Nonlinear delay line with a constant characteristic impedance

Abstract

It is shown that for a lossless nonlinear transmission line in which both the series inductance per unit length L(i), and the shunt capacitance per unit length C(v), are amplitude dependent, the phase velocity is given by u = 1/?{L(i)C(v)} and the characteristic impedance is given by Z0 = ?{L(i)/C(v)}. By appropriate choice of the functions L(i) and C(v), there is a class of lines whose variation in phase velocity with signal amplitude is greater than in partly nonlinear lines (where only the inductance or the capacitance is nonlinear), and whose characteristic impedance is constant and not amplitude dependent. The theory of this type of line is given, together with results from an experimental lumped line which employs saturating inductors and varactor diodes. The line has a delay which is variable over the range 0.8?4?s and shows a good agreement with theory. For small-signal plus bias inputs the line behaves like a linear line, except that its delay and cutoff frequency are determined by the amplitude of the bias. For large-signal operation there is considerable distortion, and shock waves can be formed.