IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 52, NO. 2, MAY2010 487 A Combined Method for Fast Analysis of Signal Propagation, Ground Noise, and Radiated Emission of Multilayer Printed Circuit Boards Xiaomin Duan, Student Member, IEEE, Renato Rimolo-Donadio, Student Member, IEEE, Heinz-Dietrich Br¨ uns, and Christian Schuster, Senior Member, IEEE Abstract—This paper presents a method for fast and compre- hensive simulation of signal propagation, power/ground noise, and radiated emissions by combining the merits of the physics-based via model, the modal decomposition technique, the contour integral method (CIM), and the equivalence principle. The physics-based via model combined with the modal decomposition technique is an efficient technique for signal integrity analysis of multilayer PCBs and packages. The CIM can be used to calculate the voltage distribution between arbitrarily shaped power planes. Far-field ra- diation can be obtained by applying the field equivalence principle. In this paper, we integrate the four techniques to analyze all the three effects in a fast, concurrent, and holistic manner. To the best knowledge of the authors, the four techniques are integrated here for the first time. Various structures are simulated and validated with full-wave simulations up to 20 GHz. It is shown that a reduc- tion in simulation time of more than two orders of magnitude is achieved in comparison to a standard full-wave electromagnetic solver. Index Terms—Contour integral method (CIM), field equivalence principle, physics-based via and trace model, power integrity (PI), printed circuit board (PCB), signal integrity (SI). I. INTRODUCTION C ONVENTIONALLY, signal interconnects, the power de- livery network (PDN), and the electromagnetic compati- bility (EMC) of digital systems are designed and evaluated sep- arately. The interaction among them is often ignored in the early stage of the design process. However, they are in fact closely re- lated. For instance, signal transitions among different layers can excite cavity modes of power planes and cause power-ground bounce [1]. Noise can be coupled to other vias or cause radi- ated emissions through the plane edges. As the complexity of the interconnects increases and the rise/fall time reduces, their interactions become more prominent. Disregarding them may cause costly and less optimal noise suppression in a late stage of the design flow. Therefore, the trend is to unify the analyses of signal integrity (SI), power integrity (PI), and EMC. Full-wave methods, in principle, can be applied to analyze electromagnetic effects in printed circuit boards (PCBs) and packages (see for instance [2] and [3]). However, their com- putational burden grows rapidly as the system complexity and Manuscript received September 30, 2009; revised December 7, 2009. First published March 1, 2010; current version published May 19, 2010. The authors are with the Institut f ¨ ur Theoretische Elektrotechnik, Technische Universit¨ at Hamburg-Harburg, 21073 Hamburg, Germany (e-mail: xiaomin. duan@tuhh.de; renato.rimolo@tuhh.de; bruens@tuhh.de; schuster@tuhh.de). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEMC.2010.2041238 operating frequency increase. Recently, a number of techniques have been proposed for rapid analysis of PCBs and packages. These techniques exploit the planar nature of the PDN, since the cavities, sandwiched by power planes, are in general very thin in comparison to the wavelengths of interest. Some of the techniques have been applied to the analysis of via transitions and power planes such as the multilayered finite-difference method [4], the contour integral method (CIM) [5]–[7], the transmission line matrix method [8], multiple scattering meth- ods [9]–[11], as well as analytical formulations [12]–[15]. Hy- brid techniques combining different approaches for analysis of multilayer boards have been also proposed, for example in [16]–[23]. The modeling of traces connecting vias has been included using the modal decomposition technique [24], as shown for instance in [16]–[18], [22] and [23]. Segmentation techniques [25] have been applied to include multilayer power planes, e.g., in [16] and [19]. In addition, far-field radiation from one pair of power planes has been estimated via the equivalence principle in [26] and [27]. Most of the aforementioned methods focus on one or two aspects of the SI, PI, or radiated emissions analyses. In this pa- per, the authors propose and demonstrate the integration of four of the most efficient techniques, namely the physics-based via model, the modal decomposition technique, the CIM, and the equivalence principle to simulate the SI, PI, and radiated emis- sions at the same time. The combination of these four methods enables a fast system-level simulation of relatively complex PCB structures. In comparison the work of Rimolo-Donadio et al. [16], the combined method proposed here can additionally calculate the cavity field distribution for each layer as well as radiated emissions of multilayer PCBs. Application examples are demonstrated and the results are validated with full-wave simulations up to 20 GHz. II. REVIEW OF INDIVIDUAL TECHNIQUES A. Physics-Based Via Model The physics-based via model [14], [16] describes the via tran- sition crossing a pair of power planes, as depicted in Fig. 1(a). This layered approach makes use of the assumption that the field penetration through the solid planes can be neglected. Hence, the vias provide the only coupling path between cavities. The two building blocks of the model are the parallel-plate impedance Z pp and the via to plane capacitances C v [16]. The parallel-plate impedance models the current return path for vias by describing the excitation of modes inside the cavities 0018-9375/$26.00 © 2010 IEEE