Frequency multiplexing tickle tones to determine harmonic coupling weights in nonlinear systems

Obtaining the Jacobian parameters for a nonlinear system, such as in X-parameter or S-function measurement, requires excitation of tickle tones either on or slightly off of the main harmonic frequencies. Traditional off-frequency measurements involve simultaneous excitation with tickle tones both slightly above and/or below a single harmonic frequency at a time. This paper describes a multiplexing technique for the excitation of the system with perturbations at all harmonics simultaneously. This technique requires both frequency and cross-frequency noninterference for successful results from the measurements. If these conditions exist for the nonlinear system, the off-frequency multiplexing technique for tickle tones can reduce the measurements necessary to find the Jacobian matrices by a factor equal to the number of harmonics considered in the polyharmonic distortion. These methods provide exact results for memoryless polynomial nonlinearities.