Electromagnetic simulation of electronic packaging designs (95-ERP-003). 1995 LDRD final report Page: 29 of 50
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consistently lie below the analytic result for an ideal circular-cylindrical coax,
49.58 ohms, although the values are approaching this impedance uniformly with
increasing azimuthal resolution of the model; by the time n8=24, the error is
minuscule. It would appear, if these results are at least qualitatively accurate,
that the impedance of the model configuration increases, albeit by a small
amount, toward the ideal circular-cylindrical value as the number of azimuthal
sections increases. It is noted, however, that the increase from 8 to 24 sections is
only about 1%.
no ZMAxWELL4 44.56
8 48.98
12 49.41
16 49.49
20 49.52
24 49.54Table 4.3
Impedances computed with MAXWELL EMINENCE.
As a further check, Grant's version of the DSI code was used to compute
the impedance. For the purposes of this study, Grant's version differed in two
essential respects: (1) it had the capability to take advantage of the symmetry of
the INGRID mesh to compute the impedance using only a single azimuthal
section of the model, as shown in Fig. 4.5, and (2) it computed the line integrals
of Eqs. (2.6) and (2.11) somewhat differently than Brandon's version, breaking the
path integrals along each edge into two segments, dividing the edge at the
midpoint, rather than using only one segment along the edge. Using only a single
section of the whole coax cross section, it was simplest to subdivide the section in
what amounts to the x-direction in the figure. Thus, this set of simulations was
characterized by numbers of zones in the azimuthal-, radial-, and x-directions (n0
x nr x ny). With this greater resolution, it was hoped that it would be possible to
obtain more accurate values for the impedance of the faceted-face model
approximations to the ideal cylindrical coax. The results obtained from these
simulations are summarized in Table 4.4. The values obtained with this version
of the code are quite different in a couple of respects from those computed
earlier, as can be seen from the table. First, the impedances increase from below
toward the value obtained with MAXWELL EMINENCE as the resolution of the
mesh becomes greater. Second, except for a few exceptions, the impedances
approach the frequency-domain value quite uniformly as the both the azimuthal
and radial resolution is increased, in contrast to the trend with the other version25
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Swegle, J. A. Electromagnetic simulation of electronic packaging designs (95-ERP-003). 1995 LDRD final report, report, May 1996; California. (https://digital.library.unt.edu/ark:/67531/metadc667166/m1/29/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.