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Complex permittivity measurement using capacitance method from 300 kHz to 50 MHz
Measurement 46 (2013) 3796–3801
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Complex permittivity measurement using capacitance method from 300 kHz to 50 MHz Wong Jee Keen Raymond a,c,⇑, Chandan Kumar Chakrabarty a, Goh Chin Hock a, Ahmad Basri Ghani b a
Universiti Tenaga Nasional, Department of Electronic and Communication Engineering, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia TNB Research Sdn. Bhd., No. 1, Lorong Air Hitam, Kawasan Institusi Penyelidikan, 43000 Kajang, Selangor, Malaysia c University of Malaya, Department of Electrical Engineering, Faculty of Engineering, 50603 Kuala Lumpur, Malaysia b
a r t i c l e
i n f o
Article history: Received 6 September 2012 Accepted 25 June 2013 Available online 4 July 2013 Keywords: Component Complex permittivity Parallel plate capacitor Vector network analyzer VNA Dielectric constant Measurement
a b s t r a c t Complex permittivity measurement has been performed using a parallel plate capacitor and a vector network analyzer (VNA) from 300 kHz to 50 MHz. The material under test (MUT) is a flat and thin sample clamped between the capacitor plates and connected to the VNA to obtain its two port S parameters. The S parameter is converted into impedance to calculate the complex permittivity using Matlab program. Techniques used to overcome the air gap and stray capacitance was described. Measurement obtained using the proposed method was compared with the free space method to validate its accuracy. The percent difference is less than 5%. Ó 2013 Published by Elsevier Ltd.
1. Introduction Complex permittivity (e0r + je00r ) is a very useful parameter where the quality factor (e0r /e00r ) and tangent delta (e00r /e0r ) can be derived from the complex permittivity. These parameters are useful in power industry because they can be used as an indication of the power cable’s insulation quality [1,2]. Therefore there is a strong demand for complex permittivity measurement related research. There are a lot of methods developed for measuring the complex permittivity but these techniques are limited to specific frequencies, materials, and applications [3]. A list of currently known complex permittivity measurement has been described by Jarvis et al. in NIST technical note [4]. Two widely used measurement methods are resonant ⇑ Corresponding author. Tel.: +60 126045003. E-mail addresses: [email protected] (W.J.K. Raymond), [email protected] (C.K. Chakrabarty), [email protected] (G.C. Hock), [email protected] (A.B. Ghani). 0263-2241/$ - see front matter Ó 2013 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.measurement.2013.06.039
method and transmission/reflection method [5]. Resonant methods [6] have many variants such as split cylinder resonator, cavity resonator [7], Courtney technique, whispering gallery resonator and Farbry Perot resonators. Although resonant methods are highly accurate, measurements can only be done at one frequency which is the resonant frequency. Transmission/reflection method is able to measure the complex permittivity in a frequency range but requires the usage of waveguides [8–11]. Waveguides has two disadvantages. First, it is necessary to machine the sample to precisely fit the waveguide cross section with negligible air gaps. This requirement will limit the accuracy of measurements for materials which cannot be machined precisely [12]. The second disadvantage is the size limitation. Smaller sample size requires smaller waveguides which forces measurement to take place at a much higher frequency. There are plenty of research and implementation of resonant methods and transmission/reflection methods at GHz frequency range. Therefore this paper will focus on the less developed capacitance method in the MHz range.
W.J.K. Raymond et al. / Measurement 46 (2013) 3796–3801
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calibration kit before the measurement. The test fixture was connected to the VNA as shown in Fig. 1. SMA cables were used as coaxial cables to connect the fixture to the VNA. Once the test fixture is connected as shown in Fig. 1, its S parameters can be converted to impedance using Eq. (1) [15].
Z ¼ 100ð1 S21 Þ=S21
Fig. 1. Fixture and VNA connection.
The capacitance method involves sandwiching a thin material between two electrodes to form a capacitor. The typical capacitance method frequency range is from DC to 100 MHz [13]. This limitation is due to the fact that the capacitor will start to behave like an inductor above its resonance frequency which may vary for different materials. Capacitance method has several benefits which are the relatively low cost, easier sample preparation, easy to built fixture, and ability to measure at a frequency range. In this work, two round copper plates with diameter of 2.5 cm were used as the electrodes. The techniques to overcome the two main weaknesses of capacitance method i.e. stray capacitance and air gap will be discussed. The measured samples are thin, flat and has a surface area larger than the capacitor conducting plate [14]. The uniqueness of this work is the usage of VNA to measure impedance instead of LCR meter. Impedance is obtained through conversion of measured S parameter. VNA is preferred because it is more commonly available in research labs.
