System level modelling of RF power amplifiers based on large-signal measurements

Abstract

This paper demonstrates the extraction of three different system level behavioural models of power amplifiers from large signal time domain measurements. The modelling results are evaluated using a common independent CDMA2000SR1 telecommunication input signal. The capability of the models to predict long term memory effects is also evaluated by artificially modifying the bias network in one of the PA prototypes. I. INTRODUCTIONThe integration of more functionality, and thus complexity, in wireless transceivers, turned the traditional circuit level based simulation highly inefficient, which asked for system level analysis, and so reduced order models. Unfortunately, the simplicity of such reduced order models is only apparent when we have interacting nonlinearity and dynamics. This is the case of microwave power amplifiers (PAs) where an increasing interest has been seen to look for compact models that can reproduce their observable input-output behaviour without the need for the complete internal description [1]. Indeed, this model simplicity has a high cost in predictive capability and the measurements required for parameter set extraction, since we are no longer relying on any a-priori knowledge of the PA physics.Therefore, a great care is paid to the selection of the model format, since not all mathematical formulations are able to reproduce every input-output mapping encountered in nature. For example, no one would try to use a linear S-parameter matrix to reproduce nonlinear behaviour, nor would one use a polynomial, or any other static function, to account for the PA fast (time constants of the order of the carrier period) or slow dynamics (time constants of the order of the inverse of the modulated signal bandwidth). Nonlinear system identification theories have shown that the model of Fig. 1 is one of these possible general formulations as long as (i) enough delays are available in the first linear dynamic block and (ii) the nonlinear static block is a universal approximator [1].Also, because the model is built from (behavioural) inputoutput observations, it should be intuitive that its accuracy degrades when its response is tested for signal excitations that are farther and farther away from the signal, or signal class, used to extract it. For example, we should not expect that such a model can predict the response to a signal that exposes some PA property never tested during model extraction. Hence, excitation selection for model extraction and validation plays a vital role on the final model quality [2].