August 1, 1997

Computer simulation avoids EMI/EMC
problems in high-speed IC packages

Zoltan J Cendes, PhD, John Silvestro, PhD,
and Nirmal Jain, Ansoft Corp

Signal-integrity and EMI/EMC issues can be devastating in high-density, high-speed IC- package design. Simulation techniques can help you model your design and anticipate these problems.

The complexity and speed of electronic systems require that you consider electrical issues, such as signal integrity and EMI/EMC, to verify your design concepts before prototyping. Accurate signal-integrity analysis of high-density, high-speed interconnects is imperative in IC-package design. A package comprises several components that you must accurately model to predict the signal-propagation behavior of the interconnects. As the die dimensions and operating-clock frequencies increase, signal wavelengths become comparable to wire lengths and require you to model interconnects using full-wave field solvers.

Crosstalk, package resonance, reflection, and simultaneous switching noise issues are precursors to EMI/EMC issues. You can look at these factors through available simulation techniques and the example of quasistatic and full-wave analysis of a standard 208-lead QFP.

Higher clock rates make it critical to analyze package design as early as possible in the design cycle, and this situation leads to the demand for high-performance simulation tools. For crosstalk, ground bounce, and other signal-integrity issues, you can solve the static-electricity and magnetic-field problems for a given geometry and extract the R, L, and C matrices. You can then use these circuit descriptions in a circuit simulator to calculate the quantities of interest.

This technique is efficient and offers accurate results for cases in which the geometry is "electrically small": The maximum dimension is less than or equal to one-tenth the wavelength of the input signal's highest frequency component. Cases with geometry that is not electrically small--because of larger components or higher frequencies--need a full-wave electromagnetic simulation. In this situation, you typically compute coupling in scattering or S-parameters. If a design requires the level of spurious radiation, you must perform a full-wave simulation, which also lets you analyze the reciprocal problem of device susceptibility.

A typical package geometry comprises several conductors--such as leads, pc-board traces, and die pads--and several dielectric materials, such as the package body and pc-board substrates. These components typically reside in a complex, 3-D configuration, such as a 208-lead QFP (Figure 1). Calculating the field quantities excited in such a geometry is a complex task.

Several techniques are available for such a calculation. Two powerful ones are the boundary-element method (BEM) and the finite-element method (FEM). You use BEM for computing the static fields and extracting the circuit model, and you use FEM for full-wave simulation.

In BEM simulation, you use an integral-equation formulation of Maxwell's equations to compute the source terms for the field quantity of interest. In an electrostatic simulation, the sources are electric charges, whereas in a magnetostatic simulation, the sources are currents. You first break the source region into small pieces. Typically, these pieces are parts of a boundary surface, hence the name "boundary-element method."

You use simple functions to approximate the unknowns over each element. A typical approximation is to assume that the source, the charge, or another current is constant over the small element with an unknown amplitude coefficient. You substitute these terms into the integral equation, and the result is a matrix equation having a large, full matrix. Solve this equation to determine the amplitude coefficients. Once you complete this computation, you use the resulting source terms to compute the desired field quantities. Using these field quantities, you can extract the corresponding circuit parameters.

One problem with standard BEM is that as the number of unknowns increases, the solution time (the cube of the number of unknowns) also increases. Before long, the solution time becomes prohibitive. Recent advances in BEM for static-field problems center on multipole expansion (Reference 1), which, when you apply it properly, yields a dramatic speed advantage. The standard matrix procedure grows in solution time as n³, where n is the number of unknowns in the matrix equation. Meanwhile, the time with multipole acceleration increases proportional to n. This linear performance results in sizable time savings for moderate to large problems.

Several full-wave-simulation techniques are available. You can efficiently use the BEM technique for certain classes of problems, such as planar geometries (Reference 2). However, the most accurate and efficient procedure is the FEM for general 3-D geometries. An FEM calculation breaks the solution space into the FEM mesh: small, 3-D elements--typically, tetrahedrons. You then solve directly for the field quantities within each element, unlike with BEM, in which you compute the source terms. You use a simple polynomial function containing unknown amplitude coefficients to approximate the field within each element.

You then substitute these functions into a functional expression that you derive from the differential form of Maxwell's equations. Because this method solves for the field quantities themselves in the differential form of Maxwell's equations, the resulting matrix equation is sparse. You can then use a solution procedure that takes advantage of this sparseness. Once you solve this equation, you can use the resulting field quantities to compute the coupling or radiation.

