Analysis of Broad-Wall Longitudinal Slot Arrays in Standard and Reduced Height Waveguides

Transcription

1 Journal of Wireless Networking and Communications 014, 4(1): 18-5 DOI: /j.jwnc Analysis of Broad-Wall Longitudinal Slot Arrays in Standard and Reduced eight Waveguides Rintu Kumar Gayen *, Sushrut Das Department of Electronics Engineering, Indian School of ines, Dhanbad, 86004, India Abstract This paper presents method of moments based analysis of different broad-wall longitudinal slots array antennas, milled on standard or reduced height rectangular wave-guides, using ultiple Cavity odelling Technique (CT). Theoretical data for reflection coefficient, transmission coefficient, resonance length and resonance conductance have been obtained for two different two element slot arrays. The first array consists of two slots in two different waveguides whereas the second array consists of two slots in the same waveguide. The theoretical data have been compared with experimental data and Ansoft FSS s simulated data to validate the analysis. The excellent agreement obtained between the results validates the analysis. Keywords Waveguides, Slot antennas, oment ethod, Reflection Coefficients, Transmission Coefficients, Normalied Admittance, Resonance, CT 1. Introduction Studies on waveguide broad-wall longitudinal slot antennas date back before World War II. Till then a number of workers have carried out considerable investigations on the resonance and admittance properties of the structure and a detail review of it will be a literature of its own. A brief survey of these literatures has been provided in [1]. owever most of these analyses were carried out for a single slot element. Few literatures are also available on slot array [ - 5]. Bastani and Rashed-ohassed analysed planar slotted-waveguide array antennas with longitudinal slots using ethod of oments []. oment method analysis of a horiontally polaried omni directional slot array antenna was done by Sangstar and Wang [3-4]. An improved design procedure for small arrays of shunt element was provided by Elliott [5]. A three-layer DRA structure was used to achieve enhanced and broadband coupling to the waveguide in [6]. A coupled calculation technique, based on space segmentation, for the calculation of radiation from tilted rectangular waveguide slot antennas has been reported by Benko, Turocy and Pavo [7]. Cong and Dou designed dual polaried waveguide slotted array for Ka band application [8]. Lai, Zhao, Su and Liang analysed higher-order o analysis of the rectangular waveguide edge slot arrays [9]. Tolerance analysis of coupling slot of waveguide slot array was done by Jie, Yong-jin, * Corresponding author: rintukrgayen@gmail.com (Rintu Kumar Gayen) Published online at Copyright 014 Scientific & Academic Publishing. All Rights Reserved Chun shan and Wen-feng [10]. This paper presents, method of moments based analysis of different broad-wall longitudinal slots array antennas in standard and reduced height rectangular wave-guides using ultiple Cavity odeling Technique (CT) [11-1]. Theoretical data for reflection coefficient, transmission coefficient, resonance length and resonance conductance have been obtained for two different two element slot arrays. The first array consists of two slots in two different waveguides whereas the second array consists of two slots in the same waveguide. The theoretical data have been compared with experimental data and Ansoft FSS s simulated data to validate the proposed method. The excellent agreement obtained between the results validates the analysis. (a) (b) Figure 1. Fabricated antennas (a) two slots in two different waveguides and (b) two slots in the same waveguide. Formulation and Analysis The fabricated antennas are shown in figure 1 and the top views of the arrays are shown in figure with details of different parameters that will be used in the analysis. The corresponding cavity modelling and details of magnetic

