Materials Measurement
Techniques & Applications
Dr. Stoyan Ganchev
Americas TM Contact Center
Agenda
85070E/85071E Product Overview
 Fundamentals
 Measurement Instruments
 Considerations in choosing a Technique and Fixture
 Measurement Techniques
 Parallel Plate
 Coaxial Probe
 Transmission Line
 Free-Space
 Resonant Cavity

Objectives
Introduce the Agilent Technologies dielectric
measurements solutions
 Provide basic education on dielectric measurements
 Provide guidance in choosing the best measurement
technique for a given application
 Give practical information for improving
measurements

Agenda
85070E/85071E Product Overview
 Fundamentals
 Measurement Instruments
 Considerations in choosing a Technique and Fixture
 Measurement Techniques
 Parallel Plate
 Coaxial Probe
 Transmission Line
 Free-Space
 Resonant Cavity

Two Products
85070E
85071E
When you order only 85070E, this will include:
Includes:
• Software
• Dielectric Probe Software on CD-Rom
• mounting bracket to connect probe to Option 001
Probe Stand or similar stand
• ECal holder to connect to mounting bracket
• Type-N male to 3.5 mm male adapter, 1250-1743
• 3.5 mm male to 2.4 mm female adapter 11901D
• foam lined walnut box
IMPORTANT:
The configuration should specify additionally the type
of probe, cable and other options (see next slide).
IMPORTANT:
Depending on the transmission line the
customer will need additionally fixture,
that may be air coaxial line or waveguide
and appropriate calibration kit. For free
space measurement the two antennas
should be purchased from third parties.
Main Options
Model Number
85070E
Description
Dielectric Probe Kit
020
High Temperature Probe
030
Slim Form Probe
050
Performance Probe
85071E
Materials Measurement Software
100
Free Space Calibration
200
Reflectivity Software
300
Resonant Cavity Software
Options for 85070E
Options (probes)
 020 - High Temperature Probe (200 MHz
to 20 GHz), includes:
 High Temperature Probe
 Calibration Short
 030 - Slim Form Probe Kit (500 MHz to
50 GHz), includes:
 3 Slim Form probes
 Calibration short
 10 mm diameter sealed probe
holder
 6 O-rings
 050 - Performance Probe Kit (500 MHz
to 50 GHz), includes:
 Performance Probe
 Calibration short
 Mounting accessories
Options (other)
 001 - Probe Stand
 002 - High Temperature Cable
 022 - 20 GHz Flexible Cable
 032 - 50 GHz Flexible Cable
 033 - Slim form probe replenishment kit,
contains 3 extra Slim Form Probes
 Security Key - (Must choose one)
 UL7 - Parallel Hardware Key
(required for Windows NT® 4.0)
 UL8 - USB Hardware Key
 85070EU-070 Software upgrade from
older version
What is in options 020 and 030 for 85070E?
020
030
Short
Short
Holder
O-rings
Probes
Probe
 020 High Temperature Probe Kit
(200 MHz to 20 GHz)
 High Temperature Probe
 Calibration Short
 030 - Slim Form Probe Kit (500 MHz to 50
GHz), Includes:
 3 Slim Form probes
 Calibration short
 10 mm diameter sealed probe holder
 6 O-rings
What is in option 050 for 85070E?
050
Short
Probe
 050 Performance Probe Kit (500
MHz to 50 GHz)
 Performance Probe
 Calibration Short
85070E Configurations
85070E
Chose probe, one, two or all three
020 - High temperature
030 - Slim form probe 050 - Performance probe
Chose cable
022 - 20 GHz Flexible Cable
032 - 50 GHz Flexible Cable
002 - High Temperature Cable
Chose security key (one)
UL7 - Parallel Security Key
UL8 - USB Security Key
Options for 85071E
Options
100 - Free Space Calibration Option. Provides Gated Reflect
Line (GRL) calibration technique for free space measurement
method.
 200 Arch Reflectivity Software automates measurements made
with the NRL Arch technique
Options 100 and 200 are only compatible with PNA and 8510C
network analyzers with Time Domain Option installed.
 300 Resonant Cavity Software
 071 - Upgrade from any older version of 85071 software
 Security Key - (Must choose one)
•UL7 - Parallel Software Security Key
• UL8 - USB Software Security Key
Option 100, GRL
Gated Reflect Line (GRL) features
• converts a coaxial/waveguide 2-port calibration into a full 2-port free-space
calibration
• requires a PNA or an 8510 network analyzer with the time domain option, an
appropriate free-space fixture and a metal plate for calibration.
• includes also a gated isolation/response calibration to reduce errors from diffraction
effects at the sample edges, and multiple residual reflections between the antennas
• accurate free space measurements are now possible without expensive spot focusing
antennas, micro positioning fixturing or direct receiver access.
• the software automatically sets up all the free space calibration definitions and
network analyzer parameters.
• for PNA, additional ease and timesaving is provided with ECal.
• a guided calibration wizard steps the user through the calibration process.
New feature for 85071E:
Option 200, Reflectivity Software
Reflectivity Software
Option 200 provides a separate software program that automates NRL (Naval
Research Lab) arch measurements. The program guides you through the
complete process of setup, calibration and measurement of material absorption.
Measurements are displayed in both a graphical and tabular form — with up to
four measurements displayed simultaneously for comparison. The software
includes markers to aid in measurement analysis, and complete measurement
results and setup can be saved and recalled. Also, data can be saved in a
spreadsheet compatible file format or copied into other applications for further
analysis.
New feature for 85071E:
Option 300, Resonant Cavity Software
Resonant Cavity Software
Can control and measure dielectric properties with two types of resonators:
• Waveguide TE10n resonator using perturbation technique as described in
ASTM 2520
• Split Dielectric Post Resonator (SPDR) for measuring of substrate materials
or thin films
What more you will need?
85070E
Network Analyzer
Computer with IEEE-488 interface
card and HP-IB cable (Not required
for PNA family)
85071E
Network Analyzer
Computer with IEEE-488
interface card and HP-IB cable
(Not required for PNA family)
 Fixture
Coaxial
Waveguide
Two antennae
 NRL Arch
 Resonator(s)
Key features of both 8507xE Software
• Runs internally on the PNA series of network analyzers or on external
computer for the other network analyzer families
• View measurement results in a variety of formats
• Measurement markers simplify measurement analysis
• Split screen view shows measurement results simultaneously as a plot
and a table
• Ability to copy/paste measurement results to other applications in
either plot or table format. Data is easily shared with other Windows®
based programs or through the user programmable Component Object
Model (COM) interface
Key features (continued)
•Compatible with Windows® 98, 2000, ME, XP, or Windows NT® 4.0
(Windows NT® 4.0 requires Option UL7 Parallel Security Key)
• Supports both Agilent Technologies and National Instruments GPIB
cards (IEEE-488)
• COM interface allows the measurements to be setup, triggered and
read from a user written program.
• Compatible with a variety of network analyzer families
• 85070E is compatible with E4991A impedance analyzer
New feature 85070E: Cal refresh with ECal
Calibration Refresh with ECal will reduces drift errors
ECal
Holder
Water measurement with and
without ECal calibration refresh.
Software Menus for 85070E
File
Save or recall measurement setups or previous measurement results. Print copies of the
measurement results in a tabular or graphical format.
Edit
Copy the measurement results to the clipboard. Either graph or the tabular listing can be
copied. This allows your measurement results to be pasted into other applications.
View
Select the section you want to view. Selections include the toolbar, status bar, table of the
measurement data and chart of the measurement data.
Calibration
Select the frequency range, number of points, linear or log sweep. Guided calibration
sequence; choice of calibration materials or user-specified; refresh calibration for single
standard or ECal; recalibration versus temperature; automatic refresh on or off.
Software Menus for 85070E (continued)
Measure: Trigger a measurement.
Chart: Select the format to be displayed on the chart. Choices include er’, er’’, loss
tangent and Cole-Cole. Set Graticule scale factors or “autoscale”. Select from linear,
semi-log or log-log representations.
Table: Choose between different tabular formatting (er` and er`` or er` and tand)
Display: Display current measurement data; save/display up to 3 memory traces;
compare data to reference trace with trace math. Turn the marker on or off.
Preferences: Select your preference of fonts, colors and annotations used to plot and list
the measurement data.
Help: On-line help including the product manual.
Toolbar: Provides single click access to the most important menu items.
Visual Basic Example
Dim material As AUTOMATION8507XLib.Automation85070
Private Sub Calibrate_Click()
Call material.CalibrateProbe
End Sub
Private Sub Form_Load()
Set material = CreateObject("AUTOMATION8507X.Automation85070")
Call material.Init
End Sub
Private Sub Measure_Click()
Dim num As Long
Dim er As Single
Dim ei As Single
Dim f As Single
Call material.TriggerProbe
Call material.GetMeasurement(5, f, er, ei)
End Sub
Compatible HP/Agilent Network
and Impedance Analyzers
 PNA, PNA-L
45 MHz to 110 GHz
 ENA, ENA-L
300 KHz to 8.5 GHz
 E4991A
up to 3 GHz (with 85070E)
Legacy Network Analyzer Families
 8712/14 , 8719/20/22, 8510B/C
Notes:
1. Options 100 and 200 of 85071E work only with PNA or
8510 with time domain option.
2. Out of support instruments “should” work with 85070/1E,
but it is not warranted, because the compatibility has not
been established.
PC Requirements
 Windows® 95, 98, Me, NT 4.0 or NT 2000, XP
 GPIB interface card with a compatible driver
(Agilent SICL or National Instruments 488.2M)*
 CD drive
*
Note, the 8507xE can be installed and run on a PNA series analyzer
eliminating the need for both a PC and a GPIB card. To install the 8507xE
on a PNA analyzer a PC with a CD drive is required to copy the 85070E
installation files from the supplied CD to 3.5-inch disks or a USB CD drive
to hook to PNA.
Customer Downloadable Demos Available
on the Web
Agenda
85070E/85071E Product Overview
 Fundamentals
 Measurement Instruments
 Considerations in choosing a Technique and Fixture
 Measurement Techniques
 Parallel Plate
 Coaxial Probe
 Transmission Line
 Free-Space
 Resonant Cavity