ð1Þ
The impedance measured by this method is the combinations of MUT impedance and fixture impedance. The fixture impedance must be removed to prevent systematic error in future calculations. The fixture impedance consists of residual impedance and stray admittance as depicted in Fig. 2 [16]. To determine the stray admittance, an open circuit was created at the MUT. This will cause the stray admittance to be huge and the residual impedance to be negligible. Hence the impedance measured when MUT is open will be the stray admittance. The residual impedance was measured when the test fixture was shorted. This will cause the stray admittance to be shorted and the measured impedance value will be the residual impedance. The MUT impedance Zmut can be determined once the residual impedance and stray admittance is known using the following equation.
Z mut ¼ ðZ measured Z s Þ=ð1 Y o ðZ measured Z s ÞÞ
ð2Þ
2.2. Converting impedance to complex permittivity The test fixture sandwiching the MUT can be modeled as a capacitor that has an equivalent circuit shown in Fig. 3. The equivalent circuit can be modeled as a series model or parallel model. Impedance to permittivity conversion requires the parallel model. Conversion between parallel and series model can be done using Eqs. (4) and (5).
Tan d ¼ xRs C s ¼ 1=ðxRp C p Þ
ð3Þ
2. Measurement theory
C p ¼ C s =ð1 þ ðTan dÞ2 Þ
ð4Þ
2.1. Converting S parameters to impedance
Rp =Rs ¼ 1 þ 1=ðTan dÞ2
ð5Þ
In this work, the S parameters were measured using Agilent’s E5070 vector network analyzer (VNA). Full two port calibration was performed using the Agilent 85032B
Y ¼ G þ jxC p
ð6Þ
Fig. 2. Test fixture’s impedance model.
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W.J.K. Raymond et al. / Measurement 46 (2013) 3796–3801
Fig. 3. Equivalent circuit of capacitor with MUT as dielectric core.
e00r ¼ t=ðxARp eo Þ
ð7Þ
e0r ¼ tC p =ðAeo Þ
ð8Þ
was modeled as a capacitor in parallel with the MUT capacitance. Therefore the stray capacitance could be eliminated by measuring the capacitance with and without the sample and subtracting the results as in Fig. 4. The stray capacitance could also be eliminated using guard electrodes [14]. Guard electrodes are very effective in eliminating stray capacitance but it will increase the complexity of the test fixture and the overall cost. In this work the stray capacitance which is part of the test fixture residual admittance was eliminated during the test fixture impedance removal. 2.4. Elimination air gap
A is the area of the capacitor electrode, while t is the sample thickness. eo is the permittivity of free space and its value is 8.8542 1012 F/m. The measured impedance of the MUT was converted to the parallel representation using Eqs. (4) and (5). Once Rp and Cp were known, Eqs. (7) and (8) were then used to calculate the complex permittivity. Matlab was used to perform all the calculations required to obtain the complex permittivity.
Research by Mattar et al. [17] shows that measurement accuracy is severely affected by the air gap between the MUT and capacitor electrodes. It is necessary to eliminate air gap in order to get accurate measurements. Air gaps are layers or pockets of air that exist between the MUT and capacitor conducting electrodes. An inevitable thin layer of air gaps will exist due to roughness of the MUT and the electrodes surface regardless how tight the MUT is clamped. Air gap can be modeled as a capacitor in series with the MUT capacitance, as illustrated in Fig. 5.
2.3. Eliminating stray capacitance
1=C measured ¼ 1=C mut þ 1=C ag
Stray capacitance is also known as the fringing or edge capacitance. There are two methods to remove stray capacitance, by using the subtraction technique and guard electrodes. For the subtraction technique, the stray capacitance
C mut ¼ emut eo A=t mut
ð10Þ
C ag ¼ eo A=tag
ð11Þ
Fig. 4. Stray capacitance removal.
Fig. 5. Air gap equivalent circuit.
