Implementing the Split Cylinder Resonator Method€¦ · Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials June 19 2008 Implementing the Split

Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials

June 19 2008

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

Shelley Blasdel Begley

Group/Presentation TitleAgilent Restricted

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Outline

• Overview of the Split Cylinder Method

• A Walk Through the Process

Qo

fo

f

Qs

fs


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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


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Split Cylinder Resonator System

Split Cylinder Resonator with

sample

connected between ports.

Network Analyzer

GP-IB or LAN

Computer

(not required for PNA)

NIST or Agilent

Software


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NIST fixture Agilent fixture

Sample


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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


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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 Sample

Higher Order Mode


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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


Higher Order Mode


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Measure Empty Split Cylinder Resonator


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S21 of TE011 Mode

Resonator should be loosely coupled

Adjust peak between 55-65dB

Measure Empty Split Cylinder Resonator

Agilent SoftwareAgilent Software guide


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Frequency and Quality Factor determination

Cycleper t Energy Los

Resonancein StoredEnergy 2π=Q


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Scalar Techniques

• 3dB Bandwidth

• Weighted Least Squares (WLS)

• Resonant Curve Area (RCA)

S21

f

fQ

∆= 0

∆f

3dB

f0


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Vector Technique

• Circle Fit

S21

fo

o

o

l

j

f

fft

tjQ

deLfT

−=

++=

−

2

1)(

2 δ


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Method 3dB WLS RCA Circle Fit

Average 75073.28 74082.27 74120.70 74241.30

Standard Dev. 760.37 239.12 221.78 113.04

Percent 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

Qo

fo

f

Qs

fs

Start

Measure

Empty SCR

Frequency & Q

Measure

Sample Thickness

Measure

Sample Filled SCR

Frequency & Q

End

Calculate

Permittivity


Higher Order Mode


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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

Measure Sample Thickness


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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


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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


Higher Order Mode


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Measure Sample Filled Resonator

f0

fsQ

o

fo

f

Q

s

fs

=


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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.dat

Number of TE0n Modes in Model

Radius 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


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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

χωχω

χωε

χωε

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


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Measure Sample Filled Frequency and Q

Agilent Software


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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


Higher Order Mode


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Calculate Permittivity

Agilent Software


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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


Higher Order Mode


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Higher Order Modes

TE011


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Double Peak in Search Span


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Interfering Modes


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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


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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


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Thank You for listening

Qo

fo

f

Qs

fs

Start

Measure

Empty SCR

Frequency & Q

Measure

Sample Thickness

Measure

Sample Filled SCR

Frequency & Q

End

Calculate

Permittivity


Higher Order Mode More information atwww.agilent.com/find/materials


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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.


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Appendix


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NIST Software Inputs

CalcFoInput.dat






SplitCInput.dat





Conductivity of Split-Cylinder Resonator (S/m)

Resonant Frequency of TE0np Mode (Hz)

Quality Factor of TE01np Mode



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Definition of Permittivity

"'

0rrr jεεε

ε

εκ −===

storage loss

'rε

Measure of how much

energy from an external

electric field is stored in the

material.

"rε

Measure of how much

energy from the electric field

is lost.

Permittivity describes the interaction of a material in the presence

of an electric field.


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Definition of Loss Tangent

'

"

tan

r

r

ε

εδ =

CycleperStoredEnergy

CycleperLostEnergy

QD ===

1tanδ

Dissipation FactorD Quality FactorQ

rε

'

rε

''

rε

Documents

Implementing the Split Cylinder Resonator Method€¦ · Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials June 19 2008 Implementing the Split