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A novel pin impedance-based figure of merit with mutual coupling (PMC-FOM) is proposed for effectiveness assessment of a decoupling capacitor. The algorithm is based on the relative location of the capacitor on parallel plates and takes into account mutual coupling by extending the existing scalar expressions to matrix relations. New analytical relations are developed for the calculation of derivatives as required for the iterative solution of the problem. The relations for resonant parallel plates of regular shapes are extended to the practical case of polygonal shapes. It is demonstrated that a capacitor’s effective zone can hardly be delimited with a simple circle when mutual interaction with other capacitors is considered. In fact, the presence of other capacitors deforms the circular zone to an irregular contour. The proposed method is analyzed with several benchmark examples and the results are validated for efficiency and accuracy by comparing with alternate methods including a commercial electromagnetic (EM) simulator. [ABSTRACT FROM AUTHOR]

A multiobjective evolutionary method is proposed for the optimization of surface mount device (SMD) multilayer ceramic chip (MLCC) capacitors used for decoupling on printed circuit boards (PCBs) with resonant power–ground plane pairs. The proposed approach provides options for designers to meet power integrity specifications by employing uniform-valued capacitors that help to reduce the bill-of-material (BOM) cost and mitigate the part procurement risk. It is also shown that uniform MLCC capacitors with variable distance from power pins can have a similar decoupling effect to an assortment of capacitors. By simultaneously optimizing the pin-capacitor distance and value, the proposed method is shown to allow for the allocation of fewer decoupling capacitors under the ball-grid-array (BGA) pin field of an integrated circuit (IC) device. [ABSTRACT FROM AUTHOR]

A semi-analytical method is proposed to evaluate the effectiveness of a decoupling capacitor on resonant power and ground planes. New expressions are developed relating the pin impedance to relative placement of a capacitor with associated angular and distance parameters. To speed up the solution of resulting transcendental equations, a 2-D iterative technique is proposed, which yields the effective distance as well as the angle between a decoupling capacitor and a power pin. The partial derivatives of the corresponding Jacobian matrix are analytically derived. Numerical examples are presented to demonstrate the validity of the proposed method, which also investigates the effect of plane edges on pin impedance. [ABSTRACT FROM AUTHOR]

A genetic algorithm (GA)-based method is proposed for simultaneous optimization of decoupling capacitors assigned to multiple pins of a ball-grid array (BGA) package on a printed circuit board. A noise susceptibility parameter is introduced as the basis of a new set of GA fitness functions. Performance of several fitness functions is comparatively tested and discussed in case studies. The accuracy of the developed expressions is tested against full-wave electromagnetic simulation results. The proposed method is particularly useful for predicting the number and placement of decoupling capacitors under the BGA area of integrated circuit devices in early design stages and serves as a complement to rigorous algorithms that are used in the final phase of the design. [ABSTRACT FROM AUTHOR]

Crossing strip junctions form an important discontinuity problem in differential signaling an pose a major challenge for signal integrity modeling throughout an analysis in high-speed designs. An analytical framework is proposed to characterize differential transmission lines including the effect of crossing strip junctions for broadband circuit analysis. A new analytical model is proposed to include the finite thickness in the existing models for characterization of asymmetric striplines. The proposed modular representation of the differential line segments with discontinuity effects allows for an entire high-speed transmission channel with crossing lines to be modeled in a cascaded fashion for efficient signal integrity analysis. [ABSTRACT FROM AUTHOR]

With rapidly increasing switching speeds and surge current requirements, placement of local decoupling capacitors is becoming critically important in high-speed low-power designs. In this paper, utilizing the driving-point impedance (viewed from the device pin) as a metric, a new method is presented for the placement of decoupling capacitors in parallel-plate power ground pairs of high-speed circuits. In the proposed approach, instead of using the traditional trial-and-error method to identify an appropriate placement distance, the process is formulated in the form of a transcendental function. The resulting function is solved using Newton–Raphson (N-R) iterations to give a direct solution for the distance. Also, an analytical representation based on Hankel functions for the driving point impedance and its derivatives is developed to speed up the N-R iterations. The proposed method is validated by comparing the results with the full-wave electromagnetic simulations. [ABSTRACT FROM PUBLISHER]

