# Memory in Microwave Power Amplification Systems

All communication systems, in particular transmitters, have inherent nonlinearities that limit their usefulness and range of applications. For example, the input power level in microwave amplifiers must be kept below a certain level to ensure operation in a region of sufficiently linear amplification. Ignoring this requirement leads to the generation of significant intermodulation products caused by amplitude and phase nonlinearities. The types of nonlinear systems can be briefly classified as:

- • Nonlinear systems without memory
- • Nonlinear systems effectively without memory
- • Nonlinear systems with memory.

Each type of system produces distinct nonlinear effects. These three types of systems and their effects are characterized in the following subsections [5-8].

## Nonlinear Systems without Memory

Systems belonging to this category have the following three characteristics:

- • The output instantaneously responds to the input
- • The system does not have a frequency response
- • There are no phase nonlinearities.

Nonlinearities without memory are sometimes called resistive nonlinearities. Indeed, a nonlinear circuit without energy storage elements cannot possess memory.

When such a system is driven with a narrow band amplitude modulated signal *X(t)* at carrier frequency *ю* represented by:

where, *A(t)* is the envelope of the signal and *в* is initial constant phase of the signal. The output signal of the system includes an infinite number of harmonic components and the bandpass component, y(t), around *w* can be described by:

where *G* [A(t)] represents the AM/AM (amplitude modulation to amplitude modulation) conversion characteristics of the system and can be seen as an envelope- dependent gain function.

A necessary requirement for inclusion in the memoryless category is that *G* [A(t)] should not depend on frequency. In other words, the magnitude response of the system is “flat” in the frequency domain. The effects of memoryless nonlinearities are:

- • Generation of nonlinear amplitude distortion,
- • Generation of harmonic frequencies and intermodulation products,
- • A possible shift in the system’s DC operating point due to even-order distortions.

Examples of this type of nonlinearity are the piecewise-linear limiter and the ideal comparator. An appropriate representation for such characteristics is the relatively simple, classic power (Taylor) series; for this reason, series based formulations are often used in nonlinear modeling of systems. It should be understood that no real system can ever be truly without memory due to the always-present reactive (capacitive and inductive) elements in any electronic circuits.