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

This paper presents a general method for computing transient sensitivities using both direct and adjoint methods in controlled explicit event driven simulation algorithms that employ piecewise linear device models. Sensitivity information provides first order assessment of circuit variability with respect to design variables and parasitics. This information is particularly useful for noise analysis, timing rule generation, and circuit optimization. Techniques for incorporating transient sensitivity into adaptively controlled explicit simulation, a general piecewise linear simulator, are presented. Sensitivity computation includes algorithms to handle instantaneous charge redistribution due to the discontinuous conductance models of the piecewise linear elements, and the loss of simulation accuracy due to the nonmonotonic responses in autonomous adjoint circuits with nonzero initial conditions. Results demonstrate the efficiency and accuracy of the proposed techniques.

Matrix-implicit Krylov-subspace methods have made it possible to efficiently compute the periodic steady-state of large circuits using either the time-domain shooting-Newton method or the frequencydomain harmonic balance method. However, the harmonic balance methods are not so efficient at computing steady-state solutions with rapid transitions, and the low-order integration methods typically used with shooting-Newton methods are not so efficient when high accuracy is required. In this paper we describe a Time-Mapped Harmonic Balance method (TMHB), a fast Krylovsubspace spectral method that overcomes the inefficiency of standard harmonic balance in the case of rapid transitions. TMHB features a non-uniform grid to resolve the sharp features in the signals. Results on several examples demonstrate that the TMHB method achieves several orders of magnitude improvement in accuracy compared to the standard harmonic balance method. The TMHB method is also several times faster than the standard harmonic balance method in reaching identical solution accuracy. 1

This paper presents a general method for computing transient sensitivities using the adjoint method in event driven simulation algorithms that employ piecewise linear device models. Sensitivity information provides first order assessment of circuit variability with respect to design variables and parasitics. This information is particularly useful for noise stability analysis, timing rule generation, and circuit optimization. Techniques for incorporating adjoint transient sensitivity into ACES, a general piecewise linear simulator, are presented. Sensitivity computation includes algorithms to handle instantaneous charge redistribution due to the discontinuous conductance models of the piecewise linear elements, and the loss of simulation accuracy due to the non-monotonous responses in autonomous adjoint circuits with non-zero initial conditions. Results demonstrate the efficiency and accuracy of the proposed techniques.