Memory Effects in Microwave Co

Overview
Designers 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.