TEM Transmission lines' properties, the construction techniques, types, uses in the circuits, mathematical representation, limitations and their solutions are described

2.  Has two conductors running parallel
 Can propagate a signal at any frequency
 Becomes lossy at high frequency
 Can handle low or moderate amounts of power
 Does not have signal distortion, unless there is loss
 May or may not be immune to interference
 Does not have Ez or Hz components of the fields (TEMz)
Properties
Coaxial cable (coax)
Twin lead
(shown connected to a 4:1
impedance-transforming balun)
Transmission Line

3. CAT 5 cable
(twisted pair)
The two wires of the transmission line are twisted to reduce interference and
radiation from discontinuities.
Transmission Line

4. Transmission Lines
Microstrip
h
w
εr
εr
w
Stripline
h
Transmission lines commonly kept on printed-circuit boards
Coplanar strips
hεr
w w
Coplanar waveguide (CPW)
hεr
w

5. Microstrip line is the simplest formation.
A microwave integrated circuit
Microstrip line
Transmission Line

6. 6
• Transverse Electromagnetic (TEM):
– coaxial lines
– microstrip lines (quasi tem)
– strip lines and suspended substrate
•Metallic waveguides:
– rectangular waveguides
–circular waveguides
Transmission Media

7. Parallel -plate Two-wire Coaxial
a
b
TEM Transmission Lines

8.  Lumped circuits: resistors, capacitors, inductors
neglect time delays
(phase)
account for propagation and
time delays (phase change)
Transmission-Line Theory
 Distributed circuit elements: transmission lines
We need transmission-line theory whenever the length of
a line is significant compared with a wavelength.

9. z∆
( ),i z t
+ + + + + + +
- - - - - - - - - -
( ),v z tx x xB
R∆z L∆z
G∆z C∆z
z
v(z+z,t)
+
-
v(z,t)
+
-
i(z,t) i(z+z,t)
TEM Transmission Line

10. ( , )
( , ) ( , ) ( , )
( , )
( , ) ( , ) ( , )
i z t
v z t v z z t i z t R z L z
t
v z z t
i z t i z z t v z z t G z C z
t
∂
= + ∆ + ∆ + ∆
∂
∂ + ∆
= + ∆ + + ∆ ∆ + ∆
∂
R∆z L∆z
G∆z C∆z
z
v(z+z,t)
+
-
v(z,t)
+
-
i(z,t) i(z+z,t)
TEM Transmission Line

11. Hence
( , ) ( , ) ( , )
( , )
( , ) ( , ) ( , )
( , )
v z z t v z t i z t
Ri z t L
z t
i z z t i z t v z z t
Gv z z t C
z t
+ ∆ − ∂
= − −
∆ ∂
+ ∆ − ∂ + ∆
= − + ∆ −
∆ ∂
Now let ∆z=0:
v i
Ri L
z t
i v
Gv C
z t
∂ ∂
= − −
∂ ∂
∂ ∂
= − −
∂ ∂
“Telegrapher’s
Equations”
TEM Transmission Line

12. To combine these, take the derivative of the first one
with respect to z:
2
2
2
2
v i i
R L
z z z t
i i
R L
z t z
v
R Gv C
t
v v
L G C
t t
∂ ∂ ∂ ∂ 
= − −  ÷
∂ ∂ ∂ ∂ 
∂ ∂ ∂ 
= − −  ÷
∂ ∂ ∂ 
∂ 
= − − − ∂ 
∂ ∂ 
− − − ∂ ∂ 
Switch the
order of the
derivatives.
TEM Transmission Line

13. ( )
2 2
2 2
( ) 0
v v v
RG v RC LG LC
z t t
∂ ∂ ∂ 
− − + − = ÷
∂ ∂ ∂ 
The same equation also holds for i.
Hence, we have:
2 2
2 2
v v v v
R Gv C L G C
z t t t
∂ ∂ ∂ ∂   
= − − − − − −   ∂ ∂ ∂ ∂   
TEM Transmission Line

14. At high frequency, discontinuity effects can become important.
Limitations of TEM Transmission Line
Bend
incident
reflected
transmitted
The simple TL model does not account for the bend.
ZTH
ZL
Z0
+-

15. At high frequency, radiation effects can become important.
We want energy to travel from the generator to the load, without radiating.
The extended fields may cause interference with nearby objects. (This may be
improved by using “twisted pair.”)
ZTH
ZL
Z0
+-

16. To reduce radiation effects of the twin lead at discontinuities:
h
1) Reduce the separation distance h (keep h << ).
2) Twist the lines (twisted pair).
Solution
CAT 5 cable
(twisted pair)