Permittivity measurements using

coaxial probes

A Degree Thesis Submitted to the Faculty of the Escola Tècnica d'Enginyeria de Telecomunicació de Barcelona

Universitat Politècnica de Catalunya by

Bartomeu Oliver Riera

In partial fulfilment of

the requirements for the degree in Telecommunications Systems ENGINEERING

Advisor: Joan O’Callaghan Castella Barcelona,

May 2016

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I hereby declare that except where specific reference is made to the work of others, the contents of this dissertation are original and have not been submitted in whole or in part for consideration for any other degree or qualification in this, or any other university. This dissertation is my own work and contains nothing which is the outcome of work done in collaboration with others, except as specified in the text.

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Abstract The main objective of this thesis is to characterize, using the ADS software, the coaxial probe provided by the faculty ETSETB and utilize such probe in order to calculate the permittivity of different materials.

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Resumen El objetivo principal de esta tesis el de caracterizar, con el programa ADS, la sonda coaxial proporcionada por la facultad de la ETSETB y utilizar-la para el calculo de la permitividad de diferentes materiales.

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Resum L’objectiud’aquestatesiseseldecaracteritzar,ambelprogramaADS,lasondacoaxialproporcionadaperlafacultatdel’ETSETBIutilitzar-lapercalcularlapermitivitatendiferentsmaterials.

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Table of contents

Abstract....................................................................................................................................3

Resumen...................................................................................................................................4

Resum........................................................................................................................................5Revisionhistoryandapprovalrecord.......................¡Error!Marcadornodefinido.

Tableofcontents...................................................................................................................6

ListofFigures.........................................................................................................................7ListofEquations....................................................................................................................8

ListofTables...........................................................................................................................81 Introduction.....................................................................................................................9

2 Background...................................................................................................................102.1 Permittivity........................................................................................................................102.2 SingleanddoubleDebyemodels................................................................................112.3 Theopen-endedCoaxialforpermittivitymeasurement....................................112.4 Differencewithothermethods....................................................................................142.5 ADSsoftwareforequivalentcircuitfitting..............................................................172.5.1 ADSgeneralities.........................................................................................................................172.5.2 Optimizationmethods............................................................................................................17

3 BroadbandfittingofDebyemodels.......................................................................193.1 EquivalentcircuitsforDebyemodels.......................................................................193.2 Open-endedaircapacitance.........................................................................................203.3 Fittingresults....................................................................................................................28

4 Unconstrainedmeasurementsofpermittivity..................................................344.1 De-embeddingtheeffectsoftheprobe.....................................................................344.2 DeterminingPermittivity..............................................................................................35

5 Conclusion......................................................................................................................37Annex:Matlabcalculations.............................................................................................42

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List of Figures Figure1:Complexpermittivityvectordiagram[1]..............................................................10Figure2:Probeendfields[26]......................................................................................................12Figure3:Coaxialprobe[1]..............................................................................................................12Figure4:Equivalentopen-endedcoaxiallinecircuit[5]....................................................13Figure5:Permittivitymeasurementsystemexample[7].................................................13Figure6:SingleDebyemodelequivalentcircuit....................................................................19Figure7:Equivalentcircuitendedinshortcircuit................................................................20Figure8:Optimizationofshortcircuit.......................................................................................21Figure9:Equivalentcircuitendedinopencircuit................................................................22Figure10:Optimizationofopencircuit.....................................................................................22Figure11:Equivalentcircuitofthepurewatermeasurementsupto500MHz.......24Figure12:Optimizationwiththewatermeasurementsupto500MHz......................24Figure13:Equivalentcircuitofthe2-propanolmeasurementsupto500MHz.......25Figure14:Optimizationwiththe2-propanolmeasurementsupto500MHz...........25Figure15:Equivalentcircuitofthemethanolmeasurementsupto500MHz..........26Figure16:Optimizationwiththemethanolmeasurementsupto500MHz..............26Figure17:Equivalentcircuitoftheacetonemeasurementsupto500MHz..............27Figure18:Optimizationwiththeacetonemeasurementsupto500MHz..................27Figure19;LSMofC = Cf+ ε'C0....................................................................................................28Figure20:Equivalentcircuitofthepurewatermeasurementsupto10GHz..........29Figure21:Optimizationwiththepurewatermeasurementsupto10GHz..............29Figure22:Equivalentcircuitofthe2-propanolmeasurementsupto10GHz.........30Figure23:Optimizationwiththe2-propanolmeasurementsupto10GHz..............30Figure24:Equivalentcircuitofthemethanolmeasurementsupto10GHz.............31Figure25:Optimizationwiththemethanolmeasurementsupto10GHz.................31Figure26:Equivalentcircuitoftheacetonemeasurementsupto10GHz................32Figure27:Optimizationwiththeacetonemeasurementsupto10GHz.....................32Figure28:EquivalentcircuittocharacterizetheS-Parametersoftheprobe...........34Figure29:S-parametersconversiondiagram[16].................................................................35Figure30:dBresponseofthecoaxialprobeendedwithashortcircuit......................38Figure31:MatlabscriptforpermittivitycalculationusingDebyemodel..................42Figure32:ScatteringparametersMatlab..................................................................................42Figure33:ReflectioncoefficientsMatlab..................................................................................42Figure34:ReflectioncoefficientsoftheM.U.TMatlab........................................................43Figure35:MatlabscriptforpermittivitycalculationusingDebyemodel..................43

