antiresonate at the crystal reso-nant frequencyfR, the product of A by the antiresonantimpedance will be finite and can be made equal toR,R,. Under these conditions a large change in R,R,will not change the frequency since no phase shift re-quiring a shift in frequency will occur. This analysisdoes not take account of the change in dielectric con-stant with voltage for the tube capacitances enteringthe circuit but it has been found experimentally thatthis effect is small and does not alter appreciably themaximum stability conditions. Even when dissipationis associated with all of the elements, this relation isstill true as can be demonstrated with reference toFigs. 10(A) and 10(B).As shown by (18), the ratio of Rp/R, =,u-1, which

is the maximum value possible. Hence, the output willbe greatest at the voltage-stabilized point also. SinceR, will be considerably smaller than Rp an increase inoutput can be obtained by making the ratio of thetransformer output impedance to its input impedance

Fig. 10-Impedances at crystal resonance for phase-reversing oscillator.

less than unity. For this case the frequency and ampli-tude equations become

1P XA XB + XCRg, 2XA + XB XC _

XAXBXC

=2XA + XB + XC(19)

XA4,2XBXCRR

XA + XB + XC

October468

Mason and Fair: Crystal Control for Ultra-Short Waves

where 4)2= impedance transformation ratio=M2/P2=where M is the mutual inductance of the transformer,and P the primary inductance. For XB very small orfor oscillations near the resonant frequency

R~ --;4 /_RRA2.A. (20)

R 02 0~~~~'2XA +X

Hence, the ratio of Rp/R, will be a maximum and con-sequently the output will be a maximum when 4) = 2/,u.If the resistances of the elements, as represented by

Li C1 A

Ql B~~~~~~~~~0~~~~~~~~~~~~*,ch/

X e g /A

CO~~~~~~~B

(A) (8)

Fig. 11-Use of crystal in bridge circuit.

Fig. 10(B), are taken account of this transformationratio for maximum output will be less. The stabilitywith reactance tuning will also be increased by usinga step-down transformer since the impedance of thecrystal will effectively be increased compared to theimpedance of the tuning reactance. Hence, it requiresa larger change in tuning of the plate reactance to causea given frequency change in the oscillator.

IV. OSCILLATOR CIRCUITS FOR USE WITH

HIGH-FREQUENCY HARMONIC CRYSTALS

Neither of these two standard types of circuits canbe used directly with high-harmonic-type crystals onaccount of the fact that the sign of the reactance doesnot become positive in the resonance region. Theycould be used to control the frequency by using thecrystal as a negative reactance, but in that case it isdifficult to locate the control in the resonance region.We note, however, on examining the equivalent circuitof a crystal shown in Fig. 1, that the reason the re-actance does not go positive is that the series-resonantarm is shunted by a very large condenser. If this con-denser could be neutralized, the remaining impedancearm would consist of a simple tuned circuit whichchanges from negative to positive reactance at theresonant frequency.

In crystal-filter work6 it has been shown that thestatic capacitance of a crystal can be balanced out byincorporating the crystal in a lattice network of ca-pacitances as shown in Fig. 11 (A). The drawing showstwo crystals having the same constants but they canbe represented actually by a single crystal with twosets of plates. By virtue of the network theorem shownin Fig. ll(B), the static capacitances of the crystaltogether with the balancing condenser CB can be re-

6 See W. P. Mason, 'Resistance compensated band-pass crystalfilters for unbalanced circuits," Bell Sys. Tech. Jour., vol. 16,pp. 423-436; October, 1937.

moved to the end of the lattice leaving a network ofreactances. In this network the series arms are theresonance series arms of the equivalent representationof the crystal, and the shunt arms are the static ca-pacitance of the crystal.