2 Journal of Wireless Networking and Communications 014, 4(1): current at the apertures are shown in figure 3. The electric field at the slot may be assumed to be X-directed and can be expressed in terms of a sum of i weighted sinusoidal basis functions, e p, defined over the entire length of the slot as follows: i E (x,y, ) = uˆ x p 1 = E ip, p π sin L y b On aperture "i" L s 0 Elsewhere ( ws s ) δ( ) Using the above electric field distribution the magnetic currents can be obtained by the application of equivalence principle. At the region of slot, the tangential components of the magnetic field should be identical. This result in the following boundary conditions:- for the array1 wvg1 1 cav1 1 ( ) ( ) cav1 inc ( ) = ( ) = (1) cav1 1 cav1 ext () ext 3 0 ( ) = ext ext 3 cav 3 cav 4 0 cav 3 cav 4 wvg 4 = 0(4) for the array ( 4 ) wvg ( 1 ) cav1 ( 1 ) ( ) = ( ) = ( ) = ( ) = wvg (5) cav1 inc cav1 1 cav1 ext ext 3 0 (6) ext ext 3 cav 3 cav 4 0 (7) wvg 1 cav 3 cav 4 (8) wvg 4 inc The field components of equation (1) (8) are given by (3) (a)

3 0 Rintu Kumar Gayen et al.: Analysis of Broad-Wall Longitudinal Slot Arrays in Standard and Reduced eight Waveguides (b) Figure. Top views and details of different parameters of the arrays (a) two slots in two different waveguides and (b) two slots in the same waveguide (a) (b) Figure 3. Details of different regions and magnetic currents at the apertures of the arrays, shown in figure

4 Journal of Wireless Networking and Communications 014, 4(1): ext i WL s s i k kx ( ) p, 1/ x s p= 1 ( ) ( x ) j sin kl s if p is even jkx ( ) ( ) jk x ws k cos k ws L s if p odd ( kx x ) e e dk dk pπ Lsk 1 pπ ( ) = E Sinc k W π kη k k k ( ) wvg i i jεmεnws p, array1 p= 1 m= 0n= 0 ηγ mn x ( π) ( ) cos n = E k ab 1 S p mπ mπ mπ cos ( xs a) sin c Ws cos ( x a) a a a pπ pπ k sin ( Ls ) Ls Ls sinh ( mn ) if p even γmnls γ ( k γ mn ) S( p) e cosh( γmn) if p odd nπ cos ( y b) b inc πx β j = j sin e a cav i jωε i mπ ( ) = E p, k k p= 1 m= p= 1 L s { mn ( )} { mn ( )} { mn ( )} { mn ( )} ( 1) { } mπ nπ sin ( Ls) cos ( x Ws) Ls W s Γ mn sin Γ mn cos Γ y t cos Γ y t y > y for m = p cos Γ y t cos Γ y t y > y and n = 0 0 otherwise where a is the guide width, t is the slot / waveguide wall thickness, and S ( p) = pπ ( L s γ mn ) The method of moments is applied with Galerkin s specialiation [13] to solve equation (1) (8) and hence to enable the i determination of the E p,. 3. Results On the basis of the formulation, ATLAB codes have been written to compute the reflection coefficients, transmission coefficients, resonance length and resonance conductance of the antennas. The results are presented below: The magnitude of the S parameters of both the arrays for slots length = 16 mm, width = 1 mm, thickness = 1.7 mm, Z WS Z W0 = 0 mm, X WS X W0 = 4.13 mm (for array1),

5 Rintu Kumar Gayen et al.: Analysis of Broad-Wall Longitudinal Slot Arrays in Standard and Reduced eight Waveguides 1 mm (for array) have been obtained and compared with FSS and measured data in figure 4 and figure 5 over a frequency range 8. G to 1.4 G. Figure 4. Comparison of theoretical data for the magnitude of reflection coefficient with FSS and measured data of the antennas Figure 6. Variation of complex reflection coefficients with frequency for the slot array antennas developed on standard and reduced height waveguides over 8 to 1 G Figure 5. Comparison of theoretical data for the magnitude of transmission coefficient with FSS and measured data for the proposed structures Figure 7. Variation of complex transmission coefficients with frequency for the slot array antennas developed on standard and reduced height waveguides over 8 to 1 G