Origin of Microwave Dielectric Measurements
Why now, 60 years later, are these
measurements still so important?
Why make measurements?
Development of
new materials
Controlling a
manufacturing
process
Incoming inspection
of materials
Shorter design cycles
Higher performance
Reduced scrap
Extremely Diverse Applications
“Materials” can mean just about anything. They are produced or used by
many diverse industries. For example, customers use network analyzers to
measure:
radar-absorbing “stealth” coatings
disposable diapers
cookie dough
moisture in asphalt roads
ceramics for microwave sintering/annealing
washed coal
cement
biological tissues (including blood, brain tissue simulation)
many, many others
What can these people have in common???
Only one thing: Need to measure the dielectric properties!!!
Industries, Products, Measurement Needs
Industries
Products
Measurement Needs
Traditional
Dielectrics
er and/or r
Substrates
Reflection , Transmission 
Ferrites
High accuracy
Absorbing materials
Wide frequency
Non-traditional, but technical
Chemical
Plastics
er and/or r
Ceramics
Adhesives
Ceramic sintering/annealing
Composite Materials Polymers
Compositions analysis
Paints/Films
Temperature dependence
Semiconductors/Superconductors Cure/Polymerization
Ceramics
Relaxation effects
Non-traditional, not technical
Food, Packaging
Food, Processing, Packaging
Research, Control,
Forest, Paper
Wood, Paper, Fiber
Optimization
Rubber
Rubber
Microwave processing
Cement, Concrete
Cement
Heating, Cooking, Drying
Bio, Medicine,
Medical therapy
Moisture content
Drugs
Analysis, Diathermy
Electronics
Microwaves
Communications
Aerospace/Defense
List of Applications
Application
Notes
Electronics
Capacitors; inductors; substrates, PC boards; ferrites, isolators,
circulators; antenna lenses; magnetic recording heads; dielectric
resonators and filters; etc
Absorbers
RFI/EMI shielding; absorbers; packaging; mode-supressors; etc
Aerospace
Stealth; low-observables; RAM (Radiation-Absorbing-Materials);
incoming inspection of materials; RCS; radomes; anechoic
chambers; nose-cones; etc
Ceramics
Basic research; ceramic processing with microwaves (sintering,
annealing); glass; superconductors; etc
Plastics
Basic research; plastics for electronics or aerospace; microwave
food packaging; polymerization research; adhesives research
(curing); radiation-absorbing paints; composites; stealth; etc
Superconductors Basic research; device technology; etc
List of Applications (continued)
Application
Food
Notes
Agriculture
Food research; food development for home microwaves; frozen food
tempering; food preservation (spoilage) research; moisture measurements
in raw grains; microwave pest control; industrial microwave food
processing; etc
Moisture measurements; remote sensing; etc
Packaging
Microwave food packaging; microwave sealing of containers; etc
Forest
Moisture measurements in wood or paper; curing glue; paper drying; etc
Mining
Rubber
Bore-hole measurements; ore content analysis; measuring moisture in ore
or coal; microwave enhancement of coal cleaning; etc
Heating pre-forms; vulcanization; water content in raw materials; etc
Bio-MedicinePharmaceutical
Microwave-enhanced therapy; diathermy; basic research; drug research;
sensing; etc
Nondestructive In many of the above industries/applications there is a need for
Measurement or nondestructive measurement or microwave imaging. Examples:
Imaging
Ceramics, Plastics, Medicine
Parallel Plate Capacitor (DC)
+
A
V
t
+
+
+
+
+
+ +
+
C  C0 '
-
A
C0 
t
Capacitance with no
dielectric (vacuum)
C
 '  er ' 
C0
Dielectric constant or
permittivity (real)
Parallel Plate Capacitor (AC)
I
+
A
V
t
+
+
+
+
+
+ +
C
+
G
-
I  I c  I l  V ( jC0 'G )
then
if
G  C0 "
I  V ( jC0 )( ' j " )  V ( jC0 )
Permittivity (electromagnetic fields)
D eE
Definition of electric displacement
(electric flux density)
e  e *  e 0e r
1
e0 
x10 9
36
e
Absolute permittivity or permittivity
er
Relative permittivity or dielectric constant
F /m
Free space permittivity
Permittivity is complex
e
'
"
   e r  e r  je r
e0
storage
The permittivity is often called
dielectric constant, but is changing
with frequency and temperature.
loss
Permittivity
e r'
Measure of how much energy from an external electric field is stored in the material
Loss factor
e r"
Measure of how much dissipative or lossy a material is to an external field
Loss Tangent
e
''
r
er
e
e r"  "
tan d  ' 
er  '
'
r
1
Energy Lost per Cycle
tan d  D  
Q Energy Stored per Cycle
D
Dissipation Factor
Q
Quality Factor
Optical Dielectric Parameters
n*  n  jnk  n1  jk 
0 c 0
n
 

 v 2
 
k

2 
n* - complex index of refraction
n – (real) index of refraction
k – index of absorption
n  e r'
    j
for  r'  1
 - complex propagation factor
 – attenuation coefficient (factor)
 – phase coefficient
Snell’s Law and Critical Angle for Total
Internal Reflection
1
1
Snell’s Law
e1
e2
2
e in
e out
n1
e

n2
e
'
r1
'
r2
Critical angle for total reflection
'
e out
 tot 
e in'
Propagation Factor
E  E0e jt x
H  H 0e jt x
  2f
rad
The electromagnetic fields of a plane wave,
propagating through a material are function
of time t and distance x.
sec
Angular frequency  forms relation to time.
    j  j e *  *
Phase Factor
Attenuation Factor
The complex propagation factor 
describes relation to distance and
depends on the material properties.
Attenuation Factor Derivation
    j  j
2

e r'  je r''
'
For non magnetic dielectric r  1
 2  '
''
  j 2      e r  je r
  
2
2
2


After taking a square of
both sides of the above
equation
Next step is to equate the real and imaginary parts of both sides. We can find
expression for the attenuation and phase factor with respect to the real and
imaginary dielectric constant or expression of the real and imaginary dielectric
constant with respect of attenuation and phase factor.
Attenuation Factor and Phase Factor


2

2

e 
2
 1  tan d   1

2
'
r
e 
2
 1  tan d   1

2
'
r
2

  
  
'
e r    1    
 2      
2
Neper
m
   2
e  
 2  
2
rad
m
''
r
Attenuation Factor Calculation
  8.68
2

e r' 
2
 1  tan d   1

2
2

  128.64 f e  1  tan d   1


'
r
  91 f e tan d
'
r
tan d  1
dB
m
dB ,
m
f in GHz
dB ,
m
f in GHz
Attenuation Factor Calculation
0.03
  0.91 f e r' tan d
dB / cm
Teflon Example
e r'  2.1
0.02
tan d  4 10  4
0.01
0
10
20
30
f , GHz
40
50
The attenuation is in
dB/cm. This means that
attenuation of 1 cm thick
sample is calculated for
different frequencies.
Attenuation Factor Calculation (continued)
Water Example
f  3 GHz, e r'  80, tan d  0.16
  3.89 dB / cm
In the previous example for Teflon we did calculate the attenuation versus
frequency using one and the same value of the complex dielectric constant,
because the dielectric constant of Teflon will not change with the frequency like
most of the low loss materials. The dielectric properties of water though will
change substantially with frequency like most of the lossy materials. For this
reason the frequency dependence of the attenuation of water is not calculated.
Attenuation Factor Calculation (continued)
How the attenuation depends on the dielectric constant and loss tangent?
  0.91 f e r' tan d
dB
cm
f  10 GHz
0.04
dB
cm
tan d  0.001
dB
cm
f  10 GHz, e r'  2.1
3
2
0.02
tan d  0.0004
0
10
e
'
r
20
1
0
0.05
0.1
tan d
0.15
0.2
Penetration (or Skin) Depth
E  E0 e
 d
P  P0 e 2d
Field strength decays
exponentially over distance d
Power is square of the field strength
The field penetration depth or skin depth D is
the distance through homogeneous material
over which the electric field strength falls to
1/e or 0.368 or 36.8% of initial value.
E0
0.368E0
e 0 e r'
E0 e
d
D
 E0 e
1
D
1

meters
Power Penetration Depth
1
D
Dp 

2 2
The power penetration depth Dp is two
times less than the field penetration depth D.
Half-power depth
E0e
2Dhp
 0.5E0
ln( 0.5) 0.347
Dhp  

2

Inductor
Core
material
L  L0 '
R
L
' 
L0
L
L0
Real permeability
Inductance of coil in free space
Permeability is complex


  r'  j r"
0
0  4x107
H /m
Free space permeability
storage
loss
  *  0r

Absolute permeability
r
Relative permeability
Electromagnetic Field Interaction
STORAGE
Electric
Fields
Magnetic
Fields
LOSS
Permittivity
'
er  er

MUT
r 
"
je r
STORAGE
LOSS
Dielectric Constant
Permeability
'
r

"
jr
Electromagnetic Field Interaction
 or Z0
Z 
e r'
TEM
Air
e
'
0
MUT
e r'
Impedance lower
Wavelength shorter
Velocity slower
Magnitude attenuated
Z

e
'
r
0

 120
e0
d 
0
e
'
r
 or Z0 is the free-space
impedance which is
120 = 367 W.
v
c
e r'
Reflection Coefficient versus Dielectric
Constant
1
air
e0 e
Reflection coefficient 
0.9
0.8
'
r
MUT
For nonmagnetic lossless dielectric
 long
Z  Z0


Z  Z0
0.7
0.6
0.5

0.4
0.3
0.2
1  e r'
1  e r'
Z 0    120
0.1
0
10
20
30
40
50
60
70
Dielectric Constant
80
90
e
'
r
100
Z

e r'
Measuring of Infinitely Long Sample in
Waveguide
sample
air
e0

air
e
'
r
 long
No reflection here
Waveguide
flange
MUT
Waveguide matched load
2
2