ð9Þ
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W.J.K. Raymond et al. / Measurement 46 (2013) 3796–3801 Table 1 Sample’s thickness and SRF. Sample
Thickness (mm)
SRF (MHz)
Teflon PCB FR4 Glass XLPE Craft Raper
5.5 1.6 01.53 0.9 0.5 0.17
84.048 75.574 84.547 71.087 84.547 81.057
Fig. 6. Test fixture model.
Fig. 9. Super-heterodyne interferometer.
Fig. 7. Test fixture set up.
Fig. 10. Complex impedance of craft paper.
Fig. 8. Test samples.
The capacitance due to air gap can be removed from the calculations using Eq. (9) once the air gap thickness is known. It is impossible to measure the air gap thickness because it is too small. Fortunately a small layer of air is
enough to cause a noticeable change in capacitance. This behavior was used by Kim and Moon [18] to measure small displacement based on the change in capacitance. In this work, the same concept was used to measure the air gap effective thickness. First, it is required to create a layer of air between the capacitor electrodes that has the exact same thickness as the MUT. The MUT was inserted into the test fixture and clamped tightly. The fixture was locked to prevent the conducting electrodes from moving, thus keeping the distance between the electrodes constant. A layer of air identical to the thickness of the MUT was created after the MUT was carefully slid out of the fixture. Eq. (11) was used to calculate the capacitance of air (Cair,calculated) that has the same thickness as the MUT.
3800
W.J.K. Raymond et al. / Measurement 46 (2013) 3796–3801
Fig. 11. Real permittivity of samples.
Fig. 12. Imaginary permittivity of samples.
Fig. 13. Tangent delta of samples.
This value was compared to the measured air capacitance (Cair,measured). The difference in this capacitance was used to estimate the effective air gap thickness. The effective air gap thickness is given in the following equation.
tag ¼ eo A=ðC calculated C measured Þ
ð12Þ
3. Experimental setup 3.1. Fixture preparation A table clamp was used as the base of the test fixture. Two round copper plates with diameter of 2.5 cm were cut from a copper plate using metal cutter. The edges
W.J.K. Raymond et al. / Measurement 46 (2013) 3796–3801 Table 2 Average real permittivity measured.
e0r
Capacitive
Interferometer
%Difference
PCB Glass XLPE Teflon FR4 Craft paper
4.66 7.50 2.25 2.11 4.37 2.78
4.75 7.62 2.33 2.20 4.42 2.83
1.90 1.49 3.36 4.20 1.28 1.61
of the round copper plates were smoothen using sand paper. SMA connectors were soldered to the copper plates and attached to a nonconductive holder. The text fixture model and a snapshot of the setup are shown in Figs. 6 and 7. 3.2. Sample details The operational frequency range of this experiment setup is limited by the lowest frequency of the VNA and the self resonating frequency of the parallel plate capacitor. The Agilent E5070 operation frequency range is 300 kHz– 3 GHz. The capacitor self resonating frequency (SRF) was determined by observing the graph of impedance magnitude versus frequency. The SRF is the frequency where the impedance magnitude is at the minimum. By observing the SRF of all samples, they are between 70–85 MHz. Therefore measurements were taken from 300 kHz to 50 MHz to avoid being too near to the SRF. The samples used in this work are a cylindrical shaped Teflon, a thin slab of glass, commercial PCB, FR4 board, a slice of cross link polyethylene (XLPE) and oil impregnated craft paper (insulation material of PILC cable). A picture of the samples is shown in Fig. 8. The thicknesses of the samples as well as their respective SRF are given in Table 1. 4. Experiment results Measurement of the same samples are made using the super-heterodyne interferometer developed by Chakrabarty et al. [19,20] to compare the accuracy of the capacitance method introduced in this paper. The interferometer is a free space measurement technique where the real permittivity is determined by the phase shift of two generated waves. A setup of the super heterodyne interferometer is shown in Fig. 9. Fig. 10 shows the complex impedance plot of craft paper. The S parameter to impedance conversion works perfectly as the graph of impedance versus frequency as shown in Fig. 9 is identical to the typical pattern which conforms to the graph in Agilent’s measurement handbook [16]. All samples’ real and imaginary permittivity measured using the capacitance method was shown in Figs. 11 and 12. The tangent delta is shown in Fig. 13. Measured real permittivity by both the free space and capacitance method were averaged and summarized in Table 2. 5. Conclusion The capacitance method of measuring complex permittivity was successfully implemented using a parallel plate
