Smith Chart

Microwave EngineeringMicrowave EngineeringCHO, Yong HeuiCHO, Yong Heui

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Photo of Smith chart

Graphical method

Essential diagram for microwave engineering

1. Smith chart

P. Smith in 1939

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Induction of Smith chart

ir

LL

L

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j

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zz

z

Z

jXR

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e

1

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1

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z

:impedance load Normalized

1|| where||

00L

0

0

1. Smith chart

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Induction of Smith chart

2222

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)1(

2

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1

1

1z

ir

i

ir

ir

ir

ir

xr

j

jjxr

22

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111 ,

1

1

1

xxrr

ririr

Circle equations

1. Smith chart

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Constant resistance circles

1

1

1

22

2

rr

rir

1. Smith chart

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Constant reactance circles

22

2 111

xxir

1. Smith chart

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Input impedance

zjzj

zjzj

s

sinin

zjzjs

zjzjos

ee

ee

IZ

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eeZ

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00

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1

At

lj

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in e

e

e

ez

lz

1. Smith chart

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Input impedance

)5.0(chart thearound lap one

chart.Smith on the 2 of angle Clockwise

2

l

l

l

e lj

1. Smith chart

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Admittance

)2(

)2(

2

2

1

1

1

1

1

lj

lj

lj

lj

LL

e

e

e

e

zy

1. Smith chart

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2. Applications

VNA (Vector Network Analyzer)

Measurement equipment

Reflection coefficients with frequency sweep

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83 0.62,||

APoint 1 5.0

15.0

line -50 aon 5025

xr

jz

jZ

L

L

Representation of Smith chart

2. Applications