
112 Microwave Engineering
3.4.2 TE Waves
For this case, E
z
≡ 0; thus, the eld components given by Equation 3.58 become
E
j
h
H
z
ρ
ρ
∂
∂φ
= −
2
1
(3.60a)
E
j
h
H
z
φ
∂ρ
=
2
(3.60b)
H
h
H
z
ρ
γ ∂
∂ρ
= −
2
(3.60c)
H
h
H
z
φ
γ
ρ
∂
∂φ
= −
2
1
(3.60d)
3.4.3 Solution of Wave Equation
In view of Equations 3.59 and 3.60, all the eld components are related to E
z
or H
z
. E
z
and H
z
can be obtained by solving Equations 3.53a and 3.53b for E
or H. These are obtained as below.
Equations 3.53a and 3.53b can be written in differential forms in cylindri-
cal coordinates as
1 1
0
2
2
2
2
ρ
∂
∂ρ
ρ
∂
∂ρ ρ
∂
∂φ
E E
h E
z z
z
+ + =
(3.61a)
1 1
0
2
2
2
2
ρ
∂
∂ρ
ρ
∂
∂ρ ρ
∂
∂φ
H H
h H
z z
z
+ + =
(3.61b)
To obtain the solu