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List of Equations Equation1...............................................................................................................................................10Equation2...............................................................................................................................................10Equation3...............................................................................................................................................11Equation4...............................................................................................................................................11Equation5...............................................................................................................................................18Equation6...............................................................................................................................................19Equation7...............................................................................................................................................19Equation8...............................................................................................................................................19Equation9...............................................................................................................................................23Equation10............................................................................................................................................23Equation11............................................................................................................................................35Equation12............................................................................................................................................35Equation13............................................................................................................................................35Equation14............................................................................................................................................35

List of Tables Table1:Comparationbetweendifferentmeasurementmethods[9][10][11][12]

[13][14].........................................................................................................................................16Table2:ComputedcomplexpermittivityofpurewaterusingDebyemodels.[23]

[24][25].........................................................................................................................................33Table3:Computedcomplexpermittivityof2-propanolusingDebyemodels.[18]

............................................................................................................................................................33Table4:ComputedcomplexpermittivityofmethanolusingDebyemodels.[18]..33Table5:ComputedcomplexpermittivityofacetoneusingDebyemodels.[22].....33Table6:Computedcomplexpermittivityofpurewaterusingunconstrained

models.[23][24][25]..............................................................................................................36Table7:Computedcomplexpermittivityof2-propanolusingunconstrained

models.[18]..................................................................................................................................36Table8Computedcomplexpermittivityofmethanolusingunconstrainedmodels.

[18]...................................................................................................................................................36Table9Computedcomplexpermittivityofacetoneusingunconstrainedmodels.

[22]...................................................................................................................................................36Table10:ComparationbetweenDebyeandunconstrainedmethodsforwater.....37Table11:ComparationbetweenDebyeandunconstrainedmethodsfor2-propanol.

............................................................................................................................................................37Table12:ComparationbetweenDebyeandunconstrainedmethodsformethanol.

............................................................................................................................................................37Table13:ComparationbetweenDebyeandunconstrainedmethodsforAcetone.38

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1 Introduction The measurement of permittivity on dielectric materials has become more popular in the recent years due to the fact that a dielectric materials measurement can provide critical design parameter information for many electronics applications. For example, the loss of a cable insulator, the impedance of a substrate, or the frequency of a dielectric resonator can be related to its dielectric properties. The information is also useful for improving ferrite, absorber, and packaging designs. More recent applications in the area of industrial microwave processing of food, rubber, plastic and ceramics have also been found to benefit from knowledge of dielectric properties [1]. In the biomedical field, controversies on the biological effects of electromagnetic fields have existed for many years and, to date, investigators still have not identified the mechanisms by which such fields interact with the body. In order to advance our understanding of these processes, the utmost care must be taken by researchers when acquiring experimental data and performing theoretical studies, the lack of which can lead to erroneous results and inaccurate conclusions. Investigations on how the fields penetrate and propagate in the body are a function of the biological tissue’s material properties such as permittivity and conductivity. [2] [3] [4] [5] It’s also used in the food industry used to analyse various properties of the food using multiple techniques to detect, for example, the quality of the fat that some foods have and the age of the meat. [4] [5] [14] There are different techniques to measure the permittivity like the coaxial probe, the transmission line, the free space and the resonant cavity technique. Factors like material shape and form, accuracy and convenience. Some of the factors to consider are frequency range, form of the material (liquid, solid, semi-solid…) and temperature. [1]

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2 Background

2.1 Permittivity The permittivity is the ability of a material to store electrical potential energy under the influence of an electric field measured by the ratio of the capacitance of a capacitor with the material as dielectric to its capacitance with vacuum as dielectric. A material is classified as “dielectric” if it has the ability to store energy when an external electric field is applied. If a DC voltage source is placed across a parallel plate capacitor, more charge is stored when a dielectric material is between the plates than if no material (a vacuum) is between the plates. That occurs because the dielectric material increases the storage capacity of the capacitor by neutralizing charges at the electrodes. [1] The absolute permittivity is expressed like this:

𝜀 = 𝜀!𝜀! Equation 1

Where 𝜀 is the absolute permittivity, 𝜀! is the relative permittivity and 𝜀! =

!!"!

×10!! 𝐹/𝑚 is the free space permittivity. [6] The real part of permittivity (𝜀!! ) is a measure of how much energy from an external electric field is stored in a material. The imaginary part of permittivity (𝜀!!!) is called the loss factor and is a measure of how dissipative or lossy a material is. [1] [6] When complex permittivity is drawn as a simple vector diagram, the real and imaginary components are 90° out of phase.

Figure 1: Complex permittivity vector diagram [1]

The loss tangent tan 𝛿 is called tan delta, tangent loss or dissipation factor and is defined as the ratio of the imaginary part. For purely conductive losses [6]

tan 𝛿 =𝜎

𝜔𝜀!𝜀!

Equation 2

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where 𝜎 is the medium conductivity.[7]

2.2 Single and double Debye models According to the NPL report MAT 23, which presents the results of the NPL dielectric reference liquids measurements programme, for a polar liquid that exhibits single-Debye relaxation behaviour the relative complex permittivity is calculated at a given frequency 𝑓 using the Debye relaxation equation also known as the Debye relaxation function. [18]

𝜀! = 𝜀! + 𝜀! − 𝜀!

