
149Cavity Resonators
E E J h r n
q z
l
z z n nmp
=
0
( )cos( )sin ( )
mn
for TM modeϕ
π
(4.19)
The separation equations for TE and TM modes are
h h
p
l
2 2
2
=
′
+
( ) ( )
nm
for TE mode
π
(4.20)
h h
p
l
2 2
2
= +
( ) ( )
nm
for TM mo de
π
(4.21)
The resonant frequency of the cavity is given by
fr h
p
l
nm
=
′
( )
+
1
2
2
2
µε
π
( )for TE mode
(4.22)
fr h
p
l
= +
1
2
2
2
µε
π
( ) ( )
nm
for TM mo de
(4.23)
In the above equations,
′
=
′
h ha a
nm nm
( ) / and h ha a
nm nm
= ( ) ./ Also, E
0z
and
H
0z
are the amplitudes of electric and magnetic eld intensities, respectively,
of the wave travelling in the z-direction.
In Equations 4.18 through 4.23, n = 0, 1, 2,…, m = 1, 2, …