Unit-III.ppsx

Unit – III

IMPEDANCE MATCHING IN HIGH FREQUENCY LINES

Unit – III

IMPEDANCE MATCHING IN HIGH FREQUENCY LINES

Dr. T.V.Padmavathy

Professor/ECE

RMKCET

Dr. T.V.Padmavathy

Professor/ECE

Presentation Outline

Presentation Outline

Introduction

Quarter Wavelength Transformer

Single-Stub Matching Technique

Single-Stub Matching Technique- Using Smith Chart

Double-Stub Matching Technique

Double-Stub Matching Technique - Construction

Introduction

Introduction

 Impedance matching is one of the important aspects of high frequency

circuit analysis.

 To avoid reflections and for maximum power transfer the circuits have to

be impedance matched.

 Transmission line sections can be used for the purpose of impedance

matching.

 There are various impedance matching techniques are used

 Quarter Wavelength Transformer

 Single-Stub Matching Technique

 Double-Stub Matching Technique

Quarter Wavelength Transformer

Quarter Wavelength Transformer

 This technique is generally used for matching

 a resistive load to a transmission line

 for matching two transmission lines with unequal characteristic impedances

Quarter Wavelength Transformer

Quarter Wavelength Transformer

 _{Let us consider Fig(a), Introducing a section of a transmission line}

called transformer between two resistances to be matched

 The impedance seen towards right at A should be and impedance seen

towards left at B should be R.

 when seen from transmission line side it appears to be terminated in

and when seen from load resistance side it appears to be connected to a

conjugately matched load R.

 For the transformer there are two parameters to control, characteristic

impedance of the transformer section, and the length of the transformer

section.

0

Z

0

Z

 _{The input impedance of}

dissipation - less line is _Z0 Z_{0T ZL}

Z_in

Quarter Wavelength Transformer

Quarter Wavelength Transformer

0 0 0

tan

tan

Z

jZ

Z

Z

Z

jZ













_

_











4 4 2

g g g  _  _      

 _{in 0T} 0T

L jZ Z Z jZ     _{ }   2 0T in L

Z

Z

Z



Single-Stub Matching Technique

Single-Stub Matching Technique

_{A stub is a short-circuited section of a transmission line connected in}

parallel to the main transmission line.

A stub of appropriate length is placed at some distance from the

load

Impedance seen beyond the stub is equal to the characteristic

impedance.

Y_L = G_L + j B_L

Z₀ Z_0T

/ 4

l  

B_s = - B_L

l_s

Z_0s





0 tan

s s s s

Single-Stub Matching Technique

Single-Stub Matching Technique

 A susceptance is added at a distance d from the load

Z_L Y₀ = 1 / Z₀

s s

Y  jB

in

Y

1) Choose the distance d so that at this distance from the load

0

in in

Y

 

Y

jB

2) Choose the shunt susceptance so that

Z_L Y₀ = 1 / Z₀

d

s s

Y  jB

0

in

Y  Y

Single-Stub Matching Technique

Single-Stub Matching Technique

The feeding transmission line on the left sees a perfect match

0

in in

Y

 

Y

jB

 _{First mark the load admittance on the admittance smith chart (A).}

 _{Plot the constant circle on the smith chart}

 _{Move on the constant circle till you intersect the constant circle}

this point of intersection corresponds to point (B).

 The distance traversed on the constant circle is

Unit - III Impedance Matching in High

L



L

 g 1

L

 l₁

 This is the location of placing the stub on the transmission line from the load end .

 Find constant suseptance circle.

 Find mirror image of the circle to get circle

 Mark 0 - on the outer most circle (D).

 From (D) move circular clockwise upto s.c point (E) to get the stub

Advantages

• The single-stub matching technique is superior to the quarter wavelength transformer as it makes use of only one type of transmission line for the main line as well as the stub.

• This technique also capable of matching any complex load to the

characteristic impedance/admittance.

• The single stub matching technique is quite popular in matching fixed impedances at microwave frequencies.

Disadvantages

 It is not suitable for matching variable impedance

 A change in load impedance results in a change in the length as well as the location of the stub

 Even if changing length of a stub is a simpler task, changing the

location of a stub may not be easy in certain transmission line

configurations.

Double-Stub Matching Technique

Double-Stub Matching Technique

 _{To overcome the drawbacks of the single-stub matching technique,}

the double-stub matching technique is employed.

 _{The technique uses two stubs with fixed locations.}

 As the load changes only the lengths of the stubs are adjusted to

achieve matching.

jB

jB

Y

a

b

 There are two design parameters

for double stub matching:

 _{The length of the first stub line}

 _{The length of the second stub}

line

 _{In the double stub configuration,}

the stubs are inserted at predetermined  locations. 1 Stub

L

L

 In this way, if the load impedance is changed, one simply has to

replace the stubs with another set of different length.

 The length of the first stub is selected so that the admittance at the

 location of the second stub has real part equal to the characteristic

admittance of the line

 The length of the second stub is selected to eliminate the imaginary

part of the admittance at the location of insertion.

 At the location where the second

stub is inserted, the possible normalized admittances that can give matching

 Normalized admittances are found on an auxiliary circle which is obtained by rotating the unitary conductance circle counterclockwise, by an angle

Double-Stub Matching Technique - Matching Procedure

Double-Stub Matching Technique - Matching Procedure

 Find the normalized load impedance and determine the

corresponding location on the chart.

 Draw the circle of constant magnitude of the reflection coefficient |Γ|

for the given load.

 Determine the normalized load admittance on the chart.

 This is obtained by rotating -180° on the constant |Γ| circle, from the

load impedance point.

 Find the normalized admittance at location dstub1 by moving

clockwise on the constant |Γ| circle.

 Add the first stub admittance so that the normalized admittance

point on the Smith chart reaches the auxiliary circle

 _{The admittance point will move on the corresponding conductance}

circle, since the stub does not alter the real part of the admittance

 _{Map the normalized admittance obtained on the auxiliary circle to}

the location of the second stub dstub2.

 _{The point must be on the unitary conductance circle}

 _{Add the second stub admittance so that the total parallel admittance}

equals the characteristic admittance of the line to achieve exact matching condition

Double-Stub Matching Technique - Matching Procedure

Thank You