A Study on Quadratic PHD Models for Large Signal Applications

Measurement-based black box behavioral models are widely used nowadays. To handle nonlinear effects efficiently, such models often rely on approximation techniques. Polyharmonic distortion (PHD) modeling emerged as a viable approach for describing a nonlinear mapping. Typical PHD-based models, such as the well-known X-parameter model, are gained from linearization while operating on a certain large signal (LS) operational point. This limits the accuracy, especially for hard nonlinearities. However, quadratic terms can be added, which result in the quadratic PHD (QPHD) model. This enables highly accurate models for devices in strongly nonlinear operation, even in highly mismatched environments. In this paper, the accuracy of such models is investigated by predicting typical nonlinear measures, such as load-pull contours and intermodulation distortion, to assess the model accuracy for both static and dynamic stimulus. Furthermore, the LS matching problem is solved for both the X-parameter and the QPHD model. This allows to predict the optimum matching analytically, without performing load-pull analysis. To verify the accuracy of the model, the results are presented by comparing the model prediction with verification measurements for a commercially available GaN HEMT.