ELECTRICAL PROPERTIES OF DIELECTRICS - Advanced Signal Integrity for High-Speed Digital Design - page 267

3.92

tan d

0.0073

3.91

0.0072

3.90

0.0071

3.89

0.0070

3.88

e r

0.0069

3.87

2.0 4.0

Frequency, GHz

6.0 8.0

10.0

Figure 6-11 Dielectric properties versus frequency from Example 6-2.

Figure 6-11 shows a plot of the dielectric properties versus frequency. As a
double check, it can be confirmed that at 1 GHz, the relative permittivity is 3.9
and the loss tangent is 0.0073.

6.4 PROPERTIES OF A PHYSICAL DIELECTRIC MODEL

For a dielectric model to remain physical, it must predict correctly the frequency-
dependent behavior observed in real life. A common mistake in digital design
is to use transmission-line models that have frequency-invariant dielectric prop-
erties. Although this approximation works fine for low frequencies, as system
data rates increase past about 2 Gb/s, such methods will introduce large errors
into the simulations, rendering the analysis almost useless. In this section we
describe the properties that must be satisfied to ensure a physically realizable
model. Although the focus here is on dielectric models, any model is required to
pass these tests to ensure behavior consistent with nature. First, the relationship
between the dielectric permittivity and the loss tangent is discussed, and then
specific mathematical tests are introduced to ensure a model that obeys the laws
of physics.

6.4.1 Relationship Between ε and ε

In Section 5.2.3, specific relationships were shown to exist between the real and
imaginary parts of the series impedance of a transmission line in the form of
ac resistance and internal inductance. There is a similar relationship between the
real and imaginary portions of the complex permittivity, which in turn implies
a relationship between the relative dielectric permittivity ε r and the loss tan-
gent tan δ . To conceptualize the relationship, assume that the frequency range
is below 20 GHz, where measurements have shown that damping is the domi-
nant dielectric response. In this region, large polar molecules are attempting to