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capacitor fixture constructed in the laboratory. Inaccuracies caused by stray capacitance were successfully mitigated using the subtractive method. After reducing the stray components, the effective air gap thickness was estimated using the change in capacitance. The dielectric constant was measured and the results proved to be accurate by comparing with the interferometer method. The percentage error is less than 5%. These values were constant throughout the measurement frequency range. This method can also be used to determine the tangent delta for unknown dielectrics. References [1] D. Andjelkovic´, N. Rajakovic´, A new accelerated aging procedure for cable life tests, Electr. Power Syst. Res. 36 (1996) 13–19. [2] N. Bashir, H. Ahmad, M.S. Suddin, Ageing studies on transmission line glass insulators using dielectric dissipation factor test, IPEC, Conf. Proc. 2010 (2010) 1062–1066. [3] C.Y. Kuek, Measurement of dielectric material properties, Rohde & Schwarz Application Note, RAC0607-0019, 2006. [4] J.B. Jarvis, M.D. Janezic, B. Riddle, Dielectric and conductor-loss characterization and measurements on electronic packaging materials, NIST Technical Note 1520, 2001. [5] K. Sudheendran, D. Pamu, M. Ghanashyam Krishna, K.C. James Raju, Determination of dielectric constant and loss of high-K thin films in the microwave frequencies, Measurement 43 (2010) 556–562. [6] J. Sheen, Study of microwave dielectric properties measurements by various resonance techniques, Measurement 37 (2005) 123–130. [7] D.P. Singh, S. Saxena, S. Johri, H. Paudyal, M. Johri, Microwave cavity technique to study the dielectric response in 40 -n-Heptyl-4-biphenyl nematic liquid crystal at 20.900 GHz and 29.867 GHz, Measurement 44 (2011) 605–610. [8] Z. Abbas, R.D. Pollard, R.W. Kelsall, Complex permittivity measurements at Ka-band using rectangular dielectric waveguide, Instrum. Meas., IEEE Trans. on 50 (2001) 1334–1342. [9] S. Sßimsßek, C. Isßık, E. Topuz, B. Esen, Determination of the complex permittivity of materials with transmission/reflection measurements in rectangular waveguides, AEU – Int. J. Electron. Commun. 60 (2006) 677–680. [10] O.V. Bossou, J.R. Mosig, J.-F. Zurcher, Dielectric measurements of tropical wood, Measurement 43 (2010) 400–405. [11] U.C. Hasar, M.T. Yurtcan, A microwave method based on amplitudeonly reflection measurements for permittivity determination of lowloss materials, Measurement 43 (2010) 1255–1265. [12] D.K. Ghodgaonkar, V.V. Varadan, V.K. Varadan, A free-space method for measurement of dielectric constants and loss tangents at microwave frequencies, Instrum. Meas., IEEE Trans. on 38 (1989) 789–793. [13] M.G. Broadhurst, A.J. Bur, Two-terminal dielectric measurements up to 6 108 Hz, J. Res. Nat. Bur. Stand. (U.S.) 69C (1965) 165–172. [14] ASTM Standards D-150, AC loss characteristics and permittivity of solid electrical insulating materials, Electr. Insul. Mater. Stand. (1980). [15] Agilent Technologies, Impedance Measurements Evaluation EMC components with DC Bias Superimposed, Application Note, 5989– 9887EN, 2009. [16] Agilent Technologies, A guide to measurement technology and techniques, fourth ed., Impedance Measurement Handbook, 2009. [17] K.E. Mattar, D.G. Watters, M.E. Brodwin, Influence of wall contacts on measured complex permittivity spectra at coaxial line frequencies, Microwave Theory Tech., IEEE Trans. on 39 (1991) 532–537. [18] M. Kim, W. Moon, A new linear encoder-like capacitive displacement sensor, Measurement 39 (2006) 481–489. [19] G.C. Hock, C.K. Chakrabarty, M.H. Badjian, S. Devkumar, Emilliano, Super-heterodyne interferometer for non-contact dielectric measurements on millimeter wave material, RF and Microwave Conference, RFM, IEEE International, 2008, pp. 167–170. [20] Y.F. Yee, C.K. Chakrabarty, Phase detection using AD8302 evaluation board in the superheterodyne microwave interferometer for line average plasma electron density measurements, Measurement 40 (2007) 849–853.