Suppose now that we incorporate this crystal latticein the oscillator network shown in Fig. 12(A). Then asbefore we can take out the shunt capacitance of thecrystal and the balancing capacitance to the ends of thenetwork leaving the circuit shown in Fig. 12(B). As-suming perfect coupling in the transformer, the shuntcapacitance CB can be joined to Co to tune the inputcoil, and CB can be joined to C2 to tune the output coil.If we have 180-degree phase reversal in the trans-former, and tune the two end coils to antiresonance atthe resonant frequency of the crystal, the phase shiftaround the feedback path will be 360 degrees and theoscillator will oscillate at the crystal resonant fre-quency, which, as discussed in Section III, will resultin the greatest stability at the frequency of maximumoutput In case the transformer gives no change inphase, the crystal has to be put in the lattice arm togive this condition. In case the coil coupling is notunity, a small leakage-reactance coil appears. This canbe annulled at the resonant frequency of the crystal bya small series capacitance. Hence, the resultant re-actance at the resonant frequency will be the same asthat shown in Fig. 12 (B).The crystal network as shown in Fig. 11 has two

identical crystals or a crystal with two sets of plates.This is rather objectionable at high radio frequencies,since it is difficult to divide the plates for very small

Fig. 12-Unbalanced oscillator incorporating bridgecircuit with balanced crystal.

crystals. Fortunately this is not necessary for we canshow that the crystal lattice with a single crystal shownin Fig. 13(A) is equivalent to the balanced lattice withtwo crystals. This follows from the network equiva-lence of Fig. 13(B), which states that the series arm ofthe balanced lattice is equal to

B(A + C) + 2AC-= D. (21)

2B + A + C

1942 469

Proceedings of the I.R.E.

The crystal impedance C is given by (6) while A andB are

-;

WCA

- 1B = .

WCB

Inserting these values in (21), we find the equiva-lent impedance D to be given by

capable of driving a crystal at a high harmonic and ofbeing controlled by the resonance characteristic of thecrystal at that harmonic. A 180-degree phase shift isintroduced by the transformer and the resonant cir-cuits are tuned so that their antiresonant frequencies

f2 J1- ±+

f2'2(1-k'2) Q'(1-k'2)

f2 jI'--- Q

f2'2 Q' ]f2'12 =f22

Co(2CA+CB) +CACBJ'

Q'zQ - C(2(CACB) ]L CO(2CA +CB) +CACB-

k'2-2 k2Co(CA +CB)2

(Co+CA+ 2CB) [Co(2CA +CB) +CACB- k2CACB]

D=B(A

A +2B+CQi

01--

"CB

CA

(A)

(23)

(24)

(B)

Fig. 14-Unbalanced oscillator incorporatingunbalanced crystal bridge.

coincide with the resonant frequency of the crystal. Analternative arrangement is to use a transformer with nochange of phase and the crystal in a lattice arm. Thisis the condition for maximum output and maximumstabilization against voltage changes as pointed out

previously.

(B)

Fig. 13-Equivalence between balanced andunbalanced lattice networks.

Hence, the impedance of the D arms is that of a crystalwith somewhat different constants than that for theoriginal single crystal. If

COCA = CB2

the values in the above equations become

CO'= CB;

f212 f22[1(kCA2 -2;- Q =Q[1- k2CA2

[(CA+ C/) 2_ (CA +CB) 2

2 k2CACB 2 k2CACBk C2= -A_

(CA+CB) 2-k2CA2 (CA+CB) 2

(25)

(26)

If CA is nearly equal to CB, which will be the ordi-nary condition of operation, f2'2 =f22(1-k2/4);Q'=Q(1 -k2/4); k'2 =k2/2.

Since the shunting capacitance of the crystal Co' isequal to CB, all of the capacitances CB can be removedfrom the lattice arms to the ends of the circuit leavingthe equivalence shown in Fig. 14, in which the series-resonant arm representing the crystal impedance hasfour times the impedance of the single crystal used inthe lattice. The oscillator shown in Fig. 14 is then

(D)

LU L QI------E) _ _ ----

Fig. 15-Balanced and unbalanced oscillators.

