Xiaomin Duan

Circular Ports in Parallel-Plate Waveguide Analysis With Isotropic Excitations

Exact and consistent modeling of circularly shaped ports in the power/ground plane analysis under the assumption of isotropic excitations is addressed in this paper. Novel expressions are first derived for accurate calculation of the parallel-plate impedance of circular ports in the cavity resonator method. These ports are usually approximated as either rectangular or linear ones, leading to inaccurate results at high frequencies. The second part of this paper develops a novel semianalytical approach, derived from the contour integral equation, for modeling of circular ports assuming infinitely large reference planes. It will be shown that the radial waveguide method is a low frequency approximation of our approach and neglects the scattering among the open ports. The analytical solutions for infinite planes are then combined with the contour integral method to model finite-sized power planes. This improves the computational efficiency since a discretization of circular ports is avoided, especially for problems with a large number of circular ports.

A Combined Method for Fast Analysis of Signal Propagation, Ground Noise, and Radiated Emission of Multilayer Printed Circuit Boards

This paper presents a method for fast and comprehensive 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 radiation 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 reduction in simulation time of more than two orders of magnitude is achieved in comparison to a standard full-wave electromagnetic solver.

Accuracy of Physics-Based Via Models for Simulation of Dense Via Arrays

This paper studies the accuracy of the physics-based via model, specifically when applied to dense via arrays. The physics-based model uses Greens functions for cylindrical waves in radial waveguides to model the via return current paths and the coupling between vias. The effects of approximations made in this model are studied with regard to four types of modes based on an eigenmode expansion for the radial waveguide. It is found that for the mode conversion in the vicinity of the via, an accurate consideration of nonpropagating modes becomes critical with an increasing cavity height. For the interaction between vias in dense arrays, anisotropic modes have an impact for small pitches, whereas the coupling by nonpropagating modes is small for practical printed circuit board dimensions. For a data rate of 20 Gb/s, conclusions with regard to the applicability of the physics-based via model to a multilayer structure are drawn. For 80-mil pitch, a good agreement to full-wave results can be observed. Measurements have been carried out to validate this finding. For 40-mil pitch, the accuracy of the physics-based via model is not sufficient for data rates of 20 Gb/s or higher.

EM emission of differential signals across connected printed circuit boards in the GHz range

In this paper it is shown that when differential signals pass between printed circuit boards (PCBs) through connectors, common mode signals can be induced due to e.g. imbalanced current paths or asymmetrical line configurations. In the GHz range connectors are electrically large. Therefore, we describe connector pins and traces as transmission lines in order to analyze differential mode to common mode signal conversion. Two conversion mechanisms, conductor length mismatches and asymmetrical ground pin configurations, are investigated and validated against Method of Moment (MoM) simulations using the CONCEPT-II package. The common mode signal can return through ground pins or as displacement current between PCBs. Both of the mechanisms can cause EMI problems. Radiation from a daughter card on a motherboard structure are then studied using MoM for various configurations. The variation of board configurations can have little effect in the GHz range while the ground pin configuration has a much greater impact on the EMI performance.

Extension of the Contour Integral Method to Anisotropic Modes on Circular Ports

In the analysis of power/ground planes in multilayer substrates, circular ports are often used for modeling of via transitions. The electric and magnetic fields on excited ports are usually assumed to be isotropic. This assumption may not hold in certain scenarios such as vias in very close proximity, where anisotropic modes can be excited. This paper first extends voltage and current definitions of circular ports to account for the non-uniform field distribution along the port perimeter and the anisotropic propagating modes. The effect of these modes on the parallel-plate impedance can be captured in the contour integral method (CIM) by discretizing the port perimeter with line segments. However, the computation time grows rapidly as the number of modeled ports increases. Therefore, the CIM is extended here to incorporate analytical modal expressions to improve the computational efficiency based on the new port definition. The derivation starts with solutions under the assumption of infinite planes, and then is expanded to take finite plane boundaries into consideration. Application examples using the extended CIM will be demonstrated and validated against the conventional CIM with ports modeled numerically. The significance of anisotropic propagating modes for dense via arrays will also be discussed.

