Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials September 24,...

Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials

September 24, 2008

Shelley Blasdel Begley

Implementing the Split Cylinder Resonator Method for Measuring Complex Permittivity

of Low Loss Materials

Implementing the Split Cylinder Resonator Method for Measuring Complex Permittivity

of Low Loss Materials


September 24, 2008

Outline

• Definition of Permittivity

• Overview of the Split Cylinder Method

• A Walk Through the Process


September 24, 2008

Definition of Permittivity

"'

0rrr j

Permittivity describes the interaction of a material in the presence

of an electric field.


September 24, 2008


"'

0rrr j

storage

'r

Measure of how much energy from an external electric field is stored in the material.




September 24, 2008


"'

0rrr j

storage

'r




aka Dielectric ConstantDk


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"'

0rrr j

storage loss

'r


"r

Measure of how much energy from the electric field is lost.



aka Dielectric ConstantDk


September 24, 2008

Loss Tangent

'

"tan

'

"

r

r

r

'r

''r


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Loss Tangent

Dissipation Factor Quality Factor

'

"tan

'

"

r

r

CycleperStoredEnergy

CycleperLostEnergy

QD

1tan

D Q

r

'r

''r


September 24, 2008

Loss Tangent

Dissipation Factor Quality Factor

'

"tan

'

"

r

r

CycleperStoredEnergy

CycleperLostEnergy

QD

1tan

D Q

r

'r

''r

Aka Tan DeltaDf


September 24, 2008

Sensitive Resonant method for measuring complex permittivity

Useful for thin film and low loss sheet materials.

Originally proposed by Gordon Kent, improved by NIST Boulder, CO.

Adopted as IPC Standard TM-650 2.5.5.13

Overview of the Split Cylinder Method


September 24, 2008

Split Cylinder Resonator System

85072A 10GHz Split Cylinder Resonator and

sample

PNA, PNA-L, PNA-XNetwork

Analyzer

LAN

Optional Computer

Agilent 85071E-300 Software runs on

optional PC or Network Analyzer


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Side View


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Side View

fixed cylinder

half

adjustable cylinder

halfcoupling loop

sample

coupling loop

z


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Electric Field Orientation for TEmnp ModesWhere m = 0 and p is odd.

zsample

E field


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Electric Field Orientation for TEmnp ModesWhere m = 0 and p is odd.

zsample

E field

p = 3


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zsample

E field

Field orientation can be significant if sample is anisotropic


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Measure Empty and Sample filled Resonator

Real part of permittivity is a function of Frequency shiftLoss tangent is a function of decrease in Q factor Also needed: Sample thickness


Qo

fo

f

Qs

fs


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Process Flow

Qo

fo

f

Qs

fs

Start

Measure Empty SCR

Frequency & Q

Measure Sample Thickness

Measure Sample Filled SCR

Frequency & Q

End

Calculate Permittivity

New Sample Same SampleHigher Order Mode


September 24, 2008

Process Flow

Qo

fo

f

Start

Measure Empty SCR

Frequency & Q



Frequency & Q

End




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Measure Empty Split Cylinder Resonator

fixed cylinder

half

adjustable cylinder

halfcoupling loop

coupling loop

z

Agilent Software


September 24, 2008

S21 of TE011 Mode

Resonator should be loosely coupledAdjust peak between 55-65dB

Measure Empty Split Cylinder Resonator

Agilent Software Agilent Software guide


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Frequency and Quality Factor determination

Cycleper t Energy Los

Resonancein StoredEnergy 2Q


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Scalar Techniques

• 3dB Bandwidth

• Weighted Least Squares (WLS)

• Resonant Curve Area (RCA)

S21

f

fQ

0

Δf

3dB

f0


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Vector Technique

• Circle Fit

S21

fo

o

o

l

j

f

fft

tjQ

deLfT

2

1)(

2


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Method 3dB WLS RCA Circle FitAverage 75073.28 74082.27 74120.70 74241.30Standard Dev. 760.37 239.12 221.78 113.04Percent of SD 1.01 0.32 0.30 0.15

Method Comparison

• 3dB Bandwidth• Weighted Least Squares (WLS) • Resonant Curve Area (RCA)• Circle Fit


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Process Flow

Start

Measure Empty SCR

Frequency & Q



Frequency & Q

End




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Sample is assumed to be a uniform known thickness

Best results: 0.1 to 3mm thick, ideally ~1mm

Thickness uncertainty <0.02mm

Minimize imperfections due to:

Flatness

Straightness

Parallelism



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Sample thickness measurement

Conforming samples such as thin films and PCBs

• Samples will be straightened out by cylinders.

• Recommend Agilent built in micrometer or mean of multiple thickness measurements.

Rigid samples such as Ceramics

• Samples will not be straightened out by cylinders.

