Fundamentals of Fast Simulation Algorithms for RF Circuits

Designers of RF circuits such as power amplifiers, mixers, and filters make extensive use of simulation tools which perform periodic steady-state analysis and its extensions, but until the mid 1990s, the computational costs of these simulation tools restricted designers from simulating the behavior of complete RF subsystems. The introduction of fast matrix-implicit iterative algorithms completely changed this situation, and extensions of these fast methods are providing tools which can perform periodic, quasi-periodic, and periodic noise analysis of circuits with thousands of devices. Even though there are a number of research groups continuing to develop extensions of matrix-implicit methods, there is still no compact characterization which introduces the novice researcher to the fundamental issues. In this paper, we examine the basic periodic steady-state problem and provide both examples and linear algebra abstractions to demonstrate connections between seemingly dissimilar methods and to try to provide a more general framework for fast methods than the standard time-versus-frequency domain characterization of finite-difference, basis-collocation, and shooting methods