INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY, VOL.6, NO., 6(37(0%(5 2011
A Common Neural Approach for Computing Different Parameters of Circular Patch Microstrip Antennas Taimoor Khan* and Asok De Department of Electronics Engineering, Delhi Technological University, Delhi-110 042, India Tel: 011-2204846; Fax: 011-22048044; E-mail:
[email protected]
Abstract- This paper presents a single feed forward neural model for calculating the resonant frequency and radius of a circular patch. For calculating these two parameters, the proposed model is trained by Levenberg-Marquardt algorithm with the data sets of resonant frequency and radius simultaneously. The model has also been validated on some analytically generated data sets that are not included in training or testing of the neural model. The results obtained in the calculation of these two parameters from a common neural model are in conformity with the experimental results obtained by the conventional approaches. Index Term- Circular patch, Levenberg-Marquardt training algorithm, neural networks, resonant frequency and radius.
I. INTRODUCTION Applications of artificial neural networks in microstrip antennas are more than one decade old. In last one decade, different neural approaches have been proposed for calculating the single performance parameter (physical dimensions or resonant frequency) of the microstrip patches [1-7]. Mishra and Patnaik [1-2] have proposed two different neural approaches; one is based on neural network-based CAD model for designing the square patch microstrip antennas [1] and another based on neuro-spectral method for designing the rectangular patch microstrip antennas [2]. The designing of equilateral triangular microstrip antennas using artificial neural networks has been done by Gopalakrishnan and Gunasekaran [3] whereas Turker et al [4] have analyzed and designed rectangular patch microstrip antennas using neural approach. Guney et al [5] have proposed a generalized neural method for calculating the resonant frequencies of rectangular, circular and triangular patches using equivalent area concept. They have used three different algorithms, backpropagation, delta-bar-delta, and extended delta-bar-delta for training purpose. The average absolute errors in their neural model for circular patch are calculated as 0.02480 GHz, 0.06760 GHz, and 0.05170 GHz for these three algorithms respectively. It means the least average absolute error in their model is 0.02480 GHz. Ouchar et al [6] have used multilayered perceptron artificial neural networks model with backpropagation training algorithm for calculating the resonant frequencies of the circular patch and the average absolute error from this model is calculated as 0.03461
GHz. Sagiroglu et al [7] have also calculated resonant frequencies of the circular patch microstrip antennas using neural approach. They have used standard backpropagation algorithm with learning coefficient of 0.08000 and the momentum coefficient of 0.10000. The average absolute error from this model is calculated as 0.00185 GHz. Guney and Sarikaya [8-9] have used two different neural approaches; one is based on ANFIS (artificial neural network and fuzzy interference system) method [8] and another based on CNFS (concurrent neuro-fuzzy system) method [9] for calculating the resonant frequencies of rectangular, triangular and circular microstrip antennas, simultaneously. From these two models, the average absolute errors for circular patch are calculated as 0.00460 GHz and 0.00580 GHz respectively. The previously reported works [1-3] and [6-7] have been used for calculating one parameter and Turker et al [4] have calculated two different parameters (resonant frequency and physical dimensions) of the rectangular patch microstrip antennas whereas Guney et al [5] and Guney and Sarikaya [8-9] have calculated only one parameter i.e. resonant frequency of different types of patches, simultaneously using equivalent area concept. However in the available literature of microstrip antennas with neural networks [1-9] no single model has been proposed till date for designing the circular patch microstrip antenna (CPMSA) and the calculations of more than one parameter like resonant frequency and radius of the same patch (i.e. CPMSA) have not been done by anyone. The training and testing data sets in the previously reported works [1-9] have been taken directly from the available literature and no one has checked the validity of their neural models for the data sets that are not included in training or testing of the model. This paper suggests a common feed forward neural model based on multilayered perceptron for calculating the two parameters (resonant frequency and radius) of a CPMSA. The parameter selection (resonant frequency or radius) is done by considering another parameter say M where M=1 corresponds to resonant frequency and M=0 corresponds to radius calculation. The model is trained by LevenbergMarquardt training algorithm for both resonant frequency and radius calculation simultaneously. Some random numbers have been selected as initial weights and biases
IJMOT-2011-2-86 © 2011 ISRAMT
259
260
INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY, for the model. Finally, the calculated resonant frequency and the radius from the proposed model are also compared with their corresponding experimental counterparts. II. GEOMETRY OF CPMSA A CPMSA, in its simplest configuration, consists of a radiating conductive circular patch on a dielectric substrate of “relative permittivity, εr” and at “height, h”, from the ground plane as shown in Fig. 1.
