25 Guided TEM waves on TL systems
•
An
ˆ
x
polarized plane TEM wave propagating in
z
direction is depicted in the margin.
–
A pair of conducting plates placed at
x
=0
and
x
=
d
would not perturb
the Felds except that charge and current density variations would be induced
on plate surfaces at
x
=0
and
x
=
d
(on both sides) to satisfy Maxwell’s
boundary condition equations.
z
x
y
E
×
H
E
H
Unguided uniform plane
wave propagation in a
homogeneous medium
W
d
z
x
y
Plate 2
Plate 1
E
×
H
E
H
I
I
•
If charge and currents were conFned only to interior surfaces of the plates facing one
another, Felds
E
and
H
accompanying them would be restricted to the region in
between the plates, constituting what we would call
guided waves
.
–
Such a guided wave Feld conFned to the region between the plates will sat
isfy Maxwell’s equations including a minor fringing component that can be
neglected when the plate width
W
is much larger than plate separation
d
.
In the following discussion of guided waves in parallelplate
transmission lines
(TL) we will assume
W
±
d
and neglect the e±ects of fringing Felds.
–
Guided waves produce wavelike surface charge and current variations on plate
surfaces.
–
Conversely, wavelike charge and current variations on plate surfaces would
produce guided wave Felds.
It is su²cient to apply a timevarying current and/or charge density at some location
z
on a parallelplate TL — e.g., by a timevarying voltage or current source — in
order to “excite” the TL with propagating guided Felds.
How such excitations propagate away from their “source points” on TL systems will
be our main subject of study for the rest of the semester.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document•
In a parallelplate TL we ignore any fringing Felds and assume that
TEM wave Felds
W
d
z
x
y
Plate 2
Plate 1
E
×
H
E
H
I
I
E
=ˆ
xE
x
(
z,t
)
and
H
=ˆ
yH
y
(
z,t
)
occupy the region between the plates. ±or these Felds uniform in
x
and
y
, ±araday’s and Ampere’s laws reduce to scalar expressions
∇×
E
=

μ
∂
H
∂t
⇒
∂E
x
∂z
=

μ
∂H
y
∂t
and
∇×
H
=
σ
E
+
±
∂
E
∂t
⇒
∂H
y
∂z
=
σE
x
+
±
∂E
x
∂t
.
•
Now, multiply both equations by
d
and let
Note that voltage drop
V
=
±
1
2
E
·
d
l
=
E
x
d
is uniquely defned —
inde
pendent of integration path
— on constant
z
surFaces be
cause with TEM felds
B
z
=
μH
z
=0
,
and consequently circulation
²
C
E
·
d
l
=

d
dt
±
S
B
·
d
S
=0
when
C
is on constant
z
plane
and
d
S
=
±
dxdy
This is the end of the preview.
Sign up
to
access the rest of the document.
 Summer '10
 KUDEKI
 Electric charge, wave equation, ∂z ∂T, TL systems

Click to edit the document details