Direct synchronisation of a sinewave oscillator to a pulse

An analysis is given of the phenomenon of direct synchronisation of a sinewave oscillator to a rectangular pulse. The effect of an applied step function is investigated first, and the pulse is then considered as the application of a step, followed by its removal. By considering the action of the nth pulse in an applied pulse train, expressions are derived for most of the important effects, in terms of pulse size and frequency difference, both inside and outside the synchronising band. These include the synchronising bandwidth, the phase while synchronised, the form of the transient after application of the first pulse, beats and pulling effects just outside the synchronising band, and the waveform of the beats. The case in which the sinewave frequency is close to a large harmonic of the p.r.f. is also considered.