Detail transmission line

1. Guided By: Presented By:
Mr. R.J.Trivedi Suchit Bhatt
Mr. Raghuraj Singh Avnish Yadav
IC H & CD February 4-2011

2. Electromagnetic Waves (EM)
EM waves propagate in the nonconductor (dielectric) that separate the two
conductors
 For a transverse wave, the direction of propagation is perpendicular to the
direction of (charge) displacement
 EM wave is produced by the acceleration of an electric charge
IC H & CD February 4-2011

3. Transverse Electromagnetic Waves
z
In free space:
Magnetic Field
y
x Electric Field
IC H & CD February 4-2011

4. EM waves
• E & H fields are perpendicular to each other at 90 angles
• EM waves that travel along a transmission line from source to load are
called “incident waves” and those travel back “reflected waves”
IC H & CD February 4-2011

5. Key point about transmission line operation
Voltage and current on a transmission line is a function of both time
and position. I1 I2
V f z, t V1 V2
I f z, t
dz
The major deviation from circuit theory with transmission line, distributed networks
is this positional dependence of voltage and current!
IC H & CD February 4-2011

6.  Transmission-line theory is valid at any frequency, and for any type of
waveform (assuming an ideal transmission line).
 Transmission-line theory is perfectly consistent with Maxwell's
equations (although we work with voltage and current, rather than
electric and magnetic fields).
IC H & CD February 4-2011

7. Types of Transmission Lines
Balanced: two wires, twisted, untwisted, shielded, unshielded, open
wire: one conductor carries the signal and the other is the return
Unbalanced lines (where one conductor is grounded): e.g. concentric or
coaxial cable.
Transmission lines for microwave use: e.g. striplines, microstrips, and
waveguides.
IC H & CD February 4-2011

8. Equivalent Circuit of a Transmission Line
The primary constants are uniformly distributed throughout the length
of the line, hence called: distributed parameters.
For simplification, distributed parameters are put up together per a
given unit length to form an
"electrical artificial model"
IC H & CD February 4-2011

9. Equivalent Circuit of a Transmission Line:
Characteristics of a T L (uniformly distributed) are determined by:
Electrical proprieties: wire conductivity and insulator dielectric.
Physical properties: wire diameter and conductor spacing
Primary electric constants:
Series DC resistance R & Inductance L
Shunt Capacitance C & Conductance G
IC H & CD February 4-2011

10. z z
Circuit Model:
R z L z
G z C z
IC H & CD
z
February 4-2011

11. Four fundamental parameters that characterize any transmission line:
z These are “per unit length” parameters.
C = capacitance/length [F/m] capacitance between the two wires
L = inductance/length [H/m] inductance due to stored magnetic energy
R = resistance/length [ /m] resistance due to the conductors
conductance due to the filling material
G = conductance/length [S/m] between the wires
IC H & CD February 4-2011

12. Transmission Line Equivalent Circuit
R L R L L L
Zo Zo
C G C G C C
“Lossy” Line Lossless Line
R j L L
Zo Zo
G j C C
IC H & CD February 4-2011

13. (coaxial cable)
r a
z d= conductivity of dielectric [S/m].
b
m = conductivity of metal [S/m].
2 0 r 2 d
C F/m G S/m
b b
ln ln
a a
0 b 1 1 1
L ln H/m R /m
2 a m 2 a 2 b
2
(skin depth of metal)
m
IC H & CD February 4-2011

14. Relation Between L and C:
2 0 r 0 b
C F/m L ln H/m
b 2 a
ln
a
LC 0 0 r
1
Speed of light in dielectric medium: cd
1
LC 2
cd
This is true for ALL transmission lines.
IC H & CD February 4-2011

15. 2
characteristic impedance of a coax. C 0 r
F/m
b
ln
a
0 b
L ln H/m
2 a
r a
z b
1 0 1 b
Z0 ln
2 0 r
a
0 b
ln
Z0
L 2 a 60 b
C 2 0 r
Zo ln
b r
a
ln
a
IC H & CD February 4-2011

16. Transmission-Line Input Impedance
The input impedance at a distance l from the load is:
ZL jZ o tan( l )
Zi Zo
Zo jZ L tan( l )
When the load is a short circuit, Zi = jZo tan ( l).
For 0 < l < /4, shorted line is inductive.
For l = /4, shorted line = a parallel resonant circuit.
For /4 < l < /2, shorted line is capacitive.
IC H & CD February 4-2011

17. T-L Input Impedance
When the load is an open circuit,
Zi = -jZo cot ( l)
For 0 < l < /4, open circuited line is capacitive.
For l = /4, open-line = series resonant circuit.
For /4 < l < /2, open-line is inductive.
IC H & CD February 4-2011

18. Transmission Line Summary
or is equivalent to:
l < /4 l > /4
or is equivalent to:
l > /4 l < /4
/4
= Zo ZL
l = /4 Zo’
= /4-section Matching
Transformer
IC H & CD February 4-2011

19. IC H & CD February 4-2011

20. IC H & CD February 4-2011