I. WHY INTERPOLATION?
An electromagnetic (EM) simulator has been an indispensable tool for signal integrity analysis for both high-frequency analog and high-speed digital design. Actually, the importance of EM simulators has been increasing.
Since EM simulation may take time ranging from seconds to hours or even days, speeding up the simulation has been one of the major objectives of any EM software developers. Although IE3D, a commercial EM simulator from Zeland Software, is very fast, a faster scheme based on interpolation of real EM simulation data to generate ones at other dimensions is useful for interactive analysis and tuning in real time. The following flow represents the proposed process involving EM simulation and interpolation.
II. MICROSTRIP VIA
The first example to demonstrate the usefulness of the proposed process is a simple microstrip via as shown in Fig.1. The via connects micrstrip line with a via pad of 130μm by 130μm to ground under a GaAs substrate with 100μm thickness. IE3D predicted the inductance per unit height (pL/μm) of the via at 0.1327 at 4GHz that closely agrees with measured value at 0.124 . The small difference is likely due to different pad size used in simulation and measurement. A critical step to prepare the structure for tuning is to define variable(s) to control it. Via diameter is chosen as a variable to investigate its influence on the via’s inductive behavior. The structure was swept in frequency from 1GHz to 50GHz with 50 sampling points and in diameter from 20 μm to 130 μm with 56 sampling points using IE3D on a dual-core machine with 2GB RAM and 2.19GHz clock frequency. The sweep only took 834 seconds.
Fig.1. 3D view of a micrstrip via shorting to the ground (not shown).
Fig.2. S11 versus frequency as the via diameter changes (D=75+2*Radius).
III. THREE BOND WIRES IN PARALLEL
As shown in Fig.3, the second example is three bond wires in parallel above a dielectric layer under which a ground plane is assumed. Of course, IE3D has no problem in handling bond wires going one layer to another.
Fig.3. 3D view of three bond wires in parallel.
For simplicity, the spacing between two adjacent wires is chosen as a variable. Obviously, the spacing predominantly determines the coupling from one wire to another. The structure was swept in frequency from 0.1GHz to 10GHz with 100 sampling points and in spacing from 5 μm to 30 μm with 26 sampling points using IE3D on the same computer. The sweep only took 1427 seconds. With these data in place, we can just move the slider to change the spacing and see the change of the couplings as shown in Fig.4. As a validity check, real EM simulated data for S=17.5 μm is also shown in the figure. It is seen that interpolated data at S=17.5 μm agree very closely with those simulated numerically.
Fig.4. S15 and S16 versus frequency as the spacing changes (S=30-Spacing).
Interpolation using EM simulation data has been proven to be a valid and effective way for fast analysis and real-time tuning of high-frequency or high-speed structures.
 M. E. Goldfarb and R. A. Pucel, “Modeling via hole grounds in microstrip,” IEEE Microwave and Guided Wave Letters, vol.1, no.6, pp.135-137, June 1991.