Yoshitaka Toyota

Convergence acceleration and accuracy improvement in power bus impedance calculation with a fast algorithm using cavity modes

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 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. 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.

Modeling of gapped power bus structures for isolation using cavity modes and segmentation

Resonance characteristics of gapped power bus structures with a slit or a gap were studied, using a fast algorithm based on a full cavity-mode resonator model and the segmentation method. Inductance and capacitance models were used to account for a field coupling along the slit and across the gap, respectively. The effectiveness of the segmentation method and the inductance model for the slit has been demonstrated by good agreement between the calculated and measured results, while the capacitance model for the gap is shown to be useful when the coupling between the segments is relatively weak.

A simple method for measuring the relative permittivity of printed circuit board materials

This paper presents a simple method to measure the relative permittivity of glass-epoxy printed circuit boards (PCBs). In this method, the relative permittivity as a function of frequency is measured using an actual PCB. In order to estimate the relative permittivity, the reflection coefficient is measured with a network analyzer. The relative permittivity is calculated by observing the frequencies of the resonant cavity modes. We show that the relative permittivity of an FR-4 sample decreases from 4.3 to 4.2 at frequencies from 300 MHz to 2 GHz.

Experimental model validation of mode-conversion sources introduced to modal equivalent circuit

We have developed a modal-equivalent-circuit model with mode-conversion sources for clarifying the mode-conversion mechanism and considering countermeasures against common-mode noise by means of circuit analysis based on the proposed model. The modal equivalent circuit is divided into separate normal-mode and common-mode circuits obtained by applying the mode-decomposition technique to an actual circuit. The separate circuits are connected with the mode-conversion sources at the interface where two transmission lines with different current division factors (h) are connected. This model suggests that the mode conversion that occurs is likely related to the common-mode current and the normal-mode voltage at the interface and the difference in the current division factors (Δh). This paper validates the model experimentally. First, it is validated by changing the grounding conditions of a simple cable interconnection system. Next, the mode-conversion mechanism suggested by the mode-conversion sources is experimentally examined by matching on common mode and replacing a two-wire cable with a coaxial cable so that Δh becomes almost 0. Circuit simulation results obtained using the modal equivalent circuit with the mode-conversion sources agree well with measured results and this also demonstrates the models validity.

Finite difference modeling of multiple planes in packages

Power/ground planes in electronic packaging can be a major factor for noise coupling. There can be noise coupling not only in the transversal direction between two planes, but also vertically from one plane pair to another through the apertures and via holes. Due to the large size of the power/ground planes, it is difficult to analyze them using full-wave simulators. It is known that the finite difference solution of the Helmholtz equation provides a faster approach with a comparable accuracy. This paper presents new circuit models for a single plane pair based on the finite difference method: T- and X-models. It also presents a modeling approach for multiple plane pairs that are coupled through apertures

Power current model of LSI and parameter identification for EMI simulation of digital PCBs

A power current model of LSIs for EMI simulation of digital printed circuit boards, and a parameter identification method based on the model are presented. The model consists of equivalent internal impedance and an equivalent internal current source. The equivalent internal impedance is obtained by measuring the impedance between the power and ground terminal of an LSI by means of an impedance analyzer, and an equivalent internal source is obtained from the measured current through the power terminal under the conditions of known external impedance. Furthermore, it is shown that simulation results generated using this model have good agreement with the results of measurements made under a range of external impedances.

Analysis of resonance characteristics of a power bus with rectangle and triangle elements in multilayer PCBs

One of the major sources of radiated EMI is attributed to power bus resonance in a printed circuit board (PCB). A fast algorithm, combined with the segmentation method, is applied for calculating resonance characteristics of a power bus whose pattern consists of several segments of rectangles and/or right-angled triangles. Good agreement between the calculated and measured results demonstrates the usefulness and accuracy of the fast algorithm and the segmentation method.

Verification of common-mode-current prediction method based on imbalance difference model for single-channel differential signaling system

In a differential transmission line, a large common-mode current is excited due to its asymmetry. In this paper, the authors demonstrate experimentally the common-mode current and verify the imbalance difference model that was proposed for prediction of the common-mode current reduction. Experimental results show that the reduction of common-mode current of about 20 dB is achieved by changing the position of the transmission line. In addition, the differences that are calculated using the imbalance difference model are in agreement with the measured ones within 2 dB.

Prediction of EMI from two-channel differential signaling system based on imbalance difference model

In a differential transmission line, a large common-mode radiation is excited due to asymmetry. To suppress the radiation, the differential line must be designed electrically symmetric. In this paper, the imbalance difference model, which was proposed by the authors for estimation of common-mode radiation, is extended to apply the differential signaling system. The authors focus on two pairs of differential transmission lines with asymmetric property, which consists of an adjacent return plane and signal lines which are placed close to an edge of the return plane. The authors define five transmission modes; two normal modes, two primary common modes and a secondary common mode. In these transmission modes, the secondary common mode radiation is dominant, and the authors evaluate the radiation using the imbalance difference model. To reduce the common-mode radiation, placing a guard trace which has the same potential as that of the return plane, we can control the imbalance and reduce common-mode radiation even the transmission line has asymmetry. The reduction of common-mode radiation can be estimated quantitatively by calculation of the imbalance of the transmission line.

Prediction of electromagnetic emissions from PCBs with interconnections through common-mode antenna model

A motherboard-daughterboard structure with a connector is known to have another source of common-mode radiated emissions, and the emissions depend on the connector’s signal/ground pin configuration. In order to estimate the amount of radiated emissions from the structure, a commonmode antenna model is described. The model consists of an excitation source and an antenna element, and it calculates radiated emissions from PCBs not only quickly but accurately for practical use. In modeling the board interconnection via a connector, we added two common-mode excitation sources at each end of the connector. The electromagnetic emissions estimated by the model agreed with the measurements within an error of 6 dB around peak emission levels between 300 and 600 MHz.