Parametric Amplification along Nonlinear Transmission Lines

A pump signal propagating along a dispersionless transmission line with a distributed nonlinear capacitance is subject to deformation, since different parts of the signal move with different velocities. This process of deformation will eventually result in the formation of an electromagnetic shock wave. The deformation will affect the parametric amplification process. If a small signal consisting of a positive pulse, short compared to the pump cycle, is added to the pump signal at the input end, then it is shown that the small signal at the output must be non‐negative. All other small signals, including in particular those with sinusoidal time variation, can be regarded as superpositions of these short pulses. As a consequence it is shown that, in general, a sinusoidal signal will not be increased in its fundamental frequency component, by traveling down the line together with the pump signal. There are certain exceptional frequencies, multiples of one half the pump frequency, where a suitably phased small signal may be increased at its fundamental frequency, but not by a sufficient amount to be of practical interest.