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Dominant mode resonant frequency of circular microstrip antennas with and without air gap
1.
INTERNATIONAL JOURNAL OF
ELECTRONICS AND International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), pp. 111-122 IJECET © IAEME: www.iaeme.com/ijecet.html Journal Impact Factor (2011): 0.8500 (Calculated by GISI) ©IAEME www.jifactor.com DOMINANT MODE RESONANT FREQUENCY OF CIRCULAR MICROSTRIP ANTENNAS WITH AND WITHOUT AIR GAP B.Ramarao1 M.Aswini2 D.Yugandhar1 Dr.P.V.Sridevi3 1. Associate professor Dept of E.C.E. Aditya Institute of Technology and Management, TEKKALI AP.-532201 2. M.Tech(student), Dept of E.C.E., Aditya Institute of Technology and Management, TEKKALI AP.-532201 e-mail: maswini407@gmail.com 3. Associate professor, Dept of E.C.E.,AU College off Engg. VISAKHAPATNAM-533001 ABSTRACT Circular microstip antennas offer performance similar to that of rectangular geometries. In some applications such as arrays, circular geometries offer certain advantages over other configurations .Recent experimental results have shown that circular disk microstrip elements may be easily modified to produce a range of impedance, radiation pattern and frequency of operation. In this paper an improved analytical model is presented for calculating the resonant frequency of circular microstrip antennas with and without air gaps. Unlike the previous models, the present one is widely applicable to all patch diameters—from very large to very small compared to the height of the dielectric medium below the patch and also to the substrates covering the entire range of dielectric constants. The computed results for different antenna dimensions and modes of resonance are compared with the experimental values Key word: Microstrip antenna. I INTRODUCTION The concept of microstrip radiators was first proposed by Deschamps as early as 1953. The first practical antennas were developed in the early 1970’s by Howell and Munson. Since then, extensive research and development of microstrip antennas and arrays, exploiting the numerous advantages such as light weight, low volume, low cost, 111
2.
International Journal of
Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME planar configuration, compatibility with integrated circuits, etc., have led to diversified applications and to the establishment of the topic as a separate entity within the broad field of microwave antennas. Various types of flat profile printed antennas have been developed-- the microstrip antenna, the stripline slot antenna, the cavity backed printed antenna and the printed dipole antenna. I.I Definition of a microstrip antenna As in figure, a Microstrip antenna in its simplest configuration consists of a radiating patch on one side of a dielectric substrate (εr≤ 10), which has a ground plane on the other side. The patch conductors, normally of copper and gold, can assume virtually any shape, but conventional shapes are generally used to simplify analysis and performance prediction. Ideally, the dielectric constant, εr of the substrate should be low (εr ~ 2.5), so as to enhance the fringe fields which account for the radiation. However, other performance requirements may dictate the use of substrate materials whose dielectric constants may be greater than 5. Various types of substrates having a large range of dielectric constants and loss tangents have been developed. Flexible substrates are also available which make it possible to fabricate simple conformal wraparound antennas. Figure 1.1 Microstrip Antenna configuration II. DESIGN OF SINGLE PATCH MICROSTRIP ANTENNA Circular microstrip antennas offer performance similar to that of rectangular geometries. In some applications such as arrays, circular geometrics offer certain advantages over other configurations. Recent experimental results have shown that circular disk microstrip elements may be easily modified to produce a range of impedances, radiation patterns, and frequencies of operation. 112
3.
International Journal of
Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME Figure 2.1 II.I Analysis of a microstrip disk antenna The different methods used for the calculation of radiation fields and input impedance are • Simple cavity model • Cavity model with source • Modal expansion model • Wire grid model • Green’s function method The cavity model is the simplest method used for predicting adequately the radiation characteristics of circular shaped microstrip antennas. The methods of analyzing microstrip disk antennas appear in ascending order of complexity. Thus the cavity model is the simplest, while Green’s function method is the most involved. In all cases, the substrates thickness h is assumed to be much less than λ0. Parameters of circular disk antennas: A circular disk operating in the dominant mode is the most prevalent circular microstrip antenna configuration. The following is a design procedure for this configuration. Element radius: The first design step is to select a suitable substrate of appropriate thickness. Bandwidth and radiation efficiency increase with substrate thickness, but excess thickness is undesirable if the antenna is to have a low profile and be conformal. The three most commonly used substrate materials are duroid (εr = 2.32) , rexolite (εr = 2.6) and alumina (εr = 9.8) . Since the relative dielectric constants of rexolite and duroid are close to each other, the design curves below will be limited to duroid and alumina. For a known dielectric substrate at a specified operating frequency fr, the radius of the microstrip disk element is: 113
4.
