Fundamentals of Nonlinear Behavioral Modeling for RF and Microwave Circuits

The memory effects, also known as dispersive effects, designate changes in the circuit response according to the excitation signal speed. This originates from the frequency filtering behavior of various building components like matching networks, gain control (AGC) loops, and the biasing network, as well as from heating and trapping effects inside the semiconductor bulk.
There is extensive work on modeling the memory mechanisms in microwave devices, especially for power amplifiers. The earlier works [4 11] have dealt with the memory effects resulting from the frequency selectivity in the amplifier pass-band, henceforth called short-term memory (STM) effects. In later work [12 24], it is observed that in narrowband integrated amplifiers, intermodulation (IMD) characteristics are found that cannot be explained by the amplifier band-pass filtering components. These are the long-term memory (LTM) effects.
Figure 3.7 gives a coarse illustration of the origins of the two memory mechanisms in an integrated circuit structure. The STM memory (also designated as high-frequency memory) is characterized by relatively short time constants, usually lower than a nanosecond. These are the time constants that define the microwave cutoff frequency of transistors and group delay in matching network and filters. The STM effects can be visualized by driving the circuit with a single-tone (sinusoid) signal and observing, for example, the input-output transducer gain as the excitation frequency is swept throughout the pass-band. This is illustrated in Figure 3.8(a), where we observe that the amplifier gain varies with both input power and frequency.