# AM/AM and AM/PM Characteristics

The P_{out} vs. P_{in} characteristic is a basic and incomplete means of characterizing nonlinear transmitters and PAs driven by modulated signals. Indeed, a more comprehensive representation that includes amplitude as well as phase information is needed. In the most general case, a dynamic nonlinear transmitter is fully described by a set of four characteristics, namely the amplitude modulation to amplitude modulation (AM/AM) characteristic, the amplitude modulation to phase modulation (AM/PM) characteristic, the phase modulation to phase modulation (PM/PM) characteristic, and the phase modulation to amplitude modulation (PM/AM) characteristic. PA distortions are amplitude dependant and phase modulated signals (having constant amplitudes) are not affected by the PA distortions. Thus, PAs are mainly characterized by their AM/AM and AM/PM characteristics. Conversely, transmitters might exhibit PM/AM and PM/PM distortions that are mainly due to the gain and phase imbalances in the frequency up-conversion stage and/or when the transmitter has a non-flat frequency response over a bandwidth equal to that of the input signal. Contrary to the AM/AM and AM/PM distortions generated by the unavoidably nonlinear behavior of the PA, the PM/AM and PM/PM distortions can be minimized by a careful design of the transmitter. So far, these have often been considered to have an insignificant impact on the performance of a behavioral model or a digital predistorter. With the adoption of multi-carriers and multi-band power amplification systems where the bandwidth of the signal to be transmitted is large enough to observe on a non-flat frequency response of the PA, the contribution of the PM/AM and PM/PM is becoming more significant and their inclusion in next generation behavioral models and predistorters is becoming inevitable.

Let’s consider a DUT driven by a modulated input signal. *x _{in}* and

*x*refer to the baseband complex waveforms corresponding to the DUT’s input and output signals, respectively. The in-phase and quadrature components of the signals

_{out}*x*and

_{in}*x*are defined as:

_{out}Under the assumption that this DUT, to be modeled or equivalently linearized, does not exhibit PM/AM and PM/PM distortions, its instantaneous complex gain, G, is solely a function of the input signal’s magnitude and is given by:

where | G( |x_{in} |) | and G( |x_{in} |) represent the magnitude and phase of the instantaneous complex gain *G(lx _{in}* ), respectively; and are expressed as a function of the input and output complex baseband waveforms according to:

The AM/AM characteristic of the DUT is obtained by plotting the magnitude of its instantaneous gain (|G(|x_{in}|)|), typically expressed in dB, as a function of the DUT’s instantaneous input power. It is also possible, though less conventional to report the AM/AM characteristic as function of the DUT’s output power. Similarly, the AM/PM

Figure 1.8 Sample AM/AM characteristic of a power amplifier

characteristic of the DUT is the one that reports the phase of the instantaneous gain ( *GQx*_{in})), usually expressed in degrees, as a function of the DUT’s input or output power. Sample AM/AM and AM/PM characteristics are reported in Figures 1.8 and 1.9, respectively. These figures provide insightful information about the nonlinear behavior of the DUT. In fact, the shape of the AM/AM and AM/PM characteristics provide information about how severe the nonlinearity of the DUT is. Similarly, the dispersion of these two characteristics is a qualitative indication about the memory effects of the device.