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Shock Waves in Nonlinear Transmission Lines and Their Effect on Parametric Amplification

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The propagation of a periodic signal on a transmission line with a nonlinearity in the distributed capacitance is examined. The signal is deformed during its propagation and electromagnetic shock waves are generated. It is pointed out that the shock wave will form in a distance which is short for any parametric amplification purposes. The subsequent growth of the shock and its decay, due to the inevitable dissipation associated with a shock, are analyzed assuming that the capacitance variations are small compared to the total capacitance. The propagation of a small deviation from a signal which is perfectly periodic in time is also examined, and it is shown that the small deviation may spread out in time but cannot be changed in its sign. This result was invoked in an earlier paper demonstrating the impossibility of parametric amplification on dispersionless nonlinear lines.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:4 ,  Issue: 4 )

Date of Publication:

Oct. 1960

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