Equivalent Circuit Description for...

Bachelor Thesis

Equivalent Circuit Description for SMD-Components

By

Owais Imam

Supervised byProf. Dr.-Ing. Klaus Solbach

Department of Microwave and RF- Technology

University of Duisburg-EssenDuisburg, 07.07.2008

07.07.2008 Owais Imam2

Contents of the Thesis

Introduction to SMD ComponentsAim of the ThesisS-Parameters and CalibrationEquivalent circuit models and measurements for different types of SMD resistors as well as capacitorsSimulations and ResultsConclusion


Introduction to SMD Components

Through-Hole Technology



Surface Mounted Technology (SMT)



Advantages of SMDsLimitations of SMDsWhy use Surface Mounted TechnologyIdentifying SMDsSoldering SMD ComponentsSMT needs more skills


Aim of the Thesis

To calculate the parasitic elements for:0603 type resistors0805 type resistors0603 type capacitors0805 type capacitors

Frequency range from 50 MHz to 10 GHz


S-Parameters and Calibration

What are S-Parameters?Why do we need S-Parameters forcalculating the Parasitic Elements?CalibrationImportant considerations


Equivalent circuit models and measurements

Introduction to SMD ResistorsResistor Model for measuring S-Parameters



Micro-Strip Gap

Electronic Component on Micro-strip gap

07.07.2008 Owais Imam10


Equivalent circuit of the Model

Simplified circuit of the Model

CC5C=? pF

CC3C=? pF

CC6C=? pF

CC2C=? pF

CC4C=? pF

RR1R=47 Ohm

LL1

R=L=? nH

CC1C=? pF

CC2C=? pF

CC3C=? pF

LL1

R=L=? nH

CC1C=? pF

RR1R=47 Ohm

07.07.2008 Owais Imam11


S-Parameter (S11 & S22) measurements of 0603 type 51 Ohms Resistor

2 4 6 80 10

-9

-8

-7

-10

-6

freq, GHz

dB

(S(1

,1))

2 4 6 80 10

-9

-8

-7

-10

-6

freq, GHz

dB

(S(2

,2))

ΩΩ

07.07.2008 Owais Imam12


S-Parameter (S21 & S12) measurements of 0603 type 51 Ohms Resistor

2 4 6 80 10

-6

-5

-4

-7

-3

freq, GHz

dB

(S(2

,1))

2 4 6 80 10

-7

-6

-5

-4

-8

-3

freq, GHz

dB

(S(1

,2))

07.07.2008 Owais Imam13


Introduction to SMD Capacitors

Capacitor Model for measuring S-Parameters

Equivalent circuit of Capacitor

07.07.2008 Owais Imam14


Simplified circuit of the Model

Simplified circuit of the capacitor model

RR1R=? Ohm

LL1

R=L=? nH

CC2C=? pF

CC3C=? pF

CC1C=1 pF

07.07.2008 Owais Imam15


S-Parameter (S11 & S22) measurements of the 0603 type 10pF capacitor

2 4 6 80 10

-50

-40

-30

-20

-10

-60

0

freq, GHzdB

(S(1

,1))

2 4 6 80 10

-30

-20

-10

-40

0

freq, GHz

dB

(S(2

,2))

07.07.2008 Owais Imam16


S-Parameter (S21 & S12) measurements of the 0603 type 10pF capacitor

2 4 6 80 10

-10

-8

-6

-4

-2

-12

0

freq, GHzdB(S

(2,1

))

2 4 6 80 10

-8

-6

-4

-2

-10

0

freq, GHz

dB(S

(1,2

))

07.07.2008 Owais Imam17

Simulations and Results

Theory of OptimizationError Function (Least Squares Method )Explanation of theSet Up

07.07.2008 Owais Imam18

Simulations and Results

Set Up VARVAR1L1=0 {o}

EqnVar

S2PSNP1File="H:\ADS\owais_prj\data\R0603_51R.ds"

21

Ref

R

R1R=51 Ohm

VARVAR3Cpar=0 {o}

EqnVarVAR

VAR2C1=0 {o}

EqnVar

GoalOptimGoal4

RangeMax[1]=6 GHz

RangeMin[1]=50 MHzRangeVar[1]="freq"Weight=Max=0Min=

SimInstanceName="SP1"Expr="dB(S12 ) - dB(S34)"

GOAL

GoalOptimGoal3

RangeMax[1]=6 GHz

RangeMin[1]=50 MHzRangeVar[1]="freq"Weight=Max=0Min=

SimInstanceName="SP1"Expr="dB(S21 ) - dB(S43)"

GOAL

Goal

OptimGoal2

RangeMax[1]=6 GHzRangeMin[1]=50 MHzRangeVar[1]="freq"Weight=

Max=0Min=SimInstanceName="SP1"Expr="dB(S22 ) - dB(S44)"

GOAL

Goal

OptimGoal1

RangeMax[1]=6 GHzRangeMin[1]=50 MHzRangeVar[1]="freq"Weight=

Max=0Min=SimInstanceName="SP1"Expr="dB(S11 ) - dB(S33)"

