ELECTROMAGNETIC FUNDAMENTALS FOR SIGNAL INTEGRITY - Advanced Signal Integrity for High-Speed Digital Design - page 59

For a perfect conductor, σ . However, since the real world limits currents

to finite densities, equation (2-7) implies that infinite conductivity will produce
infinite currents inside a perfect conductor, which is impossible; therefore, the
electric field inside the perfect conductor must be zero. If the electric field is zero,
the magnetic fields must also be zero. This allows us to deduce the boundary
conditions for both E and H at the interface between a dielectric medium and a
perfect electrical conductor (PEC). Since the fields in region A are finite and the
fields in region B (the PEC) are zero, we can deduce that the wave impinging
on the conductor must induce a wave equal but opposite to the incident wave
at the surface, so the fields in the conductor are zero. The boundary condition
at the surface (z =

=∞

0 ) of the PEC requires that the tangential electric field must
vanish for all x and y to ensure that the electric field inside the conductor is zero.
Applying the boundary conditions to both the incident and the reflected portions
of the electric field gives

E(z =

0 ) = E i (z = 0 ) + E r (z =

0 ) = a x E i + a x E r = 0

which produces the relationship between the incident and reflected electric fields
for a electromagnetic wave impinging on a PEC:

a x E i =− a x E r (2-127)

This means that when an electromagnetic wave is incident normal to a perfect
electrical conducting plane traveling in the + z -direction, it will experience a

100% reflection back toward the − z -direction with the same magnitude as the

incident wave with a negative amplitude. This is the same as saying that the
magnitude of the reflected wave will remain constant but the phase will be shifted
by 180 ◦ . This is shown in Figure 2-24.

x

Region A
(Dielectric media)

z

y

E i

Incident wave

H i

H r

Reflected wave

E r

Figure 2-24 Incident electromagnetic wave propagating in dielectric region A and
impinging on a perfect conductor, showing that 100% of the wave is reflected back
in the − z -direction.