Linearized dispersion relation and green's function for discrete-charge-transfer devices with incomplete transfer

A small-signal (linearized) theory of discrete-charge-transfer-device performance is presented for the case of incomplete charge transfer. Specifically, the dispersion relation is derived which relates the charge-transfer efficiencies presently characterizing these discrete (in space and time) devices to the usual measures of device or transmission-line performance based on the attenuation, dispersion, phase velocity, etc., of sine waves. In a more general sense this emphasizes the applicability of conventional signal theory to these new devices. The impulse solution or Green's function is then shourn to be the equivalent of a bivariate distribution in probability theory. More generally the utility of (deterministically interpreted) probability theory is emphasized by showing the equivalence of a general small-signal theory to a random-walk process.