ELECTRICAL PROPERTIES OF DIELECTRICS - Advanced Signal Integrity for High-Speed Digital Design - page 273

High e r ;
Low Z 0

trace a

Top view

Low

e r ;
High Z 0

trace b

Epoxy Pool

Glass Bundles

Cross-sectional view

Figure 6-13 Physical structure of FR4 dielectric; note how the physical position of the
transmission line with respect to the fiberglass weave dictates the impedance.

6.5.1 Physical Structure of an FR4 Dielectric and Dielectric Constant
Variation

FR4 dielectric is a composite material made from a matrix of woven bundles of
fiberglass embedded in an epoxy resin. The physical structure of FR4 is illus-
trated in Figure 6-13, which demonstrates how local material variation makes
the homogeneous dielectric assumption inaccurate when propagating signals with
multi-GHz frequency content. The reinforcing fiberglass bundles have a dielectric
constant (ε r ) of approximately 6, whereas ε r is close to 3 for the epoxy resin in
which the bundles are embedded. The bulk dielectric constant is dependent on
the glass/resin volume ratio:

ε r = ε rsn V rsn + ε gls V gls (6-39)

where ε rsn and ε gls are the dielectric permittivities and V rsn and V gls are the volume
ratios of the epoxy resin and glass.
From Figure 6-13 we see that there is a significant gap between bundles over
which a signal trace may be routed. This creates the opportunity for a differential
pair to be routed such that one trace (a) is located over a fiberglass bundle, while
the other (b) is routed above the gap between bundles. The result is that a signal
on trace a will see a higher effective dielectric permittivity ( ε r, eff ) and a lower
impedance then trace b . Furthermore, it should be noted that this is a statistically
likely scenario, since the fiber weave is usually manufactured so that the bundles
are parallel to the edge of the board. The most common layout methodology is to
route the transmission lines of the system buses at either 0 ◦ or 90 ◦ with respect to
the board edges, which maximizes the chance that spatially dependent effective
dielectric permittivity ( ε r, eff ) will be observed.
The effective dielectric permittivity variability can be shown experimentally
by using a test board structure as shown in Figure 6-14. If the structures are
designed with a center-center trace distance ( x t ) slightly larger than the expected