4 - X-parameter measurement

Summary

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.