International Journal of
Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME k a= 1/ 2 2h πk 1+ ln +1.7726 π ε r k 2h 8.794 × 109 where k = and f r is in GHz. f ε r r Disk radius as a function of frequency for various values of εr and h is determined. It may be noted that the effects of substrate thickness are insignificant for frequencies less than 2 GHz. Input impedance A reasonably accurate evaluation of the input impedance of a microstrip antenna is necessary to provide a good match between the radiating element and the feed point. The LO approach provides good agreement between the experimental results for microstrip fed disk radiators and the theoretical values. Equation ω Ζin = jΧL − C J12 (Re(κ11ρ0 )) ω2 − ω111+ j Q 2 T provides a reasonably simple basis for calculating the input impedance of a disk antenna for any coaxial feed location. For a microstrip fed element, this relation may be used with Χ L = 0. Radiation pattern As previously various mathematical models have been suggested for predicting the radiation characteristics of a circular disk microstrip radiator, the far-field expressions obtained for the cavity model are simple and adequate for practical purposes. As such the radiation patterns may be plotted either by using equations Vak 0 e − jk0r Εθ = j n cos nφ 2 r [ Jn+1 ( k0 a sin θ ) – Jn-1 ( k0 a sin θ ) ] and [Jn+1( k0 a sin θ ) + Jn-1 ( k0 a sin θ ) ] Where V=h E0 Jn (ka) and is known as the edge voltage at φ = 0 . 114
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International Journal of
Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME Or Equations Vak e− jk0r sin( 0hcosθ ) k Εθ = jn 0 cosnφ 2 r k0hcosθ [ Jn+1 ( k0 a sin θ ) – Jn-1 ( k0 a sin θ ) ] Vak0 e− jk0r sin(k0h cosθ ) And Εφ = jn cosθ sin nφ 2 r k0h cosθ [ Jn+1 ( k0 a sin θ ) + Jn-1 ( k0 a sin θ ) ] The E-plane and H-plane radiation patters for disk elements at 2 GHz and εr = 2.32, εr = 9.8 are plotted in figures. The E-pattern of a microstrip disk antenna using a high dielectric constant material such as alumina, is almost constant with scan angle. Radiation resistance, q factor and losses: The radiation resistance may be evaluated from equation 2 960 Rr = V = 2 Pr (ak0 )2 I1 for n=1 or Figure can be used to determine this, using appropriate thickness of the substrate. These curves have been computed assuming that tanδ =0.0005 and the disk metallization is of copper. The frequency selectivity of a radiating element is determined by the quality factor QT. The total Q-factor of a disk radiator is given by equation −1 1 hµf (k0a)2 I1 Q = + tanδ + Εφ = jn Vak0 e− jk0r cos nφ sin nφ T h(πfσµ) 1/ 2 { } 240(ka) − n2 2 2 r And is plotted in figure for a typical set of parameters. For εr = 2.32 and f ≥ 500 MHz, the quality factor decreases with increase in resonant frequency and substrate thickness. Similarly for εr = 9.8 and h =0.1275 cm, QT decreases with increasing resonant frequency for f ≥ 500MHz. III. RESONANT FREQUENCY OF CIRCULAR MICROSTRIP ANTENNAS WITH AND WITHOUT AIR GAPS An analytical model for calculating the resonant frequency and the input impedance of circular microstrip antennas with and without air gaps ( Figure3.1) has recently been developed and is also employed in designing some integrated antenna modules. The 115
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International Journal of
Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME formulation, though incorporating the improved results of some earlier works, is valid for the antenna parameters a/h > 2 and ε r < 10. Thus the model is not applicable to small values of a, particularly when an air gap increases the value of h ( = h 1 + h 2 in figure). Moreover, the calculation of the resonant frequency involves an erroneous equation, as discussed in the following sections. All these limitations and shortcomings are addressed in this paper to satisfy the current interests of designing active and passive antennas employing circular microstrip patches. An improved formulation is proposed to calculate an accurate, or very closely approximate, theoretical