The frequency-lock a.f.c. circuit as a means of tracking signals of changing frequency in conditions of low signal/noise ratio

A frequency-lock a.f.c. loop was used to lock to and track a weak c.w. signal of changing frequency in the presence of high levels of noise. The noise-free operation of the loop as a tracking system is discussed qualitatively from first principles, and this is followed by a theoretical analysis. The tracking performance of the loop is then considered for the case where the signal is in the presence of noise and the concepts of the `maximum rate of follow¿ and the `mean time-to-unlock¿ are introduced. An examination of the errors resulting from the noise and from changes in the signal frequency leads to a theory of the loop operation for signals in noise. A range of practical results is presented which provides agreement with this theory within the expected experimental error.