IEEE SENSORS JOURNAL, VOL. 15, NO. 10, OCTOBER 2015
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Simple Calibration and Dielectric Measurement Technique for Thin Material Using Coaxial Probe Kok Yeow You, Member, IEEE, and Yi Lung Then, Student Member, IEEE
Abstract— This paper focuses on the nondestructive dielectric measurement for thin dielectric material using open-ended coaxial probe. The probe calibration procedure requires only a measurement of a half-space air and three open standard kits. The measured reflection coefficient for thin sample, which is backed by metal plate, is taken with a vector network analyzer up to 7 GHz and the reflection coefficient is converted to relative dielectric constant and tangent loss via closed form capacitance model and simple calibration process. Index Terms— Coaxial probe, thin material measurements, effective permittivity, calibration.
I. I NTRODUCTION
A
N OPEN-ENDED coaxial probe method is the simplest, broadband and nondestructive way to measure the dielectric properties of materials. However, a significant thickness of the material is required for regular measurement using coaxial probe, since the scattering of the wave from the probe’s aperture will penetrate the material and impinge on the other layer-interface medium. Various methods have been used to derive the analytical and numerical equations of the coaxial probe in order to determine the reflected fields at the probe’s aperture which is considered the effect of the layered medium terminated at aperture [7]–[12]. Later, those equations are used to estimate the relative complex permittivity, εr of the layered medium by minimizing the difference between the measured reflection coefficient, and the analytical or numerical equations. Normally, these types of techniques require a robust and complicated mathematical calculation. Thus, this study attempts to simplify this dielectric measurement technique for thin materials, in which its thickness, h, is smaller than the diameter of the outer conductor, 2b, for the modified coaxial probe. In addition, this proposed method does not involve having to make an initial estimate of the anticipated value. The measurement technique and steps of the calibration will be described in Section II. While, the measurement results will be analyzed in Section III.
Manuscript received March 13, 2015; accepted April 21, 2015. Date of publication May 4, 2015; date of current version August 6, 2015. This work was supported by the Universiti Teknologi Malaysia Research University Grant under Grant Q.J130000.2523.04H77. The associate editor coordinating the review of this paper and approving it for publication was Prof. Sang-Seok Lee. The authors are with the Department of Communication Engineering, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia (e-mail:
[email protected]; andythenyl@ yahoo.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSEN.2015.2427873
II. C ALIBRATION AND D IELECTRIC M EASUREMENT T ECHNIQUES The coaxial probe is fabricated from a square flange SMA stub contact panel with 2a = 1.3 mm and 2b = 4.1 mm, respectively, as shown in Fig. 2 (a). The reflection coefficients, of the thin material which is backed by metal plate are measured using an Agilent E5071C network analyzer from 0.5 to 7 GHz. There are four steps of calibration and dielectric measurement procedures as below: Step 1: A full one-port calibration is implemented at the end of cable (plane A A ) using an Agilent 85052D calibration kit. Then, a normalized de-embedding formulation (1) is used to calibrate the aperture of coaxial probe (See Fig. 2 (c)). Air_ F E M B B = A A (1) Air where Air is the reflection coefficient measurement for air at plane AA , and Air_ F E M is the standard value of reflection coefficients for air at aperture probe (plane BB , obtained by using the COMSOL simulator. In the simulation, the conductor of the coaxial probe is assumed to be a perfect conductor and relative permittivity of the filled Teflon in the coaxial line equals to 2.06. Discussion of Step 1: Fig. 1 shows the comparison between the reflection coefficient of the air for the coaxial probe at measurement port (plane AA ) and probe aperture (plane BB ), respectively. The accuracy of simulated reflection coefficient, A A = Re( A A ) + j Im( A A ) is validated using measured data since both values are equally the same as shown in Fig. 1 (a). However, the reflection coefficient, B B = Re( B B ) + j Im( B B ) obtained from simulation and calibrated measurement at the plane BB’ is slightly different as shown in Fig 1 (b). In this work, the measured B B is obtained using three-standard calibration technique (air, water and methanol liquid) [5]. The derivation between the simulation and measurement results are mainly due to the standard reflection coefficient values of the air (open-circuited), water or methanol in the calibration process may not accurately represent the actual reflection coefficient values. For this reason, the simulated reflection coefficient at probe aperture is chosen as the standard values rather than using the calibrated measurement data. Step 2: The B B is measured with the aperture of the probe placed on top of a custom-made calibration kit. Three calibration kits have been made by using aluminum cubes in which the cube centers are machined to produce a concave rounded with depth, h 1 = (0.4±0.05) mm, h 2 = (0.7±0.05) mm and
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TABLE I R ELATIVE E RRORS IN C ONCAVE D EPTH AND M EASURED B B
Fig. 1. The comparison of: (a) the reflection coefficient, AA at measurement port and (b) the reflection coefficient, B B at probe aperture.
