This paper quantifies the degradation in performance of a quadrature receiver when the phase of the input target signal is time-varying and the background noise is additive Gaussian. The quadrature receiver, a conventional signal processor, consists of a replica-correlator followed by a quadratic detector. In active sonar systems with narrowband transmit signals, direct path and multipath returns from a distributed highlight target add at the receiver to produce a composite echo which has a time-varying phase over the signal duration. As a result, a mismatch in phase exists between the received signal and the replica (replica-correlator) causing a degradation in processor performance. This paper measures the amount of processor degradation using a general narrowband target signal model with random phase fluctuations which are characterized by a unimodal probability distribution and a known covariance function. The receiver degradation is presented functionally in terms of the output signal-to-noise ratio (SNR) and graphically in terms of the receiver operating characteristics (ROC) curves. When the phase is assumed to be piecewise constant from time interval-to-interval over the signal duration, it is shown that under certain conditions, the receiver output SNR diminishes by 3 dB for each doubling of the number of time intervals.