Stable Simulation of Multiport Passive Distributed Networks Using Time Marching Method

An improved time marching simulation of distributed multiport networks loaded with nonlinear devices

“…Time marching (TM) is a common approach used for simulating this kind of systems, which is present in (1) the finite‐difference time‐domain (FDTD) method (eg, previous studies), (2) the Baum‐Liu‐Tesche equations in time domain for a 2‐port case (eg, Tesche), and (3) solving the time‐domain counterparts of multiport network parameters (eg, previous studies).…”

“…The main drawback of TM is its late‐time instability, which was traditionally attributed to numerical error accumulation over time and treated with time‐averaging, use of low‐pass Finite Impulse Response (FIR) filters, or use of predictor‐corrector schemes . Nevertheless, it is shown in Becerra et al that the main cause of TM instability is the occurrence of unstable poles in deconvolution operations. These poles appear in the Z‐transform of the deconvolution kernel (usually an impulse response), and hence, the instability is solved by replacing the deconvolution kernel by its minimum phase version …”

“…Nevertheless, it is shown in Becerra et al that the main cause of TM instability is the occurrence of unstable poles in deconvolution operations. These poles appear in the Z‐transform of the deconvolution kernel (usually an impulse response), and hence, the instability is solved by replacing the deconvolution kernel by its minimum phase version …”

“…It is important to mention that an incorrect formulation of the TM equations can lead to inaccurate results when the deconvolutions are stabilized, or it can hide feedback effects that may cause instability …”

“…Recently, a stable TM formulation for multiport networks has been proposed . The main drawback of this formulation is that it requires a very large number of frequency samples to avoid time aliasing (above 2 18 for simple 2‐port topologies).…”