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  • Print publication year: 2013
  • Online publication date: October 2013

4 - X-parameter measurement


One of the key features that led to the wide adoption of S-parameters was the availability of hardware and calibration techniques capable of making quick, accurate, and repeatable S-parameter measurements. S-parameters can also be easily extracted in simulation from device or circuit models. In either case, the resulting S-parameters can immediately be used in simulation or design tools. In order to achieve similar success in the nonlinear domain, X-parameters must be easily measured and also easily extracted from simulation.

Measurement hardware

X-parameters, like S-parameters, represent the steady-state behavior of a device in the frequency domain. The linearity assumption of S-parameters, however, greatly simplifies the measurement requirements. The additional capabilities of X-parameters come at the cost of additional complexity in the measurement system as well as the modeling paradigm.

Hardware requirements

X-parameters include cross-frequency terms that capture the distortion products generated by device nonlinearities. In order to measure these terms, the measurement hardware must be capable of measuring coherent cross-frequency phase. Because S-parameters include no cross-frequency interaction (a consequence of the linearity assumption), each frequency may be measured independently with no need for a consistent time base or cross-frequency phase. Since all S-parameters are ratios of waves, there is also no need for accurate measurement of absolute power – only the relative power is needed. As a result, the hardware and calibration techniques developed for S-parameter measurement generally are not sufficient for X-parameter measurement and must be extended to include cross-frequency phase and calibrated absolute power.

Gunyan, D. B., Root, D. E., Betts, L. C., and Horn, J. M., “Large signal scattering functions from orthogonal phase measurements,” U.S. Patent 7 671 605, Mar. 2, 2010.
Root, D. E., Sharrit, D. D., and Wood, J., “Behavioral model generation,” U.S. Patent 8 170 854, May 1, 2012.
Agilent Technologies, Inc., “Advanced Design System” documentation (ADS2009U1 or later) – Working with data files – X-parameter GMDIF format. Available at .
Additional reading
“Applying error correction to network analyzer measurements,” Agilent AN 1287–3, Agilent Technologies, Inc., Santa Clara, CA, 2002.
Van den Broeck, T. and Verspecht, J., “Calibrated vectorial nonlinear-network analyzers,” in 1994 MTT-S IMS Dig., May 1994, vol. 2, pp. 1069–1072.
Verspecht, J., “Method and a test setup for measuring large-signal S-parameters that include the coefficients relating to the conjugate of the incident waves,” U.S. Patent 7 038 468, May 2, 2006.