21.396.619.27:621.3.011.21 Paper No. 1384 RADIO SECTION TWO NOTES ON THE PERFORMANCE OF RECTIFIER MODULATORS By D. G. TUCKER, D.Sc, Associate Member. {The paper was first received 25th February, and in revised form 11th June, 1952.) PREFACE The paper, which is in two parts, is a study of some aspects of the performance of rectifier modulators. Part 1 deals with the calculation of the input impedance of rectifier modulators with frequency-selective terminations; and Part 2 deals with carrier-leak control by the use of a d.c. meter. Part 1. THE INPUT IMPEDANCE OF RECTIFIER MODULATORS WITH FREQUENCY-SELECTIVE TERMINATIONS SUMMARY The input impedance of a rect ifier modulator is diff erent in its circuit relationshi ps fr om that of a passive lin ear network; for a give n input frequ ency it depends on the value of the load impedance at all the frequencies which can exist in the circuit and often also on the impedance of the signal source from which it is measured. The calculation of the input impedance appears to be impracticable in the general case; but in special cases where the terminating impe- dances ca n be restricted to zero or infin ity or t o a pure resist ance at the various frequencies which can exist in the circuit, and where the resistance/time function of the rect ifier can be expanded as a Fourier series independent of the signal frequencies—i.e. controlled solel y by the carrier—calculation is possible, and a selection of results is tabulated. (1) INTRODUCTION The input impedance of a rectifier modulator is not always —or even usually—important in itself, as the modulator is probably designed for a certain, or a minimum, conversion loss taking into account the signal source and output load impe- dances; such calculations do not involve a knowledge of the input impedance. But sometime s the input impedance i s a factor which has to be specified because of its reaction on other design considerations; examples of such cases are: {a) In carrier telephony, where the channel modulator follows the audio input circuit, which may be a cable circuit requiring to be terminated by an impedance within, say, 50% of its characteristic impedance. {b) The input impedance might be the load on a valve circuit, e.g. a cathod e foll ower , where it needs to be known if the valve performance is to be calculated. It is not generally realized that with modulators, as distinct from passive linear networks, the impedance of the signal source often influences the impedance which it sees at the modulator input. Thus it is important in speci ficat ions to state from what source impedance t he input i mpedance is to be measured. It i s not sufficient just to measure the impedance on any available bridge. When the source and load impedances vary with frequency, calculation of the input impedance is impracticable in the general case, as is the calculation of conversion loss discussed in earlier papers.* But, for a special type o f termin ation , cal- cula tion is not dif ficul t; th e special restriction is tha t termina- ting impedances must be zero, infinite or a pure resistance • UCKER, D. G.: "Rectifier Modulators with Frequency-Selective Terminations," Proceedings I.E.E., 1949, 96, Part III, p. 422; also Discussion in 1950, 97, Part III, p. 206. Written contributions on papers published without being read at meetings are invited for consideration with a view to publication. Dr. Tucker is at H.M. Underwater Detection Establishment, and was formerly at the Post Office Research Station. at the freq uenci es of all possible modulat ion product s. Most practical cases approximate in some degree to this condition, and therefore the analysis is of great value in assisting design and assessment of performance. In Section 2 a number of useful results are presented on this restricted basis. (2) SOME USEFUL RESULTS The circuits analysed are the well-known ring and shunt modulators, shown in Figs. 1.1-1.4. In these Figures, R s = Signal-source "resistance." R R — Load "resistance." These are zero, infinite, or purely resistive at all significant frequencies. r{i) = Rectifier resistance controlled entirely by the carrier voltage. The subscripts + and — in Fig. 1. 2 indicate rectifiers of opposite polarity. .Carrier^ voltage Fig. 1.1.—Ring modulator. r + (t) •VWAA- Fig. 1.2.—Effective signal circuit of ring modulator. In the analysis it is assumed that the rectifiers switch, as the carrier voltage passes through zero, from a constant forward resistance r^ to a constant back resistance r b or vice versa. Then [400]