value of the resonant frequency for any a/h value of the antenna printed on the substrate covering the entire range of dielectric constants. The theory has been verified with the experimental results available in the literature for the antennas having various patch diameters (a/h > 2) and heights of the air gap below the substrate. A set of prototype coax-fed antennas with a/h ~ 2 and a/h < 2 has been fabricated and experimentally investigated. The theory shows very close agreement with the experiment in all cases. Figure 3.1 Background The simple resonator model of a circular disk cavity given by Watkins was modified by Wolff and Knoppik incorporating the effect of the fringing fields in a disk capacitor and by introducing dynamic dielectric constant ε r , dyn defined. The latter one, along with the results obtained by Chew and Kong for the fringing fields of a circular disk capacitor, has been applied to calculate the resonant frequency of TM modes in circular microstrip antennas with and without air gaps. The effect of the air gap below the substrate, shown in Fig. 1, was accounted for by an equivalent dielectric constant of the medium below the patch given by 116
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International Journal of
Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME ε re = ( ) ε r 1 + h2 h1 (1 + ε h2 h1) r Where ε r is the dielectric constant of the substrate. For the microstrip without an air gap, h 2 /h 1 = 0 and, hence, ε re = ε r Present formulation Following the analytical model by Wolff and Knoppik, an improved formulation is presented by introducing a new effective dielectric constant εr,eff in place of the dynamic dielectric constant εr,dyn of the medium below the patch to calculate the resonant frequency of a circular microstrip antenna as α nm c f r ,nm = 2πaeff ε r ,eff Where αnm is the mth zero of the derivative of the Bessel function of order n, the value of which (α01=3.832, α11=1.841, α21=3.054, α31=4.201) determines the lowest and higher order modes as TM110, TM210, TM010, and TM310 modes. c is the velocity of light in free space, αeff is the effective radius of the circular patch defined through, and εr,eff is defined as 4ε reε r , dyn ε r , eff = ( ε re + ε r , dyn ) 2 The term εr,eff is introduced to take into account the effect of εre , the equivalent dielectric constant of the medium below the patch in combination with the dynamic dielectric 4ε reε r , dyn constant εr,dyn to improve the model. εr,eff is deduced as ε r , eff = to yield the ( ε re + ε r , dyn 2 ) resonant frequency as an average of the frequencies resulting from f r ,nm = α nm c by 2πaeff ε r ,eff substituting εre and εr,dyn separately in place of εr,eff. The evaluation of εre is straightforward, as given by , and that of εr,dyn is a function of the static main and static fringing capacitances and the mode of resonance as given by ε re = ( ) and that of εr,dyn ε r 1 + h2 h1 is a function of the static and static fringing capacitances (1 + ε h2 h1) r and the mode of resonance as given by cdyn (ε = ε 0ε re ) ε r , dyn = cdyn (ε = ε 0 ) Where cdyn is the total dynamic capacitance defined as cdyn = c0, dyn + ce, dyn 117
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International Journal of
Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME co,dyn and ce,dyn are the dynamic main and dynamic fringing capacitances of the different modes determined from the static main and static fringing capacitances co,stat and ce,stat respectively, as Where c0, dyn = γ n c0, stat Where γ n = 1.0, for n = 0 = 0.3525 =1 = 0.2865 =2 = 0.2450 =3 And 1 ce, dyn = ce, stat δ Where δ = 1, for n = 0 =2 n≠0 A comparatively recent formulation for the static capacitance of a circular microstrip disk obtained by Wheeler is applied to calculate co,stat and ce,stat since the result is much improved over the earlier ones and is widely applicable to the entire range of dielectric constants and to all a/h values of the antenna. The expression of the capacitance given by Wheeler can be more explicitly written as ε 0ε reπa 2 c= (1 + q ) h Where a is the physical radius of the patch and q = u + v + uv 1 + ε re 4 u= ε re πa / h 2 ln( p ) 1 v= + − 1 / g t = 0.37 + 0.63ε re 3t 8 + πa / h t 118
