ELECTROMAGNETIC FUNDAMENTALS FOR SIGNAL INTEGRITY - Advanced Signal Integrity for High-Speed Digital Design - page 58

x

Region A
(Dielectric media)

z

y

E i

Incident wave

H i

Direction of
propagation

Figure 2-23 Incident electromagnetic wave propagating in dielectric region A and
impinging on a perfect conductor.

be oriented in the y -direction. The incident fields propagating in medium A are
given by

E i (z) = a x E i e − jωz √ µ 0 ε 0

(2-123)

1

η E i e − jωz √ µ 0 ε 0 e jωt

H i (z) = a y

(2-124)

Since the boundary is normal to the incident waves, the reflected portion will be
reflected back in the − z -direction. Subsequently, the reflected electric field will

have the form

E r (z) = a x E r e − jω( − z) √ µ 0 ε 0

= a x E r e + jωz √ µ 0 ε 0 (2-125)

Since the electric field of the reflected wave is propagating in the − z -direction,

the magnetic field must also flip and point in the − y -direction, to maintain the

proper relationship between the electric and magnetic fields:

1

η E r e + jωz √ µ 0 ε 0 e jωt

H r (z) =− a y

(2-126)

To calculate the values of the reflected and transmitted waves we must consider
what happens when an electromagnetic field impinges on a perfect conductor.
Equation (2-7) implies that an electric field impinging on a conductor with con-
ductivity σ will produce a current density

J :

J

= σ E

(2-7)