1 + 𝑗 𝑓𝑓!

Equation 3

Where 𝜀! is the static permittivity, 𝑓! the relaxation frequency and 𝜀! the high frequency permittivity limit tabulated values. When a dielectric liquid has two dielectric relaxations is called a double-Debye and this equation becomes:

𝜀! = 𝜀! + 𝜀! − 𝜀!

1 + 𝑗 𝑓𝑓!!

+𝜀! − 𝜀!

1 + 𝑗 𝑓𝑓!!

Equation 4

Where 𝜀! is the notional high frequency permittivity limit of the lower frequency relaxation and 𝑓!! and 𝑓!! are the relaxation frequencies of the two equations

2.3 The open-ended Coaxial for permittivity measurement The open-ended coaxial probe is the method used in this thesis to measure permittivity and is basically a cut-off section of a transmission line and it’s used to measure the reflection coefficient of the material. The fields at the probe end “fringe” into the material and change as they come into contact with the MUT. This reflected signal could be related to the relative permittivity. This method is based on the fact that the reflection coefficient of an open-ended coaxial line depends on the dielectric parameters of the MUT that is attached to it and it can be used on liquid, solid or semi-solid samples. [1]

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Figure 2: Probe end fields [26]

Figure 3: Coaxial probe [1]

For calculating the complex permittivity from the measured reflection coefficient it is useful to use an equivalent circuit of an open-ended coaxial line.

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Figure 4: Equivalent open-ended coaxial line circuit [5]

Where C is the capacitance between the internal and external wire out of the coaxial structure and G is the conductance that represents the propagation losses. [8] [9] According to the document “Broadband Measurement of complex permittivity using coaxial probes” [7], a standard measurement system using the reflection method on an open-ended coaxial line consists of the network analyser, the coaxial probe and software

Figure 5: Permittivity measurement system example [7]

With the coaxial probe placed in contact with a MUT, first the calibration of the vector network analyser is performed. Then the calibration using a reference material (with the known dielectric constant 𝜀!) is done. And last the reflection coefficient of MUT is measured. [7] The measurements were done on a frequency range from 300 kHz to 10 GHz.

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2.4 Difference with other methods There are other techniques to measure the permittivity like the coaxial probe, the transmission line, the free space and the resonant cavity technique. Factors like material shape and form, accuracy and convenience determine the best method to use on each specific case. The main advantage about using the coaxial probe method to measure permittivity is that it is a non-destructive and non-invasive method. It allows Coaxial Probe method not to modify the material to be tested for every measurement. Other benefit to use this method is that it works properly in broadband, but it can be also achieved through Transmission Line method, which is better in high frequency as well.

The main difference with Free Space method is that it is a non-containing method and it is also useful for high temperature measurements. Regarding Resonant Cavity method, this method is the best for low loss materials, whereas the Coaxial Probe achieves high accuracy for high-loss materials. On the other hand, Resonant Cavity is an accurate method, but it only allows measurements at only single or at resonant frequency. Finally, concerning Parallel Plate method, it can be suitable for high-loss materials, but not as accurate as Coaxial Probe, but regarding low frequencies none of the other methods are not as good as Parallel Plate method. Moreover, this method allows only thin and flat materials, because it will be sandwiched inside the plates. [1][4]

On the other hand, the main drawbacks regarding Coaxial Probe method are the repetitive calibrations, which have to be performed every time you want to make a permittivity measurement and the errors, which can be caused by air gaps formed between the probe and the liquid to be tested. [1][4]

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Method Advantages Drawbacks

Coaxial Probe • Broadband frequency • Simple and convenient (non-destructive) • Best for semi-solids or liquids • Simple sample preparation • Isotropic and homogeneous material • High accuracy for high loss materials

• Air gaps causes errors • Repetitive calibrations

Transmission Line • High frequency • Support for both solids & liquids • Anisotropic material.

• Cannot use below few GHz, due to practical sample length limitation • Sample preparation is difficult (fills fixture cross section)

Free Space • Wide frequency range support • Non-contacting • Easy sample preparation • Moderate accuracy for high-loss & low-loss • Best for large flat and solid materials • Useful for high temperature

• Diffraction problem (from material edges) • Low end limited by practical sample size

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Method Advantages Drawbacks

Resonant Cavity • Support for both solids & liquids • Most accurate method • Suitable for low loss materials • No repetitive calibration procedure • High temperature capability • Best for low loss materials

• Measurements at only single or at resonant frequency • Suitable for small size samples

Parallel Plate • Higher accuracy • For thin, flat surface samples • Suitable for high-loss materials • Measurements relatively easier

• Support for low frequency (best results) • Electrode polarization effect

Table 1: Comparation between different measurement methods [9] [10] [11] [12] [13] [14]

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2.5 ADS software for equivalent circuit fitting

The equivalent circuit of the coaxial probe consists of three elements, a transmission line, the capacitance between the internal and the external wire out of the coaxial structure and a conductance that represents the propagation loses. These capacitance and conductance are frequency dependent and also depend on the dimensions of the probe being the conductance an RC series. This equivalent circuit is recreated on the Advanced Design System (ADS) software in order to manipulate it.

