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A genetic neural network based large-signal model for GaN HEMT transistor suitable for designing power amplifiers (PAs) is presented along with its parameters extraction procedure. This model is relatively easy to construct and implement in CAD software and requires only DC and S-parameter measurements. The modeling procedure was applied to a 4-W packaged GaN-on-Si HEMT and the developed model is validated by comparing its large-signal simulation to measured data. The model has been employed for simulating a switching-mode inverse class-F power amplifier. Very good agreement between the amplifier simulation and measurement shows the validity of the model.