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Complex permittivity measurement using capacitance method from 300 kHz to 50 MHz Wong Jee Keen Raymond a,c,⇑, Chandan Kumar Chakrabarty a, Goh Chin Hock a, Ahmad Basri Ghani b a
Universiti Tenaga Nasional, Department of Electronic and Communication Engineering, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia TNB Research Sdn. Bhd., No. 1, Lorong Air Hitam, Kawasan Institusi Penyelidikan, 43000 Kajang, Selangor, Malaysia c University of Malaya, Department of Electrical Engineering, Faculty of Engineering, 50603 Kuala Lumpur, Malaysia b
a r t i c l e
i n f o
Article history: Received 6 September 2012 Accepted 25 June 2013 Available online 4 July 2013 Keywords: Component Complex permittivity Parallel plate capacitor Vector network analyzer VNA Dielectric constant Measurement
a b s t r a c t Complex permittivity measurement has been performed using a parallel plate capacitor and a vector network analyzer (VNA) from 300 kHz to 50 MHz. The material under test (MUT) is a flat and thin sample clamped between the capacitor plates and connected to the VNA to obtain its two port S parameters. The S parameter is converted into impedance to calculate the complex permittivity using Matlab program. Techniques used to overcome the air gap and stray capacitance was described. Measurement obtained using the proposed method was compared with the free space method to validate its accuracy. The percent difference is less than 5%. Ó 2013 Published by Elsevier Ltd.
1. Introduction Complex permittivity (e0r + je00r ) is a very useful parameter where the quality factor (e0r /e00r ) and tangent delta (e00r /e0r ) can be derived from the complex permittivity. These parameters are useful in power industry because they can be used as an indication of the power cable’s insulation quality [1,2]. Therefore there is a strong demand for complex permittivity measurement related research. There are a lot of methods developed for measuring the complex permittivity but these techniques are limited to specific frequencies, materials, and applications [3]. A list of currently known complex permittivity measurement has been described by Jarvis et al. in NIST technical note [4]. Two widely used measurement methods are resonant ⇑ Corresponding author. Tel.: +60 126045003. E-mail addresses: [email protected] (W.J.K. Raymond), [email protected] (C.K. Chakrabarty), [email protected] (G.C. Hock), [email protected] (A.B. Ghani). 0263-2241/$ - see front matter Ó 2013 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.measurement.2013.06.039
method and transmission/reflection method [5]. Resonant methods [6] have many variants such as split cylinder resonator, cavity resonator [7], Courtney technique, whispering gallery resonator and Farbry Perot resonators. Although resonant methods are highly accurate, measurements can only be done at one frequency which is the resonant frequency. Transmission/reflection method is able to measure the complex permittivity in a frequency range but requires the usage of waveguides [8–11]. Waveguides has two disadvantages. First, it is necessary to machine the sample to precisely fit the waveguide cross section with negligible air gaps. This requirement will limit the accuracy of measurements for materials which cannot be machined precisely [12]. The second disadvantage is the size limitation. Smaller sample size requires smaller waveguides which forces measurement to take place at a much higher frequency. There are plenty of research and implementation of resonant methods and transmission/reflection methods at GHz frequency range. Therefore this paper will focus on the less developed capacitance method in the MHz range.
W.J.K. Raymond et al. / Measurement 46 (2013) 3796–3801
3797
calibration kit before the measurement. The test fixture was connected to the VNA as shown in Fig. 1. SMA cables were used as coaxial cables to connect the fixture to the VNA. Once the test fixture is connected as shown in Fig. 1, its S parameters can be converted to impedance using Eq. (1) [15].
Z ¼ 100ð1 S21 Þ=S21
Fig. 1. Fixture and VNA connection.
The capacitance method involves sandwiching a thin material between two electrodes to form a capacitor. The typical capacitance method frequency range is from DC to 100 MHz [13]. This limitation is due to the fact that the capacitor will start to behave like an inductor above its resonance frequency which may vary for different materials. Capacitance method has several benefits which are the relatively low cost, easier sample preparation, easy to built fixture, and ability to measure at a frequency range. In this work, two round copper plates with diameter of 2.5 cm were used as the electrodes. The techniques to overcome the two main weaknesses of capacitance method i.e. stray capacitance and air gap will be discussed. The measured samples are thin, flat and has a surface area larger than the capacitor conducting plate [14]. The uniqueness of this work is the usage of VNA to measure impedance instead of LCR meter. Impedance is obtained through conversion of measured S parameter. VNA is preferred because it is more commonly available in research labs.
ð1Þ
The impedance measured by this method is the combinations of MUT impedance and fixture impedance. The fixture impedance must be removed to prevent systematic error in future calculations. The fixture impedance consists of residual impedance and stray admittance as depicted in Fig. 2 [16]. To determine the stray admittance, an open circuit was created at the MUT. This will cause the stray admittance to be huge and the residual impedance to be negligible. Hence the impedance measured when MUT is open will be the stray admittance. The residual impedance was measured when the test fixture was shorted. This will cause the stray admittance to be shorted and the measured impedance value will be the residual impedance. The MUT impedance Zmut can be determined once the residual impedance and stray admittance is known using the following equation.
Z mut ¼ ðZ measured Z s Þ=ð1 Y o ðZ measured Z s ÞÞ
ð2Þ
2.2. Converting impedance to complex permittivity The test fixture sandwiching the MUT can be modeled as a capacitor that has an equivalent circuit shown in Fig. 3. The equivalent circuit can be modeled as a series model or parallel model. Impedance to permittivity conversion requires the parallel model. Conversion between parallel and series model can be done using Eqs. (4) and (5).
Tan d ¼ xRs C s ¼ 1=ðxRp C p Þ
ð3Þ
2. Measurement theory
C p ¼ C s =ð1 þ ðTan dÞ2 Þ
ð4Þ
2.1. Converting S parameters to impedance
Rp =Rs ¼ 1 þ 1=ðTan dÞ2
ð5Þ
In this work, the S parameters were measured using Agilent’s E5070 vector network analyzer (VNA). Full two port calibration was performed using the Agilent 85032B
Y ¼ G þ jxC p
ð6Þ
Fig. 2. Test fixture’s impedance model.
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W.J.K. Raymond et al. / Measurement 46 (2013) 3796–3801
Fig. 3. Equivalent circuit of capacitor with MUT as dielectric core.
e00r ¼ t=ðxARp eo Þ
ð7Þ
e0r ¼ tC p =ðAeo Þ
ð8Þ
was modeled as a capacitor in parallel with the MUT capacitance. Therefore the stray capacitance could be eliminated by measuring the capacitance with and without the sample and subtracting the results as in Fig. 4. The stray capacitance could also be eliminated using guard electrodes [14]. Guard electrodes are very effective in eliminating stray capacitance but it will increase the complexity of the test fixture and the overall cost. In this work the stray capacitance which is part of the test fixture residual admittance was eliminated during the test fixture impedance removal. 2.4. Elimination air gap
A is the area of the capacitor electrode, while t is the sample thickness. eo is the permittivity of free space and its value is 8.8542 1012 F/m. The measured impedance of the MUT was converted to the parallel representation using Eqs. (4) and (5). Once Rp and Cp were known, Eqs. (7) and (8) were then used to calculate the complex permittivity. Matlab was used to perform all the calculations required to obtain the complex permittivity.
Research by Mattar et al. [17] shows that measurement accuracy is severely affected by the air gap between the MUT and capacitor electrodes. It is necessary to eliminate air gap in order to get accurate measurements. Air gaps are layers or pockets of air that exist between the MUT and capacitor conducting electrodes. An inevitable thin layer of air gaps will exist due to roughness of the MUT and the electrodes surface regardless how tight the MUT is clamped. Air gap can be modeled as a capacitor in series with the MUT capacitance, as illustrated in Fig. 5.
2.3. Eliminating stray capacitance
1=C measured ¼ 1=C mut þ 1=C ag
Stray capacitance is also known as the fringing or edge capacitance. There are two methods to remove stray capacitance, by using the subtraction technique and guard electrodes. For the subtraction technique, the stray capacitance
C mut ¼ emut eo A=t mut
ð10Þ
C ag ¼ eo A=tag
ð11Þ
Fig. 4. Stray capacitance removal.
Fig. 5. Air gap equivalent circuit.