2.5.1 ADS generalities The Advanced Design System (ADS) is an electronic design software system that provides an integrated design environment to designers of RF electronic products. This software system is produced by Keysight Technologies and supports every step of the design process (schematic, frequency domain and time domain circuit simulation, and electromagnetic field simulation) allowing the user to fully characterize and optimize an RF design.

2.5.2 Optimization methods The optimization is a method implemented on the ADS software that simulates and tries to achieve a set performance goal. There are different optimization types available according to the ADS support information [15]: The Random optimization: The Random optimizer uses the Random search method to arrive at new parameter values by using a random-number generator, that is, by picking a number at random within a range. The Random optimizer uses the Least-Squares error function to minimize the average weighted violation for the desired responses. So the value for the error function represents the average weighted violation for the desired responses and the value of zero indicates that all of the intended performance goals have been reached. The Random optimizer guarantees to find at least one local minimum result. It also has the probability to find the global minimum result. The Random optimizer is probably the best optimizer when the number of optimization variables is large. The Gradient optimization: The Gradient optimizer uses the Gradient search method to arrive at new parameter values using the gradient information of the network's error function.

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The Gradient optimizer guarantees to find a local minimum result. A design that is optimized by the gradient optimizer has the least sensitivity (more stable) to slight variations in its parameter values. The Gradient optimizer is the best optimizer to use for simple circuits with straightforward requirements; that is, the larger number of function evaluations will not slow the optimization appreciably, but the optimizer will converge on a solution quickly. Quasi-Newton Optimization: The Quasi-Newton optimizer uses the Quasi-Newton search method to arrive at new parameter values. The Quasi-Newton search method uses the second-order derivatives of the error function and the gradient to find a descending direction.

Much like the optimizers using the gradient search method, an iteration in the optimizers using the Quasi-Newton search method consists of many function evaluations. Therefore, a single iteration using the Quasi-Newton search method takes longer than an iteration in the optimizers using the Random search method. The Quasi-Newton optimizer uses the Least-Squares error function to minimize the average weighted violation for the desired responses and guarantees to find a local minimum result. The optimization goal used it’s the absolute value of the subtraction S(1,1) from the measurement minus the reflection coefficient from the simulated circuit created on the ADS in order to get the minimum error possible. Also is set a minimum and maximum frequencies for the optimization to make it the most accurate and fast as possible. In this case only one goal and limit are going to be set but it is possible to use more than one fixing different weights depending on the range of importance of every case. The goal used in this case is the corresponding with the expression below, which will be minimised through optimization:

𝑆(1,1)𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − 𝑆(1,1)𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑒𝑑!

Equation 5

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3 Broadband fitting of Debye models

3.1 Equivalent circuits for Debye models If the MUT measured on the coaxial probe has low 𝜎 and the frequency used is small, below 500MHz, the load impedance can be expressed as:

𝑌! = 𝑗𝜔𝐶!𝜀! + 𝑗𝜔𝐶! Equation 6

At a relative low frequencies the permittivities are bigger than 1 being 𝜀! ≫ 1, due to this the 𝐶! is negligible because 𝜀!𝐶! ≫ 𝐶!. The resulting expression of the load impedance is:

𝑌! = 𝑗𝜔𝐶!𝜀! Equation 7

On the other hand, the equivalent circuit of the coaxial probe for the single Debye model consists of three elements, a transmission line, the capacitance between the internal and the external wire out of the coaxial structure and a conductance that represents the propagation loses. These capacitance and conductance are frequency dependent, being the conductance an RC in series.

Figure 6: Single Debye model equivalent circuit

The load impedance of this equivalent circuit is:

𝑌! = 𝑗𝜔𝐶! + 𝑗𝜔𝐶!

1 + 𝑗𝜔𝑅!𝐶!

Equation 8

Using the equation that is used to calculate the complex permittivity for a polar liquid that exhibits single Debye relaxation behavior. [18], the load impedance

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expressions of the MUT, 𝑌!, and the respective equivalent circuit, 𝑌!, can be equalized obtaining the relative permittivity.

𝜀! = 𝜀! + 𝜀! − 𝜀!

1 + 𝑗 𝑓𝑓!

Equation 3

𝑌! = 𝑗𝜔 [𝐶! + 𝐶!

1 + 𝑗𝜔𝑅!𝐶!]

Equation 8

𝑌! = 𝑌! if 𝐶! = 𝜀!𝐶!

𝐶! = (𝜀! − 𝜀!)𝐶! 𝑓! =

!!!!!!!

3.2 Open-ended air capacitance The first thing that is necessary to obtain the open-ended air capacitance of the coaxial probe is to characterize it. In order to do that, a set of measurements of the coaxial probe ended with a short and an open circuit are taken. With these measurements, the transmission line is optimized ended in a short and a capacitance representing an open-ended line. Doing this, the transmission line is being characterized and later on the S parameters can be obtained.

Figure 7: Equivalent circuit ended in short circuit.

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Figure 8: Optimization of short circuit.

On the up left graphic is represented the power in dB of the reflection coefficient of both signals from 0 GHz to 10 GHz, the blue lines are always the simulated signals and the red ones the measured data from the real measurements. The up right graphic represents the phase of the signals, the bottom left the real part and the bottom right the imaginary part. This graphic representation structure is the same in all of the optimizations. This optimization is made using the random optimization method because is the fastest one due to the high number of optimization parameters that the transmission line has. The second optimization is made between the transmission line ended with a capacitance and the coaxial probe measurements using the gradient optimization method because there is only one parameter to optimize, the capacitance value.

