
92 Microwave Engineering
∂
∂
∂
∂
∂
∂
γ ωµ
E
y
E
z
E
y
E j H
z
y
z
y x
− = + = −
(3.5a)
∂
∂
∂
γ ωµ
E
E
E
E j H
x z z
x y
− = + = +
(3.5b)
∂
∂
∂
∂
ωµ
E
x
E
y
j H
y
x
z
− = −
(3.5c)
Similarly, the wave Equations 7.2a and 7.2b for E
z
and H
z
in differential
form (for
σ
= 0) are
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
γ ω µε
2
2
2
2
2
2
2
2
2
2
2 2
E
x
E
y
E
z
E
x
E
y
E E
z z z z z
z z
+ + = + + = −
(3.6a)
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
γ ω µε
2
2
2
2
2
2
2
2
2
2
2 2
H
x
H
y
H
z
H
x
H
y
H H
z z z z z
z z
+ + = + + = −
(3.6b)
Substitution of (i) H
y
from Equation 3.5b in Equation 3.4a, (ii) H
x
from
Equation 3.5a in Equation 3.4b, (iii) Equation 3.4b in Equation 3.5a and (iv)
Equation 3.4a in Equation 3.5b and some mathematical manipulations lead
to the following:
E
h
E
x
j
h
H