Unit-I.ppsx

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Unit – I

TRANSMISSION LINE Theory

Unit – I

TRANSMISSION LINE Theory

Dr. T.V.Padmavathy

Professor/ECE

RMKCET

Dr. T.V.Padmavathy

Professor/ECE

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Presentation Outline

 Introduction

 Types of Transmission Lines

 _{Analysis of differences between Low and High Frequency}  _{Transmission Line Parameters}

 _{Transmission Line Equations}

 _{Characterization of a Long Lossless Line}  _{Parameters for Lossless Transmission Lines}  _{Infinitely Long Transmission Line}

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Introduction

Stationary charges electrostatic fields

Steady currents magnetostatic fields

Time-varying currents electromagnetic fields

 Only in a non-time-varying case can electric and magnetic fields be

considered as independent of each other.

 In a time-varying (dynamic) case the two fields are interdependent.

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 In an electronic system, the delivery of power requires the connection of two

wires between the source and the load.

 At low frequencies, power is considered to be delivered to the load through

the wire.

 In the microwave frequency region, power is considered to be in electric and

magnetic fields that are guided from lace to place by some physical

structure.

 Any physical structure that will guide an electromagnetic wave place to

place is called a Transmission Line.

Introduction

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Introduction

 A transmission line is a two-port network connecting a generator

circuit at the sending end to a load at the receiving end

 Unlike in circuit theory, the length of a transmission line is of utmost

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Types of Transmission Lines

 Two wire line

 Coaxial cable

 Waveguide

 Rectangular

 Circular

 Planar Transmission Lines

 Strip line

 Microstrip line

 Slot line

 Fin line

 Coplanar Waveguide

 Coplanar slot line

Two wire line

Coaxial cable

Parallel – Plate Line

Waveguide

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Analysis of differences between Low and High

Frequency

Analysis of differences between Low and High

Frequency

 At low frequencies, the circuit elements are lumped since voltage and current waves affect the entire circuit at the same time.

 At microwave frequencies, such treatment of circuit elements is not possible since voltage and current waves do not affect the entire circuit at the same time.

 The circuit must be broken down into unit sections within which the circuit elements are considered to be lumped.

 This is because the dimensions of the circuit are comparable to the wavelength of the waves according to the formula:

where,

c = velocity of light

f = frequency of voltage/current

f

c

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Transmission Line Parameters

 The transmission line is divided into small units where the circuit

elements can be lumped.

 _{Assuming the}_{resistance of the lines is zero, then the transmission}

line can be modeled as an LC ladder network with inductors in the series arms and the capacitors in the shunt arms.

 _The_{value of inductance and capacitance}_{of each part determines}

the velocity of propagation of energy down the line.

 _{Time taken for a wave to travel one unit length is equal to}

 _{Impedance at any point is equal to}

 

s

LC

T



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Transmission Line Equations

- Resistance per unit length(Ohm/cm)

- Conductance per unit length (mho/cm)

- Inductance per unit length (H / cm)

- Capacitance per unit length (F / cm)

0 R 0 G 0 L 0 C







G j C



V

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 Two wave components with amplitudes V+ and V- traveling in the direction of +z and -z

Transmission Line Equations



   



     













I

e

V

e

V

z

I

e

V

e

V

z z z z    

1

Where propagation constant and characteristic impedance are

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Transmission Line Parameters

From the solutions to the transmission line equations





₀ 0 0

L

j

R

I

V

I

V

Z





 

 

This ratio is called characteristic impedance Z0

 and are the two most important parameters of a transmission

line.

 They depend on the distributed parameters (RLGC) of the line itself

0

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Characterization of a Long Lossless Line

 For a lossless line, the line resistance is assumed to be zero.

 The characteristic impedance then becomes a pure real number

and it is often referred to as the surge impedance.

 _{The propagation constant becomes a pure imaginary number.}

The term surge impedance loading or SIL is often used to indicate

the nominal capacity of the line.

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Parameters for Lossless Transmission Lines

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Parameters for Lossless Transmission Lines

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Infinitely Long Transmission Line

 For an infinitely long transmission line, there can be no reflected

wave (backward travelling wave)

 _{An infinite long transmission line, there is only a forward travelling}

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Terminated Transmission Line

Note the two coordinate systems and their relation:

z = measuring from the left to the right

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 In the z coordinate system,

 _{In the}_ℓ₍_ℓ_{= -}_z_{) coordinate system,}

The characteristic impedance of transmission line is given by :

Terminated Transmission Line

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 The reflection coefficient at ℓ = 0 is:

Terminated Transmission Line

 As ΓL is obtained at ℓ = 0 (the load position), it is called the reflection

coefficient at the load.

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• By Solving these two equations

Substituting the expressions for and into the equations for the voltage and current,



0

V V₀

Terminated Transmission Line

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 Using V(ℓ) and I(ℓ), we can obtain the impedance Z(ℓ) at an arbitrary

point ℓ on the transmission line as:

Terminated Transmission Line

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