Heinz-Dietrich Brüns

Physics-Based Via and Trace Models for Efficient Link Simulation on Multilayer Structures Up to 40 GHz

Analytical models for vias and traces are presented for simulation of multilayer interconnects at the package and printed circuit board levels. Vias are modeled using an analytical formulation for the parallel-plate impedance and capacitive elements, whereas the trace-via transitions are described by modal decomposition. It is shown that the models can be applied to efficiently simulate a wide range of structures. Different scenarios are analyzed including thru-hole and buried vias, power vias, and coupled traces routed into different layers. By virtue of the modal decomposition, the proposed method is general enough to handle structures with mixed reference planes. For the first time, these models have been validated against full-wave methods and measurements up to 40 GHz. An improvement on the computation speed of at least two orders of magnitude has been observed with respect to full-wave simulations.

Numerical Electromagnetic Field Analysis for EMC Problems

Much progress has been made in the use of computational electromagnetics for the analysis of electromagnetic compatibility (EMC) problems during recent years. This paper reviews the improvements in some of the most important techniques of the field: the method of moments, the finite-difference time-domain method, the finite-element method, the transmission-line matrix method, and the partial-element equivalent-circuit method. The results of computer codes on the basis of such methods have to be validated, and some of the respective possibilities are addressed.

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.

Including Stripline Connections into Network Parameter Based Via Models for Fast Simulation of Interconnects

Comprehensive physics-based via models are extended to consider traces connecting vias in PCB and package structures (stripline connection). The traces routed between two power planes are described by modal decomposition to account for the contribution of the parallel plate mode and the stripline mode. The analytical formulation for two vias connected by a trace is provided in this work. It results in a fully parameterized 4-port network, formed by the parallel connection of four 4-by-4 admittance matrices corresponding to: the parallel plate mode, the stripline mode, a coupling factor resulting from the superposition of the two modes, and the capacitances between the via barrel and the power planes. With this novel formulation, good correlation with respect to full-wave simulations could be observed up to 20 GHz, with a remarkable improvement on the computation speed (up to three orders of magnitude).

Simulation of Via Interconnects Using Physics-Based Models and Microwave Network Parameters

In this paper, the simulation of via interconnects in multilayered printed circuit boards (PCBs) and packages combining physics-based via models and microwave network theory will be discussed. The description of the via in terms of network parameters, partitioning of the system, and combination of partial results will be addressed. Two alternatives to combine the results are compared, namely multiplication of ABCD matrices and the segmentation method based on S-parameters. The goal of this work is to develop a fast and accurate modeling strategy for via arrays in the multi-gigabit range, extensible to an arbitrary number of elements, and suitable for automation and design optimization. The obtained results show good agreement with respect to 3D electromagnetic field simulations and measurements up to 20 GHz. Hence, this approach is a promising technique for efficient system-level simulation of interconnects.

Crosstalk analysis in high density connector via pin fields for digital backplane applications using a 12-port vector network analyzer

In this paper the authors present results from the crosstalk analysis of a high density single ended connector and its associated card via array obtained with 12-port vector network analyzer (VNA) measurements in the bandwidth from 10 MHz up to 20 GHz. The device under test used for this paper is typical for a high end mainframe processor node to node link scenario consisting of daughter cards plugged into a backplane card by using a multipin connector. In previous studies the authors have shown that mainly the connector via pin field is impacting the electrical link performance. Here, the measurements have shown that the via pin field constitutes a complex crosstalk problem depending on the orientation and the distance between victim and aggressor via, the common coupled via lengths, and the local power/ground environment.

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.

Energy-Aware Signal Integrity Analysis for High-Speed PCB Links

This paper proposes a novel approach to evaluate design alternatives for high-speed links on printed circuit boards. The approach combines evaluations of signal integrity and link input power. For a comprehensive analysis, different link designs are made comparable through the application of identical constraints, with the link input power as the single figure of merit for a systematic, quantitative comparison of design alternatives. The analysis relies upon a combination of efficient physics-based via and trace models, statistical time-domain simulation, and an analytical input power evaluation, which allows it to handle links consisting of a large number of channels while fully taking into account interchannel crosstalk. The proposed approach is applied to study two fundamental design decisions at the PCB level-single-ended versus differential signaling and signal-to-ground via ratios of 1:1 versus 2:1-for a link consisting of 2048 vias and up to 175 striplines with an aggregate data rate of 1 Tb/s. It is found that both design decisions have a considerable impact on the required input power of the link.

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.