Other circuits for which the same process can be ap-plied are shown in Fig. 15. Some of these circuits areunbalanced and some balanced. At ultra-high fre-quencies it is often desirable to use balanced circuits

:-j(l-k2)-Co'co

where

= CO(2CA +CB) +CACBCO+CA +2CB

470 October

4Mason and Fair: Crystal Control for Ultra-Short Waves

and double pentodes' such as the 240H have beendeveloped for this purpose. For such systems it is de-sirable to use balanced oscillator circuits, and most ofthe experimental work recorded here has been donewith the circuits of Fig. 15(C) and Fig. 15(E). Fig.15(C) is especially advantageous for the crystal and all

CIRCUIT DIAGRAM

eCa>eL

INLANG NGCAPACITY, C8

SECTION A-A

Fig. 16-Crystal bridge.

of the balancing capacitors can be put in one self.contained structure, as shown in Fig. 16, which can beenclosed in a metal vacuum-tube holder and evacuatedto eliminate the effects of air damping and humidity onthe crystal and bridge balance. The dielectric em-ployed is usually fused quartz on account of its lowloss and similar temperature variation of dielectricconstant to that of crystalline quartz. In some casesseries condensers have been placed on each side of thebridge to control the amount of feedback. The variable

With this arrangement, it was found possible todrive crystals at harmonics as high as the 23rd andfrequencies as high as 197 megacycles or 1.5 meterswavelength. Furthermore, by taking the second elec-trical harmonic of the oscillator, a frequency of 300megacycles or 1 meter was obtained with good output.This probably does not represent the upper limit forby using circuits with more gain the loss inserted bythe crystal circuit can be overcome and the oscillatorbe crystal controlled to even higher frequencies.The adjustment of this oscillator is not difficult. The

crystal bridge is left unbalanced first and the oscillatorwill oscillate uncontrolled by the crystal. Its frequencyis determined by the resonance of the coil-condensersystems on the ends. The frequency is adjusted to asomewhat lower frequency than that of the desiredmode of the crystal and the coils are tuned for maxi-

50

~J4

J 400hJ

I~3 5

z

cr

4)

et

0U

z

7

0 Cr ~~~~~~~150

5 10055 60 65 70 75 80 85 55 60 65 70 75 80 85

GRID TUNING CAPACITY (VERNIER DIAL READING)

Fig. 18-Effect of grid and plate tuning onfrequency of oscillator.

cr~cr 2

0

FREQUENCY-120 MC. _TOTAL GRID CAPACITY- 21.3,a, z

DIAL SCALE 0033 f/ DIV.

200f 2 -- SX X So>0

o0 20 40 60 80 100 120 140 160 180GRID TUNING CAPACITY (VERNIER DIAL READING)

Fig. 17-Effect of grid tuning onfrequency of oscillator.

tuning condensers are sometimes made with one com-

ponent having a negative temperature coefficient tocompensate for the positive coefficient of the metaltuning coils. This insures that the oscillator gain willremain at its maximum value over a wide temperaturerange.

V. EXPERIMENTAL RESULTS

In the experimental results obtained, the circuit ofFig. 15(C), with a self-contained bridge, has usuallybeen employed since it was desirable to work theoscillator into a balanced 240H pentode amplifier.In order to make the crystal control at high radio fre-quencies it is necessary to employ a circuit with as

much gain as possible at the high frequencies. Thisindicates that high-frequency pentodes should be em-

ployed; accordingly, 954 acorn pentodes were used.