1 
 
 
*
e 
1       
1     2a    2a 
  complex reflection coefficient (s11)
  free-space wavelength
a  broad waveguide dimension
Dielectric Properties (at 3 GHz)
Low Loss
Lossy
100
TiO 2
50
Salt
Water
Water
Steak
20
'
er
Alumina
10
Alcohol
PC Board
5
Quartz
Mylar
2
Ice
10%
Teflon
0%
Air
1
.00001
.0001
20%
Wood
.001
tan d
.01
" '
 er / er
.1
1
Dielectric Mechanisms vs. Frequency
Ionic
Conductivity
e
'
r
Electric Polarization
Dipolar
(Rotational)
+
+
+
-
-
-
Atomic
Ionic
e
10
3
10
6
Electronic
''
r
10
9
10
MW
12
10
IR
V
f, Hz
15
UV
Dipole and Hydrogen Atom in Electric Field
T
F
E

F

The static electric field will exercise
torque on the electric dipole which
will tend to align this dipole in the
direction of the field. If the field
changes the direction, so will the
torque. The friction accompanying
the orientation of the dipole will
contribute to the dielectric losses.
E
-
H
+
+
-
Electronic polarization causes
distortion of the electron orbit in the
presence of electric field.
Debye Relaxation for Water at 30oC
es  e
Debye equation : e ( )  e  
1  j
e r' , e r''
e s  76.47
The static (DC) value of
dielectric constant or e for f = 0
'
er
60
e   4.9
40
the optical (infinite frequency)
dielectric constant or e for f = 
20
  2f the angular frequency
  7.2 p sec
0.1
e r"
1
10
the relaxation time
100
f, GHz
e
Cole-Cole Plots (Water)
"
r
o
20 C
40
23.7
9.14
Increasing
f (GHz)
34.9
30
34.9
o
60 C
4.63
23.7
20
3.25
9.14
10
4.63
1.74
0.58
0
0
10
e r'
Cole-Cole Plot Explanation
e r"
Increasing
f (GHz)
30
e r" max 
20
es  e
 35.8
2
es  e
e ( )  e  
1  j
10
Center
0
10
e   4.9
20
30
40
50
60
70
'
er
e s  76.47
Relaxation Time 
Water at 20o C
100
e
Time  required for 1/e of a
perturbed (aligned) system to return
to equilibrium (random state).
'
s
10
e
''
s
1
1
10
fc = 22 GHz
 = 7.2 psec)
100
e
'

e
''

f, GHz
Dipolar (orientation
polarization)
+
-
1
1


 c 2f c
Other Empirical Models
Only few materials exhibit pure relaxation properties with single
relaxation time that are described with the Debye equation.
es  e
e    e  
1
1   j 
es  e
e    e  

1  j 



The Cole-Cole model is
used in determination of
user defined standard for
coaxial dielectric probe.
Cole-Davidson model
the relaxation time constant
the relaxation width (distribution parameter)
distribution parameter that leads to asymmetric distribution of 
Comparison Between the Different Models
e
"
r
Debye
30
Cole-Cole  = 0.2
20
Cole-Davidson
 = 0.5
10
10
20
30
40
50
60
70
'
er
Agenda
85070E/85071E Product Overview
 Fundamentals
 Measurement Instruments
 Considerations in choosing a Technique and Fixture
 Measurement Techniques
 Parallel Plate
 Coaxial Probe
 Transmission Line
 Free-Space
 Resonant Cavity

Measurement Instruments



LCR Meters and Impedance Analyzers
Impedance/Material Analyzer
Network Analyzers
4294A Precision Impedance Analyzer
16451B 16452B and 16454A Fixtures


Frequency Range: 40 Hz to 110 MHz.
Allows highly accurate measurements of various materials such as printed
circuit boards, ceramic and insulating materials (16451B Dielectric Test Fixture),
liquids (16452A Liquid Test Fixture) and magnetic materials (16454A Magnetic
Material Test Fixture).
Permittivity Measurements using the 4294A

System Configuration
 4294A Precision
Impedance Analyzer
 16451B Dielectric Test
Fixture

Characteristics of Measurement System
 Frequency: 40 Hz - 30 MHz
o
o
 Operating Temperature: 0 C to +55 C
 Applicable Material Shape: A solid
which is flat and smooth.
 Applicable Material Size: Depends on
the characteristics of the test material
(MUT) and the measurement method.
 Type of Electrodes: 4 electrodes are
furnished for different types of materials.
The contacting and non-contacting
electrode methods are applicable. For
more information please refer to Product
Note 1369-1 (or old AN 16451-1, 380-1).
4294A Electrode Considerations

When using the electrodes A and B, caution must be taken when measuring
a material which is not smooth or changes thickness when pressure is
applied. If such a material is to be tested, the non-contacting method can
be used, but the material must be at least a few millimeters thick.
Electrode MUT Diameter MUT Thickness
Type
mm
mm
40 - 56
A
 10
10 - 56
B
 10

Electrode Diameter Max Frequency
mm
MHz
38
30
5
30
When testing material which has thickness of less than a few hundred
micrometers, it is recommended to apply a thin film electrode to the surface
of the material and measure with electrodes C and D. If this method is
employed, make sure that the resistance of the thin film electrode is small.
Electrode MUT Diameter MUT Thickness Electrode Diameter Max Frequency
Type
mm
mm
mm
MHz
56
5 - 50
30
C
 10
20 - 56
5 - 14
30
D
 10
Characteristics of PCB measured using
4294A and 16451B
Permittivity and Loss Tangent
of Glass Epoxy
Settings of 4294A
OSC LEVEL: 500mV
Frequency: 1kHz-30MHz
Parameters: εr´ and tan δ
BW: 5
Compensation: OPEN/SHORT/LOAD
LOAD STD: Air (3pF)
Settings of 16451B
Electrode: Type B
Measurement Method: Contacting
Characteristics of PCB measured using
4294A and 16451B
Cole-Cole Plot of Ceramic Material
Settings of 4294A
OSC LEVEL: 500mV
Frequency: 300Hz-30MHz
BW: 5
Compensation: OPEN&SHORT&LOAD
LOAD STD: Air (1pF)
Settings of 16451B
Electrode: Type C
Measurement Method: Contacting
Permeability Measurements using
4294A and 16454A
16454A Magnetic Material Test Fixture

System Configuration
 4294A Precision Impedance Analyzer
 42942A Terminal Adapter
 16454A Magnetic Material Test Fixture

Characteristics of Measurement System
 Frequency: 40 Hz - 110 MHz
o
o
 Operating Temperature: 0 C to +55 C
 Applicable Material Shape: next slide
 Applicable Material Size: next slide
For more information please refer to AN
1369-1
Applicable MUT sizes for 16454A Test Fixture
<20mm
< 8mm
5mm
3.1mm
8.5mm
3mm
Small size
Large size
Characteristics of a magnetic material
measured using 4294A and 16454A
Permeability and Loss Tangent of
Ferrite Core
Settings of 4294A
OSC LEVEL: 500mV
Frequency: 10kHz-110MHz
Parameters: μr´and tand
BW: 5
Compensation: SHORT
Settings of 16454A
Electrode: LARGE
E4991A Impedance/Material Analyzer
16453A 16454A fixtures



16453A Operating temperature: -55o C to +200o C
Frequency Range: 1 MHz to 3 GHz (E4991A) but fixtures are 1 MHz to 1 GHz only.
Provides a total solution for high-accuracy and easy measurement of surface-mount
components and dielectric materials.
85070E Dielectric Probe with E4991A




Recommended option for E4991A is option 010
Frequency range
 High temperature probe 10 MHz – 3 GHz
 Slim probe 500 MHz – 3 GHz
For ion liquids is possible electrode polarization for low frequencies
Calibration is performed in the following way
 Configure probe calibration from the software
 Calibrate at the APC7 port of the option 010 using E4991A
 From 85070E software, calibrate the end of the probe
MW Frequency Concerns
Low frequency
vs.
MW frequency
Large wavelength
Small wavelength
Lumped element
Transmission line
Simple
Complex
Low cost (compared to
high MW frequencies)
Expensive
(high MW frequencies)
Network Analyzers
Agilent Technologies PNA, PNA-L, ENA, ENA-L family of
network analyzers
(Legacy 8712/4, 8753, 8720, and 8510)
 30 kHz to 110 GHz (and above up to 325 GHz)
 Measures reflection/transmission (magnitude and phase) vs. frequency
 High accuracy
 50 ohm measurement environment
Generalized Network Analyzer
Block Diagram
Fixture
Incident
MUT
SOURCE
Reflected
SIGNAL
SEPARATION
INCIDENT
(R)
REFLECTED
(A)
TRANSMITTED
(B)
RECEIVER / DETECTOR
PROCESSOR / DISPLAY
Transmitted
T/R Versus S-Parameter Test Sets
S-Parameter Test Set
Transmission/Reflection Test Set
Source
Source
Transfer
switch
R
R
Port 1
Port 2
Fwd



B
A
B
A
Fwd
MUT
Source applies only to port 1
port 2 is always receiver
response, one-port calibrations available
Port 2
Port 1



MUT
Rev
Source can be applied to port 1 or port 2
forward and reverse measurements
two-port calibration possible
Three Versus Four-Receiver Analyzers
3 Receivers
4 Receivers
Source
Source
Transfer switch
Transfer switch
R1
R
A
B
A
B
R2
Port 1
Port 2
Fwd

MUT
TRL*, LRM* cal
Port 1
Port 2
Fwd
Rev

MUT
true TRL, LRM cal
Rev
Network Analyzer Calibration and
Measurement Accuracy
Provides insight into the sensitivity and limitations of
various materials measurement techniques.
 Vector error correction estimates then mathematically
removes systematic errors.
 Estimate systematic errors from measurements of
known calibration standards.
 Residual systematic errors a function of how well
calibration standards are known.

