ADVANCES IN EMC NUMERICAL MODELING An improved time marching simulation of distributed multiport networks loaded with nonlinear devices Juan Becerra 1 | Felix Vega 1 | Farhad Rachidi 2 1 Electrical Engineering Department, Universidad Nacional de Colombia, Bogotá, Colombia 2 EMC Laboratory, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland Correspondence Juan Becerra, Electrical Engineering Department, Universidad Nacional de Colombia, Bogotá, Colombia. Email: jmbecerrat@unal.edu.co Abstract In this paper, we present a method for obtaining stable time marching equations of distributed multiport networks with nonlinear loads. This method allows to highly decrease the number of frequency samples required by other stable TM methods. Stability is analyzed and ensured in the Z‐domain. 1 | INTRODUCTION Simulation of distributed networks is important for many disciplines of the electromagnetic compatibility. Typical examples are the evaluation of lightning performance of power lines 1 and signal integrity in high‐speed digital circuits. 2 Frequently, this type of simulations is performed in the frequency domain. However, if the network is connected to nonlinear elements such as varistors or surge protective devices, a time‐domain approach is preferable. 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 3,4 ), (2) the Baum‐Liu‐Tesche equations in time domain for a 2‐port case (eg, Tesche 5,6 ), and (3) solving the time‐domain counterparts of multiport network parameters (eg, previous studies 2,7-10 ). The main drawback of TM is its late‐time instability, 11 which was traditionally attributed to numerical error accumu- lation over time and treated with time‐averaging, 12,13 use of low‐pass Finite Impulse Response (FIR) filters, 14,15 or use of predictor‐corrector schemes. 16-18 Nevertheless, it is shown in Becerra et al 10,19 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. 10 It is important to mention that an incorrect formulation of the TM equations can lead to inaccurate results when the deconvolutions are stabilized, 20 or it can hide feedback effects that may cause instability. 10 Recently, a stable TM formulation for multiport networks has been proposed. 10 The main drawback of this formula- tion is that it requires a very large number of frequency samples to avoid time aliasing (above 2 18 for simple 2‐port topologies). This is a problem since obtaining that amount of samples is unfeasible for measurements and very costly for simulations, especially for complex systems. In this paper, we present a TM formulation that is stable and does not require a large number of frequency samples for solving the time‐domain counterparts of multiport network parameters. The paper is organized as follows. Section 2 presents a summary of the TM formulation proposed in Becerra et al 10 and explains why it requires a large amount of samples. Section 3 presents the method for obtaining a formulation with lower sampling requirements. Section 4 shows an application example. Finally, conclusions are given in Section 5. Received: 30 June 2017 Revised: 18 September 2017 Accepted: 15 November 2017 DOI: 10.1002/jnm.2315 Int J Numer Model. 2017;e2315. https://doi.org/10.1002/jnm.2315 Copyright © 2017 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/jnm 1 of 10