This document discusses transmission lines and the conditions required for distortionless transmission. It notes that losses in transmission lines can occur due to I2R loss, skin effect, and crystallization. Distortion can arise from amplitude distortion, attenuation distortion, and phase distortion. The conditions for distortionless transmission are that the attenuation constant must be zero and the phase velocity must be independent of frequency. This requires that the line's inductance and capacitance per unit length satisfy LG/RC=1/2. The document also examines propagation constants and phase velocity for lossless transmission lines. It provides examples of calculating phase velocity, propagation constant, and phase wavelength for given line parameters.

1. Course: Electromagnetic Theory
paper code: EI 503
Course Coordinator: Arpan Deyasi
Department of Electronics and Communication Engineering
RCC Institute of Information Technology
Kolkata, India
Topic: Transmission Line – Lossless Line
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2. Losses in transmission line
I2R loss: [i] due to dissipation of heat
[ii] resistive feature
[iii] small if line is terminated without generating standing wave pattern
[iv] high if line has low characteristic impedance
Skin effect: [i] due to current confinement at conductor surface subject to
application of high-frequency signal
[ii] reduces cross-sectional area with increasing frequency
Crystallization: [i] due to again of line, major factor is bending
[ii] increases with temperature, high wind and moisture
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3. Distortion in transmission line
Amplitude distortion: occurs when the medium is non-linear or when the line
parameters are functions of voltage or current
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4. Attenuation distortion: takes place when the attenuation offered by
transmission line varies with frequency
Distortion in transmission line
input
output
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5. Phase distortion: occurs when phase constant becomes a function of frequency
Distortion in transmission line
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6. Condition for Distortionless Transmission
A transmission line can be free from attenuation distortion if every component of
the transmitted wave has get same attenuation as the others as well as same phase
velocity.
This is possible if attenuation constant becomes zero and phase velocity is
independent of frequency.
( )( )
1/2
2 2 2 2 2 2 2
1
2
RG LC R L G C
   
 
= − + + +
 
 
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7. Condition for Distortionless Transmission
0
 =
( )( )
2 2 2 2 2 2 2
0
RG LC R L G C
  
 
− + + + =
 
 
( )( )
2 2 4 2 2 2 2 2 2 2 2 2
2
R G L C RGLC R L G C
   
+ − = + +
For no distortion
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8. Condition for Distortionless Transmission
2 2 4 2 2 2
2 2 4 2 2 2 2 2 2 2 2
2
R G L C RGLC
R G L C L G C R
 
  
+ −
= + + +
2 2 2 2 2 2 2
2 0
L G C R RGLC
  
+ + =
2 2 2 2
2 0
L G C R RGLC
+ + =
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9. ( )
2
0
LG RC
+ =
LG RC
=
Condition for Distortionless Transmission
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10. Propagation Constant for Lossless Line
Propagation constant is defined as
( )( )
R j L G j C
  
= + +
2 2
( )
RG LC j LG RC
  
= − + +
2 2 2
( )
RG j LC j LG RC
  
= + + +
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11. Propagation Constant for Lossless Line
2 2 2
2
RG j LC j LGRC
  
= + +
( ) ( )
2
2
j RG j LC
  
+ = +
RG
 =
LC
 
=
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12. Phase velocity
p
v


=
p
v
LC


=
1
p
v
LC
=
Phase Velocity for Lossless Line
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13. Problem 1
A lossless cable of length 100 m has inductance of 28 µH and capacitance of 20 nF. Find
propagation velocity and propagation constant at 100 KHz.
8
1
1.336 10
p
v
LC
= = 
6
28 10
/ 0.28 /
100
L H m H m

−

= =
9
20 10
/ 0.2 /
100
C F m nF m
−

= =
Soln
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14. p
v

 =
3
4.702 10 /
rad m
 −
= 
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8
1.336 10 /sec
p
v m
= 
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15. Phase Wavelength for Lossless Line
Phase wavelength
LC
 
=
2
LC



=
2
LC



=
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16. Problem 2
A distortionless line has L=333.3 nH/m, C=92.59 pF/m. Find phase wavelength at
100 MHz.
Soln
2
LC

 =

2
2 f LC

 =

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17. 1.8 m
 =
8
6
0.6 3 10
1.8
100 10
 
 = =

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