Density-Function Calculations of Noise Propagation on an Accelerated Multivelocity Electron Beam

Abstract

The propagation of noise current and voltage fluctuations through the multivelocity accelerating region immediately in front of the potential minimum has been calculated using the density-function method of analysis. Basic assumptions made include: (a) linearized one-dimensional analysis; (b) zero total ac current in the beam; (c) uncorrelated full shot noise in each velocity class at the minimum plane; (d) dc potential η(ξ) given by the Fry-Langmuir analysis. Starting at the minimum, the noise fluctuations were traced out towards positive ξ by a numerical forward-integration process using an IBM 650 electronic computer. Principal results of the computations are that Haus's noise parameters S and Π are found to vary significantly with distance between η=0 and η=4, contrary to previous assumption. The noise parameter S decreases to ∼0.7 of its initial value of kTc/2π, while the noise power Π rises from zero to ∼0.3 of the initial value of S. Exact results depend slightly on frequency. Beyond η=4 both noise parameters become invariant. The theoretical minimum noise figure of a beam type microwave amplifier, which is Fmin=1 +(2π/kT) (S-Π), is thus found to be reduced to ∼3½ db for a temperature-limited cathode instead of the commonly quoted value of 6½ db which is based on the values of S and Π at the cathode.