Shelley Begley Application Development Engineer Agilent Technologies

Shelley Begley Application Development Engineer Agilent Technologies
Electromagnetic Properties of Materials: Characterization at Microwave Frequencies and Beyond Shelley Begley Application Development Engineer Agilent Technologies Abstract: From stealth materials to dielectric substrates, microwave food products to biofuels, accurate characterization of their electromagnetic properties at microwave and mm-wave frequencies provide engineers with critical information needed for material and circuit design, modeling, research, manufacturing and quality control. Many measurement methods exist, but which to choose is often a mystery. My intent with this seminar is to clear the air by providing an overview of measurement methods, with strengths, limitations and applications of each.

Agenda Definitions Measurement Techniques Coaxial Probe Transmission Line Free-Space Resonant Cavity Summary

Loss Tangent? Dissipation Factor? Permittivity! Dielectric Constant?
Definitions Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. Permittivity relates therefore to a material's ability to transmit (or "permit") an electric field…The permittivity of a material is usually given relative to that of vacuum, as a relative permittivity, (also called dielectric constant in some cases)….- Wikipedia Loss Tangent? Dissipation Factor? Permittivity! Dielectric Constant? There are lots of different terms in use today to describe electromagnetic properties of materials. And lots of confusion on what they all mean and how they relate to each other. So, in the next few slides, I’ll give a definitions of the terms I will be using and what they mean. Permeability!

Permittivity and Permeability Definitions
(Dielectric Constant) interaction of a material in the presence of an external electric field. Permittivity (e), also called dielectric constant, and sometimes designated by the greek letter Kappa, describes the interaction of a material with an external electric field. Kappa is equivalent to epsilon sub r, and is equal to the absolute permittivity, epsilon, relative to the permittivity of free space, epsilon sub zero. And it is a complex number: epsilon sub r prime minus jay epsilon sub r double prime. Which is quite mouthful! So I will drop the sub R. When I say epsilon or permittivity, you can assume I mean the permittivity relative to free space.

(Dielectric Constant) interaction of a material in the presence of an external electric field. To make matters more confusing, the real part of permittivity can also be called dielectric constant or Dk So in an effort to minimize the ambiguity, I will say “the real part of permittivity”.

(Dielectric Constant) Permeability interaction of a material in the presence of an external electric field. interaction of a material in the presence of an external magnetic field. Permeability or mu describes the interaction of a material with an external magnetic field. And it is also a complex number.

(Dielectric Constant) Permeability interaction of a material in the presence of an external electric field. interaction of a material in the presence of an external magnetic field. Both permittivity and permeability are complex but not constant (another reason why the term dielectric constant is ambiguous). Many materials exhibit considerable change over frequency and temperature. Some materials such as iron (ferrites), cobalt, nickel and their alloys have appreciable magnetic properties for which it is valuable to measure permeability; however, many materials are non-magnetic. All materials, on the other hand, have dielectric properties. Complex but not Constant!

Electromagnetic Field Interaction
STORAGE Electric Magnetic Fields Fields Permittivity Permeability MUT When electric and magnetic fields pass through a material, each can interact with that material in two ways: First: Storage: Energy may be exchanged between the field and the material, in a bi-directional (lossless) manner This energy storage is represented by the real part of permittivity or permeability. STORAGE

Electromagnetic Field Interaction
STORAGE Electric Magnetic Fields Fields LOSS Permittivity Permeability MUT Second Loss: Energy may be permanently lost from the field, and absorbed in the material (usually as heat). This energy loss is represented by the imaginary part of permittivity and permeability. STORAGE LOSS

Loss Tangent Dissipation Factor Quality Factor
Another term we will talk about, and you will often see on data sheets is loss tangent. This is also called tan delta. When complex permittivity is drawn as a simple vector diagram, the real and imaginary components are 90o out of phase. The vector sum forms an angle delta with the real axis. If we remember our trigonometry, we recall that the tangent of an angle is equal to the side opposite to the angle divided by the side adjacent to the angle. So, in this case, is the imaginary part of permittivity, divided by the real part of permittivity. This is why the term tan delta came about. Loss tangent is also equivalent to the dissipation factor and one over the quality factor. It is a measure of the energy lost relative to the energy stored. The term Df is also commonly used for Dissipation factor. It is no wonder people get confused, all these terms mean the same thing, Loss Tangent, tan delta, Dissipation factor, and Df. Dissipation Factor Quality Factor

