Chapter 2 smith chart and impedance matching

MICROWAVE ENGNEERING
Chapter 2

Smith Chart and Impedance Matching

Huynh Phu Minh Cuong, PhD

Department of Telecommunications
Faculty of Electrical and Electronics Engineering
Ho Chi Minh city University of Technology
4/3/2015

Cuong Huynh, Ph.D.Telecommunications Engineering DepartmentHCMUT

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Chapter 2: Smith Chart and Impedance Matching
Outline
1. Introduction
2. Smith Chart




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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Cuong Huynh, Ph.D.Telecommunications Engineering DepartmentHCMUT

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1. Introduction

 Many of calculations required to solve T.L. problems involve the use of
complicated equations.
 Smith Chart, developed by Phillip H. Smith in 1939, is a graphical aid
that can be very useful for solving T.L. problems.
 The Smith chart, however, is more than just a graphical technique as it
provides a useful way of visualizing transmission line phenomenon
without the need for detailed numerical calculations.
 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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Cuong Huynh, Ph.D.Telecommunications Engineering DepartmentHCMUT

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1. Introduction

Phillip Hagar Smith (1905–1987): graduated from Tufts
College in 1928, invented the Smith Chart in 1939 while
he was working for the Bell Telephone Laboratories.
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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
Z  R  jX

Y=1/Z=G+jB

z

Z
R
X

 j
 r  jx
Z0 Z0
Z0

y

Y G
B
  j  g  jb

Y0 Y0
Y0



Z  Z0
 Re( )  j Im( )
Z  Z0



z 1
z 1
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z

1 
1 

Cuong Huynh, Ph.D.Telecommunications Engineering DepartmentHCMUT

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2. Smith Chart
Now we can write z  1   as
1 

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2. Smith Chart

 Resistance circles

 r

Center : 
,0 
1 r 

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Radius :
1 r

Cuong Huynh, Ph.D.Telecommunications Engineering DepartmentHCMUT

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2. Smith Chart

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2. Smith Chart
 Reactance circles

 1
Center :  1, 
 x

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Radius :
x

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2. Smith Chart
Resistance circles
r-circles

Unit circle

Matching point
Shorted point
Opened point

Reactance circles
x-circles

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2. Smith Chart
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.

z = r+jx



=r+i

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
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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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2. Smith Chart
Constant circle

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7.4 Smith Chart:
2. Smith
Basic
Chart
Procedures

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2. Smith Chart

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2. Smith Chart

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3. Smith Chart Applications

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3. Smith Chart Applications

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3. Smith Chart Applications

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3. Smith Chart Applications

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3. Smith Chart Applications

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3. Smith Chart Applications

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