Modern packaging design requires extensive signal integrity simulations in order to assess the electrical performance of the system. The feasibility of such simulations is granted only when accurate and efficient models are available for all system parts and components having a significant influence on the signals. Unfortunately, model derivation is still a challenging task, despite the extensive research that has been devoted to this topic. In fact, it is a common experience that modeling or simulation tasks sometimes fail, often without a clear understanding of the main reason. This paper presents the fundamental properties of causality, stability, and passivity that electrical interconnect models must satisfy in order to be physically consistent. All basic definitions are reviewed in time domain, Laplace domain, and frequency domain, and all significant interrelations between these properties are outlined. This background material is used to interpret several common situations where either model derivation or model use in a computer-aided design environment fails dramatically. We show that the root cause for these difficulties can always be traced back to the lack of stability, causality, or passivity in the data providing the structure characterization and/or in the model itself.

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Stability, Causality, and Passivity in Electrical Interconnect Models

In this paper, we present a methodology for generating guaranteed passive time-domain models of subsystems described by tabulated frequency-domain data obtained through measurement or through physical simulation. Such descriptions are commonly used to represent on- and off-chip interconnect effects, package parasitics, and passive devices common in high-frequency integrated circuit applications. The approach, which incorporates passivity constraints via convex optimization algorithms, is guaranteed to produce a passive-system model that is optimal in the sense of having minimum error in the frequency band of interest over all models with a prescribed set of system poles. We demonstrate that this algorithm is computationally practical for generating accurate high-order models of data sets representing realistic, complicated multiinput, multioutput systems.

A convex programming approach for generating guaranteed passive approximations to tabulated frequency-data

Passive macromodeling of high-speed package and interconnect modules characterized by measured/simulated data has generated immense interest during the recent years. This paper presents an efficient algorithm for transient simulation of interconnect networks characterized by measured/simulated data in the presence of other linear and nonlinear devices. A new set of linear constraints are proposed, which help in preserving the passivity of resulting macromodels. Examples are presented to demonstrate the validity and efficiency of the proposed algorithm.

A fast algorithm and practical considerations for passive macromodeling of measured/simulated data

With the continually increasing operating frequencies, complex high-speed interconnect and package modules require characterization based on measured/simulated data. Several algorithms were recently suggested for macromodeling such types of data to enable unified transient analysis in the presence of external network elements. One of the critical issues involved here is the passivity violations associated with the computed macromodel. To address this issue, a new passivity enforcement algorithm is presented in this paper. The proposed method adopts a global approach for passivity enforcement by ensuring that the passivity correction at a certain region does not introduce new passivity violations at other parts of the frequency spectrum. It also provides an error estimate for the response of the passivity corrected macromodel.

Global passivity enforcement algorithm for macromodels of interconnect subnetworks characterized by tabulated data

A new comprehensive wide-band compact-modeling methodology for on-chip spiral inductors is presented. The new modeling methodology creates an equivalent-circuit model consisting of frequency-independent circuit elements. A fast automated extraction procedure is developed for determining the circuit element values from two-port S-parameter measurement data. The methodology is extremely flexible in allowing for accurate modeling of general classes of spiral inductors on high- or low-resistivity substrate and for large spirals exhibiting distributed trends. The new modeling methodology is applied to general classes of spirals with various sizes and substrate parameters. The extracted models show excellent agreement with the measured data sets over the frequency range of 0.1-10 GHz.

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A comprehensive compact-modeling methodology for spiral inductors in silicon-based RFICs

As digital circuits approach the GHz range, and as the need for high performance wireless devices increases, new simulation tools which accurately characterize high frequency interconnects are needed. In this paper, a new macromodeling algorithm for time domain simulation of interconnects is presented. The algorithm incorporates Householder LS curve-fitting techniques. The approach generates a universal macromodeling tool that enables simulation of interconnects in a modified version of simulation program with integrated circuit emphasis (SPICE). This results in a method that conveniently incorporates accurate EM models of interconnects or experimental data into a circuit simulator. The time domain simulation results using this new tool are compared with results from other simulators.

L. Zhao

Papers

Pole-residue formulation for transient simulation of high-frequency interconnects using householder LS curve-fitting techniques