Comparison of two compact 2D-FDFD methods and their application to extraction of circuit parameters

Compact 2D FDFD (two-dimensional finite- difference frequency-domain) methods were initially proposed by other researchers to solve the propagation constant of shielded uniform guided wave structures. In this paper, firstly we compare two compact 2D FDFD methods using four and six components of electromagnetic fields, which are applied to analyzing transmission lines with open boundaries. Then we extend them to extract the frequency-dependent circuit parameters of transmission lines. These R, L, C, G circuit parameters extracted via 1D transmission line theory are readily to be used for signal integrity analysis of high-speed circuits. I. INTRODUCTION High-speed effects of interconnect structures due to the increase in operating speed and decrease of the feature size in modern VLSI circuits, have to be carefully accounted for accurate signal integrity, power integrity and EMI/EMC analysis of modern circuit systems. The use of transmission line model becomes necessary in order to accurately capture the high-speed effects of interconnects. For the purpose of creating a proper transmission line model, very often the equivalent circuit parameters (R, L, C and G) need to be known in advance (1). This paper will focus on the compact 2D FDFD methods and apply them to extraction of circuit parameters. Characterization of transmission lines has been a topic of interest for many years, especially the analysis of the basic microstrip-like transmission line. Recently the compact two dimensional finite-difference frequency domain (2D FDFD) methods have been studied by several researchers (2-5) to analyze guided wave structures. Apart from its simple formulation, the advantage of 2D FDFD method is that we can obtain all the modes and modal field distribution of a uniform guided wave structure by solving an eigenvalue problem. The compact 2D FDFD method using four (3) and six (2, 5) field components have been proposed. In this paper, we will compare these two compact 2D FDFD methods used for analysis of guided wave structures. Then we will apply them to extract circuit parameters for the purpose of signal integrity analysis of high-speed circuit systems.