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Figure 9: Equivalent circuit ended in open circuit

Figure 10: Optimization of open circuit.

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At frequencies below the onset of any dispersion of the MUT permittivity 𝜀! is nearly constants while 𝜀!! is negligible. In this limit the load impedance can be re-expressed as:

𝑌! = 1𝑅 + 𝑗𝜔𝐶!

Equation 9

𝑡𝑎𝑛𝛿 =

𝜎𝜔𝜀!𝜀!

Equation 2

𝜀!! = 𝜀!𝑡𝑎𝑛𝛿Equation 10

Where 𝑅!! = 𝐶!

!!!

and 𝐶! = 𝐶! + 𝜀!𝐶!. If, for a particular MUT, 𝜎!" = 0 the

impedance reduces to 𝑍! = 1𝑗𝜔𝐶!. [19]

The impedance of a particular probe can be characterized using two samples of known 𝜀!. Have in mind that below 10 MHz, due to the polarization effect the measured data can deviate from the model expectations and above 500 MHz, the real part of 𝑍! deviates from the modeled behaviour due to the diminished electrode polarization effects and also in part to the breakdown of the assumption that 𝜀!!!! remain real and constant. [20]

If the working frequency is set above 10 MHz and use MUT’s with low 𝜎!" the electrode polarization effects are assumed to be negligible. For that reason an initial measure of the liquids is performed in a frequency range of 10 MHz to 500 MHz. This initial measure prevents polarization effects and keeps the losses low on those liquids. The measured liquids with low 𝜎 used are methyl alcohol that has 𝜎!" ≈ 0 𝜀! = 33 at 25ºC, pure water that has 𝜀! = 78 at 25ºC and acetone with a real permittivity of 20.7 at 25º. All measurements made at a low frequency. The equivalent circuit is optimized with this new set of measurements and the new range of frequencies following the same steps as the previous optimizations.

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Figure 11:Equivalent circuit of the pure water measurements up to 500 MHz

Figure 12: Optimization with the water measurements up to 500MHz

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Figure 13:Equivalent circuit of the 2-propanol measurements up to 500 MHz

Figure 14: Optimization with the 2-propanol measurements up to 500MHz

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Figure 15:Equivalent circuit of the methanol measurements up to 500 MHz

Figure 16: Optimization with the methanol measurements up to 500MHz

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Figure 17:Equivalent circuit of the acetone measurements up to 500 MHz

Figure 18: Optimization with the acetone measurements up to 500MHz.

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With all the measured and optimization of these liquids we calculate 𝐶! and 𝐶! constants doing a LSM of 𝐶 = 𝐶! + 𝜀!𝐶!.

Figure 19; LSM of 𝑪 = 𝑪𝒇 + 𝜺!𝑪𝟎

The obtained results are 𝐶! = 66,1 𝑓𝐹 and 𝐶! = 0,7 𝑓𝐹. Three measurements are used to reduce possible errors like alterations in the permittivities of the samples due to impurities and procedure mistakes or air bubbles on the probe.

3.3 Fitting results The first thing that is necessary for the calculation of the complex permittivity of these materials is to adjust the equivalent circuit with the measurements of those materials in order to determine 𝐶!, 𝐶! and 𝑅!.

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Figure 20: Equivalent circuit of the pure water measurements up to 10 GHz

Figure 21: Optimization with the pure water measurements up to 10 GHz

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Figure 22: Equivalent circuit of the 2-propanol measurements up to 10 GHz

Figure 23: Optimization with the 2-propanol measurements up to 10 GHz

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Figure 24: Equivalent circuit of the methanol measurements up to 10 GHz

Figure 25: Optimization with the methanol measurements up to 10 GHz

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Figure 26: Equivalent circuit of the acetone measurements up to 10 GHz

Figure 27: Optimization with the acetone measurements up to 10 GHz

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With the results of the optimization, the permittivity is calculated with the values of the capacitances and the resistances. The resulting permittivities of the calculations are:

Pure Water Frequency Measured real

part Measured

imaginary part Theoretical

real part Theoretical imag. part

0.1 GHz 90.5788 0.4397 78.7395 0.0919 1 GHz 84.8937 21.6336 78.5729 3.6232 2 GHz 71.6494 36.4146 78.0759 7.2006 3 GHz 56.9513. 43.2147 77.2614 10.6882 4 GHz 44.3544 44.5843 76.1492 14.0458 5 GHz 34.6462 43.1727 74.7655 17.2382 Table 2: Computed complex permittivity of pure water using Debye models. [23] [24] [25]

2-Propanol Frequency Measured real

part Measured

imaginary part Theoretical

real part Theoretical imag. part

0.1 GHz 25.7725 0.0731 20.0614 0.8974 1 GHz 24.5029 5.4181 5.3578 5.2576 2 GHz 21.3968 9.3848 3.9972 2.9740 3 GHz 17.7237 11.5082 3.6729 2.1162 4 GHz 14.3753 12.2217 3.5193 1.6762 5 GHz 11.6575 12.1089 3.4216 1.4041

Table 3: Computed complex permittivity of 2-propanol using Debye models. [18]

