1. Shelley Blasdel Begley
Implementing the Split Cylinder Resonator Method for Measuring Complex Permittivity of Low Loss Materials
Shelley Blasdel Begley
Abstract: Implementing the Split Cylinder Resonator Method for Measuring Complex Permittivity of Low Loss Materials
Short Version:
The Split Cylinder Resonator method was recently adopted by IPC as standard test method TM for complex permittivity of low loss dielectric materials. The standard defines much of the measurement process, but leaves some critical parameters up to the user. This paper will discuss considerations needed to make the method successful: Frequency and quality factor determination from network analyzer measurements, initial estimate of the real part of permittivity, avoiding interfering modes that may degrade measurement accuracy and sample thickness measurement.
Long version
Permittivity is a complex quantity consisting of a real part (dielectric constant) and an imaginary part (loss factor). From this, the loss tangent (loss factor/dielectric constant) can be calculated. The knowledge of a material’s permittivity is becoming increasingly important to engineers and scientists involved in component, circuit board and radome design, as well as for manufacturing quality control and incoming inspection. Resonant measurement techniques are the most precise methods for determining the loss tangent of low loss materials.
The Split Cylinder Resonator method was recently adopted by IPC as standard test method TM for complex permittivity of low loss dielectric materials. The standard defines much of the measurement process, but leaves some critical parameters up to the user. This paper will discuss the following considerations needed to make this successful.
Frequency and Quality factor determination from network analyzer measurements. Process and relative strengths of different measurement techniques will be discussed.
Initial estimate of the real part of permittivity. In addition to the TE011 mode and other useful TE0np modes, a dense population of other modes exist in the split cylinder resonator which can make it difficult to select the desired response to measure. An initial value for the real part of permittivity can be used to calculate the frequency of the desired TE0np mode after the sample has been introduced into the split cylinder resonator.
Identifying interfering modes that may degrade measurement accuracy and what can be done to avoid them.
Sample thickness measurement. Considerations for various types of materials.
Author: Shelley. Begley, Agilent Technologies, Santa Rosa California.
The author would like to thank
Philip Bartley, PhD, Innovative Measurement Solutions, Inc., Portsmouth, Virginia
Michael Janezic, PhD, NIST, Boulder, Colorado
Stoyan Ganchev, PhD, Agilent Technologies, Englewood, Colorado
for their contributions to this paper and continuing support.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

2. Outline Definition of Permittivity
Overview of the Split Cylinder Method
A Walk Through the Process
Today we’ll be talking about the Split Cylinder Resonator method for measuring complex permittivity of low loss materials. First, I’ll go over the definition of permittivity and other related terms I’ll be using in the presentation. ,Then, I’ll give an overview with some general and technical information about the method. Then, we’ll take a walk through the process, with the intention of giving you a practical guide for successful implementation of the method.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

3. Definition of Permittivity
Permittivity describes the interaction of a material in the presence of an electric field.
Permittivity, is one of the fundamental electromagnetic properties of materials. It describe how a material interacts with an externally applied electric field.
Kappa, or Epsilon sub r, is the absolute permittivity relative to the permittivity of free space, and it a complex number, epsilon sub r prime minus epsilon sub r double prime. Often in speaking and writing, the sub r is dropped, and in order not to totally tung tie myself, I will also do this. So, when I say permittivity, or Epsilon, I mean the permittivity relative to free space.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

4. Definition of Permittivity
Permittivity describes the interaction of a material in the presence of an electric field.
storage
Measure of how much energy from an external electric field is stored in the material.
The real part of permittivity (er’) is a measure of how much energy from the external electric field is stored in a material. In the presence of a sinusoidally changing electric field, the energy is stored during part of the cycle, and returned to the field, in a later part of the cycle. This happens over and over as long as the field is present and changing.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

5. Definition of Permittivity
Permittivity describes the interaction of a material in the presence of an electric field.
storage
Measure of how much energy from an external electric field is stored in the material.
Other terms you’ll hear, meaning the real part of permittivity are dielectric constant and Dk.. However, Kappa, is also called sometimes dielectric constant. So, I will try to stick to the term permittivity to avoid ambiguity.
aka Dielectric Constant Dk
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

