INTERNATIONAL JOURNAL OF ELECTRICAL, ELECTRONICS AND COMPUTER SYSTEMS (IJEECS), Volume 1, Issue 2, April 2011. ISSN: 22217258(Print) ISSN: 22217266 (Online) www.ijeecs.org 1
Accurate CAD Formulation for Resonant Frequency of Equilateral Triangular Microstrip Antenna with and without Air Gap A.K.Saha, R.Nag, R.Upadhyay, A. Adhikari and S.Chattopadhyay Abstract—The resonant modes and characteristics of an equilateral triangular microstrip patch antenna with a variable air gap are theoretically and experimentally examined. Effect of varying parameters like dielectric constant of substrate, size of patch, substrate thickness and the effect of air gap height are the important factors addressed and an improved computer aided design is presented. Index Terms— Air gap height, Equilateral triangle, Microstrip antenna, Substrate thickness.
1 INTRODUCTION
T
HE triangular microstrip is the simple geometry amongst the printed antennas ever studied, and even today it finds new applications. The resonant frequency of equilateral triangular microstrip antenna (ETMA) is a critical parameter to design any wireless communication system. Many new configurations have also been studied in recent years to explore new characteristics [1], [2}, [3], [4], [5] and [6]. But, as a triangular microstrip antenna is an inherently narrow band width antenna, its operating frequency should be determined accurately. Most of the earlier formulations used cavity model analysis [7], [8], [9]. Chen et. al. reported one analysis using spectral domain method [10]. One recently reported work shows the development of one CAD formula [11] to predict the resonant frequency of ETMA. But most of the earlier formulations fail to predict the accurate resonant frequency of ETMA when the dielectric constant of the substrate becomes high. In order to alleviate the lacuna a comprehensive computer aided design (CAD) is developed to accurately estimate the dominant and the higher order resonances in an ETMA with and without air gap. Unlike, earlier theories, the present CAD can efficiently address a wide range of dielectric constant and substrate thickness of ETMA. The
mathematical derivations are based on the accurate estimation of the fringing electric fields and resulting effective dimension of the radiator. The results have been verified with our own theory and also with some earlier experiments available in open literature. Available computed values have also been compared with ours to indicate its accuracy. Simulated data have also been employed to validate the present theory for various parameters. An introduction of an air gap in between the substrate and the ground plane has been explored in [11], [12], [13] indicating the possibility of achieving tunability of a microstrip resonator. But it could not give a clear view of tunability of the antenna.
2
THEORY
A coaxially fed equilateral triangular microstrip antenna (ETMA) having side length r, printed on a substrate (r) maintaining a variable air gap with the ground plane is shown in Fig. 1. The variable air gap is determined by the finite value of h1 which can be equal to zero to degenerate the structure into a conventional form. The fringing of the electric fields at the edges of the equilateral triangular patch is accounted for in terms of extra linear dimensions r/2 in each ———————————————— side of the edges. Indeed, this parameter need to A.K.Saha,R.Nag,R.Upadhyay,A.Adhikari,S.Chattopadhyay are with the be determined precisely for accurate determinaDepartment of Electronics and Communication Engineering, tion of the antenna characteristics. To determine Siliguri Institute ofTechnology, P.O:Sukna, Siliguri,District:Darjeeling, the parameter in a simplified way, we consider PIN:734009,West Bengal,India.Common Research Group Mail:
[email protected] an equivalent square patch having length and width as L and W respectively (L = W), effective side length Leff =L+L and resonating at the same frequency as of the ETMA. This helps us
to establish a relationship amongst the fringing parameters L and r by equating the zero order resonant frequencies [14] of both the
t 0.37 0.63 re
patches as given by
p 1 0.2 r 2 h 2 0.01 r 4 h 4
f 0,r c 2 L r 2c 3r r
(1)
Following a previous work [15], we may consider that both the patches resonating at the same frequency are having identical circumference. This results in the following relations
2L 2L W 2W 3r r
(2)
Here c is the velocity of light in free space. In order to handle the degenerate mode concept for square patch antenna following [16] we can write
L W
1 0.5 r h (12)
g 4 1.35r h 5.58h r
(13)
The fringing parameters determined through (1)(13) can be employed to calculate the resonant frequency of a ETMA with a variable air gap h1 as
f r.nm 2c 3r r r,eff
n
2
m2 nm
(14)
(3)
where r,eff is the effective relative permittivity of the medium below the patch and can be obtained as [17]
(4)
r ,eff 4 re r ,dyn re r ,dyn 2 re r ,dyn
Again because of square patch,
L W
(11)
Solving (1)(4) we have the following primary relations:
(15)
W 0.75r
(5)
Here, εre is the equivalent permittivity of the twolayer dielectric medium (Fig.1) having total thickness h = (h1+h2) and is expressed as
r 2.67L
(6)
re r 1 h1 h2 1 r h1 h2
With the help of above relations, the fringing length of ETMA, ∆r is calculated using [16] as
r 1.1r
1 f 1
(7)
Where f is the fringing factor [17] which can be written more explicitly as
f a b ab
(8)
Using [17] and [16] along with the equivalence relation developed above we get
a 1 re re 2.45h r
(9)
b 2 3tln p 8 1.63r h 1 t 1 g (10)
(16)
and r,dyn is the dynamic dielectric constant defined in [18] and is calculated from [17].
