Building a resonant cavity for the measurement ... - Wiley Online Library

achieved. To manifest this phenomenon, the simulated results of axial ratio against elevation angle for the proposed antenna with and without three small triangles at the frequency of 2.4 GHz are shown in Figures 7(a) and 7(b) respectively. It can be observed that the AR distribution in the elevation direction for the proposed antenna with three small triangles is more symmetric along the elevation angle of 0° than that without three triangles. 4. CONCLUSIONS

A microstrip-fed CP square shorted ring-slot antenna has been investigated and successfully implemented. The return loss characteristic and CP radiation performance can be controlled and improved individually. The proposed antenna has several advantages at the same time which include return loss of ⫺50.44 dB at the resonant frequency of 2.4 GHz, impedance bandwidth of 930 MHz, 3-dB AR bandwidth of 310 MHz, and good broadside CP radiation patterns over a wide elevation angle range of 80° in the azimuthal directions. The proposed antenna presents excellent performances and is very suitable for wireless communication applications ACKNOWLEDGMENT

This project is supported by National Science Council under grant NSC 94 –3111-466 – 003-Y21. REFERENCES 1. H. Morishita, K. Hirasawa, and K. Fujimoto, Analysis of a cavity backed annular slot antenna with one point shorted, IEEE Trans Antennas Propag 39 (1991), 1472–1478. 2. W.S. Chen, C.C. Huang, and K.L. Wong, Microstrip-line-fed printed shorted ring-slot antenna for circular polarization, Microwave Opt Technol Lett 3 (2001), 137–140. 3. K.L. Wong, C.C. Huang, and W.S. Chen, Printed ring slot antenna for circular polarization, IEEE Trans Antennas Propag 50 (2002), 75–77. 4. J.S. Row, C.Y.D. Sim, and K.W. Lin, Broadband printed ring-slot array with circular polarization, Electron Lett 41 (2005), 110 –112. 5. B.Y. Toh, R. Cahill, and Vincent F, Fusco, Understanding and measuring circular polarization, IEEE Trans Edu 46 (2003), 313–318. © 2007 Wiley Periodicals, Inc.

Figure 7 Simulated axial ratio against elevation angle at the frequency of 2.4 GHz for the proposed antenna (a) with and (b) without three small triangles

values over a wide angle range. From Figure 5, the elevation-angle ranges with respected to lower 3-dB AR are ⫺33 to 29, ⫺43 to 47 and ⫺49 to 9°, respectively, for 2.3, 2.4 and 2.5 GHz in the upper half free space. It can be seen that the space distribution of the AR value are more symmetric at the frequencies of 2.3 and 2.4 GHz than that at the frequency of 2.5 GHz. To further manifest the symmetric distribution of axial ratio, the calculated results obtained from the depth of the ripples in these measured polarization patterns are shown in Figure 6. It can be observed that the AR pattern with respect to elevation angle is nearly symmetric along the elevation angle of 0° at the frequencies of 2.3 and 2.4 GHz. By using the three small triangles at the square-ring slot corners to perturb the magnetic current within the square-ring slot, the symmetric AR space distribution and the minimum AR position can be further controlled. In this proposed antenna, the length of c3 (4 mm) is not equal to the length of c1 and c2 (2 mm), and in this condition, a very symmetric AR space distribution can be

DOI 10.1002/mop

BUILDING A RESONANT CAVITY FOR THE MEASUREMENT OF MICROWAVE DIELECTRIC PERMITTIVITY OF HIGH LOSS MATERIALS C. P. L. Rubinger and L. C. Costa Physics Department, University of Aveiro, 3810 –193 Aveiro, Portugal Received 19 December 2006 ABSTRACT: The design of a cavity resonator implies to solve the Maxwell equations inside that cavity, respecting the boundary conditions. As a consequence, the resonance frequencies appear as conditions in the solutions of the differential equation involved. The measurement of the complex permittivity, ␧* ⫽ ␧⬘-i␧⬙, can be made using the small perturbation theory. In this method, the resonance frequency and the quality factor of the cavity, with and without a sample, can be used to calculate the complex dielectric permittivity of the material. We measure the shift in the resonant frequency of the cavity, ⌬f, caused by the insertion of the sample inside the cavity, which can be related to the real part of the complex permittivity, ␧⬘ , and the change in the inverse of the quality factor of the cavity, ⌬(1/Q) , which can be related with the imaginary part, ␧⬙. This is valid for very small perturbations of the elec-