Methanol Frequency Measured real

part Measured

imaginary part Theoretical

real part Theoretical imag. part

0.1 GHz 47.1535 0.4333 33.60 0.99 1 GHz 41.6432 15.0332 30.52 8.81 2 GHz 30.7331 21.9962 24.28 13.20 3 GHz 21.6264 22.7963 18.79 13.97 4 GHz 15.4782 21.2149 14.94 13.18 5 GHz 11.2507 18.9303 12.42 12.42

Table 4: Computed complex permittivity of methanol using Debye models. [18]

Acetone Frequency Measured real

part Measured

imaginary part Theoretical

real part Theoretical imag. part

0.1 GHz 25.1256 0.0770 21.2 0.001 1 GHz 24.8790 2.4143 21.1915 0.4048 2 GHz 24.1681 4.6832 21.1661 0.8086 3 GHz 23.0738 6.6891 21.1238 1.2103 4 GHz 21.7068 8.3595 21.0650 1.6088 5 GHz 20.1817 9.6698 20.9898 2.0031

Table 5: Computed complex permittivity of acetone using Debye models. [22]

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4 Unconstrained measurements of permittivity When the materials do not conform the Debye models another method is required to calculate the complex permittivity.

4.1 De-embedding the effects of the probe The reflection coefficient of the measurements obtained with the network analyser represents the reflection coefficient at the initial point of the coaxial probe. For the unconstrained method it’s necessary to obtain the reflection coefficient of the MUT rather than the reflection signal at probe’s input. In order to do that the value of the Scattering parameters of the coaxial probe are necessary. The Scattering parameters can be determined using the ADS software. The S parameters are obtained in every frequency point of the simulation on an excel document using this equivalent circuit on ADS.

Figure 28: Equivalent circuit to characterize the S-Parameters of the probe.

Once the S parameters had been determined, the reflection coefficient of the MUT can be calculated using the parameters conversion formulas. [16]

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Figure 29:S-parameters conversion diagram[16]

Γ!" = 𝑆!! +𝑆!"𝑆!"Γ!1 − 𝑆!!Γ!

Equation 11

Γ! = Γ!" − 𝑆!!

𝑆!"S!" − 𝑆!!𝑆!! + 𝑆!!Γ!"

Equation 12 Where Γ!" is the value of the input reflection coefficient and Γ! the reflection coefficient of the MUT.

4.2 Determining Permittivity With the constants 𝐶! and 𝐶! previously determined, and the values of Γ! derived from the measurements, the complex permittivity 𝜀! be determined according to the equations below.

𝑌! = 𝑗𝜔𝐶!𝜀! + 𝑗𝜔𝐶! =1𝑍!

1 − Γ!1 + Γ!

Equation 13

𝜀! = 𝜀! − 𝑗 𝜖!! +𝜎!"𝜔𝜀!

=1

𝑗𝜔𝑍!𝐶! 1 − Γ!1 + Γ!

−𝐶!𝐶!

Equation 14 To check if this method works correctly, different material permittivities are calculated using the constants 𝐶! and 𝐶!.

36

Pure Water Frequency Measured real

part Measured

imaginary part Theoretical

real part Theoretical imag. part

0.1 GHz 87.5948 1.3977 78.7395 0.0919 1 GHz 82.3010 21.2610 78.5729 3.6232 2 GHz 69.3415 35.8597 78.0759 7.2006 3 GHz 55.0678 42.2556 77.2614 10.6882 4 GHz 42.5375 43.6692 76.1492 14.0458 5 GHz 33.0886 42.3057 74.7655 17.2382

Table 6: Computed complex permittivity of pure water using unconstrained models. [23] [24] [25]

2-Propanol Frequency Measured real

part Measured

imaginary part Theoretical

real part Theoretical imag. part

0.1 GHz 22.6734 2.4792 20.0614 0.8974 1 GHz 22.4045 5.6384 5.3578 5.2576 2 GHz 18.9471 8.9329 3.9972 2.9740 3 GHz 15.3110 9.1366 3.6729 2.1162 4 GHz 11.6553 11.2296 3.5193 1.6762 5 GHz 10.5724 13.4533 3.4216 1.4041 Table 7: Computed complex permittivity of 2-propanol using unconstrained models. [18]

Methanol Frequency Measured real

part Measured

imaginary part Theoretical

real part Theoretical imag. part

0.1 GHz 38.0953 4.3806 33.60 0.99 1 GHz 37.6531 10.3248 30.52 8.81 2 GHz 31.4399 19.0130 24.28 13.20 3 GHz 21.4474 19.8325 18.79 13.97 4 GHz 11.4160 22.6772 14.94 13.18 5 GHz 6.8684 23.3164 12.42 12.42 Table 8 Computed complex permittivity of methanol using unconstrained models. [18]

Acetone Frequency Measured real

part Measured

imaginary part Theoretical

real part Theoretical imag. part

0.1 GHz 21.3583 0.1750 21.2 0.001 1 GHz 21.0741 0.5206 21.1915 0.4048 2 GHz 21.9535 1.5007 21.1661 0.8086 3 GHz 21.6047 2.6369 21.1238 1.2103 4 GHz 22.1873 6.6944 21.0650 1.6088 5 GHz 24.9356 13.6965 20.9898 2.0031

Table 9 Computed complex permittivity of acetone using unconstrained models. [22]

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5 Conclusion The obtained results over the calculations of the complex permittivity are not the desired, either with the broadband fitting of Debye models method or the unconstrained method. Even though the results are not the expected ones, the complex permittivity values obtained are similar between the two different methods. This may suggest that the materials measured may be contaminated and their permittivity is disturbed.

