Behavioral Modeling of Polar Power Amplifiers Based on X-parameters by Characterizing Envelope Path using Tunable Low-pass Filters

X-parameters are developed as a superset of S-parameters and they are suitable for modeling systems having only radio-frequency (RF) and DC ports. For a polar power amplifier (PA), the envelope of the input modulated signal is applied at the envelope port, which is neither an RF nor a DC port. In this case, X-parameter may fail to characterize the behavior of the envelope path and consequently the polar PA. To solve the problem, this paper proposes a method where the nonlinearity on the RF-phase path of a polar PA is characterized by X-parameters and the frequency behavior on the envelope path is modeled by a tunable low-pass filter. The two models are then combined to establish the behavioral model for the polar PA. The concept is preliminarily validated on a 2.25GHz polar PA for WCDMA/EDGE applications in a 0.18μm CMOS process. Keywords— X-parameters, behavioral modeling, polar power amplifiers, envelope tracking, CMOS technology