Network Analyzer Calibration and
Measurement Accuracy (continued)
Calibration is always important, but at high frequencies
measurement errors can be more significant


Calibration eliminates systematic (stable, repeatable) errors,
but not random or drift errors
 noise, drift, or environment
 temperature, humidity, pressure
Minimize errors with good measurement practices
 visually inspect connectors for dirt/damage
 minimize physical movement of test port cables both
during calibration and measurement
Agilent Technologies Instrument Summary
ENA, ENA-L
Network
analyzers
PNA, PNA-L
Legacy – 8712, 8753, 8720, 8510
Impedance/Material
Analyzer
E4991A
4192A, 4194A, 4263B,
4294A, 4285A, 4278A
DC
101
10 2
10 3
10 4
10 5
10 6
LCR meters
Impedance analyzers
10 7
10 8
10 9
10 10
10 11
f (Hz)
Agenda
85070E/85071E Product Overview
 Fundamentals
 Measurement Instruments
 Considerations in choosing a Technique and Fixture
 Measurement Techniques
 Parallel Plate
 Coaxial Probe
 Transmission Line
 Free-Space
 Resonant Cavity

Considerations in choosing a
Technique and Fixture
 Consider form of material sample (liquid, solid, sheet, etc.)
 General knowledge of desired measurement
Destructive versus non-destructive
Desired frequency range
Expected range of permittivity and permeability
Isotropic versus non-isotropic
 Mathematical model relating measured s-parameters and material characteristics
Limitations of model, for example perturbation theory assumes small
variation in field pattern.
 Electric field necessary in material to sense permittivity
 Magnetic field necessary in material to sense permeability
Agenda
85070E/85071E Product Overview
 Fundamentals
 Measurement Instruments
 Considerations in choosing a Technique and Fixture
 Measurement Techniques
 Parallel Plate
 Coaxial Probe
 Transmission Line
 Free-Space
 Resonant Cavity

Parallel Plate
e r'
C

A
e0
t
tan d  D
< 10 mm
10-50 mm
Liquids
LF Parallel Plate Summary
Relatively simple computation
of er from C and D
Frequency limited
to < 100 MHz
Inexpensive
Does not provide r
Works well for thin sheets,
PC boards, films, etc.
Accurate: typically
1% for er’ , and
5%  0.005 for tand
RF Parallel Plate Summary
Automatic computation
of er from C and D
Provides automatic r
Works well for thin sheets,
PC boards, films, etc.
Accurate: typically
8% for er’ < 10 , and
 0.003 for tand
Frequency limited to
1MHz to 1.8GHz
Sample must be flat,
smooth sheet
Agenda
85070E/85071E Product Overview
 Fundamentals
 Measurement Instruments
 Considerations in choosing a Technique and Fixture
 Measurement Techniques
 Parallel Plate
 Coaxial Probe
 Transmission Line
 Free-Space
 Resonant Cavity

Coaxial Probe Technique
High temperature probe
Method features
 Broadband
 Simple and convenient (Nondestructive)
 Limited er accuracy and tan d low loss
resolution
 Best for liquids or semi-solids
Slim form and Performance probes
Material assumptions:
 "semi-infinite" thickness
 non-magnetic
 isotropic and homogeneous
 flat surface
 no air gaps
High Temperature Coaxial Probe
Flange
Measuring Aperture
200 MHz – 20 GHz
Slim Coaxial Probe
500 MHz – 50 GHz
Slim Coaxial Probe
Using the probe with the 10 mm diameter sealed probe holder
Performance Coaxial Probe
Performance Probe Features
Combines rugged high temperature performance with
high frequency performance, all in one slim design.
• 0.500 – 50 GHz
• Withstands -40 to 200 degrees C
• Hermetically sealed on both ends, and can be put in autoclave
• Food grade stainless steel
Probes Comparison
Probes
High Temp
Slim Form
Performance
Frequency
200MHz – 20GHz
500MHz – 50GHz
500MHz – 50GHz
Probe Diameter
Fat
Super slim
Slim
Withstands Extreme
Temperatures
x
Capabilities
x
Complete Hermetic
Seal
x
Low Cost,
Consumable
Suggested
Applications
x
Quick check for hard
flat solids, low
frequency liquids
when big diameter is
not a problem.
Curing and other
consumable
applications, and When
cost is an issue
Medical, Chemical, Food,
Extreme Temp, Sterile,
and other applications
that need a sealed probe.
Coaxial Probe
Solids
Semisolids (Powder)
Reflection
(S11)
Liquids
S11
er
Open-Ended Coax Formulation
2b
jk m2
YL 
b
k c ln  
a
2a
b b

 
a a
0
cos
e  jk m
r 2  r ' 2  2 rr ' cos
r 2  r '2  2rr ' cos
k m   e me 0  0
ddrdr '
kc   e ce 0  0
Metal plane
erc - the dielectric constant of the dielectric
filling the coaxial line,
a and b - the inner and outer radii of the
coaxial line, and
D. V. Blackham, R. D. Pollard, “An Improved Technique for Permittivity Measurements Using a Coaxial Probe,” IEEE
Trans. on Instr. Meas., vol. 46, No 5, Oct. 1997, pp. 1093- 1099
Fringe Field for the Slim Coaxial Probe
The theory of the probe is based on
radiation from a coaxial aperture in an
infinite metal plane. It is difficult to
model the fringe fields for the slim probe.
The “genetic algorithm” is used to model
the probe. To derive the model the only
information needed is uncorrected
reflection coefficient measurements of a
variety materials with known dielectric
constant.
Dielectric Probe System
Computer
(not required for PNA)
Network Analyzer
PNA, PNA-L, ENA, ENA-L, E4991A, 4294A
Legacy 8712/14, 8752, 8753, 8719, 8720, 8722, or 8510
CH1 S11 1 U
FS
Co
r
LOG
MAG
PHAS
E
DEL
AY
SMIT
CHA
H
RT
POLA
R
Hi
d
LIN
MAG
SW
R
HP-IB
MOR
E
START
.300 000N
MHZ
85070E
Dielectric Probe
85070E Software
(Included with probe kit)
Coaxial Probe Calibration
Directivity
Three term calibration (1-port)
corrects
Tracking
Source match
Measure three known standards
Open
Short
er  1
 1
  1
User-defined
standard
(usually water)
Difference in predicted and actual value is used to correct measurement
Coaxial Probe Errors
Cable stability
Air gaps
Sample thickness
Powder measurements results depend
on packing
Allow time for cable to stabilize
Minimize cable flexing
Machine a flat sample face Probe
flatness ~ 100  inches
(sample flatness should be similar)
tmin 
20
er
mm
Recommended
minimum thickness for
high temperature probe
Uniform packing and mixing theory
Cable Phase Stability
Remeasuring Air at Various Cable Positions
er '
1.4
1.2
1.0
0.8
0.6
0
5
10
20
15
f
(GHz )
Refresh Calibration (Single Standard)
If the perturbation is small, the change can be characterized
by the measurement of a single calibration standard
c10
e10
m
e00
e11
e01
a
c01
m
a
e00
= Measured S11
= Actual S
11
= Directivity error
e11 = Source match error
e10 e01 = Reflection tracking error
c10 c01 = Perturbation term
e10e01c10c01a
m  e00 
1  e11c10c01a
Refresh Calibration for Water
80
Permittivity (real part)
70
60
calibrated at 55 deg
50
short refresh at 55 deg
air refresh at 55 deg
40
30
calibrated at 25 deg
1
Frequency (GHz)
10
Refresh Calibration for Water
70
60
calibrated at 55 deg
short refresh at 55 deg
Loss Factor
50
air refresh at 55 deg
calibrated at 25 deg
40
30
20
10
0
1
Frequency (GHz)
10
Refresh Calibration with ECal
How it works:
• Perform cal at the tip of the probe
• After the cal, with cal on, characterize
three ECal standards and store the values
• If the cable flexes or temperature
changes measure the three standards raw
and use the newly calculated error vectors.
Errors for Thin Materials
MetalBacked
+20%
1
t  tmin
2
Measurements of Stacks of Paper
Paper
e r '  2.4 tan d  0.06
%-Error
+10%
+5%
NOM
-5%
-10%
1
t  tmin
7
-20%
tmin 
FoamBacked
0
5
10
13
20
er
15
20
Thickness (mm)
Relative Measurements
3.80
rexolite
3.60
Dielectric Constant
kynar (T/R)
kynar-rexolite + 2.54
3.40
kynar
3.20
3.00
2.80
2.60
2.40
1
Frequency (GHz)
10
Relative Measurements
0.6
rexolite
kynar (T/R)
0.4
kynar-rexolite
Loss Factor
kynar
0.2
0.0
-0.2
-0.4
1
Frequency (GHz)
10
Coaxial Probe Measurement of Methanol
35
Dielectric Constant
30
25
20
15
10
measured
5
0
0.1
Cole-Cole model
1
10
Frequency (GHz)
Measured dielectric constant of methanol at 25 C compared with Cole-Cole model.
The Cole-Cole parameters are: e rs  33.7, e r  4.45,  =4.95  10-11 s and  =0.036.
Coaxial Probe Measurement of Methanol
15
Loss Factor
10
5
measured
Cole-Cole model
0
0.1
1
10
Frequency (GHz)
Measured loss factor of methanol at 25 C compared with Cole-Cole model. The
Cole-Cole parameters are: e rs  33.7, e r  4.45,  =4.95  10-11 s and  =0.036.
Reflection Coefficients at Probe Aperture
for Air, Water, and Methanol
90°
water
methanol
air
180°
0.0
270°
0.5
1.0
0°
Coaxial Probe Summary
Convenient, easy to use
Little or no sample preparation
Requires sample
thickness of > 1 cm (typical
Solids must have a flat surface
Nondestructive for
many materials
Limited accuracy in e’r
( + 5%) and low loss
resolution ( + .05 in tand)
Ideal for liquids or semisolids
Not suited to high e’r
low e”r materials
Broad frequency range
(0.2-20 GHz depending on er)
Does not provide r
Agenda
85070D/85071D Product Overview
 Fundamentals
 Measurement Instruments
 Considerations in choosing a Technique and Fixture
 Measurement Techniques
 Parallel Plate
 Coaxial Probe
 Transmission Line
 Free-Space
 Resonant Cavity