Pure Water

Frequency Unconstrained method Debye method

Real part Imaginary part

Real part Imaginary part

0.1 GHz 87.5948 1.3977 78.7395 0.0919 1 GHz 82.3010 21.2610 78.5729 3.6232 2 GHz 69.3415 35.8597 78.0759 7.2006 3 GHz 55.0678 42.2556 77.2614 10.6882 4 GHz 42.5375 43.6692 76.1492 14.0458 5 GHz 33.0886 42.3057 74.7655 17.2382

Table 10: Comparation between Debye and unconstrained methods for water.

2-Propanol

Frequency Unconstrained method Debye method

Real part Imaginary part

Real part Imaginary part

0.1 GHz 22.6734 2.4792 20.0614 0.8974 1 GHz 22.4045 5.6384 5.3578 5.2576 2 GHz 18.9471 8.9329 3.9972 2.9740 3 GHz 15.3110 9.1366 3.6729 2.1162 4 GHz 11.6553 11.2296 3.5193 1.6762 5 GHz 10.5724 13.4533 3.4216 1.4041

Table 11: Comparation between Debye and unconstrained methods for 2-propanol.

Methanol

Frequency Unconstrained method Debye method

Real part Imaginary part

Real part Imaginary part

0.1 GHz 38.0953 4.3806 33.60 0.99 1 GHz 37.6531 10.3248 30.52 8.81 2 GHz 31.4399 19.0130 24.28 13.20 3 GHz 21.4474 19.8325 18.79 13.97 4 GHz 11.4160 22.6772 14.94 13.18 5 GHz 6.8684 23.3164 12.42 12.42

Table 12: Comparation between Debye and unconstrained methods for methanol.

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Acetone

Frequency Unconstrained method Debye method

Real part Imaginary part

Real part Imaginary part

0.1 GHz 21.3583 0.1750 21.2 0.001 1 GHz 21.0741 0.5206 21.1915 0.4048 2 GHz 21.9535 1.5007 21.1661 0.8086 3 GHz 21.6047 2.6369 21.1238 1.2103 4 GHz 22.1873 6.6944 21.0650 1.6088 5 GHz 24.9356 13.6965 20.9898 2.0031

Table 13: Comparation between Debye and unconstrained methods for Acetone.

Another option that explains these results is that this coaxial probe is not capable of handle a frequency higher than 4 GHz and in consequence the characterization of the transmission line done with the ADS is incorrect.

Figure 30:dB response of the coaxial probe ended with a short circuit

On the figure it’s shown that at the frequency of 4 GHz the reflection coefficient measured has a flop and this can affect the optimization on the ADS. Another possibility to explain the results, but less likely, is that the polarization effect on the probe is bigger that the assumption made and it’s not negligible.

39

Bibliography.

• [1] “Basics of Measuring the Dielectric Properties of Materials” Keysight Technologies Application Note, Keysight Literature Number 5989-2589EN

• [2] Cooke R and Kuntz I D 1974 “The properties of water in biological

systems”. Annu. Rev. Biophys. Bioeng. 3 95-126

• [3] Mark J Schroeder, Anupama Sadasiva and Robert M Nelson “An Analysis on the Role of Water Content and State on Effective Permittivity Using Mixing Formulas” Journal of Biomechanics Biomedical and Biophysical Engineering. Volume 2, Issue 1, 2008

• [4] T. W. Athey, M. A. Stuchly and S. S. Stuchly, "Measurement of Radio

Frequency Permittivity of Biological Tissues with an Open-Ended Coaxial Line: Part I" in IEEE Transactions on Microwave Theory and Techniques, vol. 30, no. 1, pp. 82-86, Jan. 1982. oi:10.1109/TMTT.1982.1131021 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1131021&isnumber=25100

• [5] M. A. Stuchly, T. W. Athey, G. M. Samaras and G. E. Taylor, "Measurement of Radio Frequency Permittivity of Biological Tissues with an Open-Ended Coaxial Line: Part II - Experimental Results," in IEEE Transactions on Microwave Theory and Techniques, vol. 30, no. 1, pp. 87-92, Jan. 1982. doi: 10.1109/TMTT.1982.1131022 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1131022&isnumber=25100

• [6] Altschuler H.M., Dielectric Constant, Chapter IX of Handbook of Microwave Measurements, M. Sucher and J. Fox ed., Wiley 1963

• [7] ZAJÍČEK, L. OPPL, J. VRBA, BROADBAND MEASUREMENT OF

COMPLEX PERMITTIVITY Using Reflection Method and Coaxial Probes Dept. of Electromagnetic Field, Faculty of Electrical Engineering, Czech Technical University in Prague

• [8] Gabriel, S., Lau, R., W., Gabriel, C.: The Dielectric Properties of

Biological Tissues: III. Parametric Models for the Dielectric Spectrum of Tissues. Phys. Med. Biol. Vol. 41 (1996), p. 2271–2293

• [9] .P. G. a. R. N.C., "A Review of RF and Microwave Techniques for

Dielectric measurement on polar liquids," IEEE Transactions on Dielectrics and Electrical Insulation, vol. 13, pp. 727'743, 2006.