most energy is lost at 1/t
Relaxation Constant t 1 10 100 Water at 20o C f, GHz most energy is lost at 1/t t = Time required for 1/e of an aligned system to return to equilibrium or random state, in seconds. Also of interest to many applications involving liquid and polar materials, for example microwave heating, Specific Absorption Rate, chemical processing, etc.. is the relaxation constant or time, t. For dipolar dielectrics (such as water), t describes the time required for dipoles to become oriented in an electric field. (Or the time needed for thermal agitation to disorient the dipoles after the electric field is removed.) At low frequencies, the dipole rotation can follow the field easily; e’ will be high and e” will be low. As the frequency increases, the loss factor, e” increases as the dipoles rotate faster and faster. The loss factor e” peaks at the frequency 1/t. Here, the dipoles are rotating as fast as they can, and energy is transferred into the material and lost to the field at the fastest possible rate. As the frequency increases further, the dipoles can not follow the rapidly changing field and both e’ and e” fall off. t is one of the terms needed in the Debye equation that is often used to model the theoretical permittivity of polar liquids. This model works very well for water. The other terms are the predicted value of es, the DC or static value of permittivity, and e at infinity.

Techniques Transmission LIne Coaxial Probe Resonant Free Space Cavity
There are many techniques available for measuring the electromagnetic properties of materials. Here are a few common ones that we will go over today. Parallel Plate, Coaxial Probe, Resonant Cavity and Transmission Line including Free Space. These are all commercially available from Agilent. _______ Here’s an overview of the techniques we will be discussing today. Clockwise from the upper left. Parallel Plate: (sometimes called capacitance method) Uses a parallel plate capacitor, with the material sandwiched between. This method uses an impedance analyzer. It is typically used at the lower frequencies, below 1 GHz. Coaxial probe: This method uses an open ended coaxial probe, usually with a network analyzer. It is the easiest method to use for liquids, or soft semi-solids, although very flat hard solids can be measured as well. Agilent offers probes in the RF to microwave frequencies, 200MHz to 50GHz. Resonant Cavity: This method uses a resonant cavity for the sample holder, and a network analyzer to measure the resonant frequency and Q of the cavity, both empty and with the sample present. From this, permittivity can be calculated. This method has the best loss factor resolution. Transmission Line: This method can use a variety transmission “lines” for sample holders with a network analyzer. Lines can be coaxial, waveguide and even free-space is considered a transmission line technique. It is useful for a broad frequency range, from the low microwave region to mm-wave.

Which Technique is Best?
It Depends… So, technique is best? I get asked this all the time. And the answer I give is, it depends…. Which of course isn’t the answer people want to hear. But it’s the truth.

It Depends… on Frequency of interest Expected value of er and mr Required measurement accuracy It depends on Frequency of interest, Expected value, and required measurement accuracy…

It Depends… on Frequency of interest Expected value of er and mr Required measurement accuracy Material properties (i.e., homogeneous, isotropic) Form of material (i.e., liquid, powder, solid, sheet) Sample size restrictions Material properties such as whether it is homogeneous and isotropic, the form of the material– for example liquid, powder, solid, sheet material, and sample size restrictions–is the sample large or small…

It Depends… on Frequency of interest Expected value of er and mr Required measurement accuracy Material properties (i.e., homogeneous, isotropic) Form of material (i.e., liquid, powder, solid, sheet) Sample size restrictions Destructive or non-destructive Contacting or non-contacting Temperature It depends on whether its OK for the measurement destroy the sample or whether for example the sample is a product that needs to ship, whether the sample can be touched or not– with the free space measurement technique, the sample isn’t touched. And, of course temperature. Sometimes its desirable to measure a sample that is very hot or cold.. So as you can see, which technique is best depends on many things. Each method has it’s own strengths and limitations that make it more or less useful for a particular application The rest of this presentation I will give the information needed to make the best decision.