VOL.6, NO., 6(37(0%(5 2011
After many trials, it is found that the model configuration of two hidden layers with ten neurons in each layer is suitable for calculating these two parameters of the CPMSA. Logsigmoidal and Tansigmoidal have been chosen as activation functions for the first and second hidden layer respectively. The activation function in the output layer is pure linear whereas for the input layer no activation function is used. LevenbergMarquardt training algorithm [22] is adopted for training purpose. All initial weight and bias matrices have been selected randomly and rounded off between -1.0 and +1.0. The total number of iterations required for getting a mean square error (MSE) of 4×10-7 is only 364. The training period for the proposed model is less than 2 Minutes. After getting training successfully, one can calculate any parameter (resonant frequency or radius) in microseconds. For calculating the “resonant frequency, fn”, the parameters for the input layer are; M, r, h, and εr, whereas for “radius, rn” calculation these parameters are; M, f, h, and εr. Table 1: Calculated resonant frequencies and their comparison M=1 for Resonant Frequency Calculation during Training + Testing
Fig.1. Geometry of CPMSA
For the fundamental mode, the resonant frequency of the CPMSA is the function of the radius (r) of the patch, relative permittivity (εr), and height of the dielectric material (h). Now if the resonant frequency (f), relative permittivity (εr), and height of the dielectric material (h) are given, then the radius of the patch can also be calculated easily [10-14]. For calculating these two parameters (resonant frequency and radius), total forty data sets (twenty for resonant frequency and twenty for radius) have been obtained from the literature [15-21] and are given in Table 1 and Table 2 respectively. These data sets have been used in training and testing of the proposed neural model. III. PROPOSED NEURAL APPROACH A neural model for calculating the resonant frequency and radius of CPMSA is shown in Fig.2.
r(cm) 0.74000 0.77000 0.82000 0.96000 1.04000 1.07000 1.15000 1.27000 2.00000 2.99000 3.49300 3.49300 3.80000 3.97500 4.85000 4.95000 5.00000 6.80000 6.80000 6.80000
h(cm) 0.15875 0.23500 0.15875 0.15875 0.23500 0.15875 0.15875 0.07940 0.23500 0.23500 0.15880 0.31750 0.15240 0.23500 0.31800 0.23500 0.15900 0.08000 0.15900 0.31800
εr 2.65000 4.55000 2.65000 2.65000 4.55000 2.65000 2.65000 2.59000 4.55000 4.55000 2.50000 2.50000 2.49000 4.55000 2.52000 4.55000 2.32000 2.32000 2.32000 2.32000
fth(GHz) 6.63400 4.94500 6.07400 5.22400 3.75000 4.72300 4.42500 4.07000 2.00300 1.36000 1.57000 1.51000 1.44300 1.03000 1.09900 0.82500 1.12800 0.83500 0.82900 0.81500
fn (GHz) 6.63390 4.94500 6.07380 5.23250* 3.75000 4.72300 4.42480 4.06990 2.00290 1.35990* 1.56990 1.50990 1.44300 1.03000 1.09910 0.82500 1.12790 0.83500 0.82860 0.81500*
M=1 for Resonant Frequency Calculation during validation
7.11580 7.18380 5.12490 3.87170 4.49480 3.97380 2.02040
0.08000 0.31800 0.15900 0.15240 0.31800 0.20500 0.18500
2.32000 2.10000 2.32000 2.49000 2.52000 4.50000 4.55000
0.80500 0.82500 1.10790 1.41300 1.19910 1.03000 2.00290
0.79670 0.82050 1.10080 1.41530 1.18320 1.03830 2.01010
fth represents theoretical results [15-21] and fn represents neural results.
