Convergence Acceleration and Accuracy Improvement in Power Bus Impedance Calculation With a Fast Algorithm Using Cavity Modes

Abstract

Abstract-Based on the cavity-mode model, we have developed a fast algorithm for calculating power bus impedance in multilayer printed circuit boards. The fast algorithm is based on a closed-form expression for the impedance matrix of a rectangular power bus structure; this expression was obtained by reducing the original double infinite series into a single infinite series under an approximation. The convergence of the single series is further accelerated analytically. The accelerated single summation enables much faster computation, since use of only a few terms is enough to obtain good accuracy. In addition, we propose two ways to compensate for the error due to the approximation involved in the process of reducing the double series to the single series, and have demonstrated that these two techniques are almost equivalent.Index Terms-Cavity-mode model, closed-form expression for fast calculation, power bus impedance, power bus resonance.

Mitigation of Noise Coupling in Multilayer High-Speed PCB: State of the Art Modeling Methodology and EBG Technology

“…Another popular method employs a cavity model [28]- [30]. Analytical expressions are readily available for simple geometries, and fast algorithms have been developed [31], [32]. Combined with the segmentation technique [33], [34], the cavity model can be used to model arbitrarily-shaped parallel-plane cavities.…”

Efficient Calculation of Power Bus Impedance using a Fast Algorithm Together with a Segmentation Method

“…(4) is used for calculating the self-input impedance (Z ii ), it was found that for a small port dimension the convergence of the single series is still poor and thousands of terms must be computed to obtain good accuracy. We have developed a fast algorithm (11) in which the convergence of the single series was in further accelerated analytically. With the fast algorithm, using just a few terms has been sufficient to achieve good accuracy.…”

“…Based on the cavitymode model, we have developed a fast algorithm for efficiently and accurately calculating the impedance of a rectangular power bus structure (9) (11) . The fast algorithm is based on a closed-form expression for the impedance Z-matrix of a rectangular power bus structure; this expression was obtained by reducing the original double infinite series into a single infinite series under an approximation.…”

Power Integrity and Shielding Effectiveness Modeling of Grid Structured Interconnects on PCBs

“…The advantage of the TLM-based circuit model for PCB power distribution is seen, when the PCB model can be included in designing and simulating integrated circuits. Cavity resonator method is an analytical modeling technique to characterize the impedance matrix at port locations on a rectangular parallel-plane pair structure [9,10]. For arbitrary shaped parallel-plane structure, an integral-equation equivalent circuit method is proposed [11].…”