mum output at this frequency. The crystal bridge con-denser is then adjusted towards balance and the oscilla-tions will usually stop. The grid and plate coils are thentuned to the crystal frequency and the oscillator willthen be controlled only by the crystal.Some stability curves for such an oscillator were ob-

tained for a frequency of 120 megacycles or 2.4 meters.The output obtained was 80 volts across the outputimpedance of 25,000 ohms when the plate voltage was250 volts and the screen voltage 100 volts. The fre-quency variation with grid tuning for one crystal usedis shown in Fig. 17. The grid current obtained is alsoplotted on this curve. As can be seen the maximumvariation is in the order of 5 kilocycles from the pointof maximum grid current to the point where oscilla-tions ceased. The curves for plate tuning are similar tothose for grid tuning. The over-all frequency changefor both plate and grid tuning is shown in Fig. 18. Thisover-all change amounts to 10 to 12 kilocycles or about100 parts in a million. This range represents the con-trollable range of the crystal and, therefore, the maxi-mum frequency deviation which would occur for anypossible combination of circuit changes unless thebridge becomes unbalanced and the circuit oscillatesuncontrolled. Since in the extreme tuning positions theoutput is very low, the possibility of operating this far

300, 30

1942 471

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Proceedings of the I.R.E.

off frequency is not great, and the usable range is prob-ably not over one half this or + 0.0025 per cent.The change in frequency with plate voltage for this

type of circuit is quite small for the maximum output.The reason for this is pointed out in the section onstandard oscillators. When the circuit is tuned some-

TEMP COErFF 0.2 \ /I`C/1CSTABILITY = 0.07 ~'/V/Mc.

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20 30 40 50 R0 70 80 90

TEMP. COErF = S3 -4/t/MC.STABILITY= 0.09 `/vp/MC

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resonance and hence cause little trouble.It is important for this work to have the crystal of

uniform thickness in order to obtain a large output anda single response at the desired harmonic frequency.They are polished and the degree of flatness deter-mined by interference fringes. A photograph of thecrystal and holder is shown in Fig. 20. In this figuresome interference fringes are observable which snowthe degree of flatness obtained. It is difficult to extend

TEMPERATURE IN DEGREES CENTIGRADE

Fig. 19-Frequency change as a functionof temperature.

what differently, the variations may amount to 0.05to 0.1 cycle per megacycle per volt.The temperature-frequency curves for two AT plates

vibrating at their 15th harmonic are shown in Fig. 19.The average coefficient over a 50-degree-centigradetemperature range was 1.3 parts in 101 per degree centi-

Fig. 20-Photograph of crystal and holder.

grade for one and 0.2 part for another. Five crystalswere tested and all had a coefficient less than 2 parts

in 101 per degree centigrade. One remarkable feature ofthese crystals is brought out by the temperature

curves; that is, no hops in frequency were experiencedin any of the temperature runs. This appears to be dueto the fact that the coupling with harmonics of the low-frequency modes decreases with decreasing ratio ofthickness to the diameter of- the plate. This crystal was0.21 millimeter in thickness and 12 millimeters indiameter and operated on the 15th harmonic, hencethe ratio of diameter to effective thickness is 12 to0.014 or 860 to 1, and the unwanted couplings are

practically zero. Near-by frequencies may still be foundif the plate is not exactly flat but they are of the same

type and have the same temperature coefficient, withthe result that they do not come nearer the desired

Fig. 21-Photograph of crystal oscillatorand amplifier.

the flat region out to the edges since there is a tendencyfor the crystal to become convex. For this reason thediameter of the crystals is made twice that of the elec-trode area. The holder itself has very flat electrodesand is designed to center the electrodes on the crystalthus utilizing the most nearly flat portions of thecrystal.A crystal oscillator of this sort was used in conjunc-

tion with two 240H amplifying pentodes to deliver 12watts output to the antenna at 120 megacycles.A photograph of the equipment is shown in Fig. 21.After 5 hours of continuous running the frequencyhad changed about 800 cycles or 7 parts in 106. Day-to-day checks indicated frequency agreement withinseveral hundred cycles. Continuous runs indicate thatthe frequency variation under ordinary operating con-ditions should not be more than ± 25 parts in a millionor + 3 kilocycles at 120 megacycles.

472