
117Waveguides
3.4.5 Mode Designation in Circular Waveguide
In the TM case, the wave equation is solved for E
z
. At the conductor surface,
E
z
= 0 and thus J
n
(ha) = 0. In view of Equation 3.8, for a propagating wave
h
2
<
ω
2
με
. This requires that either h is small or the frequency is high. To meet
this requirement, only a few roots of J
n
(ha) = 0 will be of practical importance.
Such rst few roots are (ha)
01
= 2.405, (ha)
11
= 3.85, (ha)
02
= 5.52 and (ha)
12
= 7.02.
These roots can thus be designated as (ha)
nm
. In (ha)
nm
, the rst sufx (n) is
the order of Bessel’s function and the second sufx is the number of root.
Similarly, the rst ...