3 RESULTS The computed results are compared with different measurements, simulations and other theories. Widely varying antenna parameters have been used to verify the new formulas. Some representative results are presented in this section. Table1 compares the newly predicted resonant frequencies of dominant and some higher order modes with the results obtained from spectral domain analysis [10], cavity model analysis [9] and some earlier theory [11] and measured results [7]. The predicted results using proposed formulation shows an excellent agreement with the measured values. Our
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theory shows only 0.5% error in predicting the resonant frequencies of dominant and higher order modes while that due to [11], and CMA [9] is 1.0% and 1.4% respectively. This clearly shows the superiority of our formulation for ETMA with low dielectric constant substrate (εr =2.32). Table2 shows the same comparison between our theory and the other theories but for ETMA with thin and high dielectric constant substrate (εr =10.5). It also reveals a close correspondence with measured results and produce minimum percentage of error compared to others. The variation of resonant frequencies with substrate thickness are studied in Fig 2 and compared with the SDA MOM [10] and earlier theory [11]. The proposed formula appears to be consistent with both the theories for low dielectric constant substrate (εr =2.32) as indicated. The theory is verified for high dielectric constant substrate (εr =10.5) also, in Table3 which shows excellent agreement with earlier theories. The effect of air gap height for ETMA is also studied and presented in Fig 3. The tunability of the patch as a function of air gap height is also revealed. A set of simulated data are also given in the figure to verify the theory. Close agreement is revealed. Thus the present formula is compared with some previous theories and simulated results for zero and nonzero air gap height values, and it is found to offer minimum average percent error amongst them.
4 CONCLUSIONS Equilateral triangular microstrip patch with and without air gap has been thoroughly studied. An improved CAD is proposed and verified with several measurements and simulated data. The proposed CAD appears to be much improved and simple compared to the existing ones to design a practical antenna without involving any rigorous analysis or commercial simulators. This indeed alleviates the lacunae and inaccuracies of the commonly used design formulas. .
5 REFERENCES [1]. J.P. Damiano, J. Bennegueouche, and A. Papiemik, “Study of Multilayer Microstrip Antennas with Radiating Elements of Various Geometry,” Proc. Inst.
Elect. Eng., pt. H, vol. 137, no. 3, pp. 163–170, 1990. (Journal Proceedings) [2]. H.R. Hassani and D. MirshekarSyahkal, “Analysis of Triangular Patch Antennas Including Radome Effects,” Proc. Inst. Elect. Eng., pt. H, vol. 139, no. 3, pp. 251–256, 1992. (Journal proceedings) [3]. D. Guha and J.Y. Siddiqui, “Effect of a Cavity Enclosure on the Resonant Frequency of Inverted Microstrip Circular patch Antenna,” IEEE Trans. Antennas Propagat., vol. 52, no. 8, p. 2177, Aug. 2004.(IEEE Transactions) [4]. R.K. Vishwakarma, J.A. Ansari, and M.K. Meshram, “Equilateral Triangular Microstrip Antenna for Circular Polarization Dual Band Operation,” Indian Journal of Radio and Space Physics, vol. 35, pp. 293296, 2006.