X-parameter-based modelling of polar modulated power amplifiers

X-parameters are developed as an extension of S-parameters capable of modelling non-linear devices driven by large signals. They are suitable for devices having only radio frequency (RF) and DC ports. In a polar power amplifier (PA), phase and envelope of the input modulated signal are applied at separate ports and the envelope port is neither an RF nor a DC port. As a result, X-parameters may fail to characterise the effect of the envelope port excitation and consequently the polar PA. This study introduces a solution to the problem for a commercial polar PA. In this solution, the RF-phase path is modelled by X-parameters and the envelope path of the polar PA is simulated by a low-pass filter. The solution can be applied to a group of polar PAs who have the similar topology and design as the one in this work. Modulated signals with different channel bandwidths were applied to the model of the polar PA for simulations. The simulated error vector magnitude (EVM) and adjacent channel power ratio (ACPR) were compared with the measured data to validate the model. The maximum differences between the simulated and measured EVM and ACPR are less than 2% point and 3 dB, respectively.