Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements...
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Transcript of Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements...
Slide Presentations for ECE 329,Slide Presentations for ECE 329,Introduction to Electromagnetic Fields,Introduction to Electromagnetic Fields,
to supplement “Elements of Engineering to supplement “Elements of Engineering Electromagnetics, Sixth Edition”Electromagnetics, Sixth Edition”
byby
Nannapaneni Narayana RaoNannapaneni Narayana RaoEdward C. Jordan Professor of Electrical and Computer EngineeringEdward C. Jordan Professor of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign, Urbana, Illinois, USAUniversity of Illinois at Urbana-Champaign, Urbana, Illinois, USADistinguished Amrita Professor of EngineeringDistinguished Amrita Professor of Engineering
Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, IndiaAmrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India
6.1
Transmission Line
6.1-3
Parallel-Plate Line
Neglect fringing (d << w).
x
y
z
+-
w
d
gV t
6.1-4
, ; ,x x y yE z t H z t E a H a
dx
z
H , cE J, ,
+
- - - - -
+ + + +
6.1-5
0, ,
,
d
xx
x
V z t E z t dx
d E z t
,,x
V z tE z t
d
, ,
,s
y
I z t w J z t
w H z t
,,y
I z tH z t
w
6.1-6
yxHE
z t
-
y xx
H EEz t
- -
V Iz d t w
-
I V Vz w d t d
- -
6.1-7
Consider the circuit
V d Iz w t
-
I w w VVz d d t
- -
z
,V z t
,I z t
z z z
,V z z t
+ +
- -
,I z z tL z
G z C z
6.1-8
Then
TransmissionLine Equations
L = , inductance per unit lengthdw
G = , conductance per unit lengthwd
C = , capacitance per unit lengthwd
LV Iz t
-
G CI VVz t
- -
6.1-9
Transverse Electromagnetic (TEM) Waves
0z zE H
, ,b
aV z t z t dE l
, ,C
I z t z t dH l
a
b
Cx
yz
6.1-10
Distributed Equivalent Circuit
Assumes perfect conductors but lossy dielectric.
z
C z
L z
G z
L z
C zG z
6.1-11
Transmission-Line Equations
L = Inductance per unit length (H/m)
C = Capacitance per unit length (F/m)
G = Conductance per unit length (S/m)
LV Iz t
-
G CI VVz t
- -
6.1-12
In general, conductors are also lossy. Then, the wavesare not exactly TEM waves.
R = Resistance per unit length (/m)
LV IRIz t
- -
G CI VVz t
- -
6.1-13
Lossless Line (Perfect Conductors, Perfect Dielectric)
WaveEquation
Combining, we obtain
LV Iz t
-
CI Vz t
-
2 2
2 2LCV Vz t
6.1-14
Solution:
,
wave wave
p pV z t Af t z v Bg t z v -
-
velocity of propagation
Note, LC =
1 1LCpv
6.1-15
0
1, p pI z t Af t z v Bg t z vZ
- -
From L ,V Iz t
-
1L
I Vt z
-
1L p p
p
Af t z v Bg t z vv
- -
0Lwhere characteristic impedance of the lineC
Z
6.1-16
Thus
p pV V t z v V t z v - -
0 0
wave wave
p pV t z v V t z vI
Z Z
-- -
-
1LCpv
0LC
Z
6.1-17
Parallel-Plate Line
0dZw
w
d
d << w
L dw
C wd
6.1-18
Coaxial Cable
0 1n2bZ a
ab
L 1n2ba
2C1n b
a
6.1-19
Parallel-Wire Line
10 cosh dZ a
-
aa
2d
1L cosh da
-
1C
cosh da
-
6.1-20
Parallel-Strip Line (d/w 1)
imbedded in a homogeneous medium
w
2d
081n
4d wZw d
6.1-21
Microstrip Line
Ground Plane
Substrate, r
w
d
1 21 1 1012 2eff
r rr
dw
- -
060 81n 4
effr
d wZ w d
6.1-22
Shielded Strip Line