52 IRE TRANSACTIONS ON INSTRUMENTATION March

IF Stabilization by RegenerativeFrequency Conversion

DAVID M. MAKOWt

INTRODUCTION UC X M3 fb

r HE conicept of an oscillatory system which oneT encounters in current electroniic practice usually

embodies a single or multitube amplifier having a UDsuitable feedback circuit. In general, oscillation can bemaintained in any system where conditions exist whicheniable the output energy to be coupled back to the inputwith suitable amplitude and phase relationship.A separate class of oscillatory systems is formed using

processes of frequency conversion within the system, sothat the frequency of oscillation in one branch of thecircuit differs from that in another.' The frequencies of /C A\ _UA noscillations are usually determined by two coniditions,the total zero-phase shift condition in the oscillatorvy 2 Us fbloop and a frequency condition which establishes therelative relationship of the frequencies involved, but nottheir absolute values. Since two or more frequencies of faoscillation are present, it is often practical to provide

UA

the most effective frequency controllinig elements, forexample, high-Q stable resonant circuits, at a frequencyfor which such circuits can be built most efficiently and

Laeconomically, while the other frequencies need not becontrolled precisely in order to maintain the same rela- fa= fo-fbtive stability.The system described employs two frequency con- m

version processes in an oscillatory loop and provides bybsuitable design of the frequency determining circuitry T Uo

0fo M I X Us fb

an improved frequency stability in some branches of thesystem. In particular, the basic relationships can be ap-plied to the design of a radio receiver or radio repeater Fig. 1-Block diagram of the regenerative frequency converter. MIl,with a high stability of the intermediate and local oscil- M2 and M3 are mixers and A, B, C and D are amplifiers.lator frequency. conversion factor depends on the second input voltage

of the mixer, to be called hereafter the switching voltage,which is usually larger than the signal voltage. The

The Basic System Elements mixers M 1, M2 and MI3 have, in our case, the conversion

The system shown in Fig. 1 consists of three mixers factors a, f, and y respectively, which are smaller thanMiVl, M2, and M3, each producing the sum or the dif- unity, and are assumed to be frequency independent.ference of the frequencies of its two input voltages, and The performance of the amplifiers is characterized byof a number of amplifiers A, B, C and D placed in some their voltage amplification factors A, B, C and D andof the branches connecting the mixers. The perfOrmance the phase angles a, b, c and d respectively, both beingof a mixer can be characterized by the conversion factor, functions of frequency.which is the ratio of the output voltage at the useful For the purpose of analysis, the branches (1) and (4)frequency to the input signal voltage. The value of the are thought to be cut at the points m and n and the volt-

ages 91ILa= Ua cos(2wfat+?) and qlU = U: cos (2wrfdt+E),* Manuscript received by the PGI, August 31, 1958. Presented at where e and e7 are arbitrary phase shifts, are inserted

the IRE-URSI Spring Meeting, WNashington, D.C.; April 24-26, above the intersections mn and n respectively. The volt-

t Nati. Res. Council, Radio and Elec. Eng. Div., Ottawa, Out., ages below these intersectionls as well as the voltages inCan. all other branches of the system can be calculated and

1 D. Makow, "Novel circulit for a stable variable frequency oscil-lator,' PROC. IRE, VOl. 44, PP. 1031-1036; August, 1956. are given in Table I. The equations for equality of the

1959 Makoow: IF Stabilization by Regenerative Frequency Conversion 35

TABLE I PhaseVALUES OF VOLTAGE IN THE VARIOUS BRANCHES OF THE SYSTEM b Qd

SHOWN IN FIG. 1, CALCULATED FOR THE PURPOSE OF THE b dSTEADY-STATE ANALYSIS.

Branch Voltage b(f b) d(f d)(0) Uo cos 27rf0t(1) (above intersection m) Ua cos (2wrfatt+-q) + 900_(4) (above intersection n) Uo cos (2wrfdt+e)(8) UZJ A cos (27rfat+?+a(fJa) fb d(5) U, D cos (2wrfdt+E+d(fd)) / d X(9) U-AACcos (2rfat+7+a(fa)C(fa)) b--d / fd \ frequency(6) & (7) & (3) /3-y UO-D cos [27r(fd-fa)t+E-77 /

+d(fd) -a(fa) -c(fa) +bUfb)](1) (below intersection mn) Uo-a cos [27r(fo-fd+f4)t-.+7 -9 0°

-dyd) +aya) +C(fa) - b(fb)](4) (below intersection n) UaA*, cos [27rfdt+e+d(fd)

C(fa) +b(fb)lFig. 2-The phase-frequency characteristics of the amplifiers B and

D for the case where C is assumed to be a wideband amplifier, andabove and below the intersections m and n re- B and D to be tuned by a series and a parallel resonant circuitvoltages aoeadblwtentretosmadne- respectively.

spectively, deliver the amplitude conditions (1) and (4),the frequency condition (2) and the phase conditions(5) and (6). opposite to that in D, for example when a series and a

