The minimum detectable change in the mean noise-input power to a radio receiver

Exact expressions are given for the minimum detectable fractional change in the mean noise-input power to a radio receiver. These expressions involve only the pre-detector and post-detector filter responses and have been derived for receivers using either a vth-power instantaneous detector (half- or full-wave type) or an ideal vth-power envelope detector. Using these expressions an example, in which the pre-detector filter is a single tuned circuit and the post-detector filter is a simple rc integrator, is worked out in detail. By the use of some well justified approximations in treating this example the results are presented in simple form and show clearly the effect of pre- and post-detector-filter bandwidths, as well as the detector law, on the sensitivity of the receiver to changes in noise-input power. The results for this example are presented graphically.