The Demodulation of a Frequency-Modulated Carrier and Random Noise by a Discriminator

Abstract

With the aid of an idealized representation of the discriminator, Middleton has shown that a frequency-modulated carrier remains intelligible for smaller carrier strengths when narrow-band f-m is used and the limiter is omitted than with a limiter and/or wide-band f-m. It is, therefore, of some interest to treat the demodulation process as it actually occurs, in the absence of a limiter. Thus, the discriminator has been taken to consist of two selective circuits, both fed by the output of the intermediate-frequency amplifier, but peaked at different frequencies, feeding rectifiers whose outputs are subtracted. Each half of the device is treated in the manner used by Rice to determine the result of passing random noise and a sine wave through a rectifier; however, there is a correlation between the noise voltages fed to the two rectifiers. The signal output and the spectral distribution of the noise output are obtained first for quadratic rectification, then in the general case, which is then specialized to linear rectification. The results are applied to a case of rectangular i-f noise spectrum, and the signal-to-noise ratio is determined for the cases of narrow-band and wide-band f-m. These results are found to be very much like those for the idealized representation of the discriminator; all are compared, along with amplitude modulation, in Table I. The optimum signal-to-noise ratio for f-m without a limiter is found to obtain with narrow-band f-m when the discriminator is designed for no wider a band than necessary; this optimum signal-to-noise ratio differs very little from that for a-m.