Fig. 3. Variation in εe f f with thickness layer, h of methanol liquid which back by metallic plate.
Fig. 2. (a) Dimensions of the coaxial probe. (b) Offset open-circuit kit. (c) Calibration set-up.
h 3 = (1±0.05) mm, respectively (See Fig. 2 (b)). The effective relative permittivity, εe f f = εe f f − j εef f of the three kits is determined by using equation (2): Yo 1 − B B εe f f = (2) j ωC 1 + B B √ = [(2π)/ln(b/a)] (εo εc /μo μc ), Symbol Yo C = 2.38εo(b-a) [1] and ω are the characteristic admittance, aperture probe capacitance and the angular frequency, respectively. The εc (=2.06) and μc (=1) are the relative permittivity and relative permeability of a material for the coaxial probe measurement. Discussion of Step 2: The limited precision of the concave depth, h for the calibration kits, due to uncertainty in machining, can cause errors in the reflection
coefficient, measurement. The maximum percentage relative error of concave depth, h/ h and the corresponding relative error of the measured B B are tabulated in Table I. The relative error in the reflection coefficient, B B / B B with respect to the relative change in relative effective permittivity, εe f f , can be derived from (2) and given as: εe f f B B (3) |ξ | B B where ξ is the sensitivity coefficient which is expressed as: Yo + j ωεef f C 2 j ωC ξ = −εef f 2 . (4) Yo − j ωεef f C Yo + j ωεef f C εe f f =
Step 3: The relationship between the actual relative permittivity, εr and εe f f for a finite thickness sample is empirically expressed as: (5) εr = εe f f a1 + a2 e−h/M + a3 e−2h/M where a1 , a2 and a3 are the unknown complex coefficients, which are desired to be found. In this work, the empirical coefficient, M in (5) is found to suit the study probe,
YOU AND THEN: SIMPLE CALIBRATION AND DIELECTRIC MEASUREMENT TECHNIQUE FOR THIN MATERIAL
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Fig. 4. Prediction of |M| using (7) and the measured εe f f data from Fig. 3.
Fig. 6. The comparison of: (a) the effective relative dielectric constant, εe f f , and (b) the effective loss tangent, tan δe f f , for three different thickness of RT/duroid 5880 substrate using Eq (2) and Agilent 85070D probe.
using (2). The values of εr1 , εr2 and, εr3 are estimated by matching the measurement and simulation of B B . The results shows εr1 =1.14, εr2 =1.13, εr3 =1.08. Then, the unknown values of a1 = Re(a1 )+ j Im(a1), a2 = Re(a2 )+ j Im(a2 ) and a3 = Re(a3 ) + j Im(a3 ) are found by using Gaussian elimination routine. Discussion of Step 3: Rearrange the (5) and assume that the a1 = 1, a2 = −1 and a3 e−2h/M = 0, yields, M= Fig. 5. The values of: (a) Re(a1 ), Re(a2 ), and Re(a3 ) and (b) Im(a1 ), Im(a2 ), and Im(a3 ), respectively.