GOAL

OptimOptim1

SaveCurrentEF=no

UseAllGoals=yes

UseAllOptVars=yesSaveAllIterations=noSaveNominal=noUpdateDataset=yes

SaveOptimVars=yesSaveGoals=yesSaveSolns=noSetBestValues=yesNormalizeGoals=no

FinalAnalysis="SP1"StatusLevel=4DesiredError=0.0MaxIters=300ErrorForm=L2

OptimType=Random

OPTIM

LL1

R=L=L1 nH

C

C1C=C1 pF

TermTerm4

Z=50 Ohm

Num=4

TermTerm3

Z=50 Ohm

Num=3

C

C3C=Cpar pF

C

C2C=Cpar pF

TermTerm1

Z=50 Ohm

Num=1

Term

Term2

Z=50 OhmNum=2

S_ParamSP1

Step=100 MHzStop=10.0 GHz

Start=50 MHz

S-PARAMETERS

07.07.2008 Owais Imam19

Optimization of 0603 type 51 Ohms Resistor

2 4 6 80 10

-9

-8

-7

-10

-6

freq, GHz

dB(S

(1,1

))dB

(S(3

,3))

2 4 6 80 10

-9

-8

-7

-10

-6

freq, GHz

dB(S

(2,2

))dB

(S(4

,4))

2 4 6 80 10

-6

-5

-4

-7

-3

freq, GHz

dB

(S(2

,1))

dB

(S(4

,3))

2 4 6 80 10

-6

-5

-4

-7

-3

freq, GHz

dB

(S(1

,2))

dB

(S(3

,4))

07.07.2008 Owais Imam20

Results for 0603 type 51 Ohms Resistor

L1 (nH) C1 (pF) Cpar (pF)

Initial values 0 0 0

Optimized values

0.776 0.112 0.097

Error function 0.3128

07.07.2008 Owais Imam21


2 4 6 80 10

-9

-8

-7

-10

-6

freq, GHz

dB(S

(1,1

))dB

(S(3

,3))

2 4 6 80 10

-8.5

-8.0

-7.5

-7.0

-9.0

-6.5

freq, GHz

dB(S

(2,2

))dB

(S(4

,4))

2 4 6 80 10

-6.0

-5.5

-5.0

-4.5

-6.5

-4.0

freq, GHz

dB(S

(2,1

))dB

(S(4

,3))

2 4 6 80 10

-6.5

-6.0

-5.5

-5.0

-4.5

-7.0

-4.0

freq, GHz

dB(S

(1,2

))dB

(S(3

,4))

07.07.2008 Owais Imam22




Optimized values 1.03 0.09 0.0023


07.07.2008 Owais Imam23


2 4 6 80 10

-4.5

-4.0

-3.5

-5.0

-3.0

freq, GHz

dB(S

(1,1

))dB

(S(3

,3))

2 4 6 80 10

-4.5

-4.0

-3.5

-5.0

-3.0

freq, GHz

dB(S

(2,2

))dB

(S(4

,4))

2 4 6 80 10

-10.5

-10.0

-9.5

-9.0

-8.5

-11.0

-8.0

freq, GHz

dB(S

(2,1

))dB

(S(4

,3))

2 4 6 80 10

-11

-10

-9

-12

-8

freq, GHz

dB(S

(1,2

))dB

(S(3

,4))

07.07.2008 Owais Imam24




Optimized values

0.85 0.022 0.0062


07.07.2008 Owais Imam25






07.07.2008 Owais Imam26





Error function0.4258

07.07.2008 Owais Imam27




Optimized values 0.40

0.0380.0001


07.07.2008 Owais Imam28

Optimization of 0805 type 1pF capacitor

2 4 6 80 10

-40

-30

-20

-10

-50

0

freq, GHz

dB(S

(1,1

))dB

(S(3

,3))

2 4 6 80 10

-40

-30

-20

-10

0

-50

10

freq, GHz

dB(S

(2,2

))dB

(S(4

,4))

2 4 6 80 10

-30

-20

-10

-40

0

freq, GHz

dB(S

(2,1

))dB

(S(4

,3))

2 4 6 80 10

-30

-20

-10

-40

0

freq, GHz

dB(S

(1,2

))dB

(S(3

,4))

07.07.2008 Owais Imam29

Results for 0805 type 1pF capacitor

L1 (nH) R1 (Ohms) Cpar (pF)


Optimized values

1.004 0.753 0.048


07.07.2008 Owais Imam30


2 4 6 80 10

-40

-30

-20

-10

-50

0

freq, GHz

dB(S

(1,1

))dB

(S(3

,3))

2 4 6 80 10

-40

-30

-20

-10

-50

0

freq, GHz

dB(S

(2,2

))dB

(S(4

,4))

2 4 6 80 10

-10

-8

-6

-4

-2

-12

0

freq, GHz

dB(S

(2,1

))dB

(S(4

,3))

2 4 6 80 10

-10

-8

-6

-4

-2

-12

0

freq, GHz

dB(S

(1,2

))dB

(S(3

,4))

07.07.2008 Owais Imam31




Optimized values

0.495 0.404 0.028


07.07.2008 Owais Imam32


2 4 6 80 10

-50

-40

-30

-20

-10

-60

0

freq, GHz

dB(S

(1,1

))dB

(S(3

,3))

2 4 6 80 10

-50

-40

-30

-20

-10

-60

0

freq, GHz

dB(S

(2,2

))dB

(S(4

,4))

2 4 6 80 10

-2.0

-1.5

-1.0

-0.5

-2.5

0.0

freq, GHz

dB(S

(2,1

))dB

(S(4

,3))

2 4 6 80 10

-2.0

-1.5

-1.0

-0.5

-2.5

0.0

freq, GHz

dB(S

(1,2

))dB

(S(3

,4))

07.07.2008 Owais Imam33




Optimized values

0.174 0.127 0.014


07.07.2008 Owais Imam34




Optimized values

0.746 0.684 0.065


07.07.2008 Owais Imam35




Optimized values

0.384 0.376 0.031


07.07.2008 Owais Imam36




Optimized values

0.125 0.109 0.014


07.07.2008 Owais Imam37

END

THANK YOU FOR YOUR ATTENTION!

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