Index Reduction of FM Waves by Feedback and Power-Law Nonlinearities

As is known, it is possible to design feedback systems t h a t reduce t h e index of an FM wave by an explicit use of power-law nonlinearities based on certain simple trigonometric identities. Circuits which use feedback to achieve subharmonic operation, and which are stable under changes in the input frequency over at least a limited range, have been built, tested, and described in the literature. 1 T h e y have the behavior predicted by t h e trigonometric identities. Some of them depend 011 nonlinear conversion of a signal containing harmonics of 6 into one containing only the first harmonic, and others depend on the inverse process of generating harmonics. Our purpose is to discuss the problem of " m o d e s " (i.e., different responses to the same excitation) in these systems, and the problem of t h e stability of the interesting subharmonic modes. We also indicate an application to frequency modulation: by incorporating the principle on which the systems are based into a frequency modulation receiver, one obtains circuits with some of t h e properties and advantages of t h e FM demodulator with feedback 2 3 proposed by J. G. Chaffee. However, 589