Transient simulation based on state variables and waves

Abstract

This article reports a new method for transient analysis of nonlinear circuits based on nonlinear device state variables and waves at their ports. The method is based on relaxation and thus does not require large matrix decompositions if time step is constant. The use of waves results in guaranteed convergence for any linear passive circuit and some types of nonlinear circuits. Additionally, the formulation using waves ensures that nonlinear devices are always excited with a physically meaningful input, i.e., the amount of power transmitted to nonlinear devices is bounded. The method was implemented in the fREE-DA TM circuit simulator. The formulation, its properties, and a convergence analysis of the proposed method are presented first, followed by case studies. V C 2011 Wiley Periodicals, Inc.Int J RF and Microwave CAE 21:314-324, 2011.

Wave-based transient analysis using block Newton-Jacobi

“…(17) that is performed just once. The performance of the proposed approach is compared with the original (plain relaxation) wavebased transient analysis, type: WaveTran [1], and the statevariable transient analysis, type: Tran2 which uses the formulation of Eq. (3) [7].…”

“…All vectors in Eqs. (1) and (2) have the same size equal to the number of ports of the nonlinear network (n s ). Applying numerical integration and discrete convolution on the standard MNA equation and employing connectivity information between the linear and nonlinear subnetwork the following error function is obtained (the full derivation can be found in [1])…”

“…Different relaxation methods have been previously proposed for circuit simulation [5]. The greatest advantage of the approach presented in [1] compared to the traditional fixed-point iteration approaches using voltages and currents is that the power delivered to nonlinear devices at any iteration is bounded [2]. Convergence is guaranteed for any linear passive circuit and some types of nonlinear circuits.…”

“…Recently a new wave-based transient analysis aimed to microwave circuits was introduced in Reference [1]. This transient analysis formulation is based on fixed-point iterations of waves at the ports of nonlinear devices.…”

“…[1], the method proposed in [2] was further developed with parameterized nonlinear device models, implemented in the fREEDA TM [6] simulator and tested with a wider variety of circuits. This paper presents for the first time an alternative formulation of the transient analysis aimed to microwave circuits presented in [1] that uses a block Newton-Jacobi approach to accelerate the convergence of the nonlinear equations. Other methods to solve these equations exist but the Newton-Jacobi approach is attractive because its implementation requires relatively minor modifications to the original fixed-point method and shares the advantage of exploiting the latency of the circuit.…”