Stability of Frequency Feedback Receivers Under Steps in Input Frequency

The frequency feedback (or frequency compression) demodulator for FM signals was proposed by J. G. Chaffee 1 in 1937. After some 1503 1504 T H E BELL SYSTEM TECHNICAL J O U R N A L , M A Y - J U N E 1971 twenty-five years, Chaffee's idea was found to have a particularly fitting application in the satellite communications experiments Echo 2 and Telstar, 3 in which there was a high premium on detecting a lowpower wide-band FM signal in noise. Nevertheless, since its invention, little progress has been made in the mathematical analysis of this circuit. Approximate methods of analysis and synthesis have been proposed, and some of them experimentally verified as useful. 4,5 However, except for unpublished works by S. 0. Rice and T. R. Williams, the nonlinear character of the circuit away from equilibrium positions has not been considered. It is the aim of this paper to formulate briefly one of the problems arising in the analysis of the FM with feedback (FMFB) receiver, namely that of stability of its response to step changes in input frequency. We shall write equations describing this response and present results about local and global stability of solutions for simple cases.