Chapter 2 smith chart and impedance matching

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4/3/2015 Cuong Huynh, Ph.D.Telecommunications Engineering DepartmentHCMUT 1

1

Huynh Phu Minh Cuong, PhD

hpmcuong@hcmut.edu.vn

Department of Telecommunications Faculty of Electrical and Electronics Engineering

Ho Chi Minh city University of Technology

Chapter 2

Smith Chart and Impedance Matching

MICROWAVE ENGNEERING

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 Smith Chart Description

 Smith Chart Characteristics

 Z-Y Smith Chart

3 Smith Chart Applications

 Determining Impedance and Reflection Coefficients

 Determining VSWR

 Input Impedance of a Complex Circuit

 Input Impedance of a Terminated Transmission Line

4 Impedance Matching

 Matching with Lumped Elements

 Single-Stub Matching Networks

 Double-Stub Matching Networks

 Quarter-wave Transformer

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 A microwave engineer can develop a good intuition about transmission line and impedance-matching problems by learning to think in terms of the Smith chart

 From a mathematical point of view, the Smith chart is simply a representation of all possible complex impedances with respect to coordinates defined by the reflection coefficient

 The domain of definition of the reflection coefficient is a circle of radius

1 in the complex plane This is also the domain of the Smith chart

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2 Smith Chart

The initial goal of the Smith chart is to represent a reflection coefficient and its corresponding normalized impedance by a point, from which the conversion between them can be easily achieved

To do so, we start from the general definition of reflection coefficient

00

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Now we can write as z 1

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1 Center : ,0 :

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2 Smith Chart

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Resistance circles r-circles

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For the constant r circles :

1 The centers of all the constant r

circles are on the horizontal axis –

real part of the reflection coefficient

2 The radius of circles decreases

when r increases

3 All constant r circles pass

through the point r =1, i = 0

4 The normalized resistance r = 

is at the point r =1, i = 0

For the constant x (partial) circles:

1 The centers of all the constant x

circles are on the r =1 line The

circles with x > 0 (inductive

reactance) are above the r axis; the

circles with x < 0 (capacitive) are

below the r axis

2 The radius of circles decreases when absolute value of x increases

3 The normalized reactances x =  are at the point r =1, i = 0

z = r+jx   = r+ i

2 Smith Chart

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2 Smith Chart

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2 Smith Chart

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2 Smith Chart

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2 Smith Chart

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Constant  circle

2 Smith Chart

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7.4 Smith Chart: Basic Procedures 2 Smith Chart

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2 Smith Chart

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2 Smith Chart

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Given R and ZR  Find the Voltage Standing Wave Ratio (VSWR)

The Voltage standing Wave Ratio or VSWR is defined as

The normalized impedance at a maximum location of the standing wave pattern is given by

This quantity is always rea l and ≥ 1 The VSWR is simply obtained

on the Smith chart, by reading the value of the (real) normalized impedance, at the location dmax where  is real and positive

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Keep in mind that the equality

is only valid for normalized impedance and admittance The actual

values are given by

where Y0=1 /Z0 is the characteristic admittance of the transmission line

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The Smith chart can be used for line admittances, by shifting the space reference to the admittance location After that, one can move

on the chart just reading the numerical values as

representing admittances

Let’s review the impedance - admittance terminology:

Impedance = Resistance + j Reactance

Admittance = Conductance + j Susceptance

On the impedance chart, the correct reflection coefficient is always represented by the vector corresponding to the normalized

impedance Charts specifically prepared for admittances are

modified to give the correct reflection coefficient in correspondence

of admittance

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2 Smith Chart: Y Smith Chart

1 1

y y



 



z z

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1 : Z-Smith C.

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2 Smith Chart Z-Y Smith Chart

1 : Z-Smith C.

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Since related impedance and admittance are on opposite sides of the same Smith chart, the imaginary parts always have different sign

Therefore, a positive (inductive) reactance corresponds to a

negative (inductive) susceptance , while a negative (capacitive)

reactance corresponds to a positive (capacitive) susceptance

Numerically, we have

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Find Impedance of a complex circuit using Smith Chart

C1 10p

R 50

L

22.5nH

C2 12p

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Find Impedance of a complex circuit using Z-Smith Chart

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L

22.5nH

C2 12p

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Find Impedance of a complex circuit using ZY-Smith Chart

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Impedance Matching

 Using lump elements

 Using transmission lines

 ADS Smith Chart tool

Maximum power transfer

Z S

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How to design an impedance matching network using Smith Chart ?

Z L

Impedance Matching Network

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ZL

ZS

Z s

Z L

 Find a path from Z L to Z s

 Realize the circuit according

to the path

Stubs can be used to realize

reactance/susceptance

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ZL

ZS

Z s

Z L

 Find a path from ZL to Zs

 Realize the circuit

according to the path

Stubs can be used to

realize

reactance/susceptance

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ZL

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ZL

ZS

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ZL

ZS

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54

Double-Stub Matching

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How to construct the

path on the Smith chart ?

d  

100 100

2 2 50

L

j

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How to construct the

path on the Smith chart ?

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