IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 45, NO. 10, OCTOBER 1997 1911 An FDTD–Touchstone Hybrid Technique for Equivalent Circuit Modeling of SOP Electronic Packages Yinchao Chen, Member, IEEE, Paul Harms, Member, IEEE, Raj Mittra, Life Fellow, IEEE, and Wendemagegnehu T. Beyene, Member, IEEE Abstract—The electromagnetic-field behavior within electronic packages used for high-speed digital-circuit or high-frequency analog-circuit applications often cannot be accurately modeled by using a quasi-static approximation, and a frequency-dependent analysis is sometimes needed for accurate modeling. In this paper, we employ the finite-difference time-domain (FDTD) approach, in conjunction with the commercially available software called Touchstone, to model the generic 24-pin silicon on plastic (SOP). The model for the package includes many details, such as the plastic encasement, bonding pads, and wires. The frequency responses of the package are tested against the results obtained with only the FDTD algorithm. It is shown that by extracting the equivalent-circuit elements from the field data, the hybrid FDTD–Touchstone technique allows greater flexibility in deriving a circuit configuration at the expense of fine tuning the circuit to reproduce the response of the package. It is hoped that the technique presented in this paper will lead to more accurate circuit simulations of complex packaging configurations than has been possible up to this point, by using quasi-static analyses. Index Terms—Electronic packaging, equivalent circuits, FDTD, silicon on plastic (SOP) package. I. INTRODUCTION T HE electromagnetic characterization of electronic pack- ages containing high-speed digital or high-frequency ana- log circuits is of great practical interest [1]–[11], [14], and often these packages cannot be modeled accurately by using the quasi-static approximation. The methodology that is typ- ically employed for modeling electronic packages entails the following steps. 1) The package geometry is subdivided such that it is manageable to model by using quasi-electrostatic and quasi-magnetostatic analysis tools which ignore the cou- pling between the electric and magnetic fields. 2) The equivalent capacitance and inductance are deter- mined separately for each subsection, and the coupling between these subsections is ignored. Manuscript received November 3, 1996; revised June 10, 1997. Y. Chen is with the Department of Electronic Engineering, Hong Kong Polytechnic University, Hong Kong. P. Harms is with the Georgia Tech Research Institute, Atlanta, GA 30332- 0800 USA. R. Mittra is with the Applied Research and Electromagnetic Communication Research Laboratories, Electrical Engineering Department, Pennsylvania State University, University Park, PA 16802 USA. W. T. Beyene is with the Department of Electrical and Computer Engineer- ing, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA. Publisher Item Identifier S 0018-9480(97)07394-8. 3) The lumped circuits are connected together to develop an equivalent-circuit package configuration, which can be inserted into a circuit simulator. 4) The model is adjusted on an as-needed basis to match the available measurements. The finite-difference time-domain (FDTD) method [10]–[13] is a general-purpose Maxwell solver which is well-suited for modeling the frequency-dependent behavior of electronic packages. The field solution can in turn be used to generate an equivalent circuit comprising self and mutual inductances and capacitances, as well as resistances and conductances, in a form that can be directly inserted into a circuit simulator such as SPICE. Since the integrated- circuit chip typically contains many components, it would be very time consuming to accurately model all of them using the FDTD method described in [11]. In this paper, we investigate the problem of extracting such an equivalent circuit of a generic silicon-on-plastic (SOP) package shown in Fig. 1(a), by employing the full-wave solver FDTD method, in conjunction with the commercially available software Touchstone [14]. 1 In Section II, the package model will be described. In Section III, the equivalent circuits will be given for four dif- ferent bond-wire configurations of the package. In Section IV, the equivalent circuits generated by using Touchstone will be presented and validated by demonstrating that their fre- quency response approximates that directly computed via FDTD method in the frequency range of interest. II. MODELING THE SOP PACKAGE The first step in analyzing the SOP package, shown in Fig. 1(a) and (b), is to generate a mesh or a discretized model that describes the geometry of the package. A uniform-grid FDTD approach is used, and the unit cell size is chosen to be 0.0254, 0.0500, 0.0500 mm along the -, -, and -directions, respectively, to ensure adequate spatial resolution. The entire computational domain consists of (181 176 30) cells. The physical size of the computational volume is about 4.6 8.8 1.5 mm , and symmetry is used where possible to reduce the size of the computational domain. To simplify computations and for purposes of illustrating this approach, the mesh is truncated with first-order Mur absorbing-boundary 1 Touchstone, EEsof Inc., Westlake Village, CA 91362. 0018–9480/97$10.00  1997 IEEE