Parameterized model order reduction of delayed systems using an interpolation approach with amplitude and frequency scaling coefficients

When the geometric dimensions become electrically large or signal waveform rise times decrease, time delays must be included in the modeling. We present an innovative PMOR technique for neutral delayed differential systems, which is based on an efficient and reliable combination of univariate model order reduction methods, amplitude and frequency scaling coefficients and positive interpolation schemes. It is able to provide parameterized reduced order models passive by construction over the design space of interest. Pertinent numerical examples validate the proposed PMOR approach.

1 Introduction

Complex high-speed systems require 3-D electromagnetic (EM) methods [1], [2] as analysis and design tools. Large systems of equations are usually generated by the use of these methods and model order reduction (MOR) techniques are crucial to reduce the complexity of EM models and the computational cost of the simulations, while retaining the important physical features of the original system [3], [4]. Over the last years, the development of methods to build reduced order models (ROMs) of EM systems has been intensively investigated, with applications to interconnects, vias and high-speed packages [5], [6].