Error-Signal Response of a Phase-Locked Loop to a Coherent Chirp Signal

A new theory which describes the transient response of a PLL to a periodic ramp voltage applied to the VCO for generating a coherent chirp signal has been presented. With the appropriate choice of loop parameters and the ramp voltage rate to make the value of the normalized loop natural frequency within the range (0, 1), the PLL's equation can be simplified to a nearly linear differential equation. Its asymptotic solution can be obtained by the perturbation method as ε is a rather small value. Computer simulation results in agreement with the analysis have been obtained. Its application to generate a coherent linear frequency modulation waveform using a high-gain second-order PLL is considered.