• [10] Agilent Technologies, "Basics Of Measuring The Dielectric

Properties Of Material," CA, USA2006.

40

• [11] G. S. V. R. M.S.Venkatesh, "An Overview of Dielectric Properties

Measuring Techniques," The Journal of The Canadian Society for Bioengineering (CSBE), vol. 47, pp. 7.15'7.30, 2005.

• [12] S. N. Shyam Narayan Jha, K. Basediya, A. Sharma, Rajiv Jaiswal,

Pranita Kumar, Ramesh Bhardwaj, Rish, "Measurement techniques and application of electrical properties for nondestructive quality evaluation of foods—a review," Journal of Food Science and Technology, vol. 48, pp. 387'411, 2011.

• [13] F. H. S. Wee, P. J. Suhaizal, A. H. M. Nornikman, H. Ezanuddin, A.

A. M., "Free space measurement technique on dielectric properties of agricultural residues at microwave frequencies," in Microwave and Optoelectronics Conference (IMOC), 2009 SBMO/IEEE MTT'S International, 2009, pp. 183'187.

• [14] S. Clerjon and J.'L. Damez, "Microwave sensing for an objective

evaluation of meat ageing," Journal of Food Engineering, vol. 94, pp. 379'389, 2009.

• [15] Keysight Software support system of the Advanced Design System

program. http://edadocs.software.keysight.com/display/support/ADS+Product+Documentation#content--412530656

• [16] Sophocles J. Orfanidis ECE Department Rutgers University 94 Brett

Road Piscataway, NJ 08854-8058 “Electromagnetic Waves and Antennas” Ch.14: S-Parameters

• [17] OPPL, L. Measurement of Dielectric Properties. Dissertation Thesis,

CTU in Prague, Dept. of EM field, 2001. (in Czech)

• [18] A. P. Gregory and R. N. Clarke, “Tables of the complex permittivity of dielectric reference liquids at frequencies up to 5GHz”, National Physical Laboratory Technical Report, January 2012

• [19] Stuchly, M. A. and S. S. Stuchly, “Coaxial line reflection methods for

measuring dielectric properties of biological substances at radio and microwave frequencies — A review,” IEEE Trans. Instrum.Meas. Vol. 29, No. 3, 176–183, 1980.

• [20] Progress In Electromagnetics Research B, Vol. 40, 159–183, 2012

PERMITTIVITY MEASUREMENTS OF BIOLOGICAL SAMPLES BY AN OPEN-ENDED COAXIAL LINE J. S. Bobowski and T. Johnson School of Engineering, University of British Columbia Okanagan, 3333 University Way, Kelowna, British Columbia V1V 1V7, Canada

41

• [21] Baker-Jarvis, J., M. D. Janezic, P. D. Domich, and R. G. Geyer, “Analysis of an open-ended coaxial probe with lift-off for non-destructive testing,” IEEE Trans. Instrum. Meas., Vol. 43, No. 5, 711–718, 1994.

• [22] NBS, “Tables of dielectric dispersion data for pure liquids and dilute

solutions”, National Bureau of Standards circular 589, U.S. Dept. of Commerce, Washington, DC.

• [23] D. Or and J. M. Wraith, “Temperature effects on soil bulk dielectric

permittivity measured by time domain reflectometry: A physical model,” Water Resources Research vol. 35, pp. 371-383, 1999.

• [24] A. Stogryn, “Equations for calculating the dielectric constant of saline

water,” IEEE Transactions on Microwave Theory and Techniques vol. MIT-19, pp. 733-736, 1971.

• [25] F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote

Sensing: Active and Passive, vol. III: From Theory to Applications. Dedham, MA: Artech House, Inc., 1986.

• [26] Camelia Gabriel “PERMITTIVITY PROBE MODELLING”, Armstrong

Laboratory. Department of Physics King's College London Strand, London WC2R 2LS,UK. 1991.

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Annex: Matlab calculations To facilitate and accelerate the procedure of obtaining the complex permittivity, the calculations of the different methods are done using the Matlab software. In section 3-Broadband fitting of Debye models the complex permittivity is calculated using the next script.

Figure 31: Matlab script for permittivity calculation using Debye model

Where 𝐶!, 𝐶! and 𝑅! are the values of the elements of the equivalent circuit and 𝐶! is the value of the open-ended capacitance of the coaxial probe. In section 4-Unconstrained measurement of permittivity, the equations are solved using MATLAB. Vector variables are used to accommodate the 1601 frequency points acquired by the network analyser from 300 KHz to 10 GHz The values of the S parameters of the coaxial probe are imported into the Matlab program for each of the 1601 points of frequency and converted to polar using this algorithm.

Figure 32: Scattering parameters Matlab

After that the reflection coefficients measured of the coaxial probe are also going to be import using the same process and also convert it to the algebraic form.

Figure 33: Reflection coefficients Matlab

using Γ! = !!"!!!!

!!"!!"!!!!!!!!!!!!!" to calculate Γ!.

43

Figure 34: Reflection coefficients of the M.U.T Matlab

With a simple Matlab script the permittivities are calculated.

Figure 35: Matlab script for permittivity calculation using Debye model