Three-Tone Characterization of Nonlinear Memory Effects in Radio-Frequency Power Amplifiers

A stepped three-tone measurement technique based on digitally modulated baseband signals is used in characterizing radio-frequency power amplifiers (PAs). The bandwidths of the stepped measurement were 8.8 MHz for the input signal and 26.4 MHz for the output signal. A PA designed for third-generation mobile telecommunication system was analyzed. The amplitude and phase of the third-order Volterra kernel were determined from the identified intermodulation products. The properties of the Volterra kernel along certain paths in the 3-D frequency space were analyzed and compared to some box models for nonlinear systems. The main symmetry of the third-order Volterra kernel of this PA was found to be of the type given by the cascaded quadratic nonlinearities with a linear filter in between (a Hammerstein-Wiener system), and frequency dependence, i.e., memory effects, was found to be due to the effects at the baseband.