Measurement Techniques vs. Frequency and Material Loss
High Coaxial Probe Transmission line Medium Free Space In an attempt to simplify, here is chart that shows the measurement techniques we will discuss mapped on a chart. The axis are two important determining factors in deciding which technique to choose. On the x-axis we have frequency of interest, from the low MHz to 500GHz– quite a span! And on the y-axis is how lossy the material under test will be At the bottom we have low loss materials and at the top, high loss materials. Resonant Cavity Low Frequency 50 MHz 5 GHz 20 GHz 40 GHz 60 GHz 500+ GHz Low frequency RF Microwave Millimeter-wave

High Coaxial Probe Medium The coaxial probe technique frequency range is 200MHz to 50GHz. It is best for characterizing permittivity of lossy materials. Examples are human phantoms for Specific Absorption Rate tests, tissue samples for medical research… Low Frequency 50 MHz 5 GHz 20 GHz 40 GHz 60 GHz 500+ GHz Low frequency RF Microwave Millimeter-wave

High Coaxial Probe Medium Bio-and chemical samples. Also any sample with a high water content, such as food products that will be heated in a microwave, and many other materials that will be dried using microwaves. Low Frequency 50 MHz 5 GHz 20 GHz 40 GHz 60 GHz 500+ GHz Low frequency RF Microwave Millimeter-wave

High Coaxial Probe Transmission line Medium Free Space The transmission line technique has a frequency range of from around 50MHz to about 75GHz. Above 75GHz, it gets difficult to fit a sample into the microwave transmission line that is used as a sample holder. If you know anything about waveguide sizes, you know how small waveguide in this frequency range is, 75Ghz waveguide is approximately 1x2 mm. So at higher frequencies, free space technique– which is just a variation of the transmission line technique– becomes more practical because everything, including the required sample size, becomes larger and easier to work with. With the free space technique, we can go all the way up to 500GHz and even beyond. By contrast, on the low frequency end, free space becomes more difficult because things become very large. The free space technique works at low frequencies, but at 3-6Ghz, a sample would have to be a few feet wide and at that point it can become easier to fit the sample into a transmission line. Unless of course the sample is a large sheet of material, in which free space may still be a practical solution. Both these techniques are best for characterizing permittivity as well as permeability of medium loss materials. High loss materials can be measured too if the sample is kept relatively thin. Examples of materials suitable for transmission line technique are hard solid materials that can be machined to fit inside a transmission line sample holder, sand, dirt or other powders that can conform to fit inside. Common materials measured with the free space technique are various types of radar absorbing materials such as low observable coatings for military aircraft, as well as other coatings such as painted car bumper materials for collision avoidance. Low Frequency 50 MHz 5 GHz 20 GHz 40 GHz 60 GHz 500+ GHz Low frequency RF Microwave Millimeter-wave

High Coaxial Probe Transmission line Medium Free Space In addition, free space technique is often used for measuring permittivity of radome materials– materials used to cover antenne. Even though these materials are usually fairly low loss, the form factor of the large sheet of radome material fits the technique well and the accuracy of the real part of permittivity is usually adequate for the application. Low Frequency 50 MHz 5 GHz 20 GHz 40 GHz 60 GHz 500+ GHz Low frequency RF Microwave Millimeter-wave

High Coaxial Probe Transmission line Medium Free Space For the highest accuracy permittivity measurements for very low loss materials, the resonant cavity technique is used. The common frequency range for this technique is in the 1Ghz to 20Ghz range, although higher frequency resonant fixtures are available. At high frequencies it can become difficult to separate out the useable resonant frequency modes. Resonant Cavity Low Frequency 50 MHz 5 GHz 20 GHz 40 GHz 60 GHz 500+ GHz Low frequency RF Microwave Millimeter-wave

Coaxial Probe System Calibration is required Computer
(Optional for PNA or ENA-C) Network Analyzer (or E4991A Impedance Analyzer) GP-IB, LAN or USB 85070E Dielectric Probe The next technique we’ll talk about is the Coaxial Probe technque. A typical coaxial probe system consists of a vector network analyzer, and an open ended coaxial probe. The tip of the probe is immersed into a liquid sample under test, or can be pressed against a solid sample and then S11 or reflection coefficent is measured with the network analyzer. Since the math needed to calculate calulate permittivity from the reflection coeffient measurements is not trivial, software is used. This can be run on an external PC or for Agilent PNA series or ENA C network analyzers the software can be run directly on the instrument. Agilent offers a complete solution including probes, calibration short and the software application for these measurements The software controls the network analyzer to calibrate the instrument, set up the measurements, calculate and display the results. In addition there is an application programmable interface into the software so that measurements can be further automated by the user for customized applications. 85070E Software (included in kit) Calibration is required

