Interpolation and extrapolation capabilities of non-linear behavioural models

This paper demonstrates how the Poly Harmonic Distortion (PHD) modelling framework is effective in its ability to interpolate or extrapolate non-linear measured data and thereby improve the quality and speed of measurement systems. Fundamental interpolation was verified and demonstrated using a 7-coefficient model extracted from a sparse set of fundamental impedances (19 points). It was shown that a relatively low order polynomial was required to capture the second harmonic space. Interpolation accuracy was however increased by including more coefficients. Second harmonic extrapolation was carried out on measured data and shown to be accurate to an average confidence of 99% when 6 model coefficients were extracted on a 0.7 reflection coefficient circle and then used to predict data on a 1.0 reflection coefficient circle. Measurements were carried out using an open loop active load-pull system operating at a fundamental frequency of 9GHz, on a 0.5W 10×75μm GaAs PHEMT device.