Transmission Line Technique
Waveguide
Coax
Material assumptions:
 sample fills fixture cross section
 no air gaps at fixture walls
 smooth, flat faces, perpendicular to long axis
 homogeneous
Method features:
 Broadband - low end limited by practical sample length
 Limited low loss resolution
 Measures magnetic materials
 Anisotropic materials can be measured in waveguide
 Coaxial line supports planar TEM mode (free space)
Transmission Line
Waveguide
l
Reflection
(S11)
Transmission
(S21 )
Coax
S11
er
S 21
r
Waveguide Section with Samples
Air Coaxial Section with Samples
Transmission Line System
Computer
(not required for PNA)
Network Analyzer
PNA, PNA-L, ENA, ENA-L
Legacy 8712/14, 8752, 8753, 8719, 8720, 8722, or 8510
CH1 S11 1 U
FS
Co
r
LOG
MAG
PHAS
E
DEL
AY
SMIT
CHA
H
RT
POL
AR
LIN
MAG
Hi
d
SW
R
MOR
E
START
.300 000N
MHZ
HP-IB
85071E
Materials Measurement
Software
Transmission Line Fixture
(coaxial, waveguide, or free-space set up)
Transmission Line Algorithms in 85071E
Algorithm
Measured
Optimum
Length
Output
Nicolson-Ross
(PN 8510-3)
S11,S21,S12,S22
(or S11,S21)
g/4
er and r
Precision (NIST)
S11,S21,S12,S22
ng/4
er
S21,S12
(S21)
ng/4
er
Fast
Short-circuited
back
S11
g/2
er
Arbitrary dielectric
back
S11
g/2
er
Nicolson-Ross Measurement Model
Region 1:
Region 2:
Region 1:
V1, I1, Z0
V2, I2, Zs
V3, I3, Z0
V2
Vi
V1
V2
Air
Boundary
conditions
V3
MUT
Air
l 0
1) V1  V2
ld
3) V2  V3
2) I1  I 2
4) I 2  I 3
A.M. Nicolson, G.F. Ross, "Measurement of the intrinsic properties of materials by time-domain techniques,"
IEEE Trans. on Instrum. Meas., vol. IM-19, Nov 1970, pp. 377-82
Nicolson-Ross Measurement Model
Continued
Boundary conditions
(system of 4 equations)
Related quantities
1) Vi  V1  V2  V2
2)


  jd
2

2

1
1 
Vi  V1 
V2  V2
Z0
Zs
3) V e

V e
jd


3
V

1   jd
1 
 jd
4)
V2 e  V2 e  V3
Zs
Z0
Zs
1
Z  Z0 Z0
 s

Zs  Z0 Zs  1
Z0
Zs 1 

Z0 1  
V1
s11 
Vi
T e
j
V3
s21 
Vi

re r d
c
Nicolson-Ross Measurement Model
Continued
Solution of the system
1 

T

1 

1 
T
1 
material
interface
bulk
material
material
interface
Flow graph can be used
also to solve the system

Nicolson-Ross Measurement Model
Continued
K
T 
K 1
2
2
2
S11
 S 21
1
K 
2 S11
From only one measurement the
solution is not unique. We need
to know either approximate
value of the dielectric constant
or perform another measurement
(measurement of reversed Sparameters or another sample
with different length.
S11  S 21  
1  S11  S 21 
r 
1 
1
1
 1   

2
2
0
 1
1  2



2  0
 2
c 
er  
r
c
 1
1
 1 


ln
 2d  T  
2
 

2
Phase Rotation
Calibration planes
360 f 0
For
a
b
For
L sample holder
S11
S 21
  2a
 fc 
1   
 f0 
c
2
f 
360 f 0 1   c 
 f0 
  a  b 
c
2
- phase shift
f0 – measurement frequency
fc – cutoff frequency (fc = 0 for coaxial measurement)
c – velocity of light
Nicolson-Ross Assumptions and Features





Single mode propagation assumed
– valid when homogenous sample fills cross section of transmission line
and sample interfaces are perpendicular to longitudinal axes
– practical measurements of solids usually limited to low values of
dielectric constant (<~15 for 7mm coaxial measurements)
Can determine both permittivity and permeability
Important to understand sources of error.
Measurement of both forward and reverse s-parameters yields redundant
information to enable sample position invariance.
For low loss materials, sample thicknesses near ng/2 cause discontinuities
in the measurement results
Nicolson-Ross - Measurements
Nicolson-Ross Model
Measurement Requirements
S-parameter test set
TR test set
 Measurement of S11, S21, S22, and S12
 Full 2-port calibration
 Approximate sample position
 Measurement of S11 and S21
 One path 2-port calibration
 Exact sample position
and
• One sample
• g/4 wavelength sample thickness is optimum
Precision NIST Algorithm
Model requirements:
S-parameter test set only
 Measurement of S11, S21, S22, and S12
 Full 2-port calibration
 Approximate sample position
 One sample
 ng/2 wavelength sample thickness is optimum
 Sometimes has a problem converging to an answer when
the measurement errors in S11 and S22 is large.
1.
2.
J. Baker-Jarvis, M.D. Janezic, R.F. Riddle, R.T. Johnk, P. Kabos, C. Holloway, R.G. Geyer, C.A. Grosvenor, “Measuring
the Permittivity and Permeability of Lossy Materials: Solids, Liquids, Metals, Building Materials, and Negative-Index
Materials,” NIST Technical Note 15362005
http://www.boulder.nist.gov/div818/81801/properties/Pages/publications.html
J. Baker-Jarvis, E. Vanzura, W. Kissick. “Improved Technique for Determining Complex Permittivity with the
Transmission/Reflection Method.” IEEE Transactions on Microwave Theory and Techniques, vol 38, no. 8, pp. 10961103, August 1990.
Fast Algorithm
S-parameter test set
TR test set
 Measurement of S11, S21, S22, and S12
 Full 2-port calibration
 Approximate sample position
 Measurement of S11 and S21
 One path 2-port calibration
 Exact sample position
and
• One sample
• g/4 wavelength sample thickness is optimum
• This technique minimizes the difference between the measured and calculated values of S21.. The sample is
assumed to be non-magnetic.
• Often converges to a solution when the NIST model fails. This is because it doesn’t depend on S11. The error
in measuring S11 is often a order of magnitude worst than when measuring S21.
Weakness of both the NIST and Fast Models
• Both models computes the wrong solution when the phase shift of
S21 is greater than -360 degrees at the first measurement frequency.
• This can often be overcome by computing the group delay and
computing an estimate of the permittivity.
• An alternative is to provide the model with an approximate value of
the permittivity.
Short-Circuited Back
Model requirements:
Any test set
 Measurement of S11
 S11 1 - port calibration
 Defined sample position
 One sample
 g/2 wavelength sample thickness is optimum
Arbitrary Dielectric Back
Model requirements:
MUT
Any test set
 Measurement of S11
 S11 1 - port calibration
 Defined sample position
 One sample
 g/2 wavelength sample thickness is optimum
 Two measurements are required:
 one with backing alone and
 the other with the sample and backing together
 It is simple and best for thin film measurements.
Arbitrary
back
E-field at the short is 0
 and e Single or Double
Model requirements:
Any test set
 Measurement of S11
 S11 1 - port calibration
 Defined sample position
 Measurement requires
o Two samples backed by short or
o One shorted sample in two positions
 Optimum sample thickness:
o Selected for transmission loss of 5 dB or
less (shorter sample, lossy materials)
o About g/4 and g/2 wavelength (lower
loss materials)
Two samples backed by short
One shorted sample in two positions
Transmission-Reflection versus
Short-Circuited Back
Where possible, a transmission/reflection measurement
gives much better results:
 T/R measurements are possible with thicker samples
 T/R measurements are not compromised by errors of
relative length of the samples
Duroid Measurements
Measurements of 1.5 mm thick Duroid
5.00
short backed
4.50
Dielectric Constant
transmission/reflection
arbitrary backed
4.00
3.50
3.00
2.50
2.00
8.2
9.2
10.2
Frequency - GHz
11.2
12.2
Duroid Measurements
Measurements of 1.5 mm thick Duroid
0.6
short backed
0.5
transmission/reflection
Loss Factor
0.4
arbitrary backed
0.3
0.2
0.1
0.0
-0.1
8
9
10
Frequency - GHz
11
12
Transmission Line Measurement
Error Sources


Sample geometry
– air gaps
– sample length
Network analyzer systematic errors
– usually less important that sample geometry
– minimized when measuring longer samples
Transmission Line Measurement
Error Sources
Network analyzer
errors



Careful calibration
Use good standards
Use TRL or time
domain gating
Sample length
uncertainty

Air gaps between sample
and fixture
Measure length precisely





Use larger fixture
Focus on fit of center
conductor (coaxial) or on fit
of broad waveguide wall
Measure gap precisely and
correct in software
Fill gap with conductive
grease
Metalize sample sides
Sample Length
Minimum length
Maximum length
S21 phase shift >> S21 uncertainty
(approx. 20o )
Avoid drop-outs in Nicolson-Ross algorithm
Sample loss
 20 
Lmin  g 

360


Long samples may create multiple roots
Lmax
g

2
Optimum length for low loss materials
For Nicolson-Ross:
g
L
4
S11  max 
For Precision or Fast:
L
ng
2
S21  max 
Transmission Line Air Gaps
(Altschuler, 1963)
E field in waveguide
d
d1
d2
d3 d4
b
a
neglect gaps along a
L2

L1 
e c'  e m'


tan
d

tan
d
1

e
'
c
m
c
L3  e m L1
L2 

e c'  e m'
where
d
d
d
L1  log 2  log 4 L3  log 4
d1
d3
d1
d3
L2  log
d2
where
d
D
b
tan d c  tan d m
D
D  b  e m' b  d 
Typical Errors Caused By Air Gaps
Permittivity of material
High er materials in coaxial lines = 20% to 50%
Size of transmission line
For er = 10 and air gap = 0.25 mm (coaxial line)
Coaxial line dimensions
Error
3.0 mm
35%
7.0 mm
14%
14.0 mm
8%
25.0 mm
4%
1.625 in
3.2%
3.125 in
1.7%
Minimize Sample Holder Ambiguities
Coax


