Microwave Engineering_Lecture_2-Transmission Line Equation.ppt

Microwave Engineering Overview with basic knowledge and comprehensive overview

1. University of Engineering & Technology Peshawar
Department of Telecommunication Engineering ,Mardan Campus
1 |

2. University of Engineering & Technology Peshawar
Department of Telecommunication Engineering ,Mardan Campus
2 |
04-10-2012 First FYP Presentation,Batch-08
Transmission Lines(TLs)

3. What is a Transmission Line?What is a Transmission Line?
Transmit energy from one point to another
(source load). i.e. Connections b/w:
◦Transmitter and Antenna
◦Computer networks
◦Cable provider and TV receivers, etc.
◦Devices on PCBs @ high frequencies
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4. Wave Phenomenon on TLsWave Phenomenon on TLs
Large distance b/w Source (S) &
Destination (D) Delay-induced phase
delay
If the distance between system
components ( S & D) is of the order of
wavelength or more then we deal with
wave phenomenon like that in free space &
dielectrics.
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5. TLs....TLs....
Lumped elements: If the time delay by a wave in
traversing the elements is negligible then they are called
lumped elements, such as:
Resistor (R) Ω
Capacitor (C) F
Inductor (L) H
 Distributed Elements: Those elements or interconnects
(such as TLs) which are large enough (of the order of
wavelength or more), their (R, L, C) characteristics are
evaluated on per-unit length basis, are called distributed
elements.
Field distributions for both uniform TLs and Plane waves  TEM
(Transverse ElectroMagnetic)
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6. Types of TLsTypes of TLs
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7. Types of TLsTypes of TLs
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8. TL: Role of wavelengthTL: Role of wavelength
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Fundamentally, a transmission line is a two-port network, with each port consisting
of two terminals.
Consider a, generator connected to an RC circuit through a transmission line of
length I.

9. TLTL
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Travel delay time
Where,

10. TLTL
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12. Microwave Engineering 12

13. TL: Lumped Element ModelTL: Lumped Element Model
The model consists of four basic elements, with values
called the transmission line parameters. These are:
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14. TL: Lumped Element ModelTL: Lumped Element Model
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The prime superscript is used as a reminder that the line parameters are differential
quantities whose units are per unit length.

15. Transmission Line EquationTransmission Line Equation
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16. Transmission Line EquationTransmission Line Equation
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Node : N Node : N+1

17. Transmission Line EquationTransmission Line Equation
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18. Transmission Line EquationTransmission Line Equation
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(1)

19. Transmission Line EquationTransmission Line Equation
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Derivation of Wave equation for Transmission Line (Guided
Media):
Taking derivative of both sides of (1) w. r. t z:
(2)
I.e. Substitute it from (1) into (2)
(3)

20. Transmission Line Equation: Wave equationTransmission Line Equation: Wave equation
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(4)
(5)

21. Transmission Line Equation: Wave equationTransmission Line Equation: Wave equation
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(6)
(4)

22. Transmission Line Equation: Wave equationTransmission Line Equation: Wave equation
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23. Transmission Line Equation: Wave equationTransmission Line Equation: Wave equation
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(7)

24. Transmission Line Equation: Wave Transmission Line Equation: Wave
equationequation
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25. Transmission Line Equation: Wave Transmission Line Equation: Wave
equationequation
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26. Transmission Line Equation: Wave Transmission Line Equation: Wave
equationequation
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(7) 
(8)

27. Case I: Lossless Transmission LineCase I: Lossless Transmission Line
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28. Case I: Lossless Transmission LineCase I: Lossless Transmission Line
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29. Case I: Lossless Transmission LineCase I: Lossless Transmission Line
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30. Case II: Distortionless Transmission LineCase II: Distortionless Transmission Line
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Ideal (Lossless Transmission Line): Velocity of Propagation ≠ func (frequency)
Non- Ideal (Lossy Transmission Line): Velocity of prop.= func (freq) Dispersion
(Distortionless Line): Velocity of prop≈ Nearly Constant & Phase constant
Linear, Dispersion is negligible (if the length is not too long)

31. Case II: Distortionless Transmission LineCase II: Distortionless Transmission Line
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32. Case II: Distortionless Transmission LineCase II: Distortionless Transmission Line
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33. Generality of TL TheoryGenerality of TL Theory
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It was mentioned in the last lecture that transmission lines could be used to
model the voltage and current waves on any structure supporting only TEM
waves.
What changes from structure to structure are the values for L, C, R, and G, as
shown below in Table 2.1 for three common TEM structures:
Consequently, the values of Z0, vp,  (and ) generally all change from one
TL to another. The numerical values can also be changed within a type of
TL by varying the dimensions and construction materials

34. Termination of Transmission LinesTermination of Transmission Lines
We will now consider the termination of TLs that are excited by sinusoidal
steady state sources.
Adding terminations produces reflections so that the total voltage and current
anywhere on the TL are sums of forward and reverse propagating waves. The
voltage and current on the TL will have the form
The “lumped load” ZL that terminates the TL is considered a boundary
condition for the voltage and current

35. Termination of Transmission LinesTermination of Transmission Lines

36. Termination of Transmission LinesTermination of Transmission Lines

37. 04-10-2012 First FYP Presentation,Batch-08
Any Question…?Any Question…?

38. 04-10-2012 First FYP Presentation,Batch-08
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