Using X-Parameters to Characterize and Model Long-Term Memory Effects of Wideband Modulated Signals
Designers of power amplifiers (PAs) used in wireless communication infrastructure today face many unique challenges, not the least of which is characterizing and modeling the component’s linear and nonlinear behavior. Complicating this task are long-term memory effects that make describing the PA characteristics, and therefore designing products with the PA, much more difficult. What is a memory effect? Consider that a “memoryless” system is defined as y(t) = f(x(t)), where y(t) is the output signal, x(t) is the input signal and f is a linear or nonlinear function. Here, the output at any time depends only on the input signal value at that particular instant. In a system that has memory, this does not hold true.
The output at a given time can depend not only on the present input value, but also previous output and input values. Common symptoms that let the designer know a system has memory are when the amplifier’s measured intermodulation distortion (e.g., TOI or IM3) changes as a function of the frequency difference between the two stimulus tones, its IM3 upper and lower sidebands exhibit asymmetry, or it produces hysteretic/multi-valued AM-AM and AM-PM amplifier responses in response to modulated signals.
Modeling the memory effects of microwave components like PAs is a difficult and challenging task. Memory effects make quantifying distortion (nonlinearity) much more complicated. They also make designing for linearity for arbitrary signals much more difficult, since pre-distortion of components with memory is much harder. The first step in dealing with memory effects is the ability to characterize and model them, systematically. Only then is it possible to eliminate or even exploit memory effects in design. Doing so would enable the designer to correct for distortion, design better instruments, and correct parts that would otherwise be more useful were it not for long-term memory. For example, the desirable high frequency and high-power capabilities of a promising technology like GaN HFETs is somewhat less attractive given that the devices often exhibit significant long-term memory effects due to trapping phenomena which adversely impacts linearity. Unfortunately, until recently, no unified approach yet exists to accurately characterize, model and simulate long-term memory effects for wide bandwidth communication signals.