Multitone Multiharmonic Scattering Parameters for the Characterization of Nonlinear Networks

Abstract

This work describes a generalized multitone multiharmonic scattering parameters ( $\mathbf {M^{2}S}$ -parameters) measurement approach suitable for multiport nonlinear network characterization in the wave-variable domain. Based on the incommensurate (or offset) frequency concept, the $\mathbf {M^{2}S}$ -parameters are directly measurable quantities independent of the incident wave phases and display a mild nonlinear dependence on the incident wave amplitudes. They feature a well-defined relationship with the frequency-domain nonlinear transfer functions derived from the Volterra theory, representing a generalization to the multiinput multiharmonic case of the widely used single-input single-frequency describing function approach. The proposed framework allows to capture the nonlinear steady-state behavior from a reduced set of measurements and can be effectively exploited for performance prediction in application-like scenarios. The approach is here applied to RF transistor and power amplifier load-pull measurements, as well as to the case of broadband modulation, showing that the performance assessment of the device can be obtained in a straightforward way from the $\mathbf {M^{2}S}$ -parameters description.