Material assumptions:
Coaxial Probe Material assumptions: effectively infinite thickness non-magnetic isotropic homogeneous no air gaps or bubbles 11 Reflection (S ) The probe itself is a cut off section of coaxial transmission line that has been sealed so moisture cannot seep into it. Microwave energy generated by the network analyzer is transmitted down to the tip of the probe where some of it is absorbed by the material under test and some of it is reflected back to the network analyzer. Sensitive receivers in the network analyzer can detect small magnitude and phase differences in the reflection due to the dielectric properties of the material under test. The assumptions of the technique are that the sample is endless, or at least as far as the network analyzer can sense and that there are no reflections from the edge of the sample or the sample holder. How far into the material the field extends into the material depends on the material properties, the frequency of the measurement, and the dimensions of the probe, but it is relatively small. First approximation is a hemisphere the outer diameter of the probe. The sample is also assumed to be non-magnetic, isotropic and homogeneous. Air gaps between a solid and the probe tip, and bubbles in a liquid will cause significant errors and should be carefully controlled. er

Three Probe Designs High Temperature Probe
0.200 – 20GHz (low end 0.01GHz with impedance analyzer) Withstands -40 to 200 degrees C Survives corrosive chemicals Flanged design allows measuring flat surfaced solids. Agilent now offers three probe designs. Each has it’s own unique strengths and limitations. The High Temperature probe is Agilent’s original design. It has the lowest frequency coverage of all the probes. It can be used with an impedance analyzer down to 10MHz. It can withstand -40 to 200 degress Celsius. It is made of a stainless steel alloy with a borosilicate glass seal, so it survives relatively corrosive chemicals, although of course not all. The large flange makes it a little easier to measure solid materials.

Three Probe Designs Slim Form Probe 0.500 – 50GHz
Low cost consumable design Fits in tight spaces, smaller sample sizes For liquids and soft semi-solids only The Slim Form Probe is a super slim, low cost consumable design. Since it the outer diameter is smaller the high temperature probe, it works at higher frequencies, 500 MHz to 50Ghz. It’s relatively low cost makes it ideal for measuring materials that would destroy the probe, such as curing epoxy or cement. Because the tip is so narrow and the tip is not as flat as the other probes, it is not recommended for measuring hard solids.

Three Probe Designs Performance Probe
Combines rugged high temperature performance with high frequency performance, all in one slim design. 0.500 – 50GHz Withstands -40 to 200 degrees C Hermetically sealed on both ends, OK for autoclave Food grade stainless steel The Performance Probe combines rugged high temperature performance with high frequency performance all in one slim design. It withstands extreme temperatures like the high temperature probe, and goes to 50Ghz like the slim form probe. In addition, it is hermetically sealed on both ends making it ideal for applications that need sterile equipment because it can be autoclaved. It is made from a food grade stainless steel and borosilicate glass that can survive relatively corrosive chemicals.

Coaxial Probe Example Data
This is some example data from the Agilent 85070E Dielectric Probe Kit. The X-axis is frequency, from 500MHz to 50GHz, and in this case, the Y-axis is the real part of permittivity. Our samples are different alcohols. This was a fun experiment we did, to see if we could determine the perfect martini from dielectric measurements. The bottom blue data is straight gin, and the red data is straight vermouth. Then we used a micro pippette to get different concentrations of the vermouth in the gin. I have only two of the data traces shown here, but we measured a lot.

Coaxial Probe Example Data
Here’s a look at the same samples, only this time the Y-axis is the imaginary part of permittivity, and you can see the relaxation constant peak is at different frequencys for the gin, vermouth and combinations.

Martini Meter! Infometrix, Inc.
So, for fun, we brought the data into a Chemometric software package, Perouette by Infometrix. In this case we did a linear regression. Now we can determine what mixing ratio we like and make the perfect martini every time. We believe we can get to conserviatively 0.1% level of detection of vermouth in gin. Infometrix, Inc.

