Efficient Computation of Z-parameter for the Rectangular Planar Circuit Analysis

Abstract

The conventional eigen-mode expansion method is a commonly used approach to compute Z-parameter of a rectangular planar circuit. However a double infinite series in the method limit its computation efficiency. This paper develops a novel convergence-accelerating algorithm to improve the efficiency, which is based on a trigonometric Fourier series formula and the η-algorithm. The trigonometric Fourier series formula transforms the double infinite series into a single one and the η-algorithm can accelerate the convergence of the single infinite series. The technique has high efficiency and good accuracy, which are testified by a numerical example. I. Introduction With the operating frequencies increasing and working voltage decreasing in high-speed digital systems, the model and design of Power/Ground (P/G) planes are becoming more and more critical. In order to develop a systematic P/G design strategy, the fundamental properties of P/G plane structures need to be explored. The conventional eigen-mode expansion method is a commonly used approach to compute Z-parameter of a rectangular planar circuit. However the formula in the method involves a summation of a double infinite series, which may consume much time and computer storage to obtain sufficiently good accuracy. To improve the computation efficiency, this paper proposes a new convergence-accelerating algorithm, which is based on a trigonometric Fourier series formula [1] and the η-algorithm [2][3]. The formula was first applied to the eigenmode expansion method in paper [4], but it adopted another accelerating technique. The η-algorithm was first used to compute the Z-parameters of planar circuits in paper [5][6], but it was directly applied to the 2-D case, which was difficult to be comprehended, and its computation effi ciency was limited by the two series. In this paper, the double infinite series is first transformed into a single one by the trigonometric Fourier series formula and then the η-algorithm is adopted to accelerate the convergence of the single infinite series. The technique is easy to catch on and has high efficiency and good accuracy, which are testified by a numerical example. The organization of this paper is as follows. The eigen-mode expansion method is introduced in Section II. Section III presents the new convergence-accelerating algorithm in detail. To prove its efficiency and accuracy, in Section IV the new technique is adopted to a example. Section V draws a conclusion.