Course Notes for EE1266 Applications of fields and waves
Chapter on waveguides: Lecture 1
1
NOTES for Waveguide I
This lecture covers 7.1 and 7.2
1. Rectangular waveguides
2. Transverse magnetic TM modes
Note: In this chapter, we will go through all the derivations in the
notes in details. You are required to master them. To help you
understand the contents, we will have
• Two assignments with 4 questions each
• Five example questions will be posted online
Similar to T-lines, a waveguide is a mean to transmit high-
frequency EM signal. Waveguides are better than T-lines at higher
frequencies (3-300GHz). Transmission lines become inefficiency
due to skin effect and dielectric losses. Another difference is that
T-line supports TEM waves, support frequency from dc to any
frequency (with high loss at high frequency). Waveguide has cut-
off frequency.
1. Rectangular waveguides
The simplest waveguide is rectangular waveguides. We first
assume that the waveguide is filled with lossless materials
(e.g. air) shown below.
For any structure, given a single frequency ω, the EM wave
are described by the phasor form of wave equations.
(
)
(
)
(
)
(
)
ωμε
=
=
+
∇
=
+
∇
k
z
y
x
H
k
z
y
x
H
z
y
x
E
k
z
y
x
E
0
,
,
,
,
0
,
,
,
,
2
2
2
2
r
r
r
r
For each E-field and H-field, we have three components, so
we have to solve each of the above equation three times. This
Course Notes for EE1266 Applications of fields and waves
Chapter on waveguides: Lecture 1
2
is enormous tasks. We need to figure out a way to simplify a
bit.
First, if EM wave propagate along +z direction, it is fair to
assume that all field components follow:
z
it
i
z
it
i
e
y
x
H
z
y
x
H
e
y
x
E
z
y
x
E
γ
γ
−
−
=
=
)
,
(
)
,
,
(
)
,
(
)
,
,
(
Similar to T-line and UPW, we refer γ as propagation
constants, which is to be determined.
Second, use Maxwell’s equation in charge free, and current
free environments.
E
j
H
H
j
E
r
r
r
r
ωε
ωμ
=
×
∇
−
=
×
∇
If we write the