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 49, No. 7, July 2007

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tric field inside the cavity by the insertion of a sample. For materials with high losses, the perturbation can be very high, making impracticable the use of this technique. The solution is to use high volume cavities. In this work we report the design and the performance tests of a cavity to be used with high loss materials. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1687–1690, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop. 22506 Key words: resonant cavity; microwaves; complex permittivity; perturbation theory 1. INTRODUCTION

The cavity perturbation technique was proposed by Montgomery in 1947 [1] and further developments in both experimental and theoretical aspects have been done by several workers [2–5]. This technique is used for both liquids and solids [6 – 8] and provides simple measurement procedure, high sensitivity, and indirect evaluation of complex dielectric permittivity, as well as magnetic permeability [9, 10]. Though rigorous analysis of Maxwell’s equations is available, Murthy and Raman [11] have proposed simpler approach, assuming that the cavity was a discrete resonant circuit, arriving to the theory for the calculus of complex dielectric permittivity. The cavity perturbation technique is based on the changes in the resonant frequency and quality factor of the cavity due to the presence of a sample inside the cavity. This method was designed for fully inserted samples, but occupying a narrow volume inside the cavity [12–14]. The resonant perturbation method is widely used in the characterization of microwave dielectric properties of various materials [l5–17]. The success of this method to calculate the microwave dielectric properties relies on measuring the values of resonant frequency f and quality factor Q accurately, before and after the insertion of the sample into the cavity. The parameters of the cavity depend on the volume, geometry, mode of operation, shape, dimensions, and location of the object inside the cavity. For a given cavity and a sample of regular shape and well-defined dimensions, we can determine the permittivity of the material [18]. Microwave resonant cavities have been used for evaluating the dielectric properties of geometrically defined samples, when the cavity is calibrated with dimensionally identical sample of known permittivity. The theoretical treatment of a cavity resonator consists of solving Maxwell equations considering the continuity of boundary conditions of the cavity. The resonance frequencies appear as conditions in the solutions of the differential equation involved and are not significantly affected by the fact that the cavity walls have a finite conductivity. The small perturbation is assured since linearity between the measured perturbation and the volume of the inserted sample allows independent calculation of real and imaginary parts of permittivity. The electromagnetic field, in the cavity, must satisfy the wave equation, ⵜ 2⌽ ⫺

⭸ 2⌽ ⫽0 c 2 ⭸t 2

(1)

where ⌽ is the electric or magnetic field components of the wave and c the light speed on the medium. For the electric field E, and assuming that Ez ⫽ 0 since z is the propagation direction, we have the solution for (1) as E x ⫽ 关A 1x sin共k1 x兲兴关A2x sin共k2 y兲 ⫹ B2x cos共k2 y兲兴

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⫻ 关A3x sin共k3 z兲兴e⫺i ␻ t Ey ⫽ 关A1y sin共k1 x兲兴关A2y sin共k2 y兲 ⫹ B2y cos共k2 y兲兴关A3y sin共k3 z兲兴e⫺i ␻ t

(2)

with Ex and Ey being the x and y electric field components, A’s and B’s the amplitudes and k1 ⫽ m␲/a1, k2 ⫽ n␲/a2, k3 ⫽ p␲/a3, where a1, a2, a3 are the cavity dimensions in the x, y, z directions, respectively, and m, n, p are the number of the half wavelengths in each direction. If a2 ⬍ a1 ⬍ a3 the TE1,0,1 mode has the lowest frequency and is assigned as the dominant mode. For a typical TE1,0,p Eqs. (2) reduces to

