Abstract
A mathematical treatment is given of the wave phenomena in a travelling wave parametric amplifier. The waves are described by two coupled differential equations of the second order. By the elimination of one of the unknowns a fourth order differential equation arises. There are four waves of the signal frequency and four waves of the idler frequency, in contrast to linear transmission lines, where there are only two waves on a single frequency. The influence of the reflected waves on the stability of the amplifier is investigated, and oscillation criteria are given. Some methods to prevent oscillation are suggested.
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