A method for calculating responses of sub-nanosecond circuits with nonlinear components

A method for calculating responses of high-frequency circuits with nonlinear components is presented. The method treats the input signal to the circuit as if it were composed of many small adjacent rectangular pulses. The response to the first pulse of the input signal is calculated initially. When the second pulse arrives, a response to this pulse is then calculated by taking the response to the first pulse as setting the initial value in the circuit. Repeating this procedure, the responses to the rest of the pulses in the input signal can be calculated. The final expression for the response has the same form as that of a linear convolution but with the nonlinear coefficients which must be calculated recursively; this can be called a nonlinear convolution. Examples of applying this method are given for a transmission line with a diode load driven by a 2-GHz sine wave and a 2-GHz square wave, respectively. This method can also be used for low-frequency circuits composed of frequency-dependent elements and nonlinear components.<>