IEICE TRANS. ELECTRON., VOL.E93–C, NO.3 MARCH 2010 347 PAPER Special Section on Circuits and Design Techniques for Advanced Large Scale Integration A Universal Equivalent Circuit Model for Ceramic Capacitors Koh YAMANAGA †∗ a) , Student Member, Shuhei AMAKAWA † , Kazuya MASU † , and Takashi SATO †† , Members SUMMARY A physics-based equivalent circuit model of the ceramic capacitor is proposed, which can reproduce frequency characteristics of its impedance including the often observed yet hitherto physically unexplained kinks appearing above the primary series resonance frequency. The model can also account for parasitic effects of external inductances. In order to efficiently analyze and gain engineering insight into ceramic capacitors with a large number of metallic laminae, a two-dimensional method of mo- ments is developed that treats the laminar structure as a uniform, effective medium. It turns out that the primary resonance and the kinks can be well understood and modeled by a lossy transmission line stub with a drastic wavelength reduction. The capacitor model is completed by adding com- ponents describing the skin effect and external inductances. The modeled impedance stays within a 4% margin of error up to 5 GHz. The proposed model could greatly improve the accuracy of power distribution network simulation. key words: ceramic capacitor, moment method, equivalent circuit, induc- tance 1. Introduction Reduction of power distribution network (PDN) impedance is critically important due to recent trend of increasing power consumptions. One of the most important compo- nents for stabilizing PDN is a ceramic capacitor. The ce- ramic capacitor reduces current-loop area of a PDN by by- passing high-frequency component, thereby reducing total inductance of the PDN. In general, PDN-simulation of an electrical system in- cluding ceramic capacitors is based on a hierarchical and constructive modeling approach. Ceramic capacitor and other components such as printed circuit board (PCB) and package, etc. are separately modeled. The entire system re- sponse is calculated by connecting these models. Such a modeling is commonplace because the component suppli- ers are unwilling to reveal the internal structure and mate- rial constants of ceramic capacitors. In addition, component users would like to use simple equivalent circuit models that can reduce simulation time. Due to the fundamental importance of electrical model of ceramic capacitor, various techniques have been proposed [1], [2]. In particular, the accuracy of parasitic inductance Manuscript received July 15, 2009. Manuscript revised October 1, 2009. † The authors are with the Integrated Research Institute, Tokyo Institute of Technology, Yokohama-shi, 226-8503 Japan. †† The author is with Kyoto University, Kyoto-shi, 606-8501 Japan. ∗ The author is with Murata Manufacturing Co., Ltd. a) E-mail: yamanaga.k.aa@m.titech.ac.jp DOI: 10.1587/transele.E93.C.347 is important because a resonance frequency and high fre- quency impedance are strongly influenced [3], [4]. A small error in parasitic inductance may result in a large error in the overall PDN-impedance. The model for ceramic capac- itors must accurately express the parasitic inductance with minimum number of elements. Parasitic inductance of a ceramic capacitor is essentially determined by its physical dimension and surrounding layout patterns of the PCB [5]. Geometry-dependent model considering its return current of the component is suitable to correctly reflect different insu- lator thickness of the system board. In [5], 2-port ceramic capacitor model with explicitly parameterized ground-plane distance has been proposed (Fig. 1). Measurement-based parameter characterization for the capacitor model is proposed in [6]. Using the proposed method, we can accurately determine small parasitic induc- tance that is in general difficult to measure. In order to reproduce measured characteristics in simulations, accurate equivalent circuit model is required. In the capacitor model- ing, we have two issues. 1) Measured impedance has a few kinks in many cases above the frequency of series LC reso- nance, which cannot be explained by the skin nor proximity effects. 2) Above stated layout-pattern dependence requires multiple equivalent circuit models having different parasitic inductance for a capacitor, which is inconvenient for both model providers and model users. In this paper, we present a model that simultaneously solves above issues. In order to overcome above issues, we first introduce a new two-dimensional moment method suitable for analyzing ceramic capacitor, and investigate the relationship between frequency characteristic and its struc- ture. Then, we present a new unified structure of equivalent model which is independent of the layout patterns. Valida- tion results confirming a very good match with the measure- ment results are also presented. 2. Moment Method for Analyzing Ceramic Capacitor A surface-mount ceramic capacitor has a large number of stacked conductor plates to achieve high electrical capaci- tance as shown in Fig. 1. Even in a tiny 1005-sized (1.0 mm × 0.5 mm footprint) capacitor, it is common to include much more than 100 plates. Because the required number of meshes for the plates as well as surrounding media becomes too large to be analyzed, it is very difficult to obtain detailed frequency response accurately using three-dimensional full- wave electromagnetic analyzers. Considering the number of Copyright c  2010 The Institute of Electronics, Information and Communication Engineers