6. Definition of Permittivity
Permittivity describes the interaction of a material in the presence of an electric field.
storage
loss
Measure of how much energy from an external electric field is stored in the material.
Measure of how much energy from the electric field is lost.
The imaginary part of permittivity represents the loss of the energy from the electric field. This energy is lost to the field forever, due to heat or some other mechanism.
aka Dielectric Constant Dk
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

7. Definition of Permittivity
Permittivity describes the interaction of a material in the presence of an electric field.
Complex
but not Constant!
storage
loss
Measure of how much energy from an external electric field is stored in the material.
Measure of how much energy from the electric field is lost.
And, of course we don’t want to forget that even though often called Dielectric “Constant”, permittivity is not constant. It is not constant over frequency, temperature, humidity, substrate batch, vendor… There are a lot of things can change the permittivity and impact not only your materials electrical performance.
aka Dielectric Constant Dk
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

8. Loss Tangent
One more term that is very important to our discussion today is loss tangent. 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 (er’).
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

9. Loss Tangent Dissipation Factor Quality Factor skip
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

10. Loss Tangent Dissipation Factor Aka Tan Delta Df Quality Factor
If we remember our trigonometry, we know that in a right angle triangle, the tangent of the angle delta, is equal to the opposite side over the adjacent side. So, Loss tangent, also know as tan delta, Dissipation Factor, or Df, is the ratio of the energy lost to the energy stored per cycle. It is often used as a figure of merit for dielectric materials because it represents the relative “lossiness” of a material.
Quality Factor
Dissipation Factor
Aka Tan Delta Df
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

11. Overview of the Split Cylinder Method
Sensitive Resonant method for measuring complex permittivity Useful for thin film and low loss sheet materials. Originally proposed by Gordon Kent, improved by NIST Boulder, CO. Adopted as IPC Standard TM
Now will look at the basic components of the Split Cylinder Resonator method.
Since the Split Cylinder method is a resonant method, it has enough sensitivity to measure low loss and thin film materials. The accuracy for the real part of permittivity is around 1-2 percent and the loss tangent resolution is on the order of 10^-4.
The method was originally proposed by Gorden Kent in the 1980s for non-destructive test because the sample does not have to be machined to fit inside the resonator fixture.
The method was improved significantly in 2003 by Dr. Michael Janezic of NIST, Boulder CO, who developed a mode matching model of the split cylinder resonator that extends the frequency coverage of the fixture from the original use of just the TE011 mode to higher order odd numbered TE0np modes.
Recently, the method, using the Dr. Janezic’s model, was adopted by IPC as a standard test method for printed circuit board materials. It is currently being investigated as a standard test method for Low Temperature Co-Fired Ceramic ( LTCC) materials.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

12. Split Cylinder Resonator System
PNA, PNA-L, PNA-XNetwork Analyzer
Optional Computer
LAN
The Split Cylinder Resonator system consists of a network analyzer, Agilent PNA-series or just off the press, the new 20GHz ENA-C, with the Agilent 85072A Split Cylinder resonator connected between ports one and two. Permittivity is calculated from measurements of the frequency and Q, first with the fixture empty and then filled with the material under test. The Agilent Split Cylinder Resonator has a built in micrometer, you can see the handle on the right side of the fixture, which automatically measures the thickness of the sample as it is being loaded into the fixture.
Agilent 85071E with option 300 Resonant Cavity software provides a graphical user interface, instrument control, determines the frequency and Q using a circle fit method (which we’ll talk about later) , and calculates permittivity using the algorithms developed by Dr. Janezic at NIST, and standardized by IPC.
Agilent 85071E-300 Software runs on optional PC or Network Analyzer
85072A 10GHz Split Cylinder Resonator and sample
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

13. Overview of the Split Cylinder Method
Here’s a closer look at a side view of the Agilent Split Cylinder Resonator.
The split cylinder resonator is a cylindrical resonant cavity separated into two halves. The sample is loaded into the gap between them, which you can see clearly in this photo.
Side View
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

14. Overview of the Split Cylinder Method
Here I’ve superimposed a machine drawing of the cylinders with the sample inserted on the photograph so you can see where they are in relationship to everything else.
Side View
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

15. Overview of the Split Cylinder Method
If we take a look at just the drawing…
Side View
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