ð9Þ
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W.J.K. Raymond et al. / Measurement 46 (2013) 3796–3801 Table 1 Sample’s thickness and SRF. Sample
Thickness (mm)
SRF (MHz)
Teflon PCB FR4 Glass XLPE Craft Raper
5.5 1.6 01.53 0.9 0.5 0.17
84.048 75.574 84.547 71.087 84.547 81.057
Fig. 6. Test fixture model.
Fig. 9. Super-heterodyne interferometer.
Fig. 7. Test fixture set up.
Fig. 10. Complex impedance of craft paper.
Fig. 8. Test samples.
The capacitance due to air gap can be removed from the calculations using Eq. (9) once the air gap thickness is known. It is impossible to measure the air gap thickness because it is too small. Fortunately a small layer of air is
enough to cause a noticeable change in capacitance. This behavior was used by Kim and Moon [18] to measure small displacement based on the change in capacitance. In this work, the same concept was used to measure the air gap effective thickness. First, it is required to create a layer of air between the capacitor electrodes that has the exact same thickness as the MUT. The MUT was inserted into the test fixture and clamped tightly. The fixture was locked to prevent the conducting electrodes from moving, thus keeping the distance between the electrodes constant. A layer of air identical to the thickness of the MUT was created after the MUT was carefully slid out of the fixture. Eq. (11) was used to calculate the capacitance of air (Cair,calculated) that has the same thickness as the MUT.
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W.J.K. Raymond et al. / Measurement 46 (2013) 3796–3801
Fig. 11. Real permittivity of samples.
Fig. 12. Imaginary permittivity of samples.
Fig. 13. Tangent delta of samples.
This value was compared to the measured air capacitance (Cair,measured). The difference in this capacitance was used to estimate the effective air gap thickness. The effective air gap thickness is given in the following equation.
tag ¼ eo A=ðC calculated C measured Þ
ð12Þ
3. Experimental setup 3.1. Fixture preparation A table clamp was used as the base of the test fixture. Two round copper plates with diameter of 2.5 cm were cut from a copper plate using metal cutter. The edges
W.J.K. Raymond et al. / Measurement 46 (2013) 3796–3801 Table 2 Average real permittivity measured.
e0r
Capacitive
Interferometer
%Difference
PCB Glass XLPE Teflon FR4 Craft paper
4.66 7.50 2.25 2.11 4.37 2.78
4.75 7.62 2.33 2.20 4.42 2.83
1.90 1.49 3.36 4.20 1.28 1.61
of the round copper plates were smoothen using sand paper. SMA connectors were soldered to the copper plates and attached to a nonconductive holder. The text fixture model and a snapshot of the setup are shown in Figs. 6 and 7. 3.2. Sample details The operational frequency range of this experiment setup is limited by the lowest frequency of the VNA and the self resonating frequency of the parallel plate capacitor. The Agilent E5070 operation frequency range is 300 kHz– 3 GHz. The capacitor self resonating frequency (SRF) was determined by observing the graph of impedance magnitude versus frequency. The SRF is the frequency where the impedance magnitude is at the minimum. By observing the SRF of all samples, they are between 70–85 MHz. Therefore measurements were taken from 300 kHz to 50 MHz to avoid being too near to the SRF. The samples used in this work are a cylindrical shaped Teflon, a thin slab of glass, commercial PCB, FR4 board, a slice of cross link polyethylene (XLPE) and oil impregnated craft paper (insulation material of PILC cable). A picture of the samples is shown in Fig. 8. The thicknesses of the samples as well as their respective SRF are given in Table 1. 4. Experiment results Measurement of the same samples are made using the super-heterodyne interferometer developed by Chakrabarty et al. [19,20] to compare the accuracy of the capacitance method introduced in this paper. The interferometer is a free space measurement technique where the real permittivity is determined by the phase shift of two generated waves. A setup of the super heterodyne interferometer is shown in Fig. 9. Fig. 10 shows the complex impedance plot of craft paper. The S parameter to impedance conversion works perfectly as the graph of impedance versus frequency as shown in Fig. 9 is identical to the typical pattern which conforms to the graph in Agilent’s measurement handbook [16]. All samples’ real and imaginary permittivity measured using the capacitance method was shown in Figs. 11 and 12. The tangent delta is shown in Fig. 13. Measured real permittivity by both the free space and capacitance method were averaged and summarized in Table 2. 5. Conclusion The capacitance method of measuring complex permittivity was successfully implemented using a parallel plate
