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This paper analyzes the step and impulse response of a phase-locked loop discriminator with an optimum-type RC filter. In previous papers the multiplier in a phase-locked loop is linearized in order to obtain the optimum filter design, and the response to a large step is not considered. In this paper the system is treated as a second-order nonlinear system, and phase plane analysis is used to determine the transient response. Some very interesting results were found analytically and then verified experimentally. For example, it was found that the phase error can be greater than Â¿ and the system will still lock onto the carrier after an unusual transient response.