Note on Phase Locking to the Envelope of a Periodically Pulsed Sine Wire

A periodically pulsed sine wave in noise, typical in wildlife tracking systems, is often envelope demodulated in the signal detector. An automatic detector using correlation techniques might employ a binary (bang-bang) multiplier in the phase-lock loop to lock onto the demodulated pulse train. A threshold device in front of or incorporated into the multiplier to quantize the pulse envelope causes loop gain effects, which are analyzed in this paper. A trade off from high loop gain to low loop threshold is the result as the quantizer threshold is lowered to the point where noise envelope alone exceeds the threshold 37 percent of the time.