Transmission Line System
Computer (Optional for PNA or ENA-C) Network Analyzer GP-IB, LAN or USB Now we will move on to the Transmission line system. A typical transmission line system consists of a vector network analyzer, with appropriate calibration kit, and a sample holder connected between the two network analyzer ports. As with the coaxial probe technique, software calculates permittivity, but this time from full 2 port calibrated S-parameter measurements. Agilent offers this software and several varieties of transmission line sample holders. 85071E Materials Measurement Software Sample holder connected between coax cables Calibration is required

Transmission Line Sample Holders
Coaxial Waveguide Transmission line sample holders can be made from coaxial airlines or waveguide straight sections. Both are widely available in different frequencies from Agilent and other connector manufacturers. Samples must fit snugly inside. This technique works best for hard solids that can be machined, but it is also possible, although more difficult, to contain liquids and powders inside these using dielectric dams. Coax sample holders offer broadband frequency coverage, but it is more difficult to machine solid materials to the shape needed to fit inside. Waveguide straight sections offer banded frequency coverage, but it is much easier to machine solid materials to fit inside.

Material assumptions:
Transmission Line Material assumptions: sample fills fixture cross section no air gaps at fixture walls flat faces, perpendicular to long axis Known thickness > 20/360 λ l Reflection (S ) 11 Transmission 21 The material sample is assumed to completely fill the cross section of the fixture with no air gaps, have smooth flat faces and to be uniform throughout. Unlike the coaxial probe technique the sample is not assumed to be endless. Because we will measure both reflection and transmission through the material we need to know how thick it is. The sample must be long enough to contain enough of the wavelength to be measurable. Ideally we recommend a minimum of 20 degrees, but this is conservative and with today sensitive network analyzers, reasonable measurements can be obtained with shorter samples. er and mr

Measured S-parameters
Transmission models in the 85071E Software Algorithm Measured S-parameters Output Nicolson-Ross S11, S21, S12, S22 εr and μr NIST Precision εr Fast Transmission S21, S12 Poly Fit 1 Poly Fit 2 S12, S21 Stack Two S21, S12 (2 samples)

Measured S-parameters Single Double Thickness
Reflection models in the 85071E Software Algorithm Measured S-parameters Output Short Backed S11 εr Arbitrary Backed Single Double Thickness S11 (2 samples) εr and μr

Transmission Example Data
This is an example of transmission line data. Frequency, from GHz, is on the x-axis and we are showing the real and imaginary parts of permittivity on the y-axis. The sample is an approximately 1mm thick sheet of radar absorbing material.

Transmission Example Data
This is an example of transmission line data. Frequency, from GHz, is on the x-axis and we are showing the real and imaginary parts of permeability on the y-axis. The sample is an approximately 1mm thick sheet of radar absorbing material.

Transmission Free-Space System
Computer (Optional for PNA or ENA-C) Network Analyzer Sample holder fixtured between two antennae GP-IB, LAN or USB 85071E Materials Measurement Software The free-space technique is just a variation of the transmission line technique and uses the same algorithms to calculate permittivity and permeability. A typical free-space system consists of a vector network analyzer, two antennae facing each other with a sample holder between them. Again, software is needed to convert the S-parameter output of the network analyzer to dielectric and magnetic properties. Since calibrating a network analyzer in free space is non-trivial, Agilent developed an innovative and easy calibration process. The free-space configuration overcomes some of the difficulties of the trying to fit samples into transmission line sample holders. And, because the sample is fixture in free space, it is isolated from the other hardware in the system. This can be very useful in a variety of situations. Calibration is required

Non-Contacting method for High or Low Temperature Tests.
Because the free-space technique is non-contacting, it is useful for measuring materials, such as ceramics, that need to be heated or cooled to temperatures that would cause problems for the network analyzer, cables and connectors. The sample can be placed inside a Temperature control unit with microwave windows allowing the energy radiating from the antennae to transmit through and reflect off the sample. An alternative method is to heat the sample past the desired temperature and measure it as it cools down, which eliminates the need for the temperature chamber. Free Space with Furnace

