# Radiation Pattern Investigation of n Element Microstrip Patch

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Radiation Pattern Investigation of n Element Microstrip Patch

DUET Journal Vol. 1, Issue 3, June 2012 Radiation Pattern Investigation of n Element Microstrip Patch Antenna Array S. M. Mahfuz Alam, Md. Anwarul Abedin, Utpal Kumar Das and Md. Arifur Rahman Dept. of Electrical & Electronic Engg, Dhaka University of Engineering &Technology, Gazipur, Bangladesh E-mail: [email protected] ABSTRACT Microstrip patch antenna is widely used in aircraft, spacecraft and other application for small size, low cost and light weight. The fringing field created on patch antenna depends on the dielectric constant of patch element. The desired directivity of the antenna can be achieved by the proper design of the patch antenna array. In this paper the generalized equations of electric and magnetic field for n element patch antenna array are analyzed and effect of dielectric constant of patch element on fringing field are investigated. The results from the derived equations are compared with PCCAD 5.0 software simulation results and results from experiments. The comparison shows that the derived equations can be satisfactorily used for any n element patch antenna array and any phase displacement between two patch elements. 1. INTRODUCTION In high-performance aircraft, spacecraft, satellite and missile application, where size, weight, cost, performance, ease of installation, and aerodynamic profile are constraints, low profile antennas may be required. Presently there are many other government and commercial applications, such as mobile radio and wireless communications that have similar specifications. To meet this requirements microstrip patch antennas have been studied and researched extensively over the past many years because of its low profile structure, light weight, and low cost in fabrication. They are extremely compatible for embedded antennas in handheld wireless devices such as cellular phones, pagers etc. Some of the principal advantages of this type of antennas are low profile in nature, conformability to planar and non planar surfaces, low fabrication costs and compatibility [1]. Antenna array is used to improve performances such as gain, directivity etc. In the case of patch antenna array, it can be used to scan the beam of an antenna system and perform various other functions which would be difficult with any single element. Research has been done on radiation pattern calculation of patch antenna array by improved induced element pattern method (IIEPM) which transforms the large array calculation problem into two small array problems [2]. In this paper, a generalized equations of both electric and magnetic field for an n element patch antenna array are derived considering the phase shift between patch elements without calculating the radiation pattern by transforming large array into two Dhaka University of Engineering & Technology, Gazipur small array and this equation is valid for any number of array element operating at any frequency. 2. BASIC CHARACTERISTICS OF MICROSTRIP PATCH ANTENNA Microstrip patch antenna consists of very thin metallic strip (patch) placed a fraction wavelength above a ground plane. The patch is so designed that its pattern maximum is normal to the patch. For a rectangular patch, the length L of the element is usually λ/3< L <λ/2, where λ is wavelength. The patch and the ground plane are separated by a dielectric substrate of height h as shown in Fig. 1. L patch w t Dielectric substrate h Ground Plane Fig.1: Microstrip patch antenna There are numerous substrates that can be used for the design of microstrip antennas and their dielectric constants are usually in the range of 2.2< εr < 12 [1]. The microstrip line feed is used to feed microstrip patch antenna. The transmission line model of microstrip patch antenna is shown in Fig. 2. 23 DUET Journal Vol. 1, Issue 3, June 2012 Be = Y0 tan(β Δl) (2) Where Y0, β and Δl are the characteristic admittance, phase constant and incremental length of the patch due to fringing effect respectively. If βΔl<<1 or Δl<< λ Then the edge capacitance can be approximated as 𝐶𝑒 = 𝑣 𝛥𝑙 (3) 𝑝 𝑍𝑜 Where, 𝑣𝑝 = Fig. 2: Transmission line model 𝜔 𝛽 , 𝑣𝑝 is the phase velocity and 𝑍𝑜 is the characteristic impedance. The field distribution is identical to that of a uniform transmission line of characteristic impedance Z0 and the phase voltage Vph . The fringing fields associated with edges “01” and “23” of the patch are taken into account by Z0 and Vph. The fringing fields associated with edges “02” and “13” are represented by lumped admittances Ye (edge conductance) connected at the two ends [3]. Edge admittance is given by, Ye =Ge +jBe (1) Where Be =ωCe and Ge,Be, Ce are the edge conductance, edge susceptance and edge capacitance respectively. The edge conductance accounts for the power radiated at the radiating edges (or open ends). The edge susceptance accounts for the fringing electric field (and hence the fringing capacitance at the open end) [1]. Because of the fringing effect, the effective length of the patch of the microstrip antenna looks greater than its physical dimension as shown in Fig. 2. The dimension of the patch along its length have been extended on each end side by a distance 𝛥𝑙, which is a function of dielectric constant, 𝜖𝑟 and width to height ration (w/h) and can be expressed as [1] Normalized length, 𝛥𝑙 ℎ = 0.412 𝑤 ℎ 𝜖 𝑟 +0.3 ( +0.264) (4) The Normalized Length vs. Normalized Width Curve is drawn in Fig. 4 for various values of dielectric constant, 𝜖𝑟 . 0.7 0.65 The edge capacitance, Ce is represented in terms of an equivalent line length extension as shown in the Fig. 3. 𝜖𝑟 = 1 0.6 0.55 normalised length The transmission-line model gives good physical insight. Basically the transmission line model represents the microstrip patch antenna by two slots, separated by a low impedance (𝑍𝑜 )transmission line of length L [3]. 𝑤 ℎ 𝜖 𝑟 −0.258 ( +0.8) 𝜖𝑟 = 1.5 0.5 𝜖𝑟 = 2.45 0.45 𝜖𝑟 = 5 0.4 0.35 1 2 3 4 5 6 7 8 9 10 normalised width Fig. 4: Normalized length vs. normalized width Fig. 3: Transmission Line Model, Edge Capacitance From the theory of open ended transmission line, the edge susceptance of microstrip patch can be expressed as [3] Dhaka University of Engineering & Technology, Gazipur From Fig. 4 it is seen that for a fