Vii. Microwave Tube Research A. Noise Reduction by Means of a Lossy Beam Transformer

in which 4o is the self power spectrum of the noise voltage, To is the self power 0 0 spectrum of the noise current, A is the imaginary part of the cross power spectrum 0 of the noise voltage and current, and H is the real part of the cross power spectrum; O0 the subscript o indicates that all noise power spectra are taken at a reference plane beyond the potential minimum in the electron gun. The reference plane is chosen sufficiently far from the potential minimum that an approximate single velocity treatment of the electron flow is justified at and beyond the reference plane. In other words, the average velocity of the electrons at the reference plane must be large compared to their velocity spread. If the corresponding power spectra at an arbitrary cross-sectional plane of the electron beam are indicated by 4, 4, A, and H, and if we set S = ( \'A ) 1/ 2 , then S = So and 1 = H , as proved before (1), provided only lossless beam transformers act upon the beam. Velocity jumps, beam expansions and contractions, and the like, if analyzed under the assumption of a one-dimensional geometry, are examples of lossless beam transformers. It is of interest to know whether or not an extraction of noise power from the electron beam would lead to a lower ultimate noise figure than that given in Eq. 1. A wide class of microwave structures that extract rf power from an electron beam can be represented as lossy nonreciprocal four-terminal networks so far as their