ELECTRICAL PROPERTIES OF DIELECTRICS - Advanced Signal Integrity for High-Speed Digital Design - page 262

Orientatiional
or dipole

e′

Ionic or
molecular

Electronic

e′′

~10 9 ~10 10 − 10 14

~10 16

Frequency

Figure 6-8 Conceptual complex dielectric permittivity variations as a function of fre-
quency, showing approximate regions where each polarization mechanism exists.

most practical high-speed digital platforms built on commonly available dielectric
materials.

n

ε i

ε = ε ∞ + (6-28)

1 + j(ω/ω 2 i )

i = 1

Note that equation (6-28) is identical to the well-known Debye equation and is
often curve-fit to measured data to build a very accurate dielectric model library,
used for designing high-speed digital systems.
There is evidence based on laboratory measurements that dielectric resonances
can exist as low as 30 GHz in FR4 dielectrics, which may affect some very high
frequency designs. When designing digital systems with significant harmonics
past about 20 GHz, care should be taken to examine carefully the measured
phase delay and loss characteristics of transmission lines built on a representative
dielectric so that any resonance can be accounted for. In Chapter 9 we describe
methodologies for extracting the loss characteristics and the phase velocity from
S -parameter measurements. A dramatic narrowband increase in the loss accom-
panied by a simultaneous increase in the phase velocity is a telltale sign that a
dielectric resonance exists in the frequency of interest.
Equations (6-27) and (6-28) are much more useful than (6-26) for one very
important reason: They can be fit empirically . Since equation (6-26) requires
intimate knowledge of the atomic substructure, it is not very useful for practi-
cal applications. However, the dielectric permittivity can be measured using the
phase delay (see Chapter 9 for details), the results of which can be fit to (6-27)
by choosing the appropriate poles ( ω 1 i

and ε , to essentially
curve-fit the dielectric behavior to a physically consistent model. The particu-
lar implementation of (6-27) is dependent on the characteristics of the material.

ε ∞ and ω 2 i ),