16. Overview of the Split Cylinder Method
And zoom in a little, we can get a better look at just the two cylinder halves with the sample between them.
The cylinder half on the left side is fixed, where the cylinder half on the right side adjusts along the z axis, allowing the gap between the cylinders to accommodate varying sample thicknesses.
In order to excite resonant modes in the cavity, coupling loops are introduced through a small hole in the side of each cylinder half.
One other thing you can see from this drawing is that because of the horizontal configuration with the cylinders on their sides, the sample can extend infinitely above them. This allows for non-destructive test of large sheets of material. Where as if the cylinders were vertical, one on top of other, the support structure for that configuration would limit the size of the sample.
Not shown in this drawing, but critical to measurement performance, the horizontal configuration allows for the adjustable cylinder half to ride on a precision slide mechanism which maintains the perfect alignment with the fixed cylinder half.
Side View
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

17. Overview of the Split Cylinder Method
So, now we are looking at just the sample, as if it were still between the cylinders in the Split Cylinder Resonator. The cylinders are not in the picture so you can see the sample. And because I’m not that good of an artist.
We are going to be measuring TEnmp modes that have been excited in the resonator, where m= 0, and p, which is the number of half wavelengths along the cylinder z axis, is an odd integer. For these modes, the maximum electric field is between the two cylinder halves, where we’ve placed our sample. And, the orientation of electric field is parallel to the sample and perpendicular to the z axis of the cylinder halves.
Transverse Electric Modes for cylindrical cavities are described using cylindrical coordinates, r, θ, z, where m=r, n= θ, and p=z.
Electric Field Orientation for TEmnp Modes
Where m = 0 and p is odd.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

18. Overview of the Split Cylinder Method
;To illustrate, I’ve drawn 3, a nice odd integer, half wavelengths along the z-axis of the cylinders so you can see that the middle peak is centered where the sample is. So, for TEmnp modes when p, the number of half wavelenghs = 1 or 3, or any other odd number, the maximum field is at the sample. But, if p were an even number, for example 2, you can see the sample would be where the field was at its minimum.
Electric Field Orientation for TEmnp Modes
Where m = 0 and p is odd.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

19. Overview of the Split Cylinder Method
Recall that at these TE0n odd number p modes, the electric field orientation is parallel to the sample. This is a consideration if your material is significantly anisotropic, for example due to a glass weave or some other structure within the material, because field orientation during test will not represent the field orientation during the materials use. How much this effects the measured permittivity value depends on how anisotropic the material is. For slightly anisotropic materials, and of course for homogenous materials, such as ceramics or thin films, this is not a concern.
Field orientation can be significant
if sample is anisotropic
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

20. Overview of the Split Cylinder Method
Measure Empty and Sample filled Resonator
Real part of permittivity is a function of Frequency shift
Loss tangent is a function of decrease in Q factor
Also needed: Sample thickness Qo fo f Qs fs
So, how do we get permittivity from these TE0n odd numbered p modes that are excited in the Split Cylinder Resonator? We’re going to measure the resonant frequency and Quality factor, also called Q, of the Split Cylinder Resonator, first empty and then with the sample inserted. In this picture the blue trace shows a transmission measurement, S21, of our resonant mode’s peak in the empty Split Cylinder Resonator.
When the sample is inserted, the resonant frequency will shift downward, shown by the red trace that’s shifted to the left in this picture. The frequency shift is due to the sample’s real part of permittivity.
Also, somewhat harder to see in the picture, the peak’s Q will degrade, and that is due to the Loss Tangent the sample.
So, by making these two measurements, we can calculate permittivity and loss tangent. Using the mode matching model developed at NIST in Boulder, Colorado, permittivity and loss tangent can be calculated at the first usable mode, which is the TEnmp mode where n=0, m=1, and p= the odd integer 1, so it’s the TE011 mode, as well as higher order TE0n odd numbered p modes. In the Agilent Split Cylinder Resonator the TE011 mode is at 10GHz.
One other thing: To make the calculation, we also need to know the sample’s thickness. When the sample is loaded into the split cylinder resonator, the resonant frequency always shifts downward so the measurement frequency is always lower than the frequency of the empty split cylinder resonator. The amount of frequency shift is dependent on the real part of permittivity and thickness of the sample.
By varying the thickness of the sample, it may be possible to target a specific measurement frequency.
It is also possible that the measurement frequency may shift down into a range where interference from other non-TE modes can cause distortion and decrease the accuracy of the measurement. Increasing or decreasing the thickness of the sample may shift the measurement frequency away from the interfering mode.
The quality factor, or Q , of the split cylinder resonator will also always decrease when the sample is loaded into the split cylinder resonator. The amount of decrease is dependent on the loss tangent and the thickness of the sample. Thick or lossy materials can decrease the Q enough to cause the split cylinder resonator not to resonate properly making it difficult or impossible to measure these materials. Making samples thinner may help increase the Q factor, but for some lossy samples it may not be possible to make them thin enough to measure. Therefore the split cylinder resonator is only recommended for low loss materials.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

