DensityFunction 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 densityfunction method of analysis. Basic assumptions made include: (a) linearized onedimensional 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 FryLangmuir analysis. Starting at the minimum, the noise fluctuations were traced out towards positive ξ by a numerical forwardintegration 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 kT_{c}/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 F_{min}=1 +(2π/kT) (SΠ), is thus found to be reduced to ∼31/2 db for a temperaturelimited cathode instead of the commonly quoted value of 61/2 db which is based on the values of S and Π at the cathode.
 Publication:

Journal of Applied Physics
 Pub Date:
 October 1957
 DOI:
 10.1063/1.1722594
 Bibcode:
 1957JAP....28.1138S