Application of Fourier Transforms to Variable-Frequency Circuit Analysis

Fourier transforms are very valuable for the analysis of the behavior of passive circuits when the driving force is frequency modulated. The output current or voltage is expressed in the form of a convolution integral, which can lead either to the expansion given by Carson and Fry or, preferably, to the van der Pol expansion in terms of the values of the transfer admittance or impedance for the instantaneous frequency, and its derivatives. The proof given here lends itself to a discussion of the conditions for convergency. In certain cases, the convolution integral can be directly expressed in terms of known functions: this is the case, for instance, for broadband FM line discrimnators, an analysis of which is given.