Again, in full-wave simulators, you typically compute the coupling in terms of the S-parameters. In a full-wave simulation, you apply the signals to input or output ports in the simulation model. The S-parameters relate the signals incident on the ports to the signals reflected from the ports (Reference 3).

208-lead QFP demonstrates technique

You can use the 208-lead QFP model and a BEM solver with multipole acceleration to understand the approach (Reference 4). The package has a nonideal ground plane 4 mm from the bottom of the pins; in this case, the pins in the model are pins 23 through 30. The model also includes a die pad to weigh its effect performance.

In the crosstalk analysis (Figure 2), the RLC matrices using T-networks (Table 1) generate a subcircuit, which you use to model the package pins. A pulse with 0.5-nsec rise and fall times and a 5V amplitude drives Pin 26 while the other pins are quiet. The load and source resistances are 100 ohms, and all the other pins terminate with 100 ohms at the far and near ends. The near-end crosstalk amplitudes on pins 25, 24, and 23 are 360, 196, and 176 mV, respectively (Figure 3). The far-end crosstalk amplitudes on pins 25, 24, and 23 are 260, 166, and 160 mV, respectively (Figure 4).

The results from this study show that the crosstalk on the first neighbor is more than 10% of the signal on the active line; it falls off rapidly for the next neighbors. In designs that cannot tolerate this crosstalk, you must devise ways to decrease it. Some of your options include using a coplanar-waveguide configuration, moving the ground plane closer to the package, or using materials with lower dielectric constants.

Full-wave simulation goes even further

When doing a full-wave simulation, you typically want to know at which frequencies the device is resonant. At these frequencies, your design often encounters crosstalk and spurious-radiation problems. To illustrate these problems, reconsider Figure 1's small package geometry using a full-wave FEM solver (Reference 5). Instead of using six pins, you use two input pins on opposite sides of the package to perform the simulation.

Each pin connects to a trace on a grounded substrate. The traces are short and terminate at the end of the board in simulation ports. In full-wave simulations, you solve the coupling terms for the S-parameters. The S-parameters of interest for this case are S₁₂ or S₂₁, the coupling coefficients between the two ports.

The pins do not make a direct electric connection to the die pad; therefore, you would expect small coupling of energy from one side to the other. For most frequencies this situation is true, but where the package-pin-pc-board geometry is resonant, the coupling can be sizable. The results show that spurious radiation can also decrease.

A plot of S₁₂ for this geometry vs frequency shows less than ­10-dB coupling for all frequencies except for those in a narrow band near 2.3 GHz (Figure 5). To see what is happening at that frequency, consider two shaded plots (Figures 6 and 7). A plot of the (E·E*)^1/2 for a plane that cuts through the die at 2 GHz includes an input port on the backside of the model (Figure 6). Energy exists along the input pin, but there is little coupling to other parts of the package at 2 GHz.

For the fields at 2.3 GHz, significant coupling to the die pad occurs (Figure 7). This energy also couples to the output pin giving the large S₁₂ value in Figure 5. The increased coupling to the package structure also produces an increase in spurious radiation.

The ratio of the radiated power to input power for several frequencies of this simulation shows little radiated power except for frequencies near 2.3 GHz (Figure 8). To illustrate how this increased level of radiation can be troublesome, consider a plot of the magnitude of the vertical component of the electric field along a 3m-radius circular path, centered at the package model (Figure 9). The field quantities are in decibel-microvolts per meter vs the angle around the path.

Although there is only 1 µW of input power at 2.3 GHz, these field levels are large enough to concern a designer whose product is trying to pass today's EMC guideline. Although high frequencies were not a concern in the past, modern clock speeds of 200 MHz and above generate sizable harmonic content at 2.3 GHz and higher.

References

1. Nabors, K, S Kim, and J White, "Fast capacitance extraction of general three-dimensional structures," IEEE Transactions on Microwave Theory and Techniques, Volume 40, No. 7, July 1992.

2. Cendes, Z, et al, "EM field solver offers 3D analysis of MMICs and antennas," Microwaves and RF, April 1996.

3. Pozar, D, Microwave Engineering, Addison-Wesley Publishing Co, Reading, MA, 1990.

4. Maxwell Quick Parameter Extractor, User's Reference, Ansoft Corp, November 1994.

5. Maxwell Eminence, User's Reference, Ansoft Corp, May 1994.

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