Chakraborty, N B

Dixit, K D

English

IACS Institutional Repository

60A  NOTE ON SOME TUNABLE OSCILLATORSN. B. CHAKRABOKTY* and K. D. DIXITJ. K. Institute or Applied Physics, University of Allahabad,Allahabad {T teceA v cd , J u l y  1, 1960)ABSTRACT. Some arraugeiuontH of vollage iuniiblo Iwo-piiih oseillators cnjiublo o f largo frequency doviaiion are fbsruHsficb Po'^sibli'combinations of tbo transfer funotions of the mdividnal jiaths together with the inning equation and 1 ho constraints lor stable amplitude of oscillation arc given In some circuit arrangements the variation of Iroquoncy with modulating voltage is found to be linear over a wide range.The jireseut note discusses some cij’cuit arrangements of voltage tunable oscillators which are theoretically capable of very large frequency deviation. In practical arrangements a frequency tuning ratio of two to one and in some cases live to one have been achieved. Tuning is accomplished by means of variation of the gains of the individual paths of a two-path oscillator.Fig. t. Schematic diagram of a iwo-fcodback loop.If G - i ( p ) and are the transfer lunctious of the two paths of the feedback loop in Fig. 1 the charactei'istic equation of the loop is given byI  . . .  ( 1)Here K - i and are the gain multiplying factors and are in general variable in accordance with tlie tuning voltage. If the adder is non-idcal and has a transfer function F { p )  then Eq. (1) is modified to1 (La)The condition for proper working is that the imaginary axis be the root locus with unity feedback.In Table I some possible combinations of transfer functions together with the tuning equation and the constraints for stable amplitude of oscillation are ♦ Now at the Institute of Badio Physics and Electronics, University of Calcutta,550 N. B. Ghakrahorty and K. D, Dixitfii'oseiitod. All tlie oirciiits have the pioperty that in theory it ahonld be possible (o limt‘ their i'recpieney of operation electronically from very low to very high fretjuencieK. Fiirthet'more the magnitude of their positive fecdbai'k voltage should be independent »)f the fref|nency of resonance. In some arrangements the cuive of frequency versus modulating voltage is linear over a wide range. In a few ari'angements where the stray capacitances can be taken into account in forming the transfer fnnetious the tuidiig range can obviously bo extended to figure of merit of the tubes emjiloyed or a fraction of it deiicndiiig on the gain requiredIt will be observed that ty i^es 1-6 are practical at audio frequencies, types 1, 5 and 6 at. low and very low frequencies, while types 1 6 , 7  and S are useful at radio frequencies. In Fig. 2(a) and Fig. 2(b) are presented circuit arrangementsFipf. U(a). Schonmiic diagram of th9 furruit armngi'mcnt of type I for low anrl vovy Jow froquencioHFir, 2(1)) Soliomntic dingram of Uit I'lromt nrrangement of lype I for A. F, and R. F.oi' oscillator of type 1 for use at. low and at radio frequencies For MF an interesting form derived from type 6 making use of delay lines tan be made as shoun in Fig. 3(a) and (b). Its tuning equation iswS “  cos-i(—7\\/2) (2)Fig. 3(a). Schomatio diagram of a circuit arrangomojit of t.ype 6.Fig. 3(b). Functional diagram of typo 6.The fretpicney of excursion in this case is limited to . The linearity of modu­lation around has been observed to be quite good. It is to be noted thatA Note on Some Tunable Oscillators 551pqHbC & P pH ^ . p1 ® 1 & P p=3p ?S 1^P -2P ^ i s55 Phrt pHP pHP— — _______________ _  ,cc Oc I IoJj^H h. 'ti1 (£1 o 7 151& 1 I CO CO1 1 Ci_, 1 'Mg t-. 1 ,^n ^ CO 11 s;  ^It -e i'^ V  ^ E?r 60 tcr 'W1-T3 *f 7- l E1V CO UO<M + '\ i"S1 1 J 11K 1J- i lCO1 3 J, SH1 'hT ^ CO? iS ii  6lP 'S1'^ '1 -^ itI'l fc< - 'M1 ^1 "H 1'Mi t-1 7 1 'h t  fsh' In  ^\^- >T3 It .’f r-■ia It 1 1§ i- \iS"S 1-H wh1 ' i 1 j 1 11 H Ho lt^‘ri :j,|j,too 1 OCDss ■> ~v 'y I 'M 1CO n 1COEH I1 1 I I 1 T 1 11 3 3 3 3 fcT 3 3r^i I'lc6 r. 1^1 I n 1 1 O o1 N I I1oU 1 1 (=<T -T+ ;T f l l« . 3•-I ? 3P.3T 1?3Tluid■n1---- "  ^1’^ s 1'1 f 11 11 1T , 3; + 3H-?1 3«!?3 1 3?| + “aSto11^1 3jl<o3r“3TCS r II1ir T0n W «0 t" oc552 N* B, Chakrahorty and K, D. Dixitill arrangements of types 6, 7 and 8, means will have to be adapted to supress harmonioH.The forms 1 —5 have identical characteristic equations. However the way nonlinearities enter into the equation is different and consequently the amplitude stability and other related properties will be different. The nonlinear defining equations in the different cases are also presented in Table I. F{x) represents the nonlinear parameter basically governing the ainplitufle of oscillation.It has been found that the variation of frequency is limited in practice to a ratio of five to one in types 1—5, while in the rest it is about two to one. It is thought that this may be due to the very considerable variation of the slope of the loop phase shift. Another cause is the non-uleal behaviour of the adder.The disturbing effect of the adder can be removed in the following manner.Suiiposing that the transfer function of the adder is the modified loop,equation is(l.o)The characteristic equation of the loop in the oscillating condition will now be{pn K ){p^ ~ c)  -  0 ... (3)It will be found in this case that both Kj and arc to be varied. 'For type 1 for example and are related by(2fe+])(2-l-6) = K,h{2Jrh)-\-h{\~K^ -K,) T U N A B L E  A M P L I F I E B S... (4)It is evident that at a gain setting smaller than that recpiired for self- oscillation all the circuits can be used as tunable amplifiers and hence as spectrum analysers. The nature of the selectivity curve and the variation of the maximum output of the response curve with the tuning frequency will obviously depend on the iioint of observation of the output as well as the nature of the transfer functions. In the (bagram of Fig. 1 for example for inputs and E^ applied respectivelyat the input to circuit, circuit and the adder the voltage outputs at the corresponding output points will be given by^1... ( M(5.6)(5c)A Note on Some Tunahte Oscillators 563whereIn the arrangement of Fig. 1 , for cxaiiiplo. if be the input applied to the adder the output >^2 will be given by1 at 2J -  jM’„.The peak of leBponsc will therefore depend t)ii the tuning irtujuency. If ojr the other hand, the voltage obtained at the output of circjuit in transmittedthrough a eireuit liaviiig a transfer fuiu tioii ^ «)ue obtains a transfer cluiraeter-;H 1istie which does not depend on the tuning frequeney. It should be noted that a much simpler solution is possible for the arrangement of type 3.K K E l l  E N V. E SAudoi'son, F. B., lOfiJ, P r o c .  I .  E .  E . ,  39, 881.Delanga, O. E , 11)49, P r o c .  1 .  R .  E . ,  37, 1328.Stowari, J. L , llinS. P r o c .  I .  R .  E . ,  43, 589.

A Note on Some Tunable Oscillators

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A Note on Some Tunable Oscillators

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