Waveguide
Measure S-parameters of sample holder
using Unknown Thru Calibration and use
explicit deembedding.
 define sample holder length=0 in the
softare for computation
Use sample holder as THRU cal standard
(coaxial)
 modify cal kit definition of THRU
offset delay using value of sample
holder length
delay 
length e r air
c
Thru

Include sample holder as part of port 2
(implicit deembedding)
 define sample holder length=0 for
computation
Port 1
Port 2
Note: Implicit or explicit deembedding is best
approach to compensate for sample holder loss.
Plexiglas Measurement Results
e
'
r
25 mm
2.58
31 mm
25 mm
2.56
2.54
9
31 mm
calibrated out
sample holder
10
11
12
f, GHz
Plexiglas Measurement Results
tan d
tand
25 mm
0.005
31 mm
0.004
25 mm
31 mm
0.003
9
10
calibrated out
sample holder
11
12
f, GHz
Measured Parameter Uncertainty
Effects on Material Properties
 Length and Air gaps
– recalculate results adding and subtracting dimensional
ambiguity
 S-parameters accuracy
– Monte Carlo method such as uncertainty “noise”
Transmission Line Typical Accuracy
e r'  1  3
Coaxial line
Waveguide
2%
1%
e r'  3  10
e r'  10  30
5%
3%
 For low loss, nonmagnetic, isotropic, rigid material
 Requires precise sample machining (e.g. 0.03 mm). It will
depend on the frequency.
 Reported 2-4 times better accuracy with no air gaps
10%
5%
Transmission Line Calibration
Frequency response calibration (not recommended for materials
measurements)
 Open, short or thru only
One-port reflection calibration (3 term error correction)
 Open (offset short)/Short/Load (fixed, sliding, offset)
 ECAL
Full two-port calibration (12 term error correction)




Short/ Open (offset short)/Load (fixed, sliding, offset)/Thru
Thru/Reflect/Line
Unknown Thru
ECAL
TRL Calibration
 Thru
 Zero or non-zero length
 Reflect
 Unknown high reflect
 Same response to Port 1 and 2
Port 1
Port 2
Port 1
Port 2
 Line
 Different in length than “Thru”
 Reflectionless
Port 1
Port 2
TRL Calibration Residual Errors
 Fewer known standards required
 Simple standards (especially for non-coaxial media)
 Highest precision
Sliding
Offset
Errors
Fixed
Load
Load
Load
TRL
Directivity
-40 dB
-52 dB
-60 dB
-60 dB
Match
-35 dB
-41 dB
-42 dB
-60 dB
Residual
Tracking
0.1 dB
0.047 dB
0.035 dB
0 dB
Unknown Thru Calibration
 Do a one-port calibration on port 1
Port 1
 Do a one-port calibration on port 2
 Measure unknown thru calibration standard:
 Must be reciprocal (Sij = Sji)
 Phase known to within a quarter wavelength
 Confirm estimated electrical delay of unknown thru
Port 2
Port 1
Short
Open
Load
Short
Open
Load
Unknown
Thru
Port 2
Coaxial Transmission Line Fixtures
Agilent Technologies coaxial transmission lines (part of the
verification kits)
N type from 85055A verification kit, airline 85055-60006
7 mm from 85051B verification kit, airline 85051-60010
3.5 mm from 85053B verification kit, airline 85053-60008
2.4 mm from 85057B verification kit, airline 85057-60008
Waveguide Transmission Line Fixtures
Agilent Technologies waveguide components:
- X/P/K/R/Q/U/V/W 11644A calibration kits contain  /4
line as well as a straight waveguide section that can be
used as sample holder)
Transmission Line Summary
Provides both er and r
Simple fixtures
Broad frequency range
(0.1-110 GHz)
Adaptable to "free space"
Frequency limited to >100
MHz (banded in waveguide)
Precise sample shape required
(usually destructive)
Limited low loss resolution
Liquids and gases must
be contained
Agenda
85070D/85071D Product Overview
 Fundamentals
 Measurement Instruments
 Considerations in choosing a Technique and Fixture
 Measurement Techniques
 Parallel Plate
 Coaxial Probe
 Transmission Line
 Free-Space
 Resonant Cavity

Free Space Technique
Material assumptions:
 large, flat, parallel-faced samples ( > 10)
 homogeneous
Method features:
 Non-contacting, non-destructive
 High frequency - low end limited by practical sample size
 Useful for high temperature
 Antenna polarization may be varied for anisotropic materials
 Measures magnetic materials
Free Space Methods
Reflection
RCS
RCS (Radar Cross Section)
NRL arch
NRL Arch
Transmission
Tunnel
Tunnel
S-parameter (reflection/transmission)
Cavity
Open (Fabry-Perot) resonator
S11
er
S21
r
Free Space System
Computer
(not required for PNA)
Network Analyzer
PNA, PNA-L, ENA, ENA-L
Legacy 8712/14, 8752, 8753, 8719, 8720, 8722, or 8510
CH1 S11 1
U FS
C
or
LOG
MAG
PHA
SE
DEL
AY
SMI
CHA
TH
RT
POL
AR
LIN
MAG
Hi
d
SW
R
MO
RE
HP-IB
START
.300
000N MHZ
Antennae
85071E
Materials Measurement
Software
Fixture to hold the sample
NRL (Naval Research Lab) Arch
To Port 1 of
network
analyzer
To Port 2 of
network
analyzer

Measure s21 with the network analyzer
NRL arch is used usually to measure absorbing
materials. For absorbers is desired to know the
frequency response of reflectivity at a given angle.
Measurement with NRL Arch and
option 200 of 85071E
Free Space Set-Up
To Port 1 of
network
analyzer
Material
Sample
To Port 2 of
network
analyzer
Fixture to hold the sample and short
 Plane wave incident on homogeneous sample of infinite transverse dimensions
 Focusing lenses convert spherical waves to plane waves
Free Space High Temperature
Heating panels
Furnace
Thermal insulation
Sample
 No tolerance requirements on sample
 Sample is easily thermally isolated
 Fibrous insulation virtually transparent to microwaves
Thermocouple
Free Space Calibration
 Response calibration (reflection)
 Response and isolation calibration (transmission)
 TRL/TRM 2-port calibration
 Thru: focal points are coincident
 Reflect: metal plate at focal point
 Line or Match: focal points separated by /4 or use absorber as a match
 Time domain gating eliminates multiple reflections
 Gated Reflect Line (GRL) Calibration
Two-Port Error Correction
Reverse model
Forward model
Port 1
Port 2
ERT'
Port 1
a1
ED
S11A
E RT
ED = fwd directivity
E S = fwd source match
ERT = fwd reflection tracking
E D' = rev directivity
E S' = rev source match
E RT' = rev reflection tracking

Port 2
S21A
ES
b1

EX
S22 A
ETT
EL
b2
S21
b2
A
a1
E L'
S11A
b1
S22 A
E S'
ED'
a2
a2
S12A
ETT'
EX'
S12
A
E L = fwd load match
ETT = fwd transmission tracking
E X = fwd isolation
E L' = rev load match
E TT' = rev transmission tracking
E X' = rev isolation
Each actual S-parameter is a
function of all four measured Sparameters
Analyzer must make forward and
reverse sweep to update any one
S-parameter
S11a 
S
 ED
S
 ED '
S
 E X S12 m  E X '
( 11m
)(1  22m
E S ' )  E L ( 21m
)(
)
E RT
E RT '
E TT
E TT '
S
S
S
 E D'
 ED '
 E X S12 m  E X '
(1  11m
E S )(1  22m
E S ' )  E L ' E L ( 21m
)(
)
E RT
E RT '
E TT
ETT '
S21a 
S21m  E X
S22 m  E D '
)(1 
( E S ' E L ))
E TT
E RT '
S
S
S
 ED
 ED'
 E X S12 m  E X '
(1  11m
E S )(1  22m
E S ' )  E L ' E L ( 21m
)(
)
E RT
E RT '
E TT
ETT '
S12a 
S
 EX '
S
 ED
( 12m
)(1  11m
( E S  E L ' ))
E TT '
E RT
S
 ED
S
 ED'
S
 E X S12m  E X '
(1  11m
E S )(1  22m
E S ' )  E L ' E L ( 21m
)(
)
E RT
E RT '
E TT
E TT '
(
(
S22a 
S 22m  E D '
E RT '
)( 1 
S11m  E D
S 21m  E X S12m  E X '
ES )  E L ' (
)(
)
E RT
E TT
E TT '
S
 ED
S
 ED'
S
 E X S12m  E X '
(1  11m
E S )(1  22m
E S ' )  E L ' E L ( 21m
)(
)
E RT
E RT '
E TT
ETT '
TRM Calibration
Thru
Reflect
Match
Hard to get broadband absorbers for match
TRL Calibration
Thru
Move the antenna away to
compensate for the thickness
of the short. Move it back
for the next step.
Reflect
Move the antenna away on a
quarter-wavelength and then
back in the original position.
Line
Precise positioning fixtures are expensive
Gated Reflect Line (GRL) Calibration
Step one of two
Two port calibration at waveguide or coax input into antennas
removes errors associated with network analyzer and cables.
ECal, SOLT or TRL
Cal done here
The antennas are removed
for this calibration.
GRL Calibration Continued
Step two of two
Two additional free space calibration standards remove
errors from antennas and fixture.
Line
(empty fixture)
Reflect
(metal plate of
known thickness)
GRL Calibration – How It Works?
GRL Cal Error Model (forward only)
MUT
2-port Cal Terms
1
D
S21
Ms
Tr
2-port Cal Terms
GRL Error
Adapter
S11
Tt
S22
GRL Error
Adapter
Ml
S12
• Coax or Waveguide 2-port Cal corrects errors from end of cable back into the instrument.
• Errors from Antennas and Fixture can be thought of as being lumped into a GRL error adapter.
• The GRL error adapter is quantified by measurements of reflect and line standards.
• The original 2-port Cal is modified to correct for the error adapter.
MUT and GRL Error Adapters
After 2-Port Calibration
MUT
O21
O11
S21
O22
O12
S11
T12
S22
T22
S12
T11
T21
Six Unknowns
O21 = O12
T21 = T12
O11
T11
O22
T22
GRL Calibration – How It Works?
Time Domain of Empty Free Space Fixture
gate
Transmitting
Antenna
Receiving
Antenna
Air
MUT and GRL Error Adapters
After O11 and T11 are embedded into the original 2-Port calibration.
MUT
O21
S21
O22
O12
S11
T12
S22
T22
S12
T21
Four Unknowns
O21 =
O12
O22
T21 = T12
T22
GRL Metal Plate Standard
MUT
O21
P11  P22  1
P21  P12  0
S21
O22
O12
O 21O12
 plate_1  
1  O 22
S11
T12
S22
S12
 plate_2
T22
T21
T21T12