IV RESULTS A. During Training and Testing Fig.2. Proposed Neural Model for Resonant Frequency/Radius Calculation
The resonant frequencies and radiuses calculated during training and testing of the proposed neural model are given in Table 1 and Table 2 respectively. These tables
IJMOT-2011-2-86 © 2011 ISRAMT
261
INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY, show that the calculated parameters obtained from the proposed neural model during training and testing are closer to their corresponding experimental values. B. During Validation To check the validity of the proposed model a design procedure for CPMSA is taken as [23]:
r =
A ⎧ 2h ⎨1 + πε r A ⎩
⎡ ⎤⎫ ⎢⎣ ln 2 h + 1 . 7726 ⎥⎦ ⎬ ⎭
πA
1/ 2
(1)
Where
A=
8 . 791 × 10 9 f εr
(2)
In equations (1) and (2), the resonant frequency (f) is supplied in Hz, height of the dielectric material (h) in cm. Using these two equations total seven values of the radius (r) have been calculated for the seven randomly selected combination of f, h and εr and have also been given in Table 2. Now from the same equations (1) and (2) the resonant frequency (f) can be calculated for the given set of r, h and εr and calculated resonant frequencies in this fashion have been given in Table 1. Table 2: Calculated radiuses and their comparison M=0 for Radius Calculation during Training+ Testing
f(GHz) 6.63400 4.94500 6.07400 5.22400 3.75000 4.72300 4.42500 4.07000 2.00300 1.36000 1.57000 1.51000 1.44300 1.03000 1.09900 0.82500 1.12800 0.83500 0.82900 0.81500
h(cm) 0.15875 0.23500 0.15875 0.15875 0.23500 0.15875 0.15875 0.07940 0.23500 0.23500 0.15880 0.31750 0.15240 0.23500 0.31800 0.23500 0.15900 0.08000 0.15900 0.31800
εr 2.65000 4.55000 2.65000 2.65000 4.55000 2.65000 2.65000 2.59000 4.55000 4.55000 2.50000 2.50000 2.49000 4.55000 2.52000 4.55000 2.32000 2.32000 2.32000 2.32000
rth(cm) 0.74000 0.77000 0.82000 0.96000 1.04000 1.07000 1.15000 1.27000 2.00000 2.99000 3.49300 3.49300 3.80000 3.97500 4.85000 4.95000 5.00000 6.80000 6.80000 6.80000
rn(cm) 0.74090 0.77010 0.81880 0.96460* 1.04010 1.07250 1.14790 1.27030 2.00000 2.98190* 3.49300 3.49300 3.79990 3.97500 4.84990 4.95000 5.00000 6.80000 6.80000 6.79840*
VOL.6, NO., 6(37(0%(5 2011
V COMPARISON AND CONCLUSIONS
A comparison of the calculated and experimental results is also given in Table 1 and 2. The average absolute error in calculating the resonant frequencies is only 0.00051 GHz during training and testing in the proposed neural model whereas in previously reported neural models [59] it is calculated as 0.02480 GHz, 0.03461 GHz, 0.00185 GHz, 0.00460 GHz and 0.00580 GHz, respectively. Similarly the average absolute error is only 0.00109 cm when the radiuses are calculated from the same model during training and testing. The model is also tested on some analytically generated data sets [23] for checking its validity. The results calculated during validation of the model are also given in Table 1 and Table 2 respectively which shows that the calculated results are in very good agreement to their analytically generated counterparts. During validation, the average absolute error in resonant frequencies is 0.00766 GHz only whereas in radiuses it is 0.02149 cm only. In tables 1 and 2 the results represented by astrick are calculated during testing of the neural model shown in Fig.2. The proposed model is used for calculating two parameters of a CPMSA whereas the previously reported neural models [1-3] and [5-9] have been used for calculating only one parameter of the CPMSA. The average absolute errors in the proposed neural model are more encouraging for both the parameters. All previously reported neural models [1-9] have been trained and tested only for the data sets available in the literature. No one has checked the validity of their model. Here the beauty of the proposed model is; firstly, a common model is calculating two parameters with more encouraging errors and secondly the model is not only verifying the experimental results [15-21] but it is also validating the analytically generated data sets [23]. REFERENCES [1]
[2]
[3]
M=0 for Radius Calculation during Validation
1.10790 1.41300 1.56990 0.82500 1.03000 2.00290 6.63390
0.15900 0.15240 0.10880 0.21500 0.20500 0.18500 0.15875
2.32000 2.49000 2.50000 4.35000 4.50000 4.55000 2.45000
5.12490 3.87170 3.48780 5.05230 3.97380 2.02040 0.80250
5.09490 3.87810 3.53420 5.05980 4.00790 2.03930 0.79540
rth represents theoretical[15-21] and rn represents neural results.