• Recommend mean of multiple thickness measurements.

fixed cylinder

half

adjustable cylinder

halfcoupling loop

sample

coupling loop

z

fixed cylinder

half

adjustable cylinder

halfcoupling loop

sample

coupling loop

z


September 24, 2008

Process Flow

f

Qs

fs

Start

Measure Empty SCR

Frequency & Q



Frequency & Q

End




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Measure Sample Filled Resonator

Q

o

f

o

f

Q

s

f

s

=


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Estimate Sample Filled Frequency

Three ways to come up with initial guess:

• Theoretical or Design Value

• Independent Measurement

• Measure TE111 mode

NIST Software – CalcFoInput.datNumber of TE0n Modes in ModelRadius of Split-Cylinder Resonator (m)Length of Upper or Lower Split-Cylinder Resonator Section (m)Substrate Thickness (m)Initial Guess for Relative Permittivity of Substrate


September 24, 2008

Calculate Sample Filled Frequency

TE111 mode is the dominant mode when

03.22 radius

lengthTE111

0'

2cot

'

'

2tan

'

03.2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

a

mn

c

h

a

mn

c

a

mn

c

e

a

mn

c

a

h

h = the total length of the closed cavity, or in this case where the cylinders are equal length, 2x the length of one cylinder.a = the radius of the cylinders.χ’mn = the mth root of Bessel function of nth order


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Calculate Sample Filled Frequency

TE111 mode

Agilent Software


September 24, 2008

Measure Sample Filled Frequency and Q

Agilent Software


September 24, 2008

Process Flow

Qo

fo

f

Qs

fs

Start

Measure Empty SCR

Frequency & Q



Frequency & Q

End




September 24, 2008


Agilent Software


September 24, 2008

Process Flow

Qo

fo

f

Qs

fs

Start

Measure Empty SCR

Frequency & Q



Frequency & Q

End




September 24, 2008

Higher Order Modes

TE011


September 24, 2008

Double Peak in Search Span


September 24, 2008

Double Peak in Search Span

Agilent Software


September 24, 2008

Interfering Modes


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Split Cylinder Resonator Results

Real Part of Permittivity (Dk)

Teflon® PTFE

1.9

1.95

2

2.05

2.1

2.15

2.2

5 10 15 20 25 30

GHz

Expected Value Measured Value


September 24, 2008

Split Cylinder Resonator Results

Loss Tangent (Df)

Teflon® PTFE

-0.001

-0.0005

0

0.0005

0.001

0.0015

0.002

5 10 15 20 25 30

GHz

Expected Value Measured Value


September 24, 2008

Conclusions

• Split Cylinder Resonator is a sensitive method for measuring complex permittivity of low loss materials

• It can be confusing if you don’t know what you are doing.

• Agilent offers a turn key solution to make it fast and easy.


September 24, 2008

Thank You for listening

Start

Measure Empty SCR

Frequency & Q



Frequency & Q

End



More information atwww.agilent.com/find/materials


September 24, 2008

References[1] M.D. Janezic, ‘‘Nondestructive Relative Permittivity and Loss Tangent Measurements using a Split-Cylinder Resonator,’’Ph.D. Thesis, University of Colorado at Boulder, 2003.

[2] IPC-TM-650 Test Methods Manual Relative Permittivity and Loss Tangent Using a Split-Cylinder Resonator” Number 2.5.5.13 January, 2007.

[3] R.N. Clarke (Ed.), “A Guide to the Characterization of Dielectric Materials at RF and Microwave Frequencies,” Published by The Institute of Measurement & Control (UK) & NPL, 2003

[4] P.G. Bartley, S.B. Begley “Quality Factor Determination of Resonant Structures” IMTC 2006 – Instrumentation and Measurement Technology Conference Sorrento, Italy 24-27 April 2006

[5] M.T. Ali, M.K.M. Salleh, Md.M.Md. Zan “” Air-Filled Circular Cross Sectional Cavity for Microwave Non-Destructive Testing Transactions on Engineering, Computing and Technology Volume 18 December 2006, pg 107-112, ISSN 1305-5313

[6] M.D. Janezic, J.Krupka “Split-Post and Split-Cylinder Resonator Techniques: A Comparison of Complex Permittivity Measurement of Dielectric Substrates”. CICMT 2008 pgs 156-159.


September 24, 2008

Appendix


September 24, 2008

NIST Software Inputs

CalcFoInput.datNumber of TE0n Modes in ModelRadius of Split-Cylinder Resonator (m)Length of Upper or Lower Split-Cylinder Resonator Section (m)Substrate Thickness (m)Initial Guess for Relative Permittivity of Substrate

SplitCInput.datNumber of TE0n Modes in ModelRadius of Split-Cylinder Resonator (m)Length of Upper or Lower Split-Cylinder Resonator Section (m)Substrate Thickness (m)Conductivity of Split-Cylinder Resonator (S/m)Resonant Frequency of TE0np Mode (Hz)Quality Factor of TE01np ModeInitial Guess for Relative Permittivity of Substrate

Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials September 24,...

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