1  T22
GRL Thru Standard (Air)
A11  A22  0
A21  A12  e 0d ,  0   0e 0
 = frequency
0 = permeability of air
e0 = permittivity of air
d = thickness of the metal plate
A 21A12 O 21O12 T22
 air_1 
1  O 22 T22
MUT
O21
S21
O22
S11
O12
T12
S22
S12
 air_2
T22
T21
A 21A12 T21T12 O 22

1  T22 O 22
GRL Calibration – System Considerations
Fixture with Metal Plate
 Determine Sample Position
 Determine Sample Size
 Choose Metal Plate
Metal Plate
GRL Calibration – System Considerations
Choose Time Domain Parameters
Empty Fixture
Air at 3.5nS
Fixture with Metal Plate
Metal Plate at
3.5nS
GRL Calibration – System Considerations
Choose Number of points to Avoid Aliasing
Minumum Number of Points =
Empty Fixture
1 + Range * (Stop Frequency – Start
Frequency)
Where Range is the needed alias
free range in Seconds
Receiving
Antenna
Transmitting
Antenna
20nS
75–110 GHz Standard Gain Form System
75–110 GHz Quasi-Optical (QO) System
QO System Schematic
Additional information available at : http://www.terahertz.co.uk/TKI/Agilent/Agilent_VNA_QO.html
Measurement Results
Real part of Epsilon
Rexolite measured with 110Ghz PNA and GRL Cal
2.57
2.56
2.55
2.54
e'
2.53
2.52
2.51
2.5
Std Gain Horn
QO table
2.49
2.48
2.47
7.500E+10
8.000E+10
8.500E+10
9.000E+10
9.500E+10
1.000E+11
1.050E+11
1.100E+11
frequency (hz)
Free Space Sources of Error
 Sample
 Finite size
 Contact with conducting backplane
 Non-plane-wave illumination
 Mechanical stabilty/alignment of sample and antennae
 Quality of anechoic environment
Free Space Summary
Noncontacting, often
nondestructive
 Sample not contained
 Useful for high
temperatures
 Remote sensing
.
 GRL calibration
 Time domain gating
eliminates errors
Special calibration
considerations
 Requires connectorless
standards (TRL, LRM)
 Tightly controlled distance
from antenna to sample (TRL)
Requires large, flat, thin,
parallel faced sample
Agenda
85070D/85071D Product Overview
 Fundamentals
 Measurement Instruments
 Considerations in choosing a Technique and Fixture
 Measurement Techniques
 Parallel Plate
 Coaxial Probe
 Transmission Line
 Free-Space
 Resonant Cavity

Three Resonance Techniques
Iris-coupled end plates
Post
Sample
 ASTM 2520 (Waveguide TE10n Cavity)
 SPDR (Split Post Dielectric Resonator)
 Split Cylinder Resonator
E
MUT
Copper
Dielectric
resonator
E
MUT
Resonant versus Broadband Techniques

Resonant techniques
 high impedance environment
 reasonable measurements
possible with small samples
 measurements at only a few
frequencies
 well suited for low loss materials

Broadband techniques
 low impedance environment
 requires larger samples to obtain
reasonable measurements
 measurement at “any” frequency
Kramers-Kronig Equations
e ( )  e  
e ( )  
1

1


PV

PV
e ( )
   d
e ( )  e 
    d
Resonant versus Broadband Techniques
Primary source
of measurement
improvement
Secondary
source of
measurement
improvement
Resonant
Technique
Broadband
Technique
Frequency
stability
Vector error
correction
Vector error
correction
Frequency
stability
Resonant Cavity
l
Sample
Dielectric Resonator
Dielectric Resonator
Coupling Loop
z
h
hG
Metal Enclosure
Q0
QS
Iris-coupled end plates
f
fS
Sample
f
Q
fC
e r or r
Resonant Cavity System
Network Analyzer
PNA, PNA-L, ENA, ENA-L
Legacy 8712/14, 8752, 8753, 8719, 8720, 8722, or 8510
CH1 S11 1 U
FS
Co
r
LOG
MAG
PHAS
E
DEL
AY
SMI
CHA
TH
RT
POL
AR
LIN
MAG
Hi
d
SW
R
MO
RE
START
.300
000N MHz
Iris-coupled end plates
Sample
Cavity Fixture
Cavity Methods (Exact and Perturbation)
Resonator (absolute)
TE 01n cavity
Sample fills a significant portion of cavity volume.
Exact theories applied to cavities for low loss
materials.
Cavity perturbation
Transmission line (waveguide) cavity
Sample disturbs (without changing) fields in cavity.
f < 0.1% (recommended frequency shift of the sample)
Measure shift in resonant frequency and Q.
Waveguide Transmission Line Cavity
(ASTM 2520)
Next we will focus on resonance measurements of dielectric
properties using TE10n waveguide resonance cavity. The
method is cavity perturbation method and is base on procedure
described in ASTM 2520 document.
Transmission Line Cavity (ASTM 2520)
Based on ASTM 2520
E-field
Rectangular waveguide cavity propagates TE10n mode
 Sample placed parallel to cavity E-field
 Fibers may be inserted through a fused silica rod

“Test methods for complex permittivity (Dielectric Constant) of solid electrical insulating materials at microwave
frequencies and temperatures to 1650°,” ASTM Standard D2520, American Society for Testing and Materials
Transmission Line Cavity
Transmission Line Cavity
Odd and Even Number of Half
Wavelengths in the Resonator
E field
H field
L
Even number of half wavelengths. The
sample is in the max of the magnetic field,
for magnetic measurements.
Sample
Odd number of half wavelengths. The
sample is in the max of the electric field,
for electric measurements.
Calculation of the Resonance Frequency
0 
L
2
1 p2
 2
2
a L
b
a
f  150
2
1 p
 2
2
a L
f, GHz
a, mm
L, mm
p, number of half wavelengths on L
Cavity Perturbation Algorithm
ASTM 2520 Method
A vertical rod or bar sample is inserted in a TE10n
rectangular waveguide resonant cavity. There is no
need to calibrate the analyzer since only frequency
is measured. Scalar analyzer can be used.
empty cavity
Vc  f c  f s 
er ' 
2Vs f s
sample inserted
Qc
Qs
Vc  1
1 
  
er" 
4Vs  Qs Qc 
Vs is the volume of the sample
fs
fc
f
Vc is the volume of the empty cavity
TE10n Waveguide Cavity
0.004
9.895
9.9375
Transmission |s21|
0.0035
Sample 1
0.003
Empty cavity
Sample 2
0.0025
0.002
0.002
Sample 3
0.001
5 10 4
0
9.8
9.82
9.84
9.86
9.88
9.9
9.92
9.94
9.96
9.98
10
Frequency, GHz
TE10n Waveguide Cavity Calculations
Sample 2 is 2.9 mm x 1.57 mm plastic rod
f c  9.9375 GHz
f s  9.901 GHz
Vc  32.516 cm 3
Vs  0.046 cm 3
Qc  2105
Qs  2029
Vc  f c  f s 
e r  1 
 2.303
2Vs f s
Vc  1
1 
    0.00313
e r 
4Vs  Qs Qc 
Alternative Calculation of Losses (er”)
L, dB
L is the difference of the attenuation of
the empty and loaded with the sample
resonator. This measurement will offer
better sensitivity for low-loss materials,
but there is a need of good calibration.
Transmission
Empty cavity
9.8
9.82
9.84
9.86
9.88
9.9
9.92
9.94
9.96
9.98
10
Frequency, GHz
Vc  f c  f s 
er ' 
2Vs f s
 20L

Vc  10  1 
er" 
4Vs  Qc 


TE10n Waveguide Cavity Calculations
Comparative measurements of the tand using
Q-factor measurement (tand1) and attenuation
measurement (tand2)
Sample
Yellow
Clear
er'
4.08
2.57
Qc
3254
3254
Qs
2067
1214
tand1
7.6x10-3
3.56x10-2
L
4.29
8.9
tand2
8.4x10-3
3.77x10-2
Sources of Error for ASTM Cavity
Network analyzer frequency resolution
 Sample dimension uncertainty and parallel sides
 Approximations in analysis

Cavity Fixtures

Agilent waveguide components

X/P/K/R/Q/U/V/W 11644A calibration kits
(standard section)

