The characteristic polynomials associated with the algorithms used in digital phase detection are used to investigate the effects of additive noise on phase measurements. First, it is shown that a loss factor eta can be associated with any algorithm. This parameter describes the influence of the algorithm on the global signal-to-noise ratio (SNR). Second, the variance of the phase error is shown to depend mainly on the global SNR. The amplitude of a modulation of this variance at twice the signal frequency depends on a single parameter beta. The material presented here extends previously published results, and as many as 19 algorithms are analyzed.