On the Theory of Noise in Radio Receivers with Square Law Detectors

Abstract

For the video output V of a receiver, consisting of an i‐f stage, a quadratic detector, and a video amplifier, the probability density P(V) has been obtained for noise alone and for noise and signal. The results are expressed in terms of eigenvalues and eigenfunctions of the integral equation $${\displaystyle {\int }_0^{\infty }}\mathrm{K(t)\rho (s-t)f(t)dt=\lambda f(s)}$$ , where ρ(τ) is the i‐f correlation function (i.e., the Fourier transform of the i‐f power spectrum) and K(t) is the response function of the video amplifier (i.e., the Fourier transform of the video amplitude spectrum). Two special cases are discussed in which the integral equation can be solved explicitly. Approximations for general amplifiers are given in the limiting cases of wide and narrow videos. Some applications of the method to other problems are shown in Sections 7B and 9.