TOPICS IN HIGH-SPEED CHANNEL MODELING - Advanced Signal Integrity for High-Speed Digital Design - page 416

ε
ε

tan | δ |= (6-16b)

The definition of G ( ω ) in shown in equation (6-45):

G(ω) = tan δωC (6-45)

The reference value of the loss tangent is calculated by rearranging equation
(6-45):

G(ω ref )
C(ω ref )ω ref

tan δ(ω ref ) =

G (ω ref ) C − 1 (ω ref )
ω ref

→ tan δ(ω ref ) = (10-3)

For a microstrip line, the values extracted would be the effective dielectric
constant and effective loss tangent. This is an easy way to handle with nonho-
mogeneous dielectrics, such as in a microstrip configuration. For a stripline, the
values extracted would be equal to the bulk properties of the material, including
any nonhomogenous structures such as the fiber weave.
Next, G ( ω ref ) is scaled by the frequency-dependent loss tangent and permit-
tivity, leading to (10-4), which is the frequency-dependent conductance of a
transmission line.

ε (ω)
ε (ω ref )

tan δ(ω)
tan δ(ω ref )

ω
ω ref

=

G(ω) G(ω ref )

ω
ω ref

[ tan δ − 1 (ω ref ) ε − 1 (ω ref ) ] G (ω ref ) ε (ω) tan δ(ω) → G (ω) = (10-4)

Using this procedure, equations (10-1) and (10-4) can be used to create the
tabular transmission-line parameters that represent a frequency-dependent causal
dielectric model that is valid for the conditions described during the derivation
of the infinite-pole model in Section 6.3.5. However, it should be noted that
a transmission line using any dielectric model can be implemented using this
technique, providing the frequency-dependent behavior of ε and ε are known.

10.1.3 Generating a Tabular Conductor Model
When creating a frequency-dependent conductor model for a transmission line,
Chapter 5 will remind the reader of the four effects that must be accounted for
properly:

1. External inductance
2. Internal inductance
3. Dc resistance
4. Ac (skin effect) resistance