Transmission Free-Space
Material assumptions: Flat parallel faced samples Sample in non-reactive region Beam spot is contained in sample Known thickness > 20/360 λ l Reflection (S11 ) Transmission (S21 ) The free space technique is best for thin flat parallel faced materials, or other materials that can be formed into this shape. The sample must be far enough away from the antennae to be out of the reactive region, greater than l, ideally in far field or 2d2/l, where d is the largest dimension of the antenna .Samples must be large enough to contain the 3dB beam spot. At low frequencies, it can be a problem to get samples large enough. But, as the frequency goes up everything gets smaller, and at mm-wave frequencies its much easier to manage than trying to fit a sample into a tiny transmission line. Focused beam antennas can help control sample size requirements. In addition, they condition the beam to improve performance. Just like the transmission line technique, the sample must be thick enough to contain ideally 20 degrees of the wavelength of interest. Where at low frequencies it can be difficult to made the sample long enough, at mm-wave frequencies, samples can be very thin. In fact, it can be difficult to make them thin enough. Samples thicker than 1 wavelength can create multiple root mathematical errors. Understanding when this occurs allows the user to avoid potential errors due to this. er and mr

Free Space Example Data
This is an example of transmission free space data. Frequency, from GHz, is on the x-axis and we are showing the real part of permittivity on the y-axis. The samples is Rexolite. Three transmission models included in the 85071E software are compared, NIST Precision model, developed by Jim Baker Jarvis at NIST Boulder CO, USA; and the Fast and poly-fit models developed by Philip Bartley for HP/Agilent.

Resonant Cavity System
Computer (Optional for PNA or ENA-C) Network Analyzer GP-IB or LAN OK, were down to the last technique. The Resonant cavity system consists of a vector network analyzer, a resonant cavity fixture connected between two ports. And software to calculate permittivity from the network analyzer measurements. This time though, permittivity is calculated from two measurements of the resonant frequency and Quality Factor, also called Q factor or Q of the cavity and the normal vector network analzyer calibration is not needed. First measurement is of the empty cavity and the second is of the cavity with the sample inserted. With the resonant cavity system, we switch from multipoint broadband or banded measurement results to measurement results at a single frequency. But, the trade off is worth it if the highest accuracy and resolution is needed. Resonant Cavity Software Resonant Cavity with sample connected between ports. No calibration required

Resonant Cavity Fixtures
There are many different types of resonant structures. Pictured here are a few that Agilent’s Resonant Cavity software support. Connected to the network analyzer we see the 10Ghz Split Cylinder resonator, which was recently adopted as an IPC standard test method. The Split Post Dielectric Resonator developed by Dr. Jerzy Krupka at QWED in Poland is in the picture with the blue background, and an older ASTM waveguide resonator behind. For the Split Cylinder and the Split Post resonators the sample must be in the form of a thin flat sheet. For the ASTM resonator, the sample is a long rod or rectangle. ASTM 2520 Waveguide Resonators Agilent Split Cylinder Resonator IPC TM Split Post Dielectric Resonators from QWED

Resonant Cavity Technique
fc = Resonant Frequency of Empty Cavity fs = Resonant Frequency of Filled Cavity Qc = Q of Empty Cavity Qs = Q of Filled Cavity Vs = Volume of Empty Cavity Vc = Volume of Sample empty cavity Q c S21 f f c Here’s a closer look at how it works. Agilent software supports three methods, Split Cylinder, Split Post and ASTM all which use the same basic principle of measuring frequency and Q shift . Shown here is the ASTM math which is the easiest to understand and explain. The Q and resonant frequency of the cavity is measured, first with no sample… ASTM 2520

fc = Resonant Frequency of Empty Cavity fs = Resonant Frequency of Filled Cavity Qc = Q of Empty Cavity Qs = Q of Filled Cavity Vs = Volume of Empty Cavity Vc = Volume of Sample empty cavity sample inserted Q c Q s S21 f f f s c And then measured again with the sample inserted. ASTM 2520

fc = Resonant Frequency of Empty Cavity fs = Resonant Frequency of Filled Cavity Qc = Q of Empty Cavity Qs = Q of Filled Cavity Vs = Volume of Empty Cavity Vc = Volume of Sample empty cavity sample inserted Q c Q s S21 f f f s c When the sample is inserted into the cavity, the resonant frequency will shift downward due to the real part of permittivity… ASTM 2520

fc = Resonant Frequency of Empty Cavity fs = Resonant Frequency of Filled Cavity Qc = Q of Empty Cavity Qs = Q of Filled Cavity Vs = Volume of Empty Cavity Vc = Volume of Sample empty cavity sample inserted Q c Q s S21 f f f s c And the Q will degrade-- meaning the 3dB bandwidth of the resonance will widen, due to the imaginary part of permittivity. The resonant frequency and Q of the empty cavity are mostly determined by its dimensions. Also, the accurate determination of the volume of the sample is important. Interestingly, the vector network analyzer error correction is not important, so it makes this, the most accurate technique, also one of the easiest techniques. ASTM 2520

Resonant Cavity Example Data
This is example data from our 10GHz Split Cylinder Resonator.