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Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME 1 + 0.8(a / h ) + (0.31a / h ) 2 4 p= 1 + 0.9 a / h g = 4 + 2 .6 a / h + 2 .9 h / a In equation ε 0ε reπa 2 c= (1 + q ) h the first term is equal to the static main capacitance co,stat and the term q arises due to the fringing fields at the edge of the disk capacitor. The static fringing capacitance ce,stat thus is defined as ce , stat (ε ) =c 0, stat (ε )q Where c0, stat (ε ) = ε 0ε reπa 2 / h It can be noted that the ce,stat evaluated in equation 1 + ε re 4 u = ε re πa / h Erroneously equates the total capacitance of a microstrip disk instead of the fringing capacitance only, which is thoroughly investigated in equation aeff = a (1 + q ) . 2 Equation c = ε 0ε reπa (1 + q ) also defines the effective radius of the microstrip disk as h aeff = a (1 + q ) RESULTS The computed results are presented and compared with the previously computed values available in the literature for certain dimensions of the antenna having small a/h values .The dependence of the factor q arising due to the fringing fields at the edge of the disk capacitor on the disk parameter a/h for two єre values is verified. The fringing field is the significant function of the dielectric constant of the substrate and the dimensional parameter a/h , particularly when a/h < 3. The theoretical values of εr,eff and εr,dyn as a function of antenna dimension a/h, with εre as a parameter, are verified. The quantity εr,eff, though, becomes closer to εr,dyn at very large values of a/h , and differs significantly as a/h decreases. The parameter εr,eff introduced in the present theory thus becomes significant for all large and small values of a/h. The computed resonant frequencies of some circular patch antennas without an air gap are presented in Table 1 and compared with some theoretical results reported earlier. 119
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International Journal of
Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME More recent results are included in Table 1, where the ce,stat has been correctly evaluated following of the previous section. Wolff’s model employing Wheeler’s result for the static capacitance of circular microstrip disk is highly relevant for comparison with the present theory and is also included in Table 1. Of all the theoretical values f the resonant frequency, the present values show the closest approximation with the experimental values with 0.04%-0.64% errors. Table 2 compares the theoretical and Abbound calculated resonant frequencies of the dominant two higher order modes of a circular patch antenna with an air gap for three different air gap heights. The present theory shows the closest agreement with the experiment for all the three modes. Table 1: Theoretical and Experimental Values of Resonant Frequency For Dominant Mode of Circular Microstrip Antennas Without Airgap Antenna Parameters h1=1.5875mm;h2=0mm;€=2.65 Abbound Wolf Shen Present A (mm) (GH) (GHz) (GHz) (GHz) 11.5 4.609 4.576 4.4 5.17 10.7 4.938 4.903 47. 5.37 9.6 5.473 5.436 5.2 5.69 8.2 6.346 6.307 6.1 6.18 7.4 6.981 6.941 6.8 6.51 Table 2: Theoretical And Experimental Values Of Resonant Frequency For Dominant Mode Of Circular Microstrip Antennas With Airgap Antenna Parameters a=50mm, h1=1.5875mm, €=2.65 Present Air Gap height Abbound Mode (MHz) h 2(mm) (MHz) TM11 1153.9 1118.8 0 TM21 1927.0 1855.9 TM31 2665.3 2552.9 TM11 1298.9 1276.1 0.5 TM21 2167.0 2115.8 TM31 2994.9 2922.8 TM11 1368.0 1342.1 1 TM21 2280.8 2235.5 TM31 3150.2 3055.6 120