21. Process Flow Qo Qs f fs fo
Now we are going to walk through the measurement process, with the intent of sharing the knowledge and practical experience I gained working on the team developing the Agilent products so that you can be successful using the Split Cylinder Resonator method.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

22. Process Flow Qo f fo
First step is to measure the resonant frequency and Q of the empty Split Cylinder Resonator.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

23. Measure Empty Split Cylinder Resonator
In this step the adjustable cylinder half on the right side of the Split Cylinder Resonator fixture, is moved all the way over to the left as far as it will go, so that the two cylinders are touching and the cavity is closed. On the Agilent Split Cyinder Resonator, this by done turning the built in micrometer handle on the right side of the fixture, which moves the adjustable cylinder half on a precision slide mechanism and keeps it perfectly aligned with the fixed cylinder half. Click on the Agilent’s software big measure button, and it automatically sets up the PNA series, and now also ENAC, network analyzer with the correct frequency, number of points, IF Bandwidth and power settings to measure the TE011 mode.
Agilent Software
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

24. Measure Empty Split Cylinder Resonator
S21 of TE011 Mode
Resonator should be loosely coupled
Adjust peak between 55-65dB
The first thing we will see a narrow peak. This is S21 of the TE011 mode of the Split Cylinder Resonator which occurs at 10G, plus or minus 0.03Ghz, with a Q of greater than 20,00
The resonator is assumed to be unloaded. But because it is actually loaded by the network analyzer connected to it through the coupling loops, we must keep it as loosely coupled as possible. Since the PNA has such a low noise floor, we can set the coupling to dB and still make good measurements. On the Agilent Split Cylinder Resoantor, the coupling is easily adjusted by turning the large knobs on the top of the fixture. Adjusting to the correct value can be done by observing the resonant peak on the network analyzer display, or the Agilent software provides an easy to use graphical tool. Once the coupling is set, the Agilent software automatically triggers the measurement and stores the data for later computation.
Agilent Software
Agilent Software guide
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

25. Frequency and Quality Factor determination
So, now we have acquired our S21 data from the network analyzer. But, for the loss tangent calculation, we need to know the Q. Q is a measure of the ratio of energy stored in a resonant structure over the energy lost and it is critical to know this as accurately as possible. How do we get the most accurate Q-factor from our S-parameter measurement?
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

26. Frequency and Quality Factor determination
Scalar Techniques
3dB Bandwidth
Weighted Least Squares (WLS)
Resonant Curve Area (RCA) f0
3dB Δf
There are many ways to determine the Frequency and Q of a resonant structure from measured transmission coefficient. The most obvious way is to use the built in 3dB bandwidth function in the network analyzers, but this is not the most accurate method. Since the measurement only uses three data points, any trace noise at all can cause significant error. Other more accurate methods have been developed, Weighted Least Squares and Resonant Curve Area are two good scalar methods [4]. But, they involve additional computation not built into the network analyzer. SInce we decided our software needed to automate the Q measurement, we decided to investigate which method is the best.
S21
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

27. Frequency and Quality Factor determination
Vector Technique
Circle Fit fo
The method we chose for our software is the Circle fit method which uses both amplitude and phase information.
In the complex plane, the transmission coefficient response (measured as S21 or S12) of a resonance traces out a circle with the pole close to the origin (0,0), the resonant frequency directly opposite, and the 3dB points a quarter circle away on each side. Fitting a circle to the measurement trace minimizes the error due to noise. [3] [4] The frequency and Q can be calculated from the above equation, where:
L is a Leakage vector between the origin and the pole which cannot be seen in the above polar plot because it is too small.
d is the amplitude at resonance
e-2jδ is a phase factor
j = √-1
S21
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

