4.2. VARIATIONS IN THE DIELECTRIC CONSTANT
The dielectric constant of the PCB substrate,
r
, directly affects the signal transmission
characteristics of high-speed interconnects. Some of the characteristics that are dependent
on
r
include propagation velocity, characteristic impedance, and crosstalk. The value of
r
is
not always constant for a given material but varies as a function of frequency, temperature,
and moisture absorption. Additionally, for a composite material, the material dielectric
properties will change as a function of the relative proportions of its components [
Mumby,
1988
].
The substrate of choice for most PCBs in commercial applications is a composite called FR4,
which consists of an epoxy matrix reinforced by a woven glass cloth. This composite
features a wide range of thickness and relative compositions of glass and resin.
Consequently, the dielectric properties observed for FR4 laminates can differ substantially
from sample to sample. Most vendors will provide a value of
r
for only one frequency. To
ensure a robust digital design that will yield adequate performance over all manufacturing
and environmental tolerances, it is important to consider the variations in the dielectric
constant.
A first-order approximation of the dielectric constant of FR4 composite may be calculated as
(4.18)
where
rsn
and
gls
is the dielectric constants of the epoxy resin and the woven glass cloth
and V
rsn
and V
gls
are the volume fractions of the resin and glass cloth. The relative volume
fractions of glass to resin can change from sample to sample. Subsequently, it is possible
that different layers of a PCB board can be manufactured with samples from different lots of
FR4. Subsequently, relatively large variations in the dielectric constant are possible between
layers on the same PCB. Measurements have also shown that the dielectric constant of FR4
can vary with frequency and resin content. A typical plot of dielectric constant variations
versus frequency for a volume resin fraction of 0.724 is shown in
Figure 4.12
.
Figure 4.12: Dielectric variation with frequency for a typical sample of FR4. (Adapted
from
Mumby [1988]
.)
An approximate equation for the prediction of the relative dielectric constant of FR4 as a
function of frequency and resin content is
(4.19)