(Journal) [5]. Y. Bhomia, A. Kajla, and D. Yadav, “ VSlotted Triangular Microstrip Patch Antenna,” International Journal of Electronics Engineering, vol. 2, no. 1, pp. 2123, 2010. (Journal) [6]. C.S. Hong, “Gain Enhanced Broadband Microstrip Antenna,” Proc. Natl. Sci. Counc. ROC (A), vol. 23, no. 5, pp. 609611, 1999 [7]. J.S. Dahele and K.F. Lee, “On the Resonant Frequencies of the Triangular Patch Antenna,” IEEE Trans. Antennas Propagat., vol. AP35, pp. 100–101, Jan. 1987. (IEEE Transactions) [8]. R. Garg and S.A. Long, “An Improved Formula for the Resonant Frequency of the Triangular Microstrip Patch Antenna,” IEEE Trans. Antennas Propagat., vol. AP36, p. 570, Apr. 1988. (IEEE Transactions) [9]. D. Karabo˘ga, K. Güney, N. Karabo˘ga, and A. Kaplan, “Simple and Accurate Effective Side Expression Obtained by Using a Modiﬁed Genetic Algorithm for the Resonant Frequency of an Equilateral Triangular Microstrip Antenna,” Int. J. Electron., vol. 83, pp. 99–108, Jan. 1997. (Journal) [10]. W. Chen, K.F. Lee, and J. Dahele, “Theoretical and Experimental Studies of the Resonant Frequencies of Equilateral Triangular Microstrip Antenna,” IEEE Trans. Antennas Propagat., vol. 40, pp. 1253–1256, Oct. 1992. (IEEE Transactions) [11]. D. Guha and J.Y. Siddiqui, ”Resonant Frequency of Equilateral Triangular Microstrip Antenna with and without Air Gap,” IEEE Trans. Antennas Propagat., vol. 52, no. 8, pp. 2174–2177, 2004. (IEEE Transactions) [12]. K.F. Lee, K.Y. Ho, and J.S. Dahele, “Circular Disc Microstrip Antenna with an Air Gap,” IEEE Trans. Antennas Propagat., vol. 32, pp. 880–884, Aug. 1984. (IEEE Transactions) [13]. J.S. Dahele and K.F. Lee, “Theory and Experiments on Microstrip Antennas with Air Gaps,” Proc. Inst. Elect. Eng., pt. H, vol. 132, no. 7, pp. 455–460, Dec. 1985. (Journal Proceedings) [14]. R. Garg, P. Bhartia, I. Bahl, and A. Ittipiboon, “Mi
[15].
[16].
[17].
[18].
crostrip Antenna Design Handbook, Artech House, “Norwood, 2001. (Hand Book) D. Guha, J.Y. Siddiqui,” Resonant Frequency of Circular Microstrip Antenna Covered with Dielectric Superstrate,” IEEE Trans. Antennas Propagat., vol. 51, pp. 16491652, 2003. (IEEE Transactions) S. Chattopadhyay, M. Biswas, J.Y. Siddiqui, D. Guha,”Rectangular Microstrips with Variable Air Gap and Varying Aspect Ratio: Improved Formulations and Experiments,” Microwave and optical Tech. Lett., vol. 51, no. 1, pp. 169173, 2009. (Journal) D.Guha, “Resonant Frequency of Circular Microstrip Antennas with and without air Gaps,” IEEE Trans. Antennas Propagat., vol. 49, pp. 55 59, 2001. (IEEE Transactions) I. Wolff, and N. Knoppik, “Rectangular and Circular Microstrip Disk Capacitors and Resonators,” IEEE Trans. Microwave Theory Tech., vol. 22, pp. 857864, 1974. (IEEE Transactions)
A.K. Saha was born in Islampur, West Bengal, India on December 8, 1989. He is pursuing his B. Tech Degree in Electronics and Communication Engineering from Siliguri Institute of Technology, Siliguri under West Bengal University of Technology, West Bengal, India. He has already published paper in international conference. His area of interest includes wireless communication and antenna engineering specially microstrip antenna. R. Nag was born in Shillong, Meghalaya, India on November 18, 1989. She is pursuing her B. Tech Degree in Electronics and Communication Engineering from Siliguri Institute of Technology, Siliguri under West Bengal University of Technology, West Bengal, India. She has already published paper in international conference. Her area of interest includes Computer Networks and antenna engineering specially microstrip antenna. R. Upadhyay was born in Maldah, West Bengal, India on November 27, 1987. She is pursuing her B. Tech Degree in Electronics and Communication Engineering from Siliguri Institute of Technology, Siliguri under West Bengal University of Technology, West Bengal, India. She has already published paper in international conference. Her area of interest includes Tele communication, Digital Signal Processing, RF and Microwave Engineering. A. Adhikari was born in Jalpaiguri, West Bengal, India on April 18, 1989. She is pursuing her B. Tech Degree in Electronics and Communication Engineering from Siliguri Institute of Technology, Siliguri under West Bengal University of Technology, West Bengal, India. She has already published paper in international conference. Her area of interest includes wireless communication and Electromagnetics.