冋

冉冊册冋冉冊册冋冉冊册冋冉冊册

E x ⫽ A 1x sin

␲x a1

关B2x 兴 A3x sin

⫽ A1y sin

␲x a1

p␲z a3

e⫺i ␻ t Ey

p␲z a3

关B2y 兴 A3y sin

e⫺i ␻ t

(3)

with the resonant frequency f ⫽ ␻/2␲ given by f⫽

c

2 冑␮ r␧ r

冑冉冊冉冊 m a1

2

⫹

p a3

2

(4)

where ␮r and ␧r are the relative values of the permeability and dielectric constant, respectively. The permittivity values of a sample can be deduced from the changes in the resonant frequency ⌬f and in the inverse of the quality factor ⌬(1/Q) of a resonant cavity, when introducing a sample in the cavity, where the electric field is maximal and the magnetic field negligible. Two approximations are made based on assumptions that the fields in the empty part of the cavity are negligible and changed by the insertion of the object, and that the fields in the object are uniform over its volume. The shift in the resonant frequency of the cavity, ⌬f, caused when the sample is inserted into the cavity can be related to the real part of the complex permittivity, whereas the change in the inverse of quality factor of the cavity, ⌬(1/Q), can be related with the imaginary part, ␧⬙. The relations are simple when we consider only the first order perturbation in the electric field caused by the sample. After some mathematic manipulations [19] we obtain ⌬f ␯ ⫽ K共␧⬘ ⫺ 1兲 f0 V ⌬

冉冊

1 ␯ ⫽ 2K␧⬙ Q V

(5)

(6)

where K is a constant related to the depolarization factor, which depends upon the geometric parameters, v and V are the volumes of the sample and the cavity, respectively, and f0 is the resonance frequency of the cavity before the introduction of the sample. Using a sample of known dielectric constant, we can determine the constant K. For materials with high losses or high dielectric constant, the perturbation can be too high. The solution is to decrease the ratio v/V, that is, using very small samples or construct higher volume cavities. 2. EXPERIMENTAL

In this work, we develop a cavity resonator to measure the permittivity of materials with high losses such as polyaniline (PANI).


DOI 10.1002/mop

TABLE 1

Cavity Characteristics

a1 (mm) a2 (mm) a3 (mm) Resonant mode Resonant frequency, f0 (GHz) Q factor for the empty cavity

47.50 22.20 425.64 TE1,0,11 4.971 2044

The resonant cavity was built from a standard rectangular metallic waveguide section coupled with external waveguides through small apertures in the opposite walls. It was designed for the TE1,0,11 mode and a resonant frequency of about 5 GHz. In Table 1 we present the characteristics of the cavity and in Figure 1 an image of the cavity. To couple the microwave to the cavity we used the quarterwavelength flange joints and small circular irises (10 mm in diameter). For the measurements, we used an HP 8753D Network Analyzer with the excitation power of 1 mW. All measurements were carried out at constant temperature. The samples were introduced into the cavity through circular holes milled in the centre of the cavity. There, the electric field is in its strongest value and the insertion of the samples causes the maximal frequency shift. The sample holder consists in an 8-mm PTFE cylindrical tube. To study the linearity of the cavity, and consequently to infer the possibility to use the small perturbation theory, we carried out measurements using glass microtubes filled with distilled water. The cavity was used to calculate the permittivity of PANI and water, to confirm the performances. To synthesize PANI, chemical oxidative polymerization of aniline was carried out using ammonium persulphate as initiator in the presence of 1 M of HCl. The doping reaction was allowed to occur for about 4 h at room temperature to reach homogeneity of the process. The final product was then filtered, washed, and dried for 48 h. The obtained PANI was in its dark powder form. For the microwave measurements the PANI powder was compressed in 4-mm-diameter and 1-mm-thick disk-shaped samples.

