The sensitivity in the measurement of Gaussian noise power using a half-wave detector can suffer degradation relative to that of a full-wave detector, in cases where the bandwidth of the input waveform is not small compared to the center frequency. There are two physical mechanisms that suggest a basis for this effect. The half-wave detector responds to only half of the input waveform, resulting in possible loss of information. Also, in the half-wave detector a component of the input spectrum feeds through the diode and adds to the noise that is subsequently filtered by averaging at the detector output. This feedthrough component does not occur in full-wave detectors. The phenomena are examined using numerical simulation. The results for both linear and square-law characteristics are considered, and formulas and graphs for estimating the magnitudes of the effects are given.