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capacitor fixture constructed in the laboratory. Inaccuracies caused by stray capacitance were successfully mitigated using the subtractive method. After reducing the stray components, the effective air gap thickness was estimated using the change in capacitance. The dielectric constant was measured and the results proved to be accurate by comparing with the interferometer method. The percentage error is less than 5%. These values were constant throughout the measurement frequency range. This method can also be used to determine the tangent delta for unknown dielectrics. References [1] D. Andjelkovic´, N. Rajakovic´, A new accelerated aging procedure for cable life tests, Electr. Power Syst. Res. 36 (1996) 13–19. [2] N. Bashir, H. Ahmad, M.S. Suddin, Ageing studies on transmission line glass insulators using dielectric dissipation factor test, IPEC, Conf. Proc. 2010 (2010) 1062–1066. [3] C.Y. Kuek, Measurement of dielectric material properties, Rohde & Schwarz Application Note, RAC0607-0019, 2006. [4] J.B. Jarvis, M.D. Janezic, B. Riddle, Dielectric and conductor-loss characterization and measurements on electronic packaging materials, NIST Technical Note 1520, 2001. [5] K. Sudheendran, D. Pamu, M. Ghanashyam Krishna, K.C. James Raju, Determination of dielectric constant and loss of high-K thin films in the microwave frequencies, Measurement 43 (2010) 556–562. [6] J. Sheen, Study of microwave dielectric properties measurements by various resonance techniques, Measurement 37 (2005) 123–130. [7] D.P. Singh, S. Saxena, S. Johri, H. Paudyal, M. Johri, Microwave cavity technique to study the dielectric response in 40 -n-Heptyl-4-biphenyl nematic liquid crystal at 20.900 GHz and 29.867 GHz, Measurement 44 (2011) 605–610. [8] Z. Abbas, R.D. Pollard, R.W. Kelsall, Complex permittivity measurements at Ka-band using rectangular dielectric waveguide, Instrum. Meas., IEEE Trans. on 50 (2001) 1334–1342. [9] S. Sßimsßek, C. Isßık, E. Topuz, B. Esen, Determination of the complex permittivity of materials with transmission/reflection measurements in rectangular waveguides, AEU – Int. J. Electron. Commun. 60 (2006) 677–680. [10] O.V. Bossou, J.R. Mosig, J.-F. Zurcher, Dielectric measurements of tropical wood, Measurement 43 (2010) 400–405. [11] U.C. Hasar, M.T. Yurtcan, A microwave method based on amplitudeonly reflection measurements for permittivity determination of lowloss materials, Measurement 43 (2010) 1255–1265. [12] D.K. Ghodgaonkar, V.V. Varadan, V.K. Varadan, A free-space method for measurement of dielectric constants and loss tangents at microwave frequencies, Instrum. Meas., IEEE Trans. on 38 (1989) 789–793. [13] M.G. Broadhurst, A.J. Bur, Two-terminal dielectric measurements up to 6 108 Hz, J. Res. Nat. Bur. Stand. (U.S.) 69C (1965) 165–172. [14] ASTM Standards D-150, AC loss characteristics and permittivity of solid electrical insulating materials, Electr. Insul. Mater. Stand. (1980). [15] Agilent Technologies, Impedance Measurements Evaluation EMC components with DC Bias Superimposed, Application Note, 5989– 9887EN, 2009. [16] Agilent Technologies, A guide to measurement technology and techniques, fourth ed., Impedance Measurement Handbook, 2009. [17] K.E. Mattar, D.G. Watters, M.E. Brodwin, Influence of wall contacts on measured complex permittivity spectra at coaxial line frequencies, Microwave Theory Tech., IEEE Trans. on 39 (1991) 532–537. [18] M. Kim, W. Moon, A new linear encoder-like capacitive displacement sensor, Measurement 39 (2006) 481–489. [19] G.C. Hock, C.K. Chakrabarty, M.H. Badjian, S. Devkumar, Emilliano, Super-heterodyne interferometer for non-contact dielectric measurements on millimeter wave material, RF and Microwave Conference, RFM, IEEE International, 2008, pp. 167–170. [20] Y.F. Yee, C.K. Chakrabarty, Phase detection using AD8302 evaluation board in the superheterodyne microwave interferometer for line average plasma electron density measurements, Measurement 40 (2007) 849–853.