Complete Modeling of Large Via Constellations in Multilayer Printed Circuit Boards

This paper presents, for the first time, the comprehensive modeling of complete via constellations consisting of several thousands of vias in multilayer printed circuit boards using the physics-based approach. For each computational step of the physics-based approach, several alternatives are analyzed with regard to their computational efficiency, and calculation times are discussed as a function of the number of simulated vias. The results of this analysis are used in combination with previous studies to determine an efficient yet accurate algorithm for the simulation of large numbers of vias. The impact of the stackup configuration on the computational effort of the algorithm is analyzed, and the most computationally expensive parts of the calculation process are identified. A parallelization of the algorithms is carried out to accelerate the critical calculation tasks. As an evaluation example, simulation results for a via array consisting of 10 000 vias and eight cavities are shown. With the proposed simulation methods, the computation time for this via array is about 6.5 h per frequency point on a single CPU and about 40 min per frequency point with the parallel version running on 16 CPUs.

An Efficient Analysis of Power/Ground Planes With Inhomogeneous Substrates Using the Contour Integral Method

An efficient analysis using the contour integral method (CIM) for the modeling of inhomogeneous substrates with circular or arbitrarily shaped dielectric inclusions in planar structures is presented. It is shown how the segmentation method is applied to obtain circuit parameters as well as field values and how different boundary conditions can be implemented. Such an analysis is especially useful for the modeling of photonic crystals power/ground layers (PCPLs) in power delivery networks (PDNs) on printed circuit boards (PCBs). For circular inclusions, an analytical solution is presented, which improves efficiency and accuracy of the proposed method. An equivalent circuit model for cylindrical inclusions is derived, in order to obtain an effective capacitance for low frequencies and an estimate for parasitic effect at higher frequencies. It is shown how circular inclusions can be compared to decoupling capacitors on a basis of impedances. The method is validated with full-wave simulations showing a reduction in simulation time of about one order of magnitude.

Non-uniform currents on vias and their effects in a parallel-plate environment

This paper discusses the generation of non-uniform currents on vias and their impact on the field distribution at the via antipads as well as on the excitation of cavity modes supported by adjacent reference planes. It is shown that the influence of non-uniform currents can be relevant at frequencies above 10 GHz for typical printed circuit board dimensions. The contour integral method is applied to extract the current non-uniformity due to vias in close proximity. An identification of modes is carried out via a discrete Fourier transform. The energy content of the higher modes increases with frequency and via size. It is demonstrated by means of full-wave simulations that non-uniform via currents can lead to anisotropic electromagnetic fields in the antipad region and to the excitation of anisotropic cavity modes.

Efficient DC Analysis of Power Planes Using Contour Integral Method With Circular Elements

Contour integral method, well-known for the analysis of 2-D full-wave effects on power planes, is extended here for the computation of DC resistances of power planes. In particular, circular elements, e.g., vias and antipad holes, are treated using cylindrical modal expansion functions, which leads to a more efficient and accurate calculation than the conventional implementation by the linear discretization. For individual power planes, the method produces a resistor network consisting of only the nodes that are associated with power or ground vias, which can be further employed to formulate solutions for complete multilayer structures. The method is applied to several power plane configurations and results are validated by a 3-D finite element method solver. The efficiency of the extended method is analyzed and a reduction of the number of unknowns by a factor of four for the circular elements can be expected by the modal expansion. Good accuracy can be achieved by including up to the second higher order mode for dense clusters of antipad holes.

Differential to common mode conversion due to asymmetric ground via configurations

In this paper, the mode conversion in differential links of printed circuit boards and package structures is investigated, taking into account the ground via arrangement and trace length mismatch. The links are modeled using physics-based via and trace models that have been validated previously with full-wave methods and measurements. The very good numerical efficiency of these models allows simulations of different scenarios in minutes rather than hours compared to full-wave tools. It is shown that an asymmetric ground via configuration in the vicinity of a link end can increase the mode conversion in a comparable proportion to the trace length mismatch. The possibility to mitigate the mode conversion by compensating the trace length mismatch with asymmetric ground via configurations and vice versa is also discussed.