Phase-Sensitive Detector Nonlinearity at the Signal Detection in the Presence of Noise

The essential nonlinearity characteristics of a phase-sensitive detector are studied theoretically, assuming that the input signal is a sine wave in the presence of additive narrow-band Gaussian noise. Three interesting cases of the nonlinearity of the phase-sensitive detector characteristics are analyzed by means of the expression which has been derived for the output signal-to-input noise ratio as a function of the input signal-to-noise ratio, the reference wave-to-noise ratio, and the phase angle between the input signal and reference wave. In the first case, the detector nonlinearity NA as a function of the input signal-to-noise ratio is determined. In the second and third cases, the detector nonlinearities NB and NC as a function of the phase angle between the input signal and the reference wave are obtained. The results are presented as closed-form analytical expressions. Several interesting cases are plotted as a function of the significant parameters. Besides being important in themselves, the results are of a general interest because they may be used to estimate essential nonlinearities in some other more complicated cases.