Expressions were derived for the mean and mean square value of the output of a phase detector to which is applied a sinusoidal signal corrupted by narrow-band Gaussian noise, together with an oscillator reference of the same frequency as the signal but displaced in phase. The analysis was based on the model of a balanced phase detector composed of peak-detecting diodes producing a difference output from the two halves. Based on the above output parameters, a measure of phase detector performance was defined in terms of a noise-to-noise ratio, the square root of the output variance without signal divided by the same quantity with the signal present. The case where signal and reference are in quadrature was treated in detail, yielding curves of this ratio under varying input and reference conditions. In addition, the voltage output signal-to-noise ratio was calculated as a function of the phase angle between signal and reference, and the resulting graphs show the effects of reference level and input signal-to-noise power ratio.
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