Figure 2 water

Transmission of the cavity, with different volumes of distilled

factor is observed up to 36 ␮l, that is, up to 5.7 ⫻ 10⫺3. The conjugation of both conditions permits us to conclude that the cavity can be used up to variations of ⌬f/f0 of 0.56% and ⌬(1/Q) of about 4.2 ⫻ 10⫺3. If the measurements overcome this limit, the

3. DISCUSSION

We made measurements with water volumes in the range of 0.5– 48 ␮l. In Figure 2, we present the transmission absorption spectra of the TE1,0,11 5 GHz cavity resonator, considering empty sample holder and filled with distilled water at volumes of 1, 5, 12, 18 ␮l and in the inset 27, 36, and 48 ␮l. We fitted the experimental data using a Lorentzian curve and we calculated ⌬f/f0 and ⌬(1/Q). The obtained values of ⌬f/f0 and ⌬(1/Q) as a function of the water volume are presented in Figures 3(a) and 3(b), respectively. The error bars were calculated by the standard partial derivative method. Observing the Figure 3(a), we can infer that the shift in the resonant frequency of the cavity remains in the linear regime for measurements up to 27 ␮l of water. This corresponds to ⌬f/f0 of 0.56%. In Figure 3(b), the linearity in the inverse of the quality

Figure 1 The 5 GHz cavity resonator. The hole for the sample is in the geometric center

DOI 10.1002/mop

Figure 3 water

Calculated ⌬f/f0 and ⌬(1/Q) for different volumes of distilled


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9.

10.

11.

12. 13. 14. Figure 4 cavity

Transmission of resonant cavity for PANI, PTFE, and empty

15.

16.

sample volume should be reduced until the results fall into the linear regime. A plot of the transmission as a function of frequency is shown in Figure 4, where three different situations are included: empty cavity, cavity with PTFE, and cavity with PANI. The complex permittivity for PANI was then calculated from the analysis of these results using Eqs. (5) and (6). We obtained the values of 3.3 and 0.8 ⫻ 10⫺1 for real and imaginary parts of the complex permittivity, respectively. These values are consistent with that reported by other authors [20]. Finally, for water we determined ␧⬘ ⫽ (82 ⫾ 2) and ␧⬙ ⫽ (39.2 ⫾ 0.6). These values are in good agreement with a previous report [21]. 4. CONCLUSIONS

In summary, we designed a cavity resonator for a TE1,0,11 mode operating at 5 GHz for measurements of complex permittivity of high loss samples. The cavity was calibrated with distilled water. It was verified that the absorption characteristics remain in the linear regime for the distilled water volumes up to 27 ␮l, corresponding to relative frequency shifts, ⌬f/f0, up to 0.56% and inverse quality factor shifts, ⌬(1/Q), up to 4.2 ⫻ 10⫺3. The results for water and for a compressed PANI disc sample confirm the performance of our cavity. REFERENCES 1. G.A. Montgomery, Techniques of microwave measurements, McGraw-Hill, New York, 1947. 2. H.M. Altschuler, Handbook of microwave measurements, Vol. 2, Interscience, New York, 1963. 3. R.A. Waldron, Perturbation theory of resonant cavities, Proc IEEE 107 (1960), 272–274. 4. R.A. Waldron, Ferrites: An introduction for microwaves engineers (Marconi series D), Van Nostrand Co. Ltd., London, 1961. 5. V. Subramanian and J. Sobhanadri, New approach of measuring the Q factor of a microwave cavity using the cavity perturbation technique, Rev Sci Instrum 65 (1994), 453– 455. 6. V. Subramanian, V.R.K. Murthy, and J. Sobhanadri, Microwave conductivity studies on some semiconductors, Pramana J Phys 44 (1995), 19 –32. 7. V. Subramanian, B.S. Bellubbi, and J. Sobhanadri, A new technique of measuring the complex dielectric permittivity of liquids at microwavefrequencies, Rev Sci Instrum 64 (1993), 231–233. 8. V. Subramanian, B.S. Bellubbi, and J. Sobhanadri, Dielectric studies

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19.