ASTM standard D-2520
Customer would need to modify this standard section
of waveguide to make it a resonant cavity.
SPDR (Split Post Dielectric Resonator)
Next we will focus on the Split Post Dielectric Resonator
(SPDR). It provides an accurate technique for measuring the
complex permittivity of dielectric and ferrite substrates and
thin films at a single frequency point in the frequency range
1–20 GHz. The resonator needs to be purchased. It is not
easy to be manufactured like ASTM resonator.
SPDR (Split Post Dielectric Resonator)
SPDR Resonators for different frequencies
SPDR for 10 GHz
Cross-Section of SPDR fixture
l
Dielectric Resonator
hG
Sample
Dielectric Resonator
Coupling Loop
z
h
Metal Enclosure
Measurement Set-Up
PNA Network Analyzer with
installed 85071E software, opt. 300
SPDR fixture
Sample
Choosing the Sample Dimensions for
Known SPDR Frequency
Minimum measurable area
L
E field in plane
h
l
L
Frequency versus Permittivity and Sample
Thickness for 10 GHz Resonator
empty resonator
10.0
f, GHz
9.6
h=0.025 mm
h=0.05 mm
Max recommended
frequency shift
9.2
8.8
8.4
h=0.1 mm
h=0.2 mm
h=0.35 mm
h=0.5 mm
h=0.7 mm
h=0.97 mm
8.0
7.6
7.2
1
10
e r'
100
1000
Sample Related Dimensions of SPDR
Fixtures for Different Frequencies
f, GHz hG, mm l, mm
1
10
130
3.2
3.3
60
5
2
40
10
1
25
15
0.8
17
20
0.6
10
Lf, mm
200
 150*
 150*
 150*
 100*
 100*
* The fixture can be ordered with Lf dimension up to this value,
but is recommended to be less, if there is no special need.
Measurement of Thin Films
Thin Film on Substrate
(1) Measure only substrate
(2) Measure the substrate with the film
Measuring Thin Film not Deposited
on Substrate
f, MHz
Q
h, mm
e r'
5608.59
5601.11
5593.54
5586.08
5578.67
5571.28
5563.96
9400
8000
6890
6080
5480
4480
4970
0
0.100
0.201
0.303
0.406
0.511
0.616
empty
3.19
3.20
3.20
3.20
3.19
3.18
tand,
(x10-4)
empty
49 1
50 2
50 3
49 4
49 5
50 6
# of films
0
1
2
3
4
5
6
Permittivity Calculation
f0  f s
e  1
hf0 K s e r' , h
'
r
 
h -
sample thickness
f0, fs -
the resonant frequency of the SPDR – empty and with sample
Ks -
function computed and tabulated for specific SPDR
Loss Tangent Calculation
1
Q 1  QDR
 Qc1
tan d 
pes
measured unloaded Q-factor of the SPDR with the dielectric sample
Q
f 0 peDR0
f s peDR
QDR  QDR0

Qc  Qc0 K 2 e , h

'
r
QDR, QDR0- Q-factors depending on losses in the
dielectric resonators with and without sample

Qc,Qc0 - Q-factors depending on metal losses of the resonant
fixture with and without the sample

Electric energy filling factor of the sample
pes  he r' K1 e r' , h
Uncertainty of the Real Dielectric Constant
e r'  1 
e r'
e
h
T
h
'
r

Ks e , h
(1)
For most of the samples T is equal to one. Only for thick, large
permittivity samples the value of T increases, but always is < 2.

The most significant contribution to the overall Ks error arises
from coefficients related to the thickness and permittivity of the
dielectric resonators.
Calculation
errors
Total error
e r'
e
'
r
 
The main source of uncertainty of the real permittivity is due to
the uncertainty of the thickness of the sample under the test.
T 1
'
r
f0  f s
hf0 K s e r' , h
h
 0.15  T
h
( 2)
Exact numerical analysis has shown that the Ks errors due to
uncertainty of dielectric resonator thickness and permittivity can
practically cancel out under some conditions. In such case it is
possible to compute Ks coefficients for specific resonant
structures with uncertainties better then 0.15% .
Uncertainty of the Loss Tangent
Depends mainly on the Q-factor measurement uncertainty
Typical uncertainty of 1% with resolution of 2 x 10-5
Split Cylinder Resonator
Next we will focus on the Split Cylinder Resonator. It
provides an accurate technique for measuring the complex
permittivity of dielectric substrates and thin films at several
frequency points. The resonator is not easy to be manufactured
like ASTM resonator.
Split Cylinder Resonator Overview
• relative permittivity uncertainty: e’r ~ 1%
• loss tangent uncertainty: tand < 1x10-4
• measurements in 1 - 30 GHz range
• planar samples
• no sample machining (nondestructive)
• simple measurement procedure
• Originally proposed by Gordon Kent as nondestructive technique.
• Single-frequency technique: only TE011 resonant mode.
• Sample in maximum electric field: high measurement sensitivity
• Later the method was improved by NIST
G. Kent, “Nondestructive permittivity measurements of substrate,” IEEE Trans. Instrum. Meas., vol. 45, pp. 102-106,
Feb. 1996.
Janezic M. and Baker-Jarvis J., “Full-wave Analysis of a Split-Cylinder Resonator for Nondestructive Permittivity
Measurements,” IEEE Transactions on Microwave Theory and Techniques, vol. 47, no. 10, Oct 1999, pg. 2014-2020
Split Cylinder Resonator Overview
Upper Cylindrical Cavity Region
E
MUT
Coupling loop to
Network Analyzer
Lower Cylindrical Cavity Region
Place substrate between two halves of the split-cylinder
resonator. Measure resonant frequency f and quality factor Q
and calculate the permittivity and loss tangent of the substrate.
NIST Improvements
Developed new theoretical model for split-cylinder resonator to
improve accuracy of relative permittivity and loss tangent
measurements:
• Properly model fringing fields in substrate region.
• Include higher-order TE0np modes to broaden frequency coverage.
• Account for conductive losses of cavity walls and endplates.
Janezic M. and Baker-Jarvis J., “Full-wave Analysis of a Split-Cylinder Resonator for Nondestructive
Permittivity Measurements,” IEEE Transactions on Microwave Theory and Techniques, vol. 47, no.
10, Oct 1999, pg. 2014-2020
NIST Theoretical Model - Mode-Matching
Method
Divide geometry
into regions.
Represent fields in each region by finite sum of
normal modes with unknown mode coefficients.
Enforce boundary conditions at junction of
regions to derive system of linear equations.
Simplify system of linear equations and
resonance condition with orthogonality
relations.
NIST Resonator Design
• Precise alignment of two resonator sections.
• Easily adjustable coupling level.
• Designed for use in environmental chamber.
• Accommodates samples up to 5 mm thick.
• In-situ measurement of sample thickness.
NIST Measurement Comparison
Relative Permittivity
Loss Tangent
Split Cylinder Resonator
Advantages
• Accurate nondestructive measurement of dielectric substrates.
• No sample machining necessary.
• Broadband frequency coverage.
• Characterization of thin materials possible.
Disadvantages
• Electric field parallel to the dielectric substrate.
• Difficult to measure loss tangents below 5x10-5.
• Identification of TE0np resonant modes sometimes difficult.
Cavity Summary
Very accurate
Does not provide
broadband
frequency data
Very sensitive to low loss
(to 10-6 for some cavities)
Precise sample shape
required (usually
destructive).
SPDR and SCR methods
are nondestructive
Analysis may be
complex
Summary of Techniques
Loss
Coaxial Probe
High
Transmission Line
Free Space
Medium
Low
Parallel
Plate
50 MHz
Low frequency
Resonant Cavity
5 GHz
RF
20 GHz
Microwave
Open Resonator
Fabry-Perot
60 GHz
40 GHz
Millimeter-wave
Frequency
Measurement Technique Summary
Free Space
Cavity
Transmission
Line
Coaxial Probe
Parallel plate
DC
10 1
10
2
10
3
10
4
10
5
10
6
10
7
Frequency (Hz)
10
8
10
9
10
10
10
11
10
12
Summary of Techniques
er
Coaxial Probe
Broadband, convenient, non-destructive
Best for lossy MUTs; liquids or semi-solids
Transmission Line
e r and r
Best for lossy to low loss MUTs;
machineable solids
Non-contacting
Free Space
e r and r
Resonant Cavity
e r and r
Parallel Plate
Broadband
er
Best for high temperatures; large, flat samples
Accurate
Best for low loss MUTs; small samples,
Substrates, Thin Films
Accurate
Best for low frequencies; thin, flat sheets
Agilent Technologies Instruments and Fixtures
Transmission line software
85071E
Dielectric probe
85070E
Dielectric material test fixture
16453A
16451B
Dielectric test fixture
Liquid test fixture
16452A
Magnetic test fixture
16454A
DC
10Hz
100Hz
1kHz
10kHz
100kHz
1MHz
10MHz
100MHz
1GHz
100GHz
LCR meters/impedance analyzers
4263B, 4284A, 4285A, 4294A
E4991A
Impedance/Material Analyzer
PNA, PNA-L
Network analyzers
10GHz
ENA, ENA-L
Legacy – 8712, 8753, 8720, 8510
Which Technique is Best?
It depends on:











Frequency range
Expected value of er and r
Required measurement accuracy
Material properties (i.e., homogeneous, isotropic)
Form of material (i.e., liquid, powder, solid, sheet)
Sample size restrictions
Destructive or nondestructive
Contacting or noncontacting
Temperature
Cost
And more . . .
Appendix: Other Methods
Open-Ended Waveguide
a
b
 jk
y a
y  e 0

b  x  K 2 a  y  cos  K1 sin 
Y  G  jB 
2 
a 
a
r

  0 0
2
ab k0   
a
a b
4j
k
2
0

, K1  k0 e r

2
 
2

   , K 2  k0 e r
a

2
 
er r
dy dx
2
   , r  x2  y2 .
a
Centrally Located Substrate in a Waveguide
+ analysis is straightforward
+ no errors from air gaps
+ non-destructive for non-metalized sheets
+ simple and inexpensive
− E-fields in x-y plane of the sample (not z)
− frequency limited in the waveguide band
Line Resonators (Stripline)
Rectangular resonator
L
L
L
n

c
er  

 2 f r L  L  
2
L compensates for the extra
capacitance at the end of the line
+ industry-standard method (ASTM D3380, IPC
TM-650 2.5.5.5, MIL-P-13949E)
+ accurate and reproducible to < 1%
+ provides estimate of the dielectric losses
− destructive, large sample, sample preparation
− errors due to air gaps and fringing
− based on stripline (not microstrip)
− limited in range of measurable materials
Line Resonators (Strip and Microstrip)
Ring resonator
 nc 
er  

f
L
 r 
2
d d 

L   d1  2 1 
2 

The ring resonator is not subject
of to errors from end effects.
d1 inner diameter of the ring
d2 outer diameter of the ring
Full-Sheet Resonance
E
W
n
L
m
• entire sheet resonates
• both sides clad
• m and n are number of half wavelength
along sides W and L
7 mm
 c
er  
2 f

2
2
m
n
    
   
 L   W  
2
+ nondestructive
+ suitable to many substrates
+ not sensitive to thickness
+ simple and inexpensive
− fringing and radiation errors
− multiple modes confusing
− difficult to get the losses