Resonant vs. Broadband Transmission Methods
Low Loss materials Yes er” resolution ≤10-4 No er” resolution ≥10-2 Thin Films and Sheets 10GHz sample thickness <1mm 10GHz optimum thickness ~ 5-10mm Calibration Required Measurement Frequency Coverage Single Frequency Broadband or Banded Here’s a look at the trade offs between the Resonant technique and the Transmission technique. First consideration on the list is the suitabiliy for measuring low loss materials such as ceramic or composite substrates. The Resonant technique has better accuracy and resolution for measuring the imaginary part of permittivity and loss tangent. The resolution for the resonant technique for the Split Post and Split Cylinder technique is equal or better than For the broadband transmission technique, it’s closer to 10-2 or 3. The accuracy of the transmission techqnue is largely determined by the quality of the vector calibration. The resonant technique accuracy resolution is determined by the Q factor of the empty resonant cavity fixture. Both the Split Cylinder and the Split post resonators have a very high Q . The resonant cavity technique is particularly suited for thin film and sheet materials. For both the Split Cylinder and Split Post resonators, the ideal sample thickness is 1mm and below. The sample size requirement for the Split Cylinder stays the same, no matter what frequency, but with the Split post resonator, the sample size scales with frequency. For lower frequencies, the sample must be larger, and for higher frequencies the sample must be smaller. As I already mentioned, there is no vector calibration needed for the resonant technique, but broadband transmissions techniques do require it. And lastly, freqeuncy coverage. For the resonant technique each measurement results in one complex data point, real and imaginary parts of permittiivy. The Split Post resonator fixtures are tuned to measure one frequency mode each. So, to get data at multiple frqeuncy points, multiple fixtures must be used. With the split cylinder resoantor, it is possible to use muliple resonant frquencies in the same fixture. Which points these are are determined by the electrical properties of the material under test and the samples thickness.

Materials Ordering Convenience Specials
Model Number Description 85071E E19 E03 E04 E15 E07 Split Post Dielectric Resonators from QWED 1.1GHz 2.5GHz 5GHz 15GHz 22GHz E02 E01 E22 E18 E24 Quasi-optical products from Thomas Keating Ltd. 60-90GHz – Quasi-optical Table 75-110GHz – Quasi-optical Table 90-140GHz – Additional set of horns for above tables GHz – Additional set of horns for above tables GHz – Additional set of horns for above tables

For More Information Visit our website at:
For Product Overviews, Application Notes, Manuals, Quick Quotes, international contact information… For more information, please visit our website at where we have application notes, product overviews, manuals, pricing, as well as domestic and international contact information

References R N Clarke (Ed.), “A Guide to the Characterisation of Dielectric Materials at RF and Microwave Frequencies,” Published by The Institute of Measurement & Control (UK) & NPL, 2003 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 “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 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 J. Krupka , A.P. Gregory, O.C. Rochard, R.N. Clarke, B. Riddle, J. Baker-Jarvis, “Uncertainty of Complex Permittivity Measurement by Split-Post Dielectric Resonator Techniques,” Journal of the European Ceramic Society No. 10, 2001, pg “Basics of Measureing the Dielectric Properties of Materials”. Agilent application note EN AM. Nicolson and G. F. Ross, "Measurement of the intrinsic properties of materials by time domain techniques," IEEE Trans. Instrum. Meas., IM-19(4), pp , 1970. Improved Technique for Determining Complex Permittivity with the Transmission/Reflection Method, James Baker-Jarvis et al, IEEE transactions on microwave Theory and Techniques vol 38, No. 8 August 1990 P. G. Bartley, and S. B. Begley, “A New Technique for the Determination of the Complex Permittivity and Permeability of Materials Proc. IEEE Instrument Meas. Technol. Conf., pp , 2010.

Shelley Begley Application Development Engineer Agilent Technologies

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