IDEAL TRANSMISSION-LINE FUNDAMENTALS - Advanced Signal Integrity for High-Speed Digital Design - page 88

w = 2 h

4 e r = 1

e r = 4.5

3.9 h

3.8

h = 2.5 mils
h = 25 mils
Quasi-TEM approximation

3.7

3.6

3.5

3.4

3.3

3.2

3.1

3

1 10 100

Frequency (GHz)

Figure 3-15 Effective dielectric permittivity compared to the quasi-TEM approximation
for a 12-in. microstrip.

For most practical applications encountered in high-speed digital design, the
TEM approximations are valid and the frequency-dependent nature described
by (3-37) is ignored. For microstrip lines and other nonhomogeneous struc-
tures, when TEM propagation is assumed, it is referred to as the quasi-TEM
approximation . To demonstrate the conditions when the quasi-TEM approxima-
tion breaks down, equation (3-37) was used to calculate the frequency variation
of the relative effective dielectric permittivity ε eff for two cases, a thick and a thin
dielectric, as shown in Figure 3-15. The thin dielectric example ( h = 2 . 5 mils)

represents the transmission-line dimensions typically used to design buses on
conventional motherboards for personal computers. The thick dielectric example
( h =

25 mils) is an exaggerated case chosen to demonstrate when the TEM
approximation breaks down (however, similar dimensions are sometimes used in
radio-frequency (RF) applications where density is not as much of a concern).
Equation (3-35) was used to calculate the frequency-invariant quasistatic TEM
value for ε eff , and equation (3-37) was used to estimate the variation of ε eff with
frequency. Note that for the thin case, the deviation from the quasi-TEM approx-
imation is small up to very high frequencies, but the thick case begins to deviate
much earlier.
To evaluate when the quasi-TEM approximation breaks down, we choose a
metric of 1% error in total delay. Since the changes in ε eff will alter the velocity
as shown in equation (2-52), the errors will accumulate for longer line lengths. If
we choose a line length, the valid frequency range of the TEM approximation can
be calculated. Figure 3-16 shows the percent error in propagation delay caused by
the quasi-TEM approximation for a 12-in. microstrip. Note that for the thick case,
the quasi-TEM will induce a 1% error in delay at about 8 GHz, and the thin case
remains accurate to about 80 GHz. Consequently, for typical transmission-line