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Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME CONCLUSION A single patch circular microstrip antenna at a given resonant frequency is calculated. An improved analytical formulation based on a resonator model is presented for calculating the resonant frequency of circular microstrip antennas with and without air gaps. The formulation overcomes the limitations of the earlier models in predicting the resonant frequencies for small patch diameters (a/h<2) and higher dielectric constants of the substrate (εr>10) and is thus applicable to a wide range of patch dimensions- from very large to very small values of a/h printed on the substrate covering the entire range of dielectric constants. The theory is verified with the previously calculated results reported earlier for different dimensions of patch with a/h>2, heights of air gap, and modes of resonance. The theoretical resonant frequency for small patch dimensions with a/h=1.875 and 2.31 also shows close agreement with the previously calculated values. REFERENCES [1] K. F. Lee and J. S. Dahele, “Mode characteristics of annular-ring and circular-disc microstrip antenna with and without air gaps,” in IEEE Antennas Propagation Soc. Int. Symp. Dig., 1983, pp. 55–58. [2] K. F. Lee, K. Y. Ho, and J. S. Dahele, “Circular disc microstrip antenna with an air gap,” IEEE Trans. Antennas Propagat., vol. AP-32, pp. 880–884, Aug. 1984. [3] S. Dahele, S. Mem, and K. F. Lee, “Theory and experiment on microstrip antennas with air gaps,” Proc. Inst. Elect. Eng., pt. H, vol. 132, no. 7, pp. 455–460, Dec. 1985. [4] J. A. Navarro, L. Fun, and K. Chang, “Active integrated stripline circular patch antennas for spatial power combining,” IEEE Trans. Microwave Theory Tech., vol. 41, pp. 1856–1863, Oct. 1993. [5] “Novel FET integrated inverted stripline patch,” Electron. Lett., vol. 30, no. 8, pp. 655–657, 1994. [6] R. A. Flynt, L. Fun, J. A. Navarro, and K. Chang, “Low cost and compact active integrated antenna transceiver for system applications,” IEEE Trans. Microwave Theory Tech., vol. 44, pp. 1642–1649, Oct. 1996. [7] C. M. Montiel, L. Fun, and K. Chang, “A novel active antenna with selfmixing and wideband varactor-tuning capabilities for communication and vehicle identification applications,” IEEE Trans. Microwave Theory Tech., vol. 44, pp. 2421–2430, Dec. 1996. [8] K. L.Wong and Y. F. Lin, “Circularly polarized microstrip antenna with a tuning stub,” Electron. Lett., vol. 34, no. 9, pp. 831–832, 1998. [9] K. L. Wong and J. Y. Jan, “Broadband circular microstrip antenna with embedded reactive loading,” Electron. Lett., vol. 34, no. 19, pp. 1804–1805, 1998. [10] F. Abboud, J. P. Damiano, and A. Papiernik, “A new model for calculating the impedance of coax-fed circular microstrip antennas with and without air gaps,” IEEE Trans. Antennas Propagat., vol. 38, pp. 1882–1885, Nov. 1990. [11] I. Wolff and N. Knoppik, “Rectangular and circular microstrip disk capacitors and resonators,” IEEE Trans. Microwave Theory Tech., vol. MTT-22, pp. 857–864, Oct. 1974. [12] W. C. Chew and J. A. Kong, “Effects of friging field on the cacapacitance of circular microstrip disk,” IEEE Trans. Microwave Theory Tech., vol. MTT-28, pp. 98–104, Feb. 1980. 121
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Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME [13] J. Watkins, “Circular resonant structures in microstrip,” Electron. Lett., vol. 5, pp. 524–525, Oct. 1969. [14] H. A. Wheeler, “A simple formula for the capacitance of a disc on dielectric on a plane,” IEEE Trans. Microwave Theory Tech., vol. MTT-30, pp. 2050–2054, Nov. 1982. [15] L. C. Shen, S. A. Long, M. R. Allerding, and M. D. Walton, “Resonant frequency of a circular disc, printed-circuit antenna,” IEEE Trans. Antennas Propagat., vol. AP-25, pp. 595–596, July 1977. [16] M. S. Leong et al., “Determination of circular microstrip disc by Noble’s variational method,” Proc. Inst. Elec. Eng., vol. 128 H (M.O.A.), pp. 306–310, Dec. 1981. [17] D. Guha, “Comment on ‘A new model for calculating the impedance of coax-fed circular microstrip antennas with and without air gaps’,” IEEETrans. Antennas Propagat., vol. 48, pp. 1010–1011, June 2000. [18] T. Itoh and R. Mittra, “Analysis of microstrip disk resonator,” Arch. Eleck. Übertragung, vol. 27, no. 11, pp. 456–458, 1973. 122
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