X parameters: What are they?

High frequency designers have used S – parameters for a long time when the circuit or device is being characterized in the linear domain. However, once the device or circuit goes beyond the strictly linear domain and enters large signal or nonlinear operating modes a new set of parameters need to be used. A new paradigm is being used now called X parameter analysis, synthesis, measurement and modeling. The Wikipedia description of X parameters is :

“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 N5242A Nonlinear Vector Network Analyzer  and the W2200 Advanced Design System  in 2008. (Nonlinear vector network analyzers are sometimes called large signal network analyzers.)

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 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 simply add the values of resistors connected in series. X-parameters help solve this cascading problem: If the X-parameters of a set of components are measured individually, the X-parameters (and hence the non-linear transfer function) can be calculated of any cascade made from them. Calculations based on X-parameters are usually performed within a harmonic balance* simulator environment.”

X parameters are a useful tool to not only analyze but also to characterize circuits, devices, IC packages or other multiport networks. It is a good tool to learn and know when one works with RF circuits.

* See a tutorial paper on Harmonic Balance Simulation in this blog.

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