Simulation Techniques for Electromagnetic Interference (EMI) and Signal Integrity (SI) in High-Speed Electronic Circuits

Luca Daniel and Jacob White1
(Professor Alberto L. Sangiovanni-Vincentelli)
Semiconductor Research Corporation and MARCO Interconnect Focus Center

Electromagnetic interference (EMI) is becoming an exceptionally crucial issue in the design of modern electronic systems. Frequencies are continuously increasing, while integration trends are squeezing entire systems into extraordinarily high circuit densities. In the conventional design methodology, electromagnetic compatibility (EMC) issues are addressed only after a prototype is built. At that stage, the traditional EMC remedies are confined to adding extra components, metal shields, metal plans, or even redesigning the entire system, with a potentially significant impact both on the cost and on the time-to-market of the products. It is our firm opinion that EMC must instead be addressed as early as possible during the design phase, and not after. EMI simulation could shorten the design time, allowing the analysis of circuits before manufacturing.

Large and expensive electronic equipment can effectively employ standard EMC solutions. But smaller, high-volume, low-priced electronic devices, automotive electronics, and most of the embedded systems cannot afford those costly solutions. Such devices are the most susceptible to EMI problems and the most sensitive to post-prototype EMC added costs. Unfortunately, they are also the most difficult to simulate with respect to EMI problems since they require "full-board" capabilities, and no tool is available to date for such task.

Full-board EMI simulation capability would therefore be instrumental in promptly verifying EMC compliance during the very first stages of the design of high-speed PCBs and IC-packages. For this application, we are investigating the use of integral equation methods:

  1. Our research focuses on minimizing the number of unknowns needed to model each conductor in the system. We have found two alternative set of basis functions [1-3], requiring 16 to 20 times fewer unknowns than the classical thin filaments discretization, for the same final accuracy. In our method, we use as basis functions some of the physically admissible solutions of the diffusion equation for the current density in the interior of the conductors.
  2. We are currently implementing our method based on our new basis functions. We solve the resulting linear system using the very efficient Krylov subspace iterative methods. The complexity of the algorithm is dominated by an O(N2) matrix-vector product operation. We propose to further reduce the computational complexity of the iterative method. Fast algorithms exist for such products with complexity O(Nlog(N)). Such algorithms have been already successfully implemented in tools for the static capacitance extraction problem (FASTCAP) and for the magneto-quasi-static problem (FASTHENRY). We plan to modify and extend one such algorithm, Precorrected-FFT, to our full-wave EMI analysis problem.
Desirable results from an EMI analysis range from the characterization of the spectrum emissions observed on a measurement sphere at 10 meters, to the generation of a model of the interconnect structures for instance to be later used within a non-linear time domain simulator.

To address efficiently the first specification, we propose to use an adjoint method to calculate a set of transfer functions from the thousands of circuit inputs (e.g., the pins of the ICs) to the tens of observation points on the measurement sphere.

To address the second specification, we are working on the generation of "dynamical linear systems" that mimic the same behavior of the original interconnect structure, but have a state vector orders of magnitude smaller. In some recent papers of ours, we show how to generate guaranteed passive reduced order models from originally passive structures including dielectrics [4], and for distributed systems with frequency dependent matrices [5] (as generated for instance when accounting for substrate effects or for fullwave effects). Finally we are developping techniques for "parameterized" model order reduction techniques [6] for enabling optimization of interconnect structures.

L. Daniel, A. Sangiovanni-Vincentelli, and J. White, "Interconnect Electromagnetic Modeling Using Conduction Modes as Global Basis Functions," IEEE Topical Meeting on Electrical Performance of Electronic Packages, Scottsdale, AZ, October 2000.
L. Daniel, J. White, and A. Sangiovanni-Vincentelli, "Conduction Modes Basis Functions for Efficient Electromagnetic Analysis of On-Chip and Off-Chip Interconnect," Proc. Design Automation Conf., Las Vegas, NV, June 2001.
L. Daniel, A. Sangiovanni-Vincentelli, and J. White, "Proximity Templates for Modeling of Skin and Proximity Effects on Packages and High Frequency Interconnect," ," ICCAD, San Jose, CA, November 2002.
L. Daniel, A. Sangiovanni-Vincentelli, and J. White, "Techniques for Including Dielectrics when Extracting Passive Low-Order Models of High Speed Interconnect," ICCAD, San Jose, CA, November 2001.
L. Daniel, J. Phillips, "Guaranteed Passive Model Order Reduction for Strictly Passive and Causal Distributed Systems," Proc. Design Automation Conf., New Orleans, June 2002.
L. Daniel, C. Ong, S. Low, K. Lee, J. White, "Geometrically Parameterized Interconnect Performance Models for Interconnect Synthesis," International Symposium on Physical Design, San Diego, CA, May 2002.
1Professor, Massachusetts Institute of Technology

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