6 Journal of Wireless Networking and Communications 014, 4(1): The resonance frequency of the slot arrays with slot length = 16 mm, width = 1 mm, thickness = 1.7 mm, X S = mm, X 0 = mm, X WS X W0 = 4.13 mm (for array1), 9.51 mm (for array) and Z WS Z W0 = 0 mm, are plotted with normalied guide height in figure 1. Figure 8. Variation of resonant slot length for the slot array antennas developed on standard and reduced height waveguides over 8 to 1 G Figure 9. Variation of normalied resonance conductance for the slot array antennas developed on standard and reduced height waveguides over 8 to 1 G The variation of the complex S parameters for slots with slot length = 16 mm, width = 1 mm, thickness = 1.7 mm, X S = mm, X 0 = mm, X WS X W0 = 4.13 mm (for array1), 9.51 mm (for array) and Z WS Z W0 = 0 mm, milled on a waveguide with a =.86 mm and b = / 5.08 /.54 mm, are plotted with frequency in figure 6 and figure 7 respectively. The variation of resonant slot length and normalied resonant conductance for the slot arrays with slot width = 1 mm, thickness = 1.7 mm, X S = mm, X 0 = mm, X WS X W0 = 4.13 mm (for array1), 9.51 mm (for array) and Z WS Z W0 = 0 mm, milled on a waveguide with a =.86 mm and b = / 5.08 /.54 mm, are plotted with frequency in figure 8 and figure 9 respectively. The variation of the complex S parameters for the slot arrays with slot length = 16 mm, width = 1 mm, thickness = t = 1.7 mm, X S = 6 mm, X 0 = - 6 mm, X WS X W0 = 4.13 mm (for array1), 1 mm (for array) and Z WS Z W0 =.7 mm are plotted with frequency in figure 10 and figure 11 respectively for different guide height. Figure 10. Variation of complex reflection coefficients with frequency for the slot array antennas developed on standard and reduced height waveguides over 8 G to 1 G

7 4 Rintu Kumar Gayen et al.: Analysis of Broad-Wall Longitudinal Slot Arrays in Standard and Reduced eight Waveguides magnitude of reflection coefficient obtained for array 1 is much lower and the magnitude of reflection coefficient for array and the transmission coefficient obtained for array 1 is much higher than array. The resonance frequencies as obtained for the arrays are summaried in Table 1. Table 1. Resonance frequency of the reflection coefficient from figure 6 Arrays Guide height (b) Guide height (b) Guide height (b/) array G 9.64 G 10.5 G array 9.14 G 9.45 G G Figure 11. Variation of complex transmission coefficients with frequency for the slot array antennas developed on standard and reduced height waveguides over 8 G to 1 G Figure 1. Variation of Resonance Frequency with normalied guide height over the range 0. to 1 4. Conclusions In this paper a moment method analysis has been carried out to compare two different two element broad-wall longitudinal slots array using ultiple Cavity odeling Technique (CT). The first array consists of two slots in two different waveguides where as the second array consist of two slots in the same waveguide. The theoretical data have been compared with experimental data and Ansoft FSS s simulated data in figure 4 and figure 5 to validate the proposed method. The excellent agreement obtained between the results demonstrates that the proposed method is able to accurately and efficiently solve reflection coefficients, transmission coefficients for both arrays. Figure 6 and 7 reveals that reduction in guide height has a pronounced effect on the complex S-parameters. The resonance frequency shifts to a higher frequency as the guide height is reduced. For the same guide height, array constructed with two slots in two different waveguide (array 1) has higher resonance frequency than the array with two slots in same waveguide (array ). Furthermore the The decrease in guide height also increases the resonance length, as evident from figure 8. For the same guide height array 1 has larger resonance length than array. Reduction in guide height has also pronounced effect on the normalied resonance conductance, as evident from figure 9. The normalied resonance conductance increases with decrease in guide height, the rate of increase being higher at lower frequencies than at higher frequencies. For the same guide height the normalied resonant conductance, obtained for array is also much higher than array 1. The difference in normalied resonant conductance, however, decreases at higher frequencies. The previous structures assumed that there is no offset between the slots along the propagation direction. The effects of slot offset along propagation direction on complex S-parameters have been studied in figure 10 and 11. The effect on the magnitude of the S-parameters is almost same as before however the phase variation now becomes more complex. Figure 1 reveals that the resonance frequency decreases with increase in normalied guide height. The resonance frequency is higher in array 1 than in array. Finally, this paper demonstrates that CT can also effectively incorporate the internal and external mutual coupling, essential for the analysis of antenna arrays. In previous works [ - 10] using CT this aspect of array analysis was not studied. Therefore we can conclude that CT is applicable not only in the analysis of single slot element but also in the analysis of antenna arrays. ACKNOWLEDGEENTS The measurements were carried out in the Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology Kharagpur and the authors wish to express their gratitude to Prof. A. Bhattacharya of Indian Institute of Technology, Kharagpur, for allowing us to use the lab facility. REFERENCES [1] S. Gupta, Electromagnetic field estimation in aperture and

