Analysis of the Phase-Controlled Loop with a Sawtooth Comparator

The phase-controlled oscillator has evoked much interest in recent years. Some of its applications are to synchronism in television,1"' synchronization to a harmonic of a crystal oscillator, 3 elimination of jitter in pulse code modulation, 4 tracking filters, etc. The general phase-controlled oscillator loop is given in Fig. 1. The incoming signal and the variable oscillator have the same free-running frequency coc. The phase comparator has as its output some function / of the phase difference
,) =
,) for for n = ··· - 1 , 0 , 1 , The output of the phase comparator passes through a filter whose impulse response is h(t). The output of the filter v(t) controls the variable oscillator according to the equation at = «»(