Methods of theoretical analysis and computer modeling of the shaping of electrical pulses by nonlinear transmission lines and lumped-element delay lines

The mechanism by which high-power electrical pulses can be sharpened by propagation along nonlinear transmission lines and lumped-element delay lines is described with emphasis on the production of pulses with very fast leading or trailing edges. A survey of some of the mathematical techniques that have been applied to the propagation of electrical signals along nonlinear lines and ladder networks is presented, and the limitations of these techniques are discussed. The processes that both produce and limit pulse sharpening on nonlinear lumped-element delay lines are examined, and it is found that the wave equation, which describes the propagation of electrical signals along such networks, predicts that an electrical pulse will decompose into an array of solitons. An approximate formula for estimating the degree of pulse sharpening that can be produced on a delay line with a given number of sections is derived, and its accuracy is compared with experimental results. Numerical integration techniques for solving the nonlinear differential and difference equations that result from the mathematical analysis of nonlinear lines and networks are discussed, and the propagation of a voltage pulse along a lumped-element delay line containing nonlinear capacitors is simulated using a computer model based on an efficient algorithm