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21.

of some binary-liquid mixtures using microwave cavity techniques, Pramana J Phys 41 (1993), 9 –20. Sheng-Chum Zhu, Hai-ying Chen, and Fan-Ping Wen, Measurement theory and experimental research on microwave permeability and permittivity by using the cavity characteristic equation method, IEE Trans Magn 28 (1992), 3213–3215. A. Verma, A.K. Saxena, and D.C. Dube, Microwave permittivity and permeability of ferrite-polymer thick films, J Magn Magn Mater 263 (2003), 228 –234. V.R.K. Murthy and R. Raman, A method for the evaluation of microwave dielectric and magnetic parameters using rectangular cavity perturbation technique, Sol Stat Commun 70 (1989), 847– 850. H.A. Bethe and J. Schwinger, Perturbation theory for cavities, NRDC report D1–117, Cornell University, USA, 1943. T. Kahan, Me´thode de perturbation applique´ a l’e´tude des cavite´s e´lectromagne´tiques, Comptes Rendus 221, Paris, 1945. J. Slater, Microwave electronics, Van Nostrand Co. Ltd., New York, 1950. L. Chen, C.K. Ong, and B.T.G. Tan, A resonant cavity for highaccuracy measurement of microwave dielectric properties, Meas Sci Technol 7 (1996), 1255–1259. L.C. Costa, S. Devesa, P. Andre´, and F. Henry, Microwave dielectric properties of polybutylene terephtalate (PBT) with carbon black particles, Microwave Opt Tech Lett 46 (2005), 61– 63. L.C. Costa, A. Correia, A. Viegas, J. Sousa, and F. Henry, Dielectric characterisation of plastics for microwave oven applications, Mater Sci Forum 480 (2005), 161–164. A.W. Kraszewski and S.O. Nelson, Observations on resonant cavity perturbation by dielectric objects, IEEE Trans Microwave Theory Tech 40 (1992), 151–155. F. Henry, De´veloppement de la me´trologie hyperfre´quences et application a l⬘e´tude de l⬘ hydratation et la diffusion de l⬘eau dans les mate´riaux macromolećulaires, Ph.D. Thesis, Paris (1982). S.B. Kumara, H. Hohn, R. Joseph, M. Hajian, L.P. Ligthart, and K.T. Mathew, Complex permittivity and conductivity of polyaniline at microwave frequencies, J Eur Ceram Soc 21 (2001), 2677–2680. F. Henry, M. Gaudillat, L.C. Costa, and F. Lakkis, Free and/or bound water by dielectric measurements, Food Chem 82 (2003), 29 –34.

© 2007 Wiley Periodicals, Inc.

IMPROVING THE RADIATION CHARACTERISTICS OF A BASE STATION ANTENNA ARRAY USING A PARTICLE SWARM OPTIMIZER Z. D. Zaharis,1 D. G. Kampitaki,1 P. I. Lazaridis,1,2 A. I. Papastergiou,1 A. T. Hatzigaidas,1 and P. B. Gallion2 1 Department of Electronics, Alexander Technological Educational Institute of Thessaloniki, 57400 Thessaloniki, Greece 2 De´partement Communications et Electronique, Unite´ de Recherche Associeé au Centre National de la Recherche Scientifique, 820 Ecole Nationale Supe´rieure des Te´lećommunications, 46 rue Barrault, 75634 Paris Cedex 13, France Received 19 December 2006 ABSTRACT: A particle swarm optimization based technique is applied on linear antenna arrays used by broadcasting base stations. Both the geometry and the excitation of the antenna array are optimized by a suitable algorithm under the constraints of the maximum possible gain at the desired direction and the desired value of side lobe level. The matching condition of the elements of the antenna array is also required by the algorithm. The technique has been applied to antenna arrays composed of collinear wire dipoles and seems to be very promising for


DOI 10.1002/mop