which can be represented by a single value as 0.0006 m. The values of εe f f , M and h for the three kits are respectively replaced into (5). Thus, 3 sets of linear equations are created and expressed in matrix form as: ⎤ ⎡ ⎤⎡ ⎤ ⎡ εe f f 1 εe f f 1 e−h 1 /M εe f f 1 e−2h 1 /M a1 εr1 ⎣ εr2 ⎦ = ⎣ εe f f 2 εe f f 2 e−h 2 /M εe f f 2 e−2h 2 /M ⎦ ⎣ a2 ⎦ εr3 a3 εe f f 3 εe f f 3 e−h 3 /M εe f f 3 e−2h 3 /M (6) where εe f f 1 , εe f f 2 and εe f f 3 are the effective relative permittivity of the three kits, respectively, which are found
−h ln 1 − εr /εe f f
(7)
From (5), the value of M can be roughly determined. For instance, the values of εr in (7) for methanol is calculated using Cole-Cole model [6]. The calculated values of εr for 1 GHz and 5 GHz are respectively given as 31.26 j 9.25 and 12.13 - j 12.75. On the other hand, the values of εe f f at each corresponding distance, h are converted from measured reflection coefficient, B B using (2). The values of εe f f versus the thickness layer, h of the methanol liquid for 1 GHz and 5 GHz is plotted in Fig 3. When the metal plate distance, h is increasing from the probe aperture, the value of εe f f becomes constant and approximates to the actual relative permittivity, εr . The calculated of |M| using (7) and εe f f data from Fig. 3 is plotted in Fig. 4. Clearly, the average value of |M| is about 0.0006 m.
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Normally, the sample is considered infinitely thick if the sample has a thickness, h s ≥ 2b [3]. The measured εe f f can be further calibrated to obtain the actual permittivity, εr using step 3 and step 4 as shown in Fig. 7. Obviously, the calibrated εr for the three RT/duroid 5880 substrates are in good agreement with the expected values. In addition, the εr for FR4 (εr = 4.3, tan δ = 0.02) and RO 3206 (εr = 6.15, tan δ = 0.0027) substrates are also measured, which are close to the expected values. The average deviation of the calibrated εr and the values provided by the manufacturer are within 1.5 % over a frequency range from 0.5 GHz to 7 GHz. However, overall results of the predicted tan δ are slightly higher than the expected values. The prediction of the tan δ for low-loss samples from measured B B lacks sufficient resolution [4], since those values are too small. It is well known that resonance measurement techniques are good selections for determining low tan δ values, but such techniques cannot be used for the measurement of swept frequency. This study method is relatively simple, significantly minimal data processing time and does not require any initial estimate of the anticipated value which may cause initial value dependent error in permittivity prediction. R EFERENCES
Fig. 7. Variation in: (a) relative dielectric constant, εr , and (b) the loss tangent, tan δ, for RT/duroid 5880, FR4 and RO 3206 substrates.
The calculated complex coefficients, (a1 , a2 and a3 ) are shown in Fig 5. Obviously, the Re(a1) and Re(a2 ) are approximate to 1 and −1, respectively. Meanwhile, the Re(a3 ) is nearly equal to zero, meaning that equation (3) is more influenced by the first term, a1 and the second term, a2 rather than the third term, a3 . On the other hand, over all of the imaginary part of coefficients (Im(a1 ), Im(a2 ) and Im(a3 )) are near to zero value. Step 4: Repeat step 1 and step 2 for unknown sample with thickness of h s , backed by metal plate. Finally, the εr = εr (1− j tan δ), for the sample can be found from (8) using the previous values of a1 , a2 , a3 , M, h s and measured εe f f . Yo 1− B B a1 + a2 e−h s /M + a3 e−2h s /M . (8) εr = j ωC 1+ B B III. R ESULTS AND D ISCUSSIONS Fig. 6 shows the measured εe f f for the three different thicknesses, h s of the RT/duroid 5880 substrate (εr = 2.2, tan δ = 0.001) using step 1 and step 2 procedures, as well as using an Agilent 85070D dielectric probe with 2b = 3 mm [2]. Clearly, the measured εe f f are strongly depending on the probe dimensions and the h s of the sample.
