X-parameters are a mathematical superset of S-parameters and are used for characterizing the amplitudes and relative phase of harmonics generated by nonlinear components under large input power levels.
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X-parameters represent a new category of nonlinear network parameters for high-frequency design and were developed and introduced by Agilent Technologies as functionality included in N5242 Nonlinear Vector Network Analyzer[1][2], and the W2200 Advanced Design System in 2008. (Nonlinear vector network analyzers are sometimes called large signal network analyzers[3].)
X-parameters are applicable to both large-signal and small-signal conditions, for linear and nonlinear components. They are a mathematical superset of S-parameters[4] meaning that, in the limit of a small signal, Agilent’s X-parameters reduce to S-parameters.
They help overcome a key challenge in RF engineering, namely that nonlinear impedance differences, harmonic mixing, and nonlinear reflection effects occur when components are cascaded under large signal operating conditions. This means that there is a nonlinear and as such non-trivial relationship between the properties of the individual cascaded components and the composite properties of the resulting cascade. This situation is unlike that at DC, where one can, for example, simply add the values of resistors connected in series. X-parameters help solve this cascading problem: if you measure the X-parameters of a set of components individually, you can calculate the X-parameters (and hence the non-linear transfer function) of any cascade made from them. Calculations based on X-parameters are usually performed within a harmonic balance simulator environment[5].
X-parameters are based on the polyharmonic distortion modeling work of Dr. Jan Verspecht[6][7] and Dr. David E. Root[7].
While the X-parameter format and underlying equations are open and documented in several IEEE papers[8][9], the trademark owner Agilent also states that Given the rapidly developing state of the technology, as well as finite resources, Agilent currently can provide additional support only to key customers and strategic partners whose efforts are focused on improving the technology.