Memory Effects in Microwave Co

OverviewDesigners of power amplifi ers (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 diffi cult.  What is a memory effect? Consider that a “memoryless” system is defi ned 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 amplifi er’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 amplifi er responses in response to modulated signals.  Particularly diffi cult to deal with are long-term memory effects, where the memory persists for timescales that are many orders of magnitude longer the timescales associated with the carrier frequency or even the frequency at which the carrier is being modulated. Long-term memory effects are caused by a number of factors, including time-varying operating conditions such as dynamic self-heating, bias-line modulation and semiconductor trapping phenomena that are induced by the input signal and vary at a relatively slow rate compared to the modulation speed.