**IEEE 1770**-2021 IEEE Recommended Practce for the Usage of Terms Commonly Employed in the Field of Large- Signal Vector Network Analysis.

3.4.2 X-Parameter ® models X-Parameter® models 4 are spectral maps defining a nonlinear behavioral model in the frequency domain or the envelope domain [B11]. A spectral map is a function that maps phasors representing the input signals into phasors representing the output signals. NOTE 1—Phasors are constants for a frequency domain representation and are time dependent for an envelope domain representation. The key characteristic of an X-parameter ® model is that it is based on expressing time invariant DUT behavior in the frequency domain, as described in [B12]. Time invariant behavior means that any time delay applied to the input signals results in the same time delay applied to the output signals. In the frequency domain, the application of such a time delay corresponds to applying a phase shift to all phasors that is proportional to the frequency of the phasors, the proportionality constant being 2π times the delay. This phase shift is referred to as a linear phase shift and is equivalent to a constant shift in time. The X-parameter ® model is constructed such that the application of a linear phase shift to the input phasors results in an equivalent linear phase shift of the output phasors. An X-parameter ® model can be static or dynamic. With a static X-parameter ® model the output phasors are a function of the instantaneous input phasors. With a dynamic X-parameter ® model, the output phasors are also a function of the past input phasors. In other words, a dynamic X-parameter ® model has memory with respect to the phasors. NOTE 2—The input variables to an X-parameter ® model are typically port dc bias voltages (or currents), incident pseudo- wave phasors, A p,h (in the case of harmonically related incident signals at port p and harmonic h), and other parameters, such as temperature that are required to specify the large-signal steady state operating condition of the component.

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