Distributed Nonlinear Effects in Planar Transmission Lines

We present calculations of the third-order intercepts for planar transmission lines that contain a distributed nonlinear inductance or capacitance. We model such a transmission line as a series of small nonlinear elements that interact only weakly. This approach allows us to use simple lumped-element models to describe nonlinear effects in transmission lines longer than the effective wavelength. We use this approach to calculate the third-order intercepts for a lossless transmission line, and also for a transmission line with finite attenuation. Calculations for the lossless case agree well with third-harmonic measurements of high temperature superconducting transmission lines as a function of line length. For transmission lines with loss, the calculations agree well with third-harmonic measurements of transmission lines of variable length incorporating ferroelectric thin films.