Yaojiang Zhang

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.

An Intrinsic Circuit Model for Multiple Vias in an Irregular Plate Pair Through Rigorous Electromagnetic Analysis

An irregular plate pair with multiple vias is analyzed by the segmentation method that divides the plate pair into a plate domain and via domains. In the via domains, all the parallel-plate modes are considered, while in the plate domain, only the propagating modes are included to account for the coupling among vias and the reflection from plate edges. Boundary conditions at both vias and plate edges are enforced and all parasitic components of via circuit are expressed analytically in terms of parallel-plate modes. The work presented in this paper indicates that a previous physics-based via circuit model from intuition is a low-frequency approximation. Analytical and numerical simulations, as well as measurements, have been used to validate the intrinsic via circuit model.

A Semi-Analytical Approach for System-Level Electrical Modeling of Electronic Packages With Large Number of Vias

This paper presents a semi-analytical approach for electrical performance modeling of complex electronic packages with multiple power/ground planes and large number of vias. The method is based on the modal expansion technique and the method of moments. For the inner package domain with multiple power/ground planes and many vias, the modal expansion method is employed to compute the electromagnetic fields from which the multiport network parameters, e.g., the admittance matrix can be easily obtained. For the top/bottom domain of signal layers, the moment method is used to extract the equivalent resistance, inductance, capacitance, and conductance (RLCG) parameters. The equivalent circuit for the entire package is then generated by combining the results for both package domains. The equivalent circuit can be used in a SPICE-like simulator to study the signal and power integrity of an electronic package. Numerical examples demonstrate that the new approach is able to provide fast yet accurate signal and power integrity analysis of multilayered electronic packages.

A Novel Impedance Definition of a Parallel Plate Pair for an Intrinsic Via Circuit Model

Rigorous analysis of via-plate-pair interactions requires the impedance of a plate pair to be defined in terms of radial transmission lines on perfect magnetic conductor (PMC) ports. The plate domain is not a solid plate pair but one with multiple PMC holes where conventional impedance definitions are not suitable. A new impedance definition is proposed where port voltages and currents are expressed in terms of the inward and outward zero-order modes of a radial transmission line. Radial scattering parameters among multiple radial ports are then introduced and the transforms between the radial scattering and impedance matrices are given. An analytical formula for the radial scattering matrix in a circular plate pair is derived using the addition theorems of cylindrical waves. Furthermore, a boundary integral-equation method is developed to calculate the radial scattering matrix for any irregular plate pair. The method is validated by analytical and numerical simulations as well as measurements.

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

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.

Novel Methods for Modeling of Multiple Vias in Multilayered Parallel-Plate Structures

This paper presents novel modeling methods for accurate and efficient analysis of coupling of multiple vias in finite-sized multilayered parallel-plate structures. The new modeling methods address two open problems related to the modal expansion with the T-matrix method for the analysis of via coupling. First, a novel boundary modeling method, called the frequency-dependent cylinder layer (FDCL), is proposed to resolve the open problem of boundary modeling. In the FDCL, virtual cylinders with dynamic radii are postulated to approximate the original finite-sized boundary of parallel-plate structures. Second, a generalized T-matrix model, which is derived by the mode-matching technique, is created to characterize the coupling effect for vias penetrating more than one layer in a multilayered structure. With the two open problems successfully solved, the modal expansion with the T-matrix method incorporating the FDCL boundary modeling method and the generalized T-matrix model can now be fully utilized for efficient and accurate analysis of finite-sized multilayered parallel-plate structures with a large number of vias. Both numerical and experimental verifications are presented to validate the new modeling methods.

Estimating Radio-Frequency Interference to an Antenna Due to Near-Field Coupling Using Decomposition Method Based on Reciprocity

In mixed radio-frequency (RF) and digital designs, noise from high-speed digital circuits can interfere with RF receivers, resulting in RF interference issues such as receiver desensitization. In this paper, an effective methodology is proposed to estimate the RF interference received by an antenna due to near-field coupling, which is one of the common noise-coupling mechanisms, using decomposition method based on reciprocity. In other words, the noise-coupling problem is divided into two steps. In the first step, the coupling from the noise source to a Huygens surface that encloses the antenna is studied, with the actual antenna structure removed, and the induced tangential electromagnetic fields due to the noise source on this surface are obtained. In the second step, the antenna itself with the same Huygens surface is studied. The antenna is treated as a transmitting one and the induced tangential electromagnetic fields on the surface are obtained. Then, the reciprocity theory is used and the noise power coupled to the antenna port in the original problem is estimated based on the results obtained in the two steps. The proposed methodology is validated through comparisons with full-wave simulations. It fits well with engineering practice, and is particularly suitable for prelayout wireless system design and planning.

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.

Systematic Microwave Network Analysis for Multilayer Printed Circuit Boards With Vias and Decoupling Capacitors

An efficient microwave network method is proposed for signal and power integrity analysis of a multilayer printed circuit board with multiple vias and decoupling capacitors. The multilayer parallel plate structure is described as a cascaded microwave network. The admittance matrix of a single plate pair with ports defined in via holes both on top and bottom plates is obtained through the intrinsic via circuit model and impedance matrix between two plates. A recursive algorithm is provided to obtain the combined admittance matrix of two layers of plate pair coupled through via holes on a common plate. Decoupling capacitors are naturally treated as impedance loads to the cascaded admittance network. Numerical simulations and measurements have been used to validate the method and good agreements have been observed. While the method is as accurate as full-wave numerical solvers, it achieves much higher efficiencies both in CPU time and memory requirements.

Cascaded Microwave Network Approach for Power and Signal Integrity Analysis of Multilayer Electronic Packages

In this paper, an efficient cascaded microwave network approach is presented for power and signal integrity analysis of multilayer printed-circuit boards (PCBs) and advanced electronic packages with multiple signal traces, multiple power-ground plates, multiple vias, and external loads such as decoupling capacitors. Each parallel-plate pair, which consists of two consecutive conductor plates functioning as either power or ground in the PCBs or packages, is modeled as one individual microwave network. Equivalent circuits are used in the microwave network to model the vias, and a parallel-plate impedance matrix is formulated to account for the wave interactions between the vias and the boundary of the PCB or package. If signal traces are present in a plate pair, a modal decomposition and recombination approach is employed to model two associated modes: the transmission line mode for the signal traces, and the parallel-plate mode for the power-ground plate pair. The microwave networks for each plate pair are finally cascaded together by enforcing the continuity of the voltages and currents at the via clearance holes in the conductor plate shared by two consecutive plate pairs. Numerical validation reveals that the cascaded microwave network approach produces accurate simulation results with much less central processing unit time and memory requirements than 3-D full-wave approaches.