Investigation of a dc power delivery network, consisting of a multilayer PCB using area fills for power and return, involves the distributed behavior of the power/ground planes and the parasitics associated with the lumped components mounted on it. Full-wave methods are often employed to study the power integrity problem. While full-wave methods can be accurate, they are time and memory consuming. The cavity model of a rectangular structure has previously been employed to efficiently analyze the simultaneous switching noise (SSN) in the power distribution network. However, a large number of modes in the cavity model are needed to accurately simulate the impedance associated with the vias, leading to computational inefficiency. A fast approach is detailed herein to accelerate calculation of the summation associated with the higher-order modes. Closed-form expressions for the parasitics associated with the interconnects of the decoupling capacitors are also introduced. Combining the fast calculation of the cavity models of regularly shaped planar circuits, a segmentation method, and closed-form expressions for the parasitics, an efficient approach is proposed herein to analyze an arbitrary shaped power distribution network. While it may take many hours for a full-wave method to do a single simulation, the proposed method can generally perform the simulation with good accuracy in several minutes. Another advantage of the proposed method is that a SPICE equivalent circuit of the power distribution network can be derived. This allows both frequency and transient responses to be done with SPICE simulation.

S-parameter circuit model extraction is usually characterized by a trade off between accuracy and complexity. Trading one feature for another may or may not affect the goodness of the reconstructed S-parameter data, which are obtained from frequency domain simulations of the models extracted. However, the ultimate test for the validity of these equivalent circuit representations should be leh to eyediagram simulations, which provide useful insights, from an SI point of view, about the degradation of the signal, as it travels through the system. Physics based simplication procedures can be used to tune the models and achieve less complexity, whereas the comparisons of the eyediagrams may help to quantify the goodness ofall these circuits extracted. In fact the most accurate model is not necessary the best to be used. Kqwords-Circuit extraction; accuracy; complexi@; model order: model didation: eye-diagrams. I. I~O D U C T I O NThe versatility of equivalent models for PCB interconnect discontinuities drives an increasing demand for S-parameter circuit extraction techniques [l]. Accuracy, when compared to the original set of data, and simplicity of the model are the two features usually required from the circuits exeacted.Interconnect discontinuities, e.g. via holes, are increasingly important in high speed digital applications. The impact of these elements on the degradation of the intended signal has been studied 12-IO]. Spice based tools offer the advantage of analyzing more complex geometries, i.e., a complete signal path or multiple signal paths from one end to another one, by simply cascading the equivalent models for each element constituting the relevant geometry. Complexity, then, becomes the main issue if the advantage over time consuming 3-D full wave simulations is not to be lost.Physics-based considerations can help to reduce the model order of the equivalent circuit by meaningfully processing the S-parameter data For example, small ripples observed in frequency domain data are usually misleading, when related to the system under analysis. Removal of those features may lead to a simpler model which contains all the necessary information. The application of a Finite Impulse Response smoothing filter is an efficient way to preprocess the data, in order to implement the purpose of simplification.Finally, the comparison of the SPICE simulated eyepatterns is the optimum means to validate the different circuit models. In fact, considerations of jitter and the opening of the eye provide the necessary information to establish the quality of a model based upon a criterion, which may depend upon the particular application. E. THE EQUIVALENT CIRCUIT MODELThe via geometry under analysis is pointed out in Fig. 1 and Fig. 2. The structure consists of two 50 Ohm microstrip lines connected by a via hole in a 4-layer board as shown in Fig. 2.Each microstrip line is referenced to the closest solid plane, i.e., the ground or the power plane, such that there is no DC continuity between the two ports. Fig. 1.4-layer board w...

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