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.      

On The Problem of Using Guard Traces for High Frequency Differential Lines Crosstalk Reduction

In this paper, the problem of using guard traces for reducing crosstalk between differential transmission line pairs is investigated, both experimentally and by full-wave electromagnetic (EM) simulations. Different cases of differential lines crosstalk are treated with and without guard trace separation between the differential line pairs. Coated microstrip printed circuit board test structures including thru-reflect-line calibration standards are designed and fabricated on a high frequency laminate material, allowing direct measurement of crosstalk between adjacent differential line pairs in the absence and in the presence of guard traces stitched with vias of regular spacing. The test structures are characterized with mixed-mode scattering parameters using a physical layer test system. Different configurations (of differential line pairs) without guard trace, with floating guard traces (which are terminated and nonterminated) and with a solid guard trace separation are investigated using a High Frequency Structure Simulator (a commercial full-wave 3-D EM simulation tool). The experimental data are compared with the simulation results, and some conclusions and guidelines on the effect of guard traces for alleviating crosstalk between differential transmission lines are presented     

Efficient EM Simulation of GCPW Structures Applied to a 200-GHz mHEMT Power Amplifier MMIC

The behaviour of grounded coplanar waveguide (GCPW) structures in the upper millimeter-wave range is analyzed by using full-wave electromagnetic (EM) simulations. A methodological approach to develop reliable and time-efficient simulations is proposed by investigating the impact of different simplifications in the EM modelling and simulation conditions. After experimental validation with measurements on test structures, this approach has been used to model the most critical passive structures involved in the layout of a state-of-the-art 200-GHz power amplifier based on metamorphic high electron mobility transistors (mHEMTs). This millimeter-wave monolithic integrated circuit (MMIC) has demonstrated a measured output power of 8.7 dBm for an input power of 0 dBm at 200 GHz. The measured output power density and power-added efficiency (PAE) are 46.3 mW/mm and 4.5 %, respectively. The peak measured small-signal gain is 12.7 dB (obtained at 196 GHz). A good agreement has been obtained between measurements and simulation results.     

Full-wave simulation,design and implementation of a new combination of antenna array feed network integrated in low profile microstrip technology

In this paper, a new modified combination of antenna and array feed network integrated in low thickness microstrip technology is presented. A concept similar to the concept of coherently radiating periodic structures is used to feed a 4-element antenna array. In the feed network, a new combination of Gysel-based 3 and 5 port components as power dividers/combiners is employed to propagate the power into the antenna array so that the desired Gaussian-like amplitudes and linear phase distributions can be obtained. These multi-port components are modified to design the feed network by single-layer microstrip technology without the matching and isolation circuits and through-substrate vias. Therefore, the manufacturing cost and difficulty and design complexity are reduced, considerably. Full-wave simulations of the feed network, unit cells and the final integrated antenna array are done, step by step and the results considering all possible losses are presented. To validate the designs, two prototypes, first the feed network and second the integrated module including both antenna array and feed network designed at 3.5 GHz were fabricated and measured and the S parameters (amplitude and phase) were compared with the full-wave simulations. A good agreement between the results including impedance and radiation characteristics is shown.     

Modeling and analyzing vertical interconnections

Continual interest in miniaturization is driving electronic packaging toward three-dimensional (3-D) structures and system integration. Utilization of a third dimension allows designers much more freedom, but at the same time it leads to an increase in the complexity of signal routing. High-density of components and interconnection increases the need for electromagnetic (EM) modeling. This paper focuses on EM modeling and the analysis of vertical interconnection in a stacked 3-D package. Solder-plated polymer balls are used in vertical interconnection between interposers and laser-drilled vias through the interposers. High-frequency responses of the vertical interconnections were studied with 3-D full-wave software. Based on the EM analysis, we propose equivalent circuit models for vertical connections, which were verified with measurements. In addition, an impedance-matching technique in vertical interconnection is discussed.     

40-Gb/s Package Design Using Wire-Bonded Plastic Ball Grid Array

A 40-Gb/s packaging solution that uses low-cost wire-bonded plastic ball grid array (WB-PBGA) technology is presented. Since such a high speed was beyond the reach of conventional package designs, a new design methodology was proposed-discontinuity cancellation in both signal-current and return-current paths. The 3-D structures of bonding wires, vias, solder ball pads, and power distribution networks were optimized for the discontinuity cancellation. Two versions of four-layer WB-PBGA packages were designed; one according to the proposed methodology and the other conventionally. The proposed design methodology was verified with full-wave simulation, passive bandwidth measurement, time domain reflectometry (TDR), eye diagram measurement, and jitter analysis.     

Domain decomposition approach for capacitance computation ofnonorthogonal interconnect structures

In this paper we apply the domain decomposition approach in conjunction with the finite difference (FD) method to compute efficiently the capacitance matrixes of crossovers and via type of interconnect structures, formed by traces that are nonorthogonal in general. In the past we have applied the FD method, in conjunction with the perfectly matched layer (PML) and the impedance boundary condition for FD mesh truncation, to compute the capacitances of orthogonal interconnect configurations. In this work we extend the above approach to apply to more general geometries, e.g., vias and crossovers with arbitrary angles. The paper presents some representative numerical results and examines the convergence and efficiency issues of the proposed algorithm     

高速PCB中的过孔设计研究

传输线的不连续问题已成为当今高速数字设计研究的重点,尤其是高速多层板中的过孔结构。随着频率的增长和信号上升沿的变陡,过孔带来的阻抗不连续会引起信号的反射,严重影响系统的性能和信号完整性。文章运用全波电磁仿真软件HFSS,对多种过孔结构进行了全面的研究。通过建立三维物理模型,分析了过孔直径、过孔长度和多余的过孔短柱几种关键设计参数对高速电路的信号完整性的影响。     

Analytical Model for Optimum Signal Integrity in PCB Interconnects Using Ground Tracks

In this paper, we present analytical models for line impedance and the coupling coefficient in the presence of additional ground tracks. We use a variational analysis combined with the transverse transmission-line technique to model interconnect lines guarded by ground tracks. Using the proposed model, it would be possible for designers to reduce crosstalk in coupled lines and obtain desired line impedance, thereby ensuring optimum signal integrity. The results obtained are verified by full-wave simulations and measurements performed on a vector network analyzer. The proposed model may find applications in the design and analysis of high-speed interconnects.      

An Efficient Scheme for Processing Arbitrary Lumped Multiport Devices in the Finite-Difference Time-Domain Method

Developing full-wave simulators for high-frequency circuit simulation is a topic many researchers have investigated. Generally speaking, methods invoking analytic pre-processing of the device's V-I relations (admittance or impedance) are computationally more efficient than methods employing a numerical procedure to iteratively process the device at each time step. For circuits providing complex functionality, two-port or possibly multiport devices whether passive or active, are sure to appear in the circuits. Therefore, extensions to currently available full-wave methods for handling one-port devices to process multiport devices would be useful for hybrid microwave circuit designs. In this paper, an efficient scheme for processing arbitrary multiport devices in the FDTD method is proposed. The device's admittance is analytically pre-processed and fitted into one grid cell. With an improved time-stepping expression, the computation efficiency is further increased. Multiport devices in the circuit can be systematically incorporated and analyzed in a full-wave manner. The accuracy of the proposed method is verified by comparison with results from the equivalent current-source method and is numerically stable     

Planar distributed structures with negative refractive index

Planar distributed periodic structures of microstrip-line and stripline types, which support left-handed (LH) waves are presented and their negative refractive index (NRI) properties are shown theoretically, numerically, and experimentally. The supported LH wave is fully characterized based on the composite right/left-handed transmission-line theory and the dispersion characteristics, refractive indexes, and Bloch impedance are derived theoretically. In addition, formulas to extract equivalent-circuit parameters from full-wave simulation are given. Open (microstrip) and closed (stripline) structures with a 5/spl times/5 mm/sup 2/ unit cell operating at approximately 4 GHz are designed and characterized by full-wave finite-element-method simulations. A 20 /spl times/ 6 unit-cell NRI lens structure interfaced with two parallel-plate waveguides is designed. The focusing/refocusing effect of the lens is observed by both circuit theory and full-wave simulations. Focusing in the NRI lens is also observed experimentally in excellent agreement with circuit theory and numerical predictions. This result represents the first experimental demonstration of NRI property using a purely distributed planar structure.     

Circuit model of microstrip patch antenna on ceramic land grid array package for antenna-chip codesign of highly integrated RF transceivers

This paper presents the circuit model of a microstrip patch antenna on a ceramic land grid array (CLGA) package for the antenna-chip codesign of a highly integrated radio-frequency (RF) transceiver. The microstrip patch antenna is fed by packaging interconnect components such as bond wires, signal traces, and vias in a ground-signal-ground (G-S-G) configuration from the carried chip. The circuit model that consists of RLC lumped elements of both microstrip patch antenna and feeding interconnect components has been developed with an emphasis on verifying existing or deriving analytical formulas. The RLC values of the microstrip patch antenna are calculated with our improvements to existing computer-aided design formulas, while the RLC values of the feeding interconnect components are calculated with more efforts. In particular the C values related to the vias and signal traces require to be calculated numerically and they are calculated here with the method of moments and the conformal mapping method, respectively. The circuit model is validated with numerical simulations (High Frequency Structure Simulator) and network analyzer measurements.     

电路板上地保护走线的阻抗数学模型和串扰控制

文章提出了一种基于地保护走线的互连线的特性阻抗闭环计算公式,采用变分法结合横向传输线结构,分析地保护走线引起的两耦合信号线的耦合系数的变化。提出如何让地保护走线能很好的弥补串扰,还可以使传输线达到需求的稳定的特性阻抗。并且用高频三维电磁场仿真软件模拟仿真,并用矢量网络分析仪测量验证。     

金属接触非线性引起的无源互调效应的数值分析

针对时域物理光学方法求解无源互调问题的局限性,提出基于"场路结合"的数值分析方法,建立非线性金属结的等效电路模型并将其引入到全波方法中,通过全波方法与等效电路相结合的方式来分析系统的无源互调干扰.计算实例表明,该方法可以精确地计算由于金属接触非线性引起的无源互调及其作为二次辐射源所激发的电磁场,避免了时域方法在电大尺寸问题上计算的积累误差以及只能对处于远场区的简单微波结构的无源互调效应进行求解的问题.本文提出的场路结合数值分析方法为微波部件无源互调效应的研究提供了新的思路与方法.     

Full-wave analysis of coaxial mounting structure

An efficient full-wave spectral-domain analysis based on the integral equation method is developed for a coaxial mounting structure of a general form. Using this method, the algorithm for complex input gap impedance of such structures has been derived and the calculated data are presented. The method may be useful for designing active and passive devices mounted in a coaxial line     

An efficient approach for power delivery network design with closed-form expressions for parasitic interconnect inductances

Investigation of a dc power delivery network, consisting of a multilayer PCB using area fills for power and return, involves the distributed behavior of the power/ground planes and the parasitics associated with the lumped components mounted on it. Full-wave methods are often employed to study the power integrity problem. While full-wave methods can be accurate, they are time and memory consuming. The cavity model of a rectangular structure has previously been employed to efficiently analyze the simultaneous switching noise (SSN) in the power distribution network. However, a large number of modes in the cavity model are needed to accurately simulate the impedance associated with the vias, leading to computational inefficiency. A fast approach is detailed herein to accelerate calculation of the summation associated with the higher-order modes. Closed-form expressions for the parasitics associated with the interconnects of the decoupling capacitors are also introduced. Combining the fast calculation of the cavity models of regularly shaped planar circuits, a segmentation method, and closed-form expressions for the parasitics, an efficient approach is proposed herein to analyze an arbitrary shaped power distribution network. While it may take many hours for a full-wave method to do a single simulation, the proposed method can generally perform the simulation with good accuracy in several minutes. Another advantage of the proposed method is that a SPICE equivalent circuit of the power distribution network can be derived. This allows both frequency and transient responses to be done with SPICE simulation.     

Analyses of bounces on power distribution networks using an unconditionally stable finite-difference time-domain method

An unconditionally stable finite-difference time-domain (US-FDTD) method is utilized for analyzing the bounces on structures of power distribution networks (PDNs), which is a critical issue in the electromagnetic compatibility analysis of mobile devices. The US-FDTD method does not utilize the explicit leapfrog time scheme of conventional FDTD method and can solve problems with fine structures well, such as via, thin material and so on. By using this full-wave method, electromagnetic fields between power/ground plane pairs are analyzed and discontinuities of through-hole vias are taken into account in the modeling of PDNs.     

Analysis of Substrate Integrated Waveguide Structures Based on the Parallel-Plate Waveguide Green's Function

This paper presents the full-wave characterization of substrate integrated waveguide structures. Substrate integrated circuits are considered as an ensemble of conducting posts placed in a parallel-plate waveguide and are analyzed in terms of the cavities formed by the top and bottom conducting plates and by the walls of the metallic vias. The field inside the parallel-plate waveguide is computed by considering the dyadic Green's function expressed as an expansion in terms of vectorial cylindrical eigenfunctions and considering the scattering from the ensemble of conducting posts. Coaxial or waveguide ports are included in the analysis as equivalent magnetic current distributions. Self-admittance and mutual admittance are calculated in a form that separates the parallel-plate contribution from the field scattered by the posts. Results relevant to structures already presented in literature will be shown and compared with simulations obtained with one of the most used articles of commercial software. It will be shown that an excellent agreement with published results is achieved together with significant improvements both in computational time and memory requirements.      

Lumped-circuit model extraction for vias in multilayer substrates

Via interconnects in multilayer substrates, such as chip scale packaging, ball grid arrays, multichip modules, and printed circuit boards (PCB) can critically impact system performance. Lumped-circuit models for vias are usually established from their geometries to better understand the physics. This paper presents a procedure to extract these element values from a partial element equivalent circuit type method, denoted by CEMPIE. With a known physics-based circuit prototype, this approach calculates the element values from an extensive circuit net extracted by the CEMPIE method. Via inductances in a PCB power bus, including mutual inductances if multiple vias are present, are extracted in a systematic manner using this approach. A closed-form expression for via self inductance is further derived as a function of power plane dimensions, via diameter, power/ground layer separation, and via location. The expression can be used in practical designs for evaluating via inductance without the necessity of full-wave modeling, and, predicting power-bus impedance as well as effective frequency range of decoupling capacitors.     

Analysis and design of periodic structures for microstrip lines by using the coupled mode theory

In this work, the coupled mode theory is formulated to analyze distributed periodic structures for microstrip lines. After it, several reasonable approximations are introduced giving rise to analytical solutions for the problem. The obtained results, both numerical and analytical, are checked against measurements showing very good agreement. The proposed method is very attractive for the study of these devices since it avoids the time-consuming full-wave electromagnetic simulations customarily employed and provides analytical solutions that are very useful for analysis and synthesis purposes.