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X-Parameters: Revolutionizing nonlinear measurements in a linear world

A recent development in the measurement world is changing the way engineers design and verify linear systems and components like those commonly used in the wireless and aerospace/defense industries.


The development, X-parameters*, essentially does for nonlinear systems and components what S-parameters do for their linear counterparts.

X-parameters represent a new category of nonlinear network parameters for deterministic, high-frequency design.

Used to characterize the amplitudes and relative phase of nonlinear device behavior, they offer speed and convenience analogous to S-parameters. Unlike S-parameters, however, they are applicable to both large-signal and small-signal conditions, and can be used for linear and nonlinear components. They correctly characterize impedance mismatches and frequency mixing behavior to allow accurate simulation of cascaded nonlinear X-parameter blocks (e.g., amplifiers and mixers), in design.

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The ability to quickly and accurately measure nonlinear device behavior represents a significant advance in high-frequency design. No longer do engineers have to measure nonlinear attributes by making linear assumptions (e.g., taking S-parameters and applying nonlinear figures of merit) – all the while hoping their device isn’t so nonlinear as to be problematic, especially when it comes to simulation.

Ideally, the engineer would like to measure their device and put in a simulator to see what it would do with other devices. But, if the device’s nonlinear behavior is measured using a linear assumption, then the result of the simulation will be wrong. Moreover, the inaccuracy of the linear assumption generally forces extensive and costly empirical-based design iterations, adding substantial time and cost to the design and verification process.

X-parameters make the need for linear assumptions regarding nonlinear device behavior obsolete, but how do engineers obtain X-parameters? More importantly, how does their use impact the design flow? X-parameters can be obtained in one of two ways – either generated from a circuit-level design or through actual measurement. Once obtained, they are used to create X-parameter models that can be dropped into a component or system to start the design process or imported into a simulator.

  X-parameters can be generated from a circuit-level design in Agilent Technologies’
  Advanced Design System (ADS) software or measured using the Nonlinear Vector Network
  Analyzer (NVNA) software running inside Agilent’s PNA-X network analyzer.

These behavioral models take into account a range of different variables including source and load impedance, are fast, drop-in useable, and accurate. Because of this, they can be used in place of actual circuits with excellent accuracy and much faster simulation speed.

With current trends toward increasing energy efficiency, higher output power and longer battery life now forcing many linear devices to operate in a nonlinear fashion, the need for fast and accurate measurement of nonlinear behavior has become all the more urgent.

As a logical extension of S-parameters to include nonlinear effects, X-parameters represent the ideal solution to this dilemma. By enabling today’s engineer to deterministically design the most robust components and systems in the shortest amount of time and with the highest degree of accuracy, they are quickly becoming a key tool in the creation of linear solutions for use in a range of applications in aerospace/defense and telecommunications.

*X-parameters is a registered trademark of Agilent Technologies. The X-parameter format and underlying equations are open and documented.

For more information, visit www.agilent.com/find/eesof-x-parameters-info.