IDEAL TRANSMISSION-LINE FUNDAMENTALS - Advanced Signal Integrity for High-Speed Digital Design - page 72

e 1 E 1

q 1

e 1
e 2

q 2

e 2 E 1

Figure 3-7 Change in the orientation of an electric flux line at a dielectric boundary.

flux lines across the interface can be calculated by using the boundary conditions
for the normal and tangential components of the electric field derived in (3-5)
and (3-8). When θ 1 0, the boundary conditions of (3-5) apply. Consequently,

we need a function of θ 1 that will satisfy (3-5) when the electric field is normal to
the boundary. Since cos ( 0 ) =

=

1, the following equation will satisfy the boundary
conditions for the normal components of the electric field:

ε 1 E 1 cos θ 1 = ε 2 E 2 cos θ 2 (3-9)

90 ◦ , the boundary conditions of (3-8) apply, and since

Similarly, when θ 1 =

sin ( 90 ◦ ) = 1, the following equation will satisfy the boundary conditions for the

tangential components of the electric field:

E 1 sin θ 1 = E 2 sin θ 2 (3-10)

If E 1 is calculated from (3-10) and substituted into (3-9), the change in orientation
that the electric fields experience at a dielectric boundary can be calculated:

tan − 1 ε 2

ε 1 tan θ 1

θ 2 = (3-11)

Equation (3-11) means that the field lines will be bent farther away from the
normal to the dielectric interface in the medium with the higher permittivity .

3.2.2 Telegrapher's Equations

So far, we have concentrated primarily on the derivation and calculation of the
electric and magnetic fields. However, since this is a book targeted primarily at