ELECTRICAL PROPERTIES OF DIELECTRICS - Advanced Signal Integrity for High-Speed Digital Design - page 260

if a narrowband signal was simply turned on and off as a simplistic form of
modulation, this is equivalent to convolving the narrowband signal with a step
response, which contains an infinite number of Fourier components.
The proof that the velocity of a signal used to transmit information cannot
exceed the speed of light is too complicated to address here. However, Brillouin
[1960] showed that a signal propagating in a realistic dielectric medium cannot
exceed c .

6.3.4 Frequency-Dependent Dielectric Model: Multipole
As discussed in Section 6.1, the polarization of a realistic dielectric may consist
of any number of ionic, orientational, and electronic mechanisms, depending on
the molecular and atomic structure of the material. In general, ε and ε depend on
frequency in complicated ways, exhibiting several resonances over a wide range.
To account for this, a separate harmonic oscillator model is constructed for each
molecular or atomic resonance, and the results are combined using superposition.
Thus, for a material with n natural frequencies, the relative dielectric permittivity
is represented by summing the responses from n independent harmonic oscillator
models:

n

N i (q 2 /ε 0 m)

ε r = 1 + (6-26)

ω i − ω 2 + j(b i /m)ω

i = 1

An example is shown in Figure 6-7, where three harmonic oscillator models were
chosen arbitrarily with natural frequencies ω 1 = 20 GHz, ω 2 = 100 GHz, and

ω 3 400 GHz. Note how the permittivity tends to “stair-step” down to smaller

values as the frequency increases, separated by areas of anomalous dispersion,
producing a change in the steady-state value ( ε r ) at frequencies higher than

=

2.5

2.0

1.5

1.0

1 10 100 1000

Frequency, GHz

Figure 6-7 Example of a frequency response for a material that exhibits three atomic
or molecular resonances at 20, 100, and 400 GHz.