An Analysis of the Performance of the Oscillating Limiter Driven by FM Signals Corrupted by Noise

The behavior of the oscillating limiter (OL) driven by FM signals is surveyed, and its performance with signal corrupted by noise is investigated. For high values of the carrier-to-noise ratio (CNR), if the frequency deviation of the signal is small in comparison with the locking range of the OL, it is calculated, and experimentally verified, that a system OL discriminator is equivalent to a system bandpass limiter discriminator followed by a linear network whose frequency response has been specified. When the frequency deviation is not so small, the baseband noise power increases with it; a formula is given that allows the calculation of this power when the signal is such that the circuit operates in quasistationary fashion. For low values of the CNR, a mathematical analysis presents unsurmountable difficulties. However, heuristic argumentation leads to an interpretation of the operation of the OL in the threshold region, which is substantiated by an experimental investigation. The results of this paper enable a comparative evaluation of a system OL discriminator and a system bandpass limiter discriminator, to which the former reduces when the feedback path in the OL is open.     

Probability Density of the Click Duration in an Ideal FM Discriminator

The expression of the probability density function PClick(T) of the duration r of the clicks is determined as a function of 1) the expected number of clicks per second, Felick 2) the expected number of times per second that the noise component x(t) in phase with the carrier has instantaneous amplitude larger than that of the carrier itself 3) the probability density function peross(T) of the duration of the time intervals in which x(t) < -A 4) the probability that the values of the noise component in quadrature with the carrier will be of opposite sign at the extremes of time intervals of duration v. Using for Pcross(T) an approximate formula that holds fairly well in the range of the values of the signal-to-noise power ratio ? usually encountered, PIick(T) has been calculated for several values of a and for two shapes of the noise spectrum, Gaussian and rectangular. Finally, an expression is given for the mean value of T.     

An Extension of Viterbi's Analysis of the Cycle Slipping in a First-Order Phase-Locked Loop

The phenomenon of cycle slipping in a first-order phase-locked loop is reconsidered and a simple expression for the expected number ? of cycles slipped per second is given in the form of a rapidly converging series. In this way the computation of ? becomes much easier than with previously known formulas. A formula allowing the computation of the expected number of cycles gained or lost per second is also given. These results are obtained by extending a technique used by Viterbi. The outcome of experimental verifications of the theory is also reported.