[1] G. B. Gajda and S. S. Stuchly, “Numerical analysis of open-ended coaxial lines,” IEEE Trans. Microw. Theory Techn., vol. 31, no. 5, pp. 380–384, May 1983. [2] D. V. Blackham and R. D. Pollard, “An improved technique for permittivity measurements using a coaxial probe,” IEEE Trans. Instrum. Meas., vol. 46, no. 5, pp. 1093–1099, Oct. 1997. [3] P. De Langhe, L. Martens, and D. De Zutter, “Design rules for an experimental setup using an open-ended coaxial probe based on theoretical modelling,” IEEE Trans. Instrum. Meas., vol. 43, no. 6, pp. 810–817, Dec. 1994. [4] J. Sheen, “Comparisons of microwave dielectric property measurements by transmission/reflection techniques and resonance techniques,” Meas. Sci. Technol., vol. 20, no. 4, pp. 1–12, 2009. [5] A. Kraszewski, M. A. Stuchly, and S. S. Stuchly, “ANA calibration method for measurements of dielectric properties,” IEEE Trans. Instrum. Meas., vol. 32, no. 2, pp. 385–387, Jun. 1983. [6] A. Nyshadham, C. L. Sibbald, and S. S. Stuchly, “Permittivity measurements using open-ended sensors and reference liquid calibration— An uncertainty analysis,” IEEE Trans. Microw. Theory Techn., vol. 40, no. 2, pp. 305–314, Feb. 1992. [7] L. S. Anderson, G. B. Gajda, and S. S. Stuchly, “Analysis of an openended coaxial line sensor in layered dielectrics,” IEEE Trans. Instrum. Meas., vol. IM-35, no. 1, pp. 13–18, Mar. 1986. [8] J. Baker-Jarvis, M. D. Janezic, P. D. Domich, and R. G. Geyer, “Analysis of an open-ended coaxial probe with lift-off for nondestructive testing,” IEEE Trans. Instrum. Meas., vol. 43, no. 5, pp. 711–718, Oct. 1994. [9] S. Bakhtiari, S. I. Ganchev, and R. Zoughi, “Analysis of radiation from an open-ended coaxial line into stratified dielectrics,” IEEE Trans. Microw. Theory Techn., vol. 42, no. 7, pp. 1261–1267, Jul. 1994. [10] S. Fan, K. Staebell, and D. Misra, “Static analysis of an open-ended coaxial line terminated by layered media,” IEEE Trans. Instrum. Meas., vol. 39, no. 2, pp. 435–437, Apr. 1990. [11] Y. C. Noh and H. J. Eom, “Radiation from a flanged coaxial line into a dielectric slab,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 11, pp. 2158–2161, Nov. 1999. [12] Z. Qiu, X. Li, and W. Jiang, “On stability of formulation of openended coaxial probe for measurement of electromagnetic properties of finite-thickness materials,” J. Electromagn. Waves Appl., vol. 23, no. 4, pp. 501–511, 2009.
YOU AND THEN: SIMPLE CALIBRATION AND DIELECTRIC MEASUREMENT TECHNIQUE FOR THIN MATERIAL
Kok Yeow You (M’09) was born in 1977. He received the B.Sc. (Hons.) degree in physics from Universiti Kebangsaan Malaysia in 2001, the M.Sc. degree in microwave from the Faculty of Science in 2003, and the Ph.D. degree in wave propagation from the Institute for Mathematical Research, Universiti Putra Malaysia, in 2006. He is currently a Senior Lecturer with the Communication Engineering Department, Faculty of Electrical Engineering, Universiti Teknologi Malaysia. His main personnel research interest is in the theory, simulation, and instrumentation of electromagnetic wave propagation at microwave frequencies focusing on the development of microwave sensors for agricultural applications.
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Yi Lung Then (S’12) was born in Kuching, Sarawak, Malaysia, in 1988. He received the B.Eng. (Hons.) degree in electrical engineering from Universiti Teknologi Malaysia in 2012, where he is currently pursuing the Ph.D. degree in telecommunication engineering on the measurement of agricultural products based on microwave techniques.
