This preview shows pages 1–2. Sign up to view the full content.
1
C:\User\Teaching\505506\S11\HW02'sol.doc
PHY 506
Classical Electrodynamics II
Spring 2011
Homework 2 with solutions
Problem 2.1
(to be graded of 25 points). Calculate impedance
Z
W
of long, straight TEM transmission
lines formed by metallic electrodes with the crosssections shown in Fig. below:
(i) two round, parallel wires, separated by distance
d
>>
R
,
(ii)
microstrip line
of width
w
>>
d
,
(iii)
stripline
with
w
>>
d
1
~
d
2
,
in all cases using the macroscopic boundary conditions on metallic surfaces. Assume that the conductors
are embedded into a linear dielectric with constant
and
.
Solutions
:
(i) From the solution of Problem 2.3 with
R
1
=
R
2
=
R
, generalized to dielectric filling by the
replacement of
0
with
, the mutual capacitance per unit length is
)
/
ln(
0
R
d
C
.
The inductance
L
0
per may be found either from magnetostatics (e.g., using the generalized Ampère
law), or directly from Eq. (7.109):
R
d
C
L
ln
0
0
0
0
0
.
Combining these expressions, we get
.
,
ln
2
/
1
2
/
1
0
0
Z
R
d
Z
C
L
Z
W
This expression is close in structure to that for the coaxial cable – see Eq. (7.113) of the lecture notes,
with an extra factor of 2, due to two (rather than one) thin conductors, with distance
d
between the wires
playing the role almost similar to the diameter of the outer tube of the cable.
Practical notice: this system is very important for modern information technology. Pairs of
parallel copper wires (typically spaced by distance
d
~ 4
R
and twisted into a spiral to avoid picking up
and creating interferences) are broadly used for carrying phone and internet signals (for example, in the
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Stephens,P
 Work

Click to edit the document details