28. Frequency and Quality Factor determination
Method Comparison
3dB Bandwidth
Weighted Least Squares (WLS)
Resonant Curve Area (RCA)
Circle Fit
When we compared results from the different methods, we found the circle fitting technique [3] [4] to be the most repeatable. Since it is a vector method, it takes advantage of the vector capabilities of today’s modern network analyzers. It is the method we chose to use in Agilent Resonant Cavity Software.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

29. Process Flow
Now we are done with measuring the empty fixture. Agilent Resonant Cavity software automated the whole step.
And by the way,measuring the empty fixture only has to be done once at the 10GHz TE011 mode, even if we measure multiple samples or the same sample at a higher order mode.
So, now we are on to the next step measuring the sample thickness
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

30. Measure Sample Thickness
Sample is assumed to be a uniform known thickness
Best results: 0.1 to 3mm thick, ideally ~1mm
Thickness uncertainty <0.02mm
Minimize imperfections due to:
Flatness
Straightness
Parallelism
The sample is assumed to be a uniform, known, thickness. For best results keep sample between 0.1 and 3mm thick, ideally around 1mm. Thin film materials can be stacked to build up thickness. Thicker samples can be also measured, but accuracy is degraded.
To get the best accuracy, you need to minimize the best you can imperfections due to flatness, straightness and parallelism.
But, of course, no sample is ever going to have perfect form. Using a thickness measurement technique that will average out these imperfections will help minimize the error.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

31. Sample thickness measurement
Conforming samples such as thin films and PCBs
Samples will be straightened out by cylinders.
Recommend Agilent built in micrometer or mean of multiple thickness measurements.
Rigid samples such as Ceramics
Samples will not be straightened out by cylinders.
Recommend mean of multiple thickness measurements.
fixed
cylinder
half
adjustable
coupling
loop
sample z
One benefit of the split cylinder resonator for materials that are not totally rigid, such as printed circuit board materials or thin films is that pressure from the cylinders closing can straighten out the material. For these materials, and the built in micrometer on the Agilent Split Cylinder Resonator will have an averaging effect on the thickness measurement.
On the other hand, Rigid samples like ceramics will not be straightened out, so it is important that the material be as straight as possible to begin with. Also, the built in micrometer on the Agilent fixture will deliver the maximum material condition, if this doesn’t represent the mean thickness, it is recommended to instead use a mean of multiple measurements using a good hand held micrometer.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

32. Process Flow Qs f fs
Now we are going to measure the Split Cylinder Resonator with the sample inserted between the cylinder halves.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

33. Measure Sample Filled ResonatorQo fo f Qs fs =
Things are not quite as simple as the little diagram of the empty and filled measurements that we’ve been showing.
The PNA measurement screen shot above shows the S21 response over a wider frequency range, 8GHz to 11GHz in this case, and you can see that there is a lot going on. In the screen shot above, the green trace is the measurement of the empty fixture and the orange trace is the measurement of the fixture filled with a 3mm thick Teflon ® brand PTFE sample. The markers are showing the TE011 mode and you can see that it has indeed shifted downward.
But you can see that the trace has been complicated by modes in addition to the TE011 modes we want to measure. After the sample has been introduced to the resonator, it can be difficult to know which peak is the correct one to measure. We can’t just visually pick out the correct peak. We need a tool to estimate the frequency shift to get close before we can measure the filled fixture.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

34. Estimate Sample Filled Frequency
NIST Software –
CalcFoInput.dat
Number of TE0n Modes in Model
Radius of Split-Cylinder Resonator (m)
Length of Upper or Lower Split-Cylinder Resonator Section (m)
Substrate Thickness (m)
Initial Guess for Relative Permittivity of Substrate
Three ways to come up with initial guess:
Theoretical or Design Value
Independent Measurement
Measure TE111 mode
NIST provides algorithms that estimate the new frequency after the sample has been inserted between the split cylinders. Agilent software uses this NIST algorithm, but of course adds a graphical user interface. These are the inputs to the NIST program. They are all pretty straightforward except the last one: Initial Guess for Relative Permittivity. Isn’t relative permittivity what we are trying to measure?
The good news is there are some ways to guess intelligently.
Theoretical or design value. For example Teflon® brand PTFE is approximately 2.06.
Independent Measurement method, for example a split post dielectric resonator.
Use the TE111 mode of the Split Cylinder Resonator which is easy to find because it usually occurs at the lowest frequency. This method works well for samples with the real part of permittivity less than 20. Agilent Resonant Cavity software automates this so you don’t have to do anything but click on a button, but here’s how it works.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

