Limitations on the noise figure of microwave amplifiers of the beam type

A general model is developed for microwave amplifiers of the beam type based on the usual assumptions of a small signal, one-dimensional, single velocity flow of the electrons in the beam. The model includes arbitrary noise smoothing schemes and all amplifiers whose input and output structures have no direct rf connection; the rf coupling is provided solely by means of the modulated electron beam. A klystron, a space-charge wave amplifier, and a traveling-wave tube with a severed helix (or a helix with strong localized attenuation) are all special cases of this model. It is shown that the minimum noise figure of such an amplifier is of the form F
min
=1+2Π/kT|K| [S(z
0
,w)- K/|K| Π(z
0
,w) where S(z
0
,w) and Π(z
0
,w) are parameters of the beam noise expressed at a cross section z
0
slightly beyond the potential minimum in the electron gun, k is Boltzmann's constant, T is the temperature of the circuit, and K is a constant dependent upon the particular structures used. The dependence of K upon the microwave structures employed is discussed under restrictive assumptions about the loss in the rf structure of the amplifier. Two cases are possible. In the first case, the minimum possible value of K is unity. In the second, K is less than unity. It is shown, however, that in the latter case the available gain, G
0
, of the amplifier is given by G
0
=1/1-K