Microwave Engineering_Lecture_2-Transmission Line Equation.ppt

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

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

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
Microwave Engineering 3

Wave Phenomenon on TLs
Wave 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.

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)

Types of TLs
Types of TLs

TL: Role of wavelength
TL: Role of wavelength
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.

TL
TL
Travel delay time
Where,

TL
TL

TL: Lumped Element Model
 The model consists of four basic elements, with values
called the transmission line parameters. These are:

The prime superscript is used as a reminder that the line parameters are differential
quantities whose units are per unit length.

Transmission Line Equation

Node : N Node : N+1

(1)

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)

Transmission Line Equation: Wave equation
(4)
(5)

(6)
(4)

(7)

Transmission Line Equation: Wave
equation
equation

equation
equation

equation
equation
(7) 
(8)

Case I: Lossless Transmission Line

Case II: Distortionless Transmission Line
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)

Generality of TL Theory
Generality of TL Theory
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

Termination 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

Any Question…?
Any Question…?

Have A Nice

Microwave Engineering_Lecture_2-Transmission Line Equation.ppt

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