The Theory of FM Demodulation with Frequency-Compressive Feedback

The application of frequency-compressive feedback around an amplitude-insensitive FM demodulator promises important reductions of distortion and noise sensitivity in the demodulation of wide-band FM signals. In this paper, the basic theory of FM demodulation with frequency-compressive feedback (FCF) is presented after a brief discussion of the concept of noise threshold and of the usefulness of threshold reduction techniques in relaxing important requirements in the design of reliable communication systems. It is shown that the simultaneous presence of distortion and open-loop phase shift sets an upper bound on the amount of feedback that may be applied before inducing a rapid deterioration of system performance. This upper bound may fall well below the upper bound imposed by Nyquist's stability criterion. Thus, although the system may be stable in the usual sense, it may be incapable of tracking an applied FM signal either because of insufficient compressive action or because of open-loop phase shift that causes the distortion to rise with increased feedback. It is also shown that the system may be modeled (only approximately) by a linear feedback circuit provided that both the applied compressive action is sufficient to reduce the deviation ratio to a value much less than unity, and the SNR at the input of the feedback circuit exceeds or equals the threshold of linear output-input
S/N
relationship for a conventional FM demodulator. The linear dependence of the output SNR upon the input SNR is shown to be a necessary, but not sufficient, condition for the validity of the linear model. It is shown in this paper that the threshold of linear variation of the output SNR with the input SNR for an amplitude-insensitive FM demodulator with frequency-compressive feedback (FCF), driven directly from the linear stages of the receiver, is equivalent to that of a conventional FM demodulator that is driven from a noise bandwidth equal to one-third of the closed-loop noise bandwidth, or to the loop band-pass filter noise bandwidth, whichever is larger. When the closed-loop noise bandwidth is larger than three times the band-pass filter noise bandwidth, the band-pass filter bandwidth can be widened until it equals one third of the closed-loop noise bandwidth without changing the closed-loop noise bandwidth, provided a permissible compensating change is introduced in the loop low-pass filter. If this is done, the system will be able to accept a signal of wider deviation ratio and hence give better high
S/N
performance with the same threshold. In this sense, the FCF loop may be said to be optimized relative to the input signal if with the amount of feedback that is necessary to compress the frequency of the signal by the maximum permissible amount, the closed-loop noise bandwidth is equal to three times the noise bandwidth of the loop band-pass filter. The introduction of an amplitude limiter in front of the FCF loop is shown to raise the threshold of linear output vs input SNR back to the corresponding threshold of a conventional FM demodulator.