Efficient Approach for Order Selection of Projection-Based Model Order Reduction

Abstract

The present thrust in the electronics industry towards integrating multiple functions on a single chip while operating at very high frequencies has highlighted the need for efficient Electronic Design Automation (EDA) tools to shorten the design cycle and capture market windows. However, the increasing complexity in modern circuit design has made simulation a computationally cumbersome task. The notion of model order reduction has emerged as an effective tool to address this difficulty. Typically, there are numerous approaches and several issues involved in the implementation of model-order reduction techniques. Among the important ones of those issues is the problem of determining a suitable order (or size) for the reduced system. An optimal order would be the minimal order that enables the reduced system to capture the behavior of the original (more complex and larger) system up to a user-defined frequency. The contribution presented in this thesis describes a new approach aimed at determining the order of the reduced system. The proposed approach is based on approximating the impulse response of the original system in the time-domain. The core methodology in obtaining that approximation is based on numerically inverting the Laplace-domain of the representation of the impulse response from the complex-domain (s-domain) into the time-domain. The main advantage of the proposed approach is that it allows the order selection algorithm to operate directly on the time-domain form of the impulse response. It is well-known that numerically generating the impulse response in the time-domain is very difficult and its not impossible, since it requires driving the original network with the Dirac-delta function, which is a mathematical abstraction rather than a concrete waveform that can be implemented on a digital computer. However, such a difficulty is avoided in the proposed approach since it uses the Laplace-domain image of the impulse response to obtain its time-domain representation. The numerical simulations presented in the thesis demonstrate that using the time-domain waveform of the impulse response, computed using the proposed approach and properly filtered with a Butterworth filter, guides the order selection algorithm to select a smaller order, i.e., the reduced system becomes more compact in size. The phrase "smaller or more compact" in this context refers to the comparison with existing techniques currently in use, which seek to generate some form of time-domain approximations for the impulse response through driving the original network with pulse-shaped function (e.g., Gaussian pulse).