Conditions derived from the equality of the voltages parallel resonant circuit is used respectively. An increaseat the intersection m: of fd will then result in an increase in fb and vice versa,

in order that b = -d (see Fig. 2). If the Q values of theseUo a = Ua (1) two circuits are chosen so that the absolute changes in

fo - fd + Ia = Ia or fo = Id (2) fd and fb are equal, which is the case when condition (7)-E + a(fa) + c(fa) - d(fd) - b(fb) 0 (3) is fulfilled, the difference frequency

at the intersection n: Qb fb (7)

U0 = Ua A, (4) Qd fd

d(fd) -(fa) + b(fb) = 0 (5) (fd -fb) (fo-fb)=1, will remain unchanged. Also ifthese two circuits are constructed similarly and out of

For C(fa) = 0 the same material, they will drift in the same direction

d(fd) + b(fb =O (5') and approximately by the same amount as indicated inFig. 2, with broken lines. Then the phase condition (5')

and for b(fb) = d(fd) 0O will not be violated by this drift if the Q values of the

C(fa) 0 (5"t) two resonant circuits are equal, and the stability of fbwill therefore be considerably improved. The condition

and substituting (5) into (3) it follows that (7) and equality of the Q values can be nearly fulfilled

e = a(fa) (6) at the same time iffb andfd are approximately the same.This will be the case wherever fa is much smaller thanfo, for example when this system is used as a frequencyconverter at VHF, UHF, or SHF, where the frequency

The frequency and phase conditions (2), (5) and (6) Id =fo is the incoming modulated carrier frequency, lb isexpress relationships of interest. The value of the arbi- the substitute of the usually separately generated localtrary phase shift E is always equal to a(fa) [see (6) ]. The oscillator frequency andfa is the intermediate frequency.phase angle q cancels out in the calculation and is there- Assume next that d and b are nearly zero, which willfore not significant. The frequency Id is identical with be the case, for instance, when both D and B are broad-the input frequencyfo at all times, as expressed by (2), band amplifiers and attenuate only the undesired side-and therefore the phase angle d(fd) can be controlled by bands of the mixers M2 and M3, and c is the phase shiftthe input frequency. According to the phase condition in a stable high-Q circuit, for example in a crystal filter.(5) the phase shift (d-c+Ib) must equal zero. Then (5) simplifies to (5") and the frequency Ia is de-Assume first that c is equal to zero, which can be ful- termined mainly by the center frequency of the crystal

filled when the amlplifier C is a wideband buffer stage. filter. Variations in the input frequency will not be re-The phase angle b(fb) must then be equal and opposite flected in Ia, because the feedback loop will cause theto d(fd), see (5'), and the frequency lb will have a value frequency lb to vary simultaneously in such a way as tofor which this equality is fulfilled. Since d is determined keep fa constant. Also the value of lb is at all times de-by Id =lo, lb is then also determined by lo. Suppose the termlined as the difference of Jo and Ia, and therefore isphase frequency characteristic of the amplifier in B is not influenced by drifts in B or D. The mechanism of

54 IRE TRANSACTIONS ON INSTRUMENTATION March

stabilization of fa can be understood with the help of losses in the oscillatory loop formed by the branches 4,Fig. 3, where the phase-frequency characteristics C(fa), 5, 10, 7, and 6. The amplifiers in D and B can be usedd(fd), and b(fb) of the filters in C, D and B, respectively, also to provide additional RF amplification, if the out-are shown. It is seen that c(fa) is steeper than the latter put is taken at the frequency fd or fb, as the case couldtwo, thus indicating a high-Q filter. In order that the be in a radio link or repeater. If the output is taken atphase condition c= (d+b) is fulfilled, when the input fa however, this system can be considered as a radio re-frequency fo =fd varies, fb will have to change similarly, ceiver. In both cases, an improvement in IF stability forbecausefa will vary very little when Q,>>Qb. Any change variations in the input and local oscillator frequency isinfb as a result of a change info is reflected infa in such possible. It is observed that the phase of the voltage ina manner as to reduce the variation in fa if there were no branch (4) or (5) has a fixed relationship to the phase offeedback, and the correction is the more effective the the input voltage, according to (6). Since the voltage ingreater the ratio of deviation in fb to the change in fa,. branch (4) or (5) is of the same frequency as the input,

but of considerably higher magnitude due to IF ampli-fication in A, this system can be considered as an RF

Phase

Qc Qd and Qb

amplifier or special converter, providing an outputc=d + b (2c>' (;Qd and Qb voltage with fixed phase relationship to the input. This

property may be of interest in pulsed systems where theC (fao) d(fd) b(fb) signal envelope must bear a fixed relationship to the

carrier. Eq. (5) can take further forms besides thosey90 given by (5') and (5"). For example, in the case where

both c and d are zero, the frequency fb is solely deter-

f { < 7lb mined by the condition b(fb) =0, that is, by the filter inB. If fb is chosen for the output frequency, the system

fd=f fb frequency acts as a converter, having an output frequency not re-lated to the input frequency and its variations.

