IDEAL TRANSMISSION-LINE FUNDAMENTALS - Advanced Signal Integrity for High-Speed Digital Design - page 86

t = 0 t = t 1 t = t 2

e r = 1

E x_air

e r > 1

E x

E x_dielectric

E z

Direction of signal propagation ( + z)

Figure 3-13 The electric field develops a z -component when propagating down a
microstrip transmission line, due to the nonhomogeneous dielectric.

the fundamental concepts used throughout signal integrity analysis is that the
electric and magnetic fields are orthogonal and there are no components in the
z-direction . When waves propagate in this manner, it is called the transverse
electromagnetic mode (TEM). However, when discussing the concept of an
effective dielectric permittivity in Section 3.3.3, where the component of the
electric field propagating through the air travels faster than the component
propagating in the board material, it becomes obvious that the electric field is
no longer restricted to a single component. For example, consider Figure 3-13,
which depicts the side view of an electric field established in the x -direction at
t = 0 on a microstrip transmission line between the signal conductor and the

reference plane. As the signal begins to propagate down the line, the electric field
lines in the air will travel at a faster speed than those in the board, effectively
tilting the electric field in the z -direction. Consequently, the electric field devel-
ops a component in the z -direction which violates the assumption of the TEM
approximation.
Furthermore, as the frequencies increase, the electric field will become more
confined to the region between the microstrip and the reference plane, result-
ing in less fringing through the air, causing the effective dielectric permittivity
to increase. To understand this, refer to Figure 3-14. When a dc voltage is
applied between the signal conductor and the reference plane, the charge will
be distributed uniformly across the cross section of the signal conductor. As the
frequency of the signal is increased, the charge will tend to concentrate at the bot-
tom of the signal conductor closest to the reference plane because that is the area
of highest field concentration. This means that for a microstrip transmission line,
the electric field will tend to concentrate in the board material, which increases the
effective dielectric permittivity with increasing frequency . The charge distribution
in transmission lines is discussed in more detail in Sections 3.4.4 and 5.1.2.