S. Chattopadhyay was born in West Bengal on September 10, 1974. He received his B.Sc (Physics Honours) from University of Calcutta in 1996 and B. Tech, M. Tech degree from Institute of Radio Physics and Electronics, University of Calcutta in 1999 and 2001 respectively. He is currently working as Assistant Professor of Siliguri Institute of Technology under West Bengal University of Technology, West Bengal, India. He is also pursuing his Ph. D from The Universty of Calcutta. He is listed in Marquis Who’s Who in the World, USA, 26th Ed, 2009 and also listed in 2000 Outstanding Intellectuals of The 21st Century, UK, 2010. He is a member of IEEE Antennas and Propagation Society. He has several publications in international journals and conferences. His area of research includes microwave antennas, microstrip and integrated antennas and computer aided design of patch antennas.
r (a) h2
Dielectric (εr )
h1
Air (εr =1)
(b) Figure 1: Schematic diagram of equilateral triangular microstrip antenna structure: (a) Top view of the patch, (b) Side view of the entire structure.
Resonant ferquency (GHz)
1.35 [11] present MoM[10]
1.30 1.25 1.20 1.15 1.10 0
2
4
6
8
10 12 14 16 18
Substrate thickness (mm) Figure 2: Variation of dominant mode resonant frequency of ETMA without air gap (h1=0), with substrate thickness (h2). Parameters: r = 100 mm, Dielectric constant r =2.32
Resonant Frequency (GHz)
9.4 9.2 9.0 8.8 8.6 8.4 8.2 8.0 7.8 7.6 7.4
computed[present] simulated
0
1
2
3
4
5
Air gap height (mm) Figure 3: Variation of dominant mode resonant frequency as a function of air gap height (h1): Parameters: r =13.4 mm, εr = 2.32, substrate thickness h1=1.575 mm
TABLE 1 COMPARISON OF EARLIER THEORIES AND PRESENT MODEL FOR RESONANT FREQUENCIES OF DOMINANT AND OTHER HIGHER ORDER MODES OF ETMA (LOW DIELECTRIC Mode
SDA MoM (MHz) [10]
Computed (MHz) [11]
CMA (MHz) [9]
Measured (MHz) [7]
Present Model (MHz)
TM10
1288
1285
1281
1280
1283
TM11
2259
2226
2219
2242
2223
TM20
2610
2570
2562
2550
2566
TM21
3454
3400
3389
3400
3396
TM30
3875
3855
3843
3824
3850
1.0
1.4

0.5
Average % errors (w.r.t measured value)
CONSTANT SUBSTRATE) Parameters: εr=2.32, r = 100 mm, h1 = 0, h2 =1.59 mm
TABLE 2 COMPARISON OF EARLIER THEORIES AND PRESENT MODEL FOR RESONANT FREQUENCIES OF DOMINANT AND OTHER HIGHER ORDER MODES OF ETMA (HIGH DIELECTRIC Mode
SDA MoM (MHz) [10]
Computed (MHz) [11]
CMA (MHz) [9]
Measured (MHz) [7]
Present Model (MHz)
TM10
1522
1516
1501
1519
1513
TM11
2654
2626
2601
2637
2631
TM20
3025
3032
3003
2995
3026
TM21
4038
4011
3972
3973
4003
TM30
4518
4548
4504
4439
4509
0.6
1.2

0.7
Average % errors (w.r.t measured values)
CONSTANT SUBSTRATE) Parameters: εr =10.5, r = 41 mm, h1 = 0, h2 = 0.7 mm
TABLE 3 COMPARISON OF EARLIER THEORIES AND PRESENT MODEL FOR RESONANT FREQUENCIES OF DOMINANT MODES OF ETMA AS A FUNCTION OF SUBSTRATE THICKNESS (h2) Parameters: εr =10.5, r = 100 mm, h1 = 0 Substrate Thickness h2 (mm)
SDA MoM (GHz) [10]
Computed (GHz) [11]
Present Model (GHz)
4.0
0.64
0.63
0.6324
8.0
0.62
0.62
0.622
12.0
0.60
0.60
0.609
16.0
0.58
0.59
0.5958