/90_ A special mode of operation is observed when the fre-quency determining circuits in A, B, C and D are cen-

Fig. 3-The phase-frequency characteristics of the amplifiers B, C tered approximately to frequency values which are ra-and D for the case where C has a quartz-crystal tuning circuit and tionally related to each other. It is then found that, asB and D are wideband amplifiers, a result of locking, the frequencies in the system shift

so as to establish this fixed rational relationship. MostThe stabilization factor S, therefore, can be seen to be pronounced locking can be obtained when the frequency-primarily a function of the ratio of Q, to the sum of Qd determining circuits have a flat phase-frequency rela-and Qb as given by tionship =f(,,), i.e., when d$/dw = minimum or zero.

Operation within the locking range can be practical ifs = QC (8) the locking range exceeds considerably the possible

Qb + Qd range of frequency variation. Frequency converting andamplifying systems can then be devised having an out-

In a system where fa is the intermediate frequency, fo put frequency of the same relative stability as the fre-the incoming radio frequency carrier and fb the substi- quency of the input.tute of the usually separately generated local oscillatorfrequency, IF stabilization is possible for changes in the C. The Amplitude Relationshipfrequenciesfo and fb. Methods of IF stabilization used to A relationship between the amplitude of any one volt-date employ frequency discriminators, dc-amplifiers and age in the system and the amplitude of the input volt-reactance tubes which control the LO frequency. In the age can be derived from the conditions (1) and (4)two cases outlined above, IF stabilization is obtained by substituting the values of the conversion factors a,essentially by controlling the phase in an oscillatory A, and zy of the balanced mixers assumed in this case byloop which generates the substitute of the LO frequency. the expressions given in (9), (10) and (11) and eliminat-This phase control is accomplished by introducing a ing Ua and U~:phase angle into this loop, either in the filter in D to the 2/Ufrequency Id =fo, as shown in the first case, or in the ae=a-3 -=) 9crystal filter to the IF frequency to be stabilized, as r\W ± UB! KaRa(9shown in the second case. 2/UB \1

In both these cases, the mixer M1 performs the func- ±rt UB) v= I- (10)tion of a low-level input converter and the mixers M22 U \1and M3 are the high-level output converters. The am- 2 lc z = (11)plifier A is the IF amplifier, while D or B, or both, are 7rYZ+ Uc) K7Relow gain RE amplifiers which are required to offset the Ra, R: and Kz = load resistance of the mixer.

1959 Makow: IF Stabilization by Regenerative Frequency Conversion 35

The conversion factors a, f and Py are functions of the uPswitching voltages UB and Uc at the inputs of the mix-ers, shown in Fig. 1 by an x. The conversion factorsare, in general, small for small switching voltages and -ft +4A S4S-s2(8Q2o+7r2c)assume a constant value for large switching voltages. AFor balanced mixers (ring modulators) using diodeswith a square law characteristic, the expressions in (9), /(10) and (11) are good approximations, and represent U1-;4A-Dapproximately the behavior of any mixer when suitable a ____values for the constants K,, K, and K4 are used.CThe amplitudes of the voltages UB and Uc in branches -uo

7 and 9 respectively (see Fig. 1) are given by (12) and 4ABD(13) and in terms of the input voltage Uo by (14) and r2 4ABD)- 74 (4ABD) 4862D2C

Fig. 4-The amplitude relationship between the output voltate UUB = ByUOD (12) of M2 and the input voltage Uo.

Uc = UaA C (13) For large values of Uo, there will be a linear relationshipbetween U, and Uo as given by (19), and between any

UB = ByABUoAD (14) other voltage in the system and the input voltage, as

Uc = UoAA C (15) given by (20), (21), (22), (23), (24) and (25):2

Also, any other voltage in the system can be calculated Ua =-U0 (20)with the help of Table I. It is found, for example, thatthe voltage Uo as a function of U0 is given by (16) UP =-AUo (21)(for W= V=Z = S) and is shown in the graph of Fig. 4. 72

U2=-(UO _ S1r,) + 1/4A2 Sir3 2 S2(8BD + 7r2C) (16)zr2 4ABD () 7 K 4ABD 4B2D2C

(The minus sign leads to a solution which approaches 2zero for increasing input voltages and has no physical UA =-AUO (22)interpretation.) Below a certain value of the inputvoltage U0o, there is no real value for Uo. U08 can be 8calculated by setting the discriminant of (16) equal to 3

zero, and is given by (17). The value of the output volt-age Ug, for U08 is found by substituting (17) into (16) and Uc 2=ACUo (24)is given by (18). U 7= AU0(4

7r_ 8BDu's-= 2 + C +rI (17) UD- 4

AD UO (25)4ABDL C 7r

S / 8BDUF = -- 7r/2 + (18) ACKNOWLEDGMENT

-4A r3S The author wishes to acknowledge with appreciation

UOL = 44(U0 - (19) the most useful discuissions on the subject with H.7r2 \ 4ABD/ LeCaine and D. W. R. McKinley.