Harmonic distortion of frequency-modulated waves by linear networks

An expression is obtained connecting the distortion of the modulating signal with the distortion of the r.f. spectrum when an f.m. carrier is passed through a linear network. It is used to obtain the harmonic distortion when the signal is a single tone. In the derivation of the expression it is assumed that departures of the phase characteristic of the network from linearity with respect to frequency, and of the amplitude characteristic from constancy, are small. These assumptions are made on the ground that we are usually interested only in networks that produce small distortion of the modulation. However, it is shown that such small distortion is more generally produced by an amplitude characteristic which is sinusoidal with respect to frequency, provided that the distortion due to the phase characteristic is small. The theory could be extended straightforwardly to cover the case of small deviations from such sinusoidal characteristics, although the extension is not made in the paper.Tables of functions involved in calculating distortion by the present approach are provided, and comparison is made with the result obtained by Van der Pol using Carson and Fry's operational method, and with some measurements.