35. Calculate Sample Filled Frequency
TE111 mode is the dominant mode when
TE111
The TE111 is the dominant mode, meaning that it is the lowest frequency mode, in a split cylinder resonator when 2 times length of one cylinder divided by the radius is greater than In this case, the TE111 mode is the first occuring mode, and it is separated by a fairly large frequency range from the next occurring mode, it is an easy task using marker to peak search function in the PNA to find the frequency of this mode. We can find the permittivity by solving this equation [5].
The equation is when the resonator is closed, however it is a good approximation when the sample is thin and the permittivity is fairly low.
h = the total length of the closed cavity, or in this case where the cylinders are equal length, 2x the length of one cylinder.
a = the radius of the cylinders.
χ’mn = the mth root of Bessel function of nth order
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

36. Calculate Sample Filled Frequency
TE111 mode
Agilent Software
The TE111 method for finding the initial guess of the real part of permittivity is built into the Agilent Resonant Cavity software. Here’s a look at the graphical interface.. After inserting the sample into the Split Cylinder Resonator, simply click on the Find Estimate button.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

37. Measure Sample Filled Frequency and Q
The software drives the network analyzer, searches for the TE111 peak, calculates the real part of permittivity estimate. I
In addition, it calls the NIST algorithms and displays a list of frequencies of the sample filled Split Cylinder Resonator TE011 and higher ordered TE0n odd numbered p modes that can be used to measure complex permittivity. The first mode listed is the TE011 mode, and you can see that it has in fact shifted downward from it’s unfilled frequency of ~10.0GHz to ~9.7 GHz. At this point we can select any frequency from the list and press OK button and the software will setup the correct start and stop frequencies for the measurement.
Agilent Software
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

38. Process Flow Qo Qs f fs fo
So now that we’ve taken all the data, the Agilent Resonant Cavity software calculates the permittivity results.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

39. Calculate Permittivity
This is the easy part. The Agilent software automatically calls the NIST algorithm, calculates, and displays the result.
The Agilent graphical user interface also allows us to save our setup, save the data to a file that can be imported into a spreadsheet or other analytical tool, copy the data to the Windows clipboard. There is also an Application Programming Interface for users who want to add additional automation, such parts handling or test limits . The Measurement Wizard button takes you to a “Split Cylinder Resonators for Dummies” routine that walks a novice user though the entire process.
The Agilent Resonant Cavity Software also supports Split Post Dielectric Resonator ASTM2520 methods.
Agilent Software
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

40. Process Flow Qo Qs f fs fo
So, we’re done. Or, if we want to measure another sample, we can loop back to the measure thickness step, or if we want to measure the same sample at a higher frequency we can go back and select another frequency from the list we calculated earlier. We don’t have to measure the empty fixture again unless we think something has significantly changed, for example environmental temperature, or the fixture got significantly bumped enough to change the cylinder alignment, or we want to check that some particulate matter was introduced into the cylinders. Like microwave connectors, it’s very important to keep the cylinders clean.
Let’s now talk about measuring a sample at a higher frequency and some considerations for selecting the higher order modes.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

41. Higher Order Modes
TE011
Here’s a look at the empty 10GHz Split Cylinder Resonator over frequency range from 8GHz to 20GHz. You can see that as the frequency goes up, the mode population becomes more dense. Only a handful of these modes are the odd number TE0np modes that we can use. The TE011 mode is relatively isolated. But, as we go up in frequency, it becomes more difficult to find the correct mode to measure, and more likely that we will have interference from another mode close by.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

42. Double Peak in Search Span
Some modes we will have no problems.
But, in this case, we have two peaks in a 100MHz wide search span which the Agilent Resonant Cavity software automatically setup up when we selected the mode we wanted to measure from the list. From experience, I know that the higher frequency one on the right is the correct peak, and its easy to zoom in on it and make the measurement. But, how did I know it is the right one? It has some characteristics that give it away It is slightly closer in frequency to the frequency we chose from the list. 2. The shape is more symmetrical and the bandwidth is narrower, showing that the Q is higher. The peak on the left has a little asymmetry and the bandwidth is fairly wide.
But, when in doubt, measure both. Only one peak will give a reasonable permittivity value.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