[4] [5]
R.K. Mishra and A. Patnaik, “Neural network-based CAD model for the design of square-patch antennas”, IEEE Transaction on Antennas and Propagation, vol. 46, no. 12, pp 1890-1891, 1998. Rabindra K. Mishra, and Amalendu Patnaik, “Designing rectangular patch antenna using the neurospectral method” IEEE Transaction on Antennas and Propagation, vol. 51, no. 8, August 2003. R. Gopalakrishnan and N. Gunasekaran, “Design of equilateral triangular microstrip antenna using artificial neural networks”, IEEE International Workshop on Antenna Technology: Small Antennas and Novel Metamaterials, 2005. Nurhan Turker, Filiz Gunes and Tulay Yildirim, “Artificial neural design of microstrip antennas” Turk J Elec Engin, vol.14, no.3, 2006. Karim Guney, Seref Sagiroglu and Mehmet Erler, “Generalized neural method to determine resonant frequencies of various microstrip antennas”, International
IJMOT-2011-2-86 © 2011 ISRAMT
262
INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY, VOL.6, NO., 6(37(0%(5 2011 [6]
[7]
[8]
[9]
[10] [11] [12] [13] [14]
Journal of RF and Microwave Computer Aided Engineering, vol. 12, pp 131-139, 2002. A. Qucher, R. Aksas and H. Baudrand, “Artificial neural network for computing the resonant frequency of circular patch antennas” Microwave and Optical Technology Letters, vol. 47, pp 564-566, 2005. Seref Sagiroglu, Karim Guney and Mehmet Erler, “Resonant frequency calculation for circular microstrip antennas using artificial neural networks”, International Journal of RF, and Microwave Computer Aided Engineering, vol. 8, pp 270-277, 1998. K. Guney and N. Sarikaya, “A hybrid method based on combining artificial neural network and fuzzy interference system for simultaneous computation of resonant frequencies of rectangular, circular, and triangular microstrip antennas” IEEE Transaction on Antennas and Propagation, vol. 55, no 3, March 2007. K. Guney and N. Sarikaya, “Concurrent neuro-fuzzy systems for resonant frequency computation of rectangular, circular, and triangular microstrip antennas” Progress In Electromagnetics Research, vol. 84, pp 253-277, 2008. J. Bahl and P. Bhartia, “Microstrip antennas”, Artech House, Dedham, MA, 1980. J.R. James, P.S. Hall, and C. Wood, “Microstrip antennastheory and design”, Peter Peregrisnus Ltd., London, 1981. K.C. Gupta and A. Benalla (Editors), “Microstrip antenna design”, Artech House, Canton, MA, 1988. J.R. James and P.S. Hall, “Handbook of microstrip antennas”, IEE Electromagnetic Wave Series No. 28, Peter Peregrinus Ltd., London, 1989, Vols. 1 and 2. P. Bhartia, K.V.S. Rao, and R.S. Tomar (Editors), “Millimeter-wave microstrip and printed circuit antennas”, Artech House, Canton, MA, 1991.
[15]
[16] [17]
[18]
[19] [20]
[21] [22] [23]
J. S. Dahele and K. F. Lee, ‘‘Effect of substrate thickness on the performance of a circular-disk microstrip antenna,’’ IEEE Transaction on Antennas and Propagation, vol. 31, no. 2, pp. 358-364, 1983. J. S. Dahele and K. F. Lee, ‘‘Theory and experiment on microstrip antennas with air gaps,’’ IEE Conference Proceeding, vol. 132, no. 7, 1985, pp. 455-460. K. R. Carver, ‘‘Practical Analytical Techniques for the Microstrip Antenna,’’ Proceeding of Workshop on Printed Circuit Antennas, New Mexico State University, 1979, pp. 7.1-7.20. K. Antoszkiewicz and L. Shafai, ‘‘Impedance characteristics of circular microstrip patches,’’ IEEE Transaction on Antennas and Propagation, vol. 38, no. 6, pp. 942-946, 1990. J. Q. Howell, ‘‘Microstrip antennas’’ IEEE Transaction on Antennas and Propagation, vol. 23, pp.90-93, Jan. 1975. F. Abboud, J. P. Damiano, and A. Papiernik, ‘‘New determination of resonant frequency of circular disc microstrip antenna: application to thick substrate,’’ Electronic Letters, vol. 24, no. 17, pp. 1104-1106, 1988. T. Itoh and R. Mittra, ‘‘Analysis of a Microstrip Disk Resonator,’’ Arch Electron Ubertrugungs, vol. 27, no. 11, pp. 456-458, 1973. M. T. Hagan, and M. Menhaj, “Training feed forward networks with the Marquardt algorithms,” IEEE Transaction on Neural Networks, vol. 5, pp 989-993, 1994. C.A Balanis, “Antenna theory-analysis and design” Second Edition, John Wiley & Sons, Inc.1982.
IJMOT-2011-2-86 © 2011 ISRAMT
