A cascaded S-parameter method is proposed in this paper for signal/power integrity analysis of multiple vias in a multilayer printed circuit board (PCB). The proposed method enables efficient and accurate construction and simulation of physics-based via model for complex multilayer PCB structures involving vias. The physics-based via model describes the parasitic effects near each via region as well as mutual coupling among different vias. In this model, each via portion between two parallel plates is regarded as a three-port network with two coaxial ports and one radial port between the two plates. A procedure is first developed to obtain the S-parameters of a single plate pair, which combine the three-port via networks with the impedance matrix of the parallel-plate pair. Once the S-parameters of each plate pair are obtained, an assembling technique for cascading microwave networks is further developed. The method proposed in this paper has been validated by both simulations with a commercial circuit simulator and measurements.

Signal/Power Integrity Analysis for Multilayer Printed Circuit Boards Using Cascaded S-Parameters

A systematic approach for inductance extraction for via arrays between two parallel planes is presented. Both self and mutual inductance values are obtained based on a cavity model. The physics associated with the via inductances is analyzed, and a rigorous method is developed to derive an equivalent total inductance for multiple via arrays. Analytical equations for the equivalent total inductance are derived in closed forms for simple cases. The proposed method is corroborated with measurements, and application of the method for power distribution network designs is demonstrated.

Physics-Based Inductance Extraction for Via Arrays in Parallel Planes for Power Distribution Network Design

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

Circular Ports in Parallel-Plate Waveguide Analysis With Isotropic Excitations

In this article, we cover the fundamentals of neural networks and Bayesian learning with a focus on signal and power integrity problems arising in packaging. Rather than only focus on mathematical formulations, we explain the important concepts and the intuition behind them, thereby demystifying the use of machine learning for these problems. We also share some of the recent developments in this area along with future research directions in the context of packaging. Links to open-source downloadable software for some of the methods discussed are also provided.

Demystifying Machine Learning for Signal and Power Integrity Problems in Packaging

A hybrid 3-D and equivalent 2-D finite-element method (FEM) is proposed for signal/power integrity analysis of multiple vias in a shared anti-pad in an arbitrarily shaped parallel-plate pair. The entire domain of the plate pair is decomposed into via-domains and plate domains by virtual interfaces. Complicated fields in via-domains, due to mode conversions from transverse electromagnetic modes in anti-pads or via-holes to parallel-plate modes, are described by a 3-D FEM while in plate domains, only the zeroth-order parallel-plate modes are assumed to exist a little far away from anti-pads. Triangular prism elements are utilized in both via-domains and plate domains. It is proven that the 3-D triangular prism element can be reduced to an equivalent 2-D triangle element by a novel edge numbering process and the boundary conditions along the interfaces of via-domains and plate domains can be automatically satisfied. The accuracy of the hybrid method has been validated by comparison with other numerical methods, and its flexibility, as well as efficiency, are also demonstrated.

An Efficient Hybrid Finite-Element Analysis of Multiple Vias Sharing the Same Anti-Pad in an Arbitrarily Shaped Parallel-Plate Pair

In this paper, a closed-form expression for the impedance of an infinitely large parallel plane pair is presented. It is applicable to practical printed circuit board (PCB) design problems where there are multiple shorting vias around the signal vias of interest. With the presence of multiple shorting vias, reflections from the plane pair edges can be neglected since the shorting vias prevent the electromagnetic energy from leaking away from the local cavity around the signal vias. The self and transfer impedance expressions can be obtained using the expansion of cylindrical waves. The impedances calculated from both the rectangular cavity model and the infinitely large plane pair model for several design examples are compared to demonstrate the effectiveness of the infinite plane pair approximation.

Impedance of an infinitely large parallel-plane pair and its applications in engineering modeling

An improved multiple scattering method is developed for an irregular plate pair where via pad/antipad radius is electrically small and the spacing between any two vias is relatively large so that the axially anisotropic parallel plate modes can be neglected. The plate-pair impedance matrix, widely used as an important parameter in power integrity analysis and also a critical part for via coupling in the intrinsic and the physics-based via models, is found to be related to the addition theorems of the zero-order axially isotropic propagating modes. As the impedance matrix of an irregular plate pair can be calculated by many analytical and numerical methods, the relationship between the plate-pair impedance matrix and the addition theorems of the zero-order axially isotropic propagating modes enables the handling of both the mutual coupling among vias and the reflection from plate-pair edges. Thus, the conventional multiple scattering method, restricted to either an infinitely large or a finite circular plate pair, can be extended to irregular plates for the via structures described earlier. The assumptions of the method are discussed and several numerical examples are provided to validate the proposed improved method.

An Improved Multiple Scattering Method for Via Structures With Axially Isotropic Modes in an Irregular Plate Pair

The paper discusses current challenges and advantages of multi-level signaling for high-speed serial links, showing the differences and similarities in link-path analysis between binary and multi-level signaling. Comparison of two signaling methodologies is given from the general theory viewpoint, as well as on the basis of various tests regarding crosstalk, jitter, equalizations and different channel characteristics, such as material, impedance and overall manufacturing design sensitivity.

PAM4 signaling considerations for high-speed serial links

The paper discusses challenges of high-speed serial links using multi-level signaling and gives comparison of the performance of the various channels with different lossy materials and equalization options. Advantages and problems of multi-level signaling are shown based on the test results.

High-speed serial link challenges using multi-level signaling

Parallel plate modes are excited by the magnetic frill currents in the via holes (anti-pads). These modes are expressed as cylindrical waves. Multiple scattering of these modes among vias as well as from the edge boundaries of the plate pair are rigorously considered with the addition theorem of the cylindrical waves. An admittance matrix is derived for the via ports at the top/bottom surfaces of the via holes. Good agreement has been found between numerical simulations and the algorithm presented.

Arun Chada

Papers

Impedance of an infinitely large parallel-plane pair and its applications in engineering modeling

An Improved Multiple Scattering Method for Via Structures With Axially Isotropic Modes in an Irregular Plate Pair

PAM4 signaling considerations for high-speed serial links

High-speed serial link challenges using multi-level signaling

A concise multiple scattering method for via array analysis in a circular plate pair