Smith Chart 2.0

7/30/2019 Smith Chart 2.0

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SMITH CHART EXAMPLES

Dragica Vasileska

ASU


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Smith Chart for the Impedance Plot

jxrZZzo

+==

It will be easier if we normalize the load impedance to thecharacteristic impedance of the transmission line attached to the

load.

+=

1

1z

Since the impedance is a complex number, the reflection coefficientwill be a complex number

jvu +=

( ) 22

22

vu1

vu1r

+

=

( ) 22 vu1

v2x

+

=


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Real Circles

1 0.5 0 0.5 1

1

0.5

0.5

1

{ }Re

{ }Im

r=0r=1/3

r=1

r=2.5


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Imaginary Circles

1 0.5 0 0.5 1

1

0.5

0.5

1

{ }Re

{ }Im

x=1/3 x=1 x=2.5

x=-1/3 x=-1 x=-2.5


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Normalized AdmittancejbgYZ

Y

Yy o

o

+===

+

=1

1y

( ) 22

22

vu1vu1g++

=

( ) 22 vu1

v2b

++

=

( )22

2

g11v

g1gu

+=+

++

( ) 2

2

2

b1

b1v1u =

+++

These are equations forcircles on the (u,v) plane


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Real admittance

1 0.5 0 0.5 1

1

0.5

0.5

1

{ }Re

{ }Im

g=1/3g=1g=2.5


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Complex Admittance

1 0.5 0 0.5 1

1

0.5

0.5

1

b=-1 b=-1/3

b=2.5 b=1/3

b=1

b=-2.5

{ }Im

{ }Re


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Matching

For a matching network that contains elements

connected in series and parallel, we will need twotypes of Smith chartsimpedance Smith chartadmittance Smith Chart

The admittance Smith chart is the impedanceSmith chart rotated 180 degrees.We could use one Smith chart and flip the reflection

coefficient vector 180 degrees when switchingbetween a series configuration to a parallelconfiguration.


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TowardGenerator

Away FromGenerator

Constant

ReflectionCoefficient Circle

Full Circle is One HalfWavelength SinceEverything Repeats


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Matching Example

0=

100s

P =50Z0 M

Match 100 load to a 50 system at 100MHz

A 100 resistor in parallel would do the trick but of

the power would be dissipated in the matching network.We want to use only lossless elements such as inductorsand capacitors so we dont dissipate any power in thematching network


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Matching Example We need to go from

z=2+j0 to z=1+j0 onthe Smith chart

We wont get anycloser by addingseries impedance sowe will need to addsomething in parallel.

We need to flip overto the admittancechart

ImpedanceChart


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Matching Example y=0.5+j0

Before we add the

admittance, add amirror of the r=1circle as a guide.

AdmittanceChart


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Before we add theadmittance, add amirror of the r=1circle as a guide

Now add positiveimaginaryadmittance.

Admittance

Chart


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Before we add the

admittance, add amirror of the r=1circle as a guide

Now add positive

imaginaryadmittance jb = j0.5

AdmittanceChart

( )

pF16C

CMHz1002j50

5.0j

5.0jjb

=

=

=

pF16 100


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Matching Example We will now add

series impedance

Flip to theimpedance SmithChart

We land at on ther=1 circle at x=-1

ImpedanceChart


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Matching Example Add positive

imaginary

admittance to get toz=1+j0

ImpedanceChart

pF16

100

( ) ( )

nH80L

LMHz1002j500.1j

0.1jjx

=

=

=

nH80


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Matching Example

This solution wouldhave also worked

ImpedanceChart

pF32

100

nH160


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Mainstream vs. RF Electronics


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Substrate

Buffer

Drain

n-type active layerL

n+ cap

Gate

n+ cap

Source

Substrate

Barrier / buffer

Channel layer

Drain

BarrierL

n+ cap

Gate

n+ cap

2DEG channel

Source

MESFETMetal-Semiconductor FET

HEMTHigh Electron Mobility TransistorChannel: twodimensional electrongas (2DEG) at the inter-

face channel layer - barrier


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E. Simulation Examples Example #1

This Example gives comparison of the device output characte-

ristics of a single quantum-well structure when using drift-dif-fusion and energy balance models

Example #2

Simulation results of a pseudomorphic HEMT structure: devicetransfer and output characteristics with extraction of some

significant device parameters, such as threshold voltage,

maximum saturation current, etc.

Example #3

This is a follow-up of Example #2, in which AC analysis isperformed and the device S-parameters calculated.


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Example 1


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Example 1 (contd)


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Example 1 (contd)


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Example 2


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Example 3


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Example 3 (contd)

Smith Chart 2.0

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