ELECTRICAL PROPERTIES OF DIELECTRICS - Advanced Signal Integrity for High-Speed Digital Design - page 276

w

e r 1 e r 2

h

between bundles

over a bundle

Figure 6-17 Two-dimensional fiber-weave modeling structure.

layer is no longer sufficient. We need to modify our approach to comprehend
the localized dielectric variation. Figure 6-17 shows the profile of the cross-
sectional geometry description used as 2D field solver input for calculating the
transmission-line parameters. Simple in principle, this new approach is compli-
cated by the fact that the effective dielectric constant measured results from
the combined effect of multiple dielectrics: resin, fiberglass, solder mask, and
air. As a starting point, the effective dielectric constant of the FR4 material in
each region can be estimated from measured data using the method described in
equation 6-39 for multicomponent dielectrics. To determine the actual values of
ε r 1 and ε r 2 (see Figure 6-17), they should be varied until the delay of the 2D
simulation is equal to the measured response from the test board. Alternatively,
accurate representation of the cross section, including proper glass/resin height
ratios and solder mask thickness using a 2D electromagnetic field solver will
yield correct values of the effective dielectric permittivity.

Example 6-3 From the spatial ε r, eff variations shown in Figure 6-15, calculate the
actual (noneffective) dielectric permittivity for a trace over a bundle and between
bundles for a microstrip transmission line with a w/h ratio of 2 and t h .

SOLUTION
Step 1: Use equation (3-35) to estimate the relationship between ε r and ε r, eff .

18 . 7 ln 1

3

49 ln 2 4

+ ( 2 / 54 ) 2
2 4

1 1 2

18 . 1

a = 1 + + +

+ 0 . 432

0 . 564 ε r −

0 . 053

0 . 9
ε r +

b =

3

1 − ab

ε r + 1 ε r − 1 10

2

ε eff (u, ε r ) = + +

2 2

The relationships between ε r and ε r, eff are plotted in Figure 6-18a. The value of
ε r that corresponds to the minimum and maximum values of ε r, eff in Figure 6-15
are chosen to create equivalent cross sections to represent the case where the
trace is over a bundle and between bundles.