8 Journal of Wireless Networking and Communications 014, 4(1): slot Antennas with their equivalent network representation, PhD Dissertation, Department of Electronics & Electrical Communication Engineering, I.I.T. Kharagpur, India, [] A. Bastani and J. Rashed-ohassed, Analysis of Planar Slotted-Waveguide Array Antennas with Longitudinal Slots using the ethod of oments, IEEE Trans. Antennas Propagation., Vol. 1, pp , 004. [3] A. J. Sangstar and. Wang, Resonance properties of omni directional slot doublet in rectangular waveguide, Electronics Letters., Vol. 9, no. 1, pp , January [4] A. J. Sangstar, and. Wang, oment method analysis of a horiontally polaried omni directional slot array antenna, Proc. of IEE icrowave Antenna Propagation. Vol. 14, no. 1, pp. 1 6, February [5] R. S. Elliott, An improved design procedure for small arrays of shunt, IEEE Trans. Antennas Propagation. Vol. AP-31, pp , Jan [6] A. B. Kakade and B. Ghosh, Analysis of the rectangular waveguide slot coupled multilayer hemispherical dielectric resonator antenna, IET icrow. Antennas Propag., Vol. 6, Iss. 3, pp , 01. [7] P. T. Benko, B. L. Turócy and J. Pavo, A Coupled Analytical Finite Element Technique for the Calculation of Radiation From Tilted Rectangular Waveguide Slot Antennas, IEEE Transactions on agnetics, vol. 44, no. 6, pp , June 008. [8] Y. Cong and W. Dou, Design of Dual-Polaried Waveguide Slotted Antenna Array for Ka-band Application, Antennas Propagation and E Theory (ISAPE), pp , 010. [9] B. Lai, X. W. Zhao, Z. J. Su, and C.. Liang, igher-order o Analysis of the Rectangular Waveguide Edge Slot Arrays, IEEE Transactions on Antennas and Propagation, vol. 59, no. 11, November 011. [10] L. Jie, J. Yong-jin, Y. Chun-shan, S. Wen-feng, Tolerance Analysis of Coupling Slot of Waveguide Slot Array, icrowave, Antenna, Propagation and EC Technologies for Wireless Communications, pp , 009. [11] S. Das, Analysis of Rectangular Waveguide Based Passive Devices and Antennas using ultiple cavity odeling Technique, PhD Dissertation, Department of Electronics & Electrical Communication Engineering, I.I.T. Kharagpur, India, 007. [1] Das. S. and Chakraborty. A., A Novel odeling Technique to Solve a Class of Rectangular Waveguide Based Circuits and Radiators, Progress in Electromagnetic Research, IT, USA, Vol. 61, pp. 31-5, ay 006. [13] R. F. arrington, Field Computation by oment ethods, Roger E. Krieger Publishing Company, USA, pp. 5 7, 199.