43. Double Peak in Search Span
The Agilent Resonant Cavity software allows the user to easily change measurement frequency and search span by typing in the text box. With this we can easily zoom in the correct peak and make the measurement.
Agilent Software
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

44. Interfering Modes Interfering modes.
In this case the mode we want to measure is being interfered with by another non TE0np mode. We can see immediately that it is asymmetrical in the frequency domain. But, the frequency domain does not tell the whole story.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

45. Interfering Modes
Looking in at a Polar plot, we can see that this resonance does not draw a good circle and we will not be able to fit to it and get good frequency and Q results. Instead we have a couple of other options.
Choose another frequency from the list to measure on the same sample.
Change the thickness of the sample. This can be done by making another sample or if the sample is fairly thin to begin with, we can stack two samples together.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

46. Split Cylinder Resonator Results
This is data from measurements of a 3mm thick sample of Teflon ® brand PTFE, made with an Agilent 85072A Split Cylinder Resonator, Agilent 85071E-300 Resonant Cavity Software, and PNA network analyzer. The error bars show the typical uncertainty listed in the Agilent 85072A Technical Overview.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

47. Split Cylinder Resonator Results
This is data from measurements of a 3mm thick sample of Teflon ® brand PTFE, made with an Agilent 85072A Split Cylinder Resonator, Agilent 85071E-300 Resonant Cavity Software, and PNA network analyzer. The error bars show the estimated uncertainty.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

48. Conclusions
Split Cylinder Resonator is a sensitive method for measuring complex permittivity of low loss materials
It can be confusing if you don’t know what you are doing.
Agilent offers a turn key solution to make it fast and easy.
In Conclusion:
The Split Cylinder Resonator method has the accuracy and resolution needed to measure complex permittivity of low loss and thin materials.
It can be confusing if you don’t have the right tools.
Agilent has developed innovative tools to meet your needs and offers a turn key solution that makes this measurement technique fast and easy.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

49. Thank You for listening
More information at
I want to thank you for listening, and now I’m going to turn it over to ____. I know he has a few things to tell you and then you’ll have the opportunity to ask questions, which I’ll try to answer.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

50. References
[1] M.D. Janezic, ‘‘Nondestructive Relative Permittivity and Loss Tangent Measurements using a Split-Cylinder Resonator,’’Ph.D. Thesis, University of Colorado at Boulder, 2003.
[2] IPC-TM-650 Test Methods Manual Relative Permittivity and Loss Tangent Using a Split-Cylinder Resonator” Number January, 2007.
[3] R.N. Clarke (Ed.), “A Guide to the Characterization of Dielectric Materials at RF and Microwave Frequencies,” Published by The Institute of Measurement & Control (UK) & NPL, 2003
[4] P.G. Bartley, S.B. Begley “Quality Factor Determination of Resonant Structures” IMTC 2006 – Instrumentation and Measurement Technology Conference Sorrento, Italy April 2006
[5] M.T. Ali, M.K.M. Salleh, Md.M.Md. Zan “” Air-Filled Circular Cross Sectional Cavity for Microwave Non-Destructive Testing Transactions on Engineering, Computing and Technology Volume 18 December 2006, pg , ISSN
[6] M.D. Janezic, J.Krupka “Split-Post and Split-Cylinder Resonator Techniques: A Comparison of Complex Permittivity Measurement of Dielectric Substrates”. CICMT 2008 pgs
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

51. Appendix
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008

52. NIST Software Inputs CalcFoInput.dat Number of TE0n Modes in Model
Radius of Split-Cylinder Resonator (m)
Length of Upper or Lower Split-Cylinder Resonator Section (m)
Substrate Thickness (m)
Initial Guess for Relative Permittivity of Substrate
SplitCInput.dat
Number of TE0n Modes in Model
Radius of Split-Cylinder Resonator (m)
Length of Upper or Lower Split-Cylinder Resonator Section (m)
Substrate Thickness (m)
Conductivity of Split-Cylinder Resonator (S/m)
Resonant Frequency of TE0np Mode (Hz)
Quality Factor of TE01np Mode
Initial Guess for Relative Permittivity of Substrate
These are the inputs into NIST’s software. Some are fairly straight forward. Other’s need a bit more consideration.
Implementing Split Cylinder Resonator for Dielectric Measurement of Low Loss Materials
September 24, 2008