In this paper, a novel approach is presented for an integrated analysis of power distribution networks, including dc–dc converters, power transmission lines (PTLs), and multiple loads. The effect of power interconnects is investigated on the dynamic characteristics of a pulsewidth-modulated buck converter. A closed-form relation is developed for control-to-output transfer function including the power interconnects as a transmission line model. The effect of PTLs is demonstrated on converter’s open-loop transfer function and its stability. For analysis of distributed power loads on printed circuit board PTLs, a model is developed based on cascaded matrix representation of interconnects. The model is successfully tested against planar electromagnetic simulation results. [ABSTRACT FROM AUTHOR]

This paper introduces a new time-domain approach for compact macromodeling of multiport high-speed circuits with long delays, characterized by tabulated data. The algorithm is based on partitioning the data in the time-domain and subsequently, approximating each partition via delayed rational functions. This results in a compact low-order macromodel in the form of delayed differential equations, which can be efficiently analyzed in the time-domain using circuit simulators. [ABSTRACT FROM AUTHOR]

Electromagnetic compatibility (EMC) analysis of high-speed designs has become imperative due to rapidly in- creasing radio-frequency interference and emerging technological trends such as higher operating frequencies, denser layouts, and multifunction convergent products. In this paper, a simplified macromodel of multiconductor transmission lines (MTLs) exposed to incident fields is presented. The proposed formulation can also handle frequency dependence of resistance, capacitance, conductance, and inductance (RLGC) line parameters. The method employs the recently developed delay-extraction-based compact and passive MTL macromodel, while developing closed-form expressions for incident field analysis. An error bound for the proposed macromodel is also presented. The macromodel is simulation program with integrated circuit emphasis (SPICE) compatible and overcomes the mixed frequency/time simulation difficulties usually encountered during transient analysis, while guaranteeing the stability of the global transient simulation. The algorithm provides higher accuracy as well as significant speed gains for EMC analysis of transmission line networks as compared to the existing techniques. [ABSTRACT FROM AUTHOR]

Due to the rapid surge in operating frequencies and complexity of modern electronic designs, accurate/fast electromagnetic compatibility/interference analysis is becoming mandatory. This paper presents a closed-form SPICE macromodel for fast transient analysis of lossy multiconductor transmission lines in the presence of incident electromagnetic fields. In the proposed algorithm, the equivalent sources due to incident field coupling have been formulated so as to take an advantage of the recently developed delay extraction based passive transmission line macromodels. Also, a method to incorporate frequency-dependent per-unit-length parameters is presented. The time-domain macromodel is in the form of ordinary differential equations and can be easily included in SPICE like simulators for transient analysis. The proposed algorithm while guaranteeing the stability of the simulation by employing passive transmission line macromodel, provides significant speed-up for the incident field coupling analysis of multi-conductor transmission line networks, especially with large delay and low losses [ABSTRACT FROM AUTHOR]

Presents a time-domain macromodel for incident field coupling to lossy-multiconductor transmission lines. Basis of the model; Formulation of forcing functions; Criteria for selecting the order of approximation.

Analyzes the electromagnetic radiation and field coupling effects for nonlinear circuits with embedded full-wave modules. Employment of model-reduction-based approach to overcome the numerical stability problems associated with the finite-difference time-domain; Increase of the electromagnetic interference susceptibility and radiation efficiency.

Focuses on the simulation of high-speed microwave circuits and interconnects in the presence of incident electromagnetic interference. Analysis of incident field coupling in inhomogeneous medium; Derivation the interconnect simulation stamp; Transmission line equations with incident field excitation.

In this letter, a new method for nonlinear behavioral modeling of high-speed I/O drivers is presented, combining neural networks with driver specific circuit knowledge. In the proposed technique, the circuit knowledge of the driver is exploited to preserve the physical property of the driver. In addition, several neural network sub-models are incorporated into the overall model structure to effectively compensate the missing information in the existing buffer models, when dealing with analog input signals of various shapes. The validity and efficiency of the proposed technique are demonstrated through the modeling of a commercial I/O driver and the use of the resulting model for signal integrity simulations. [ABSTRACT FROM PUBLISHER]

We Agree with the comments that, $Z_{\mathrm {in}}$ being a complex valued function of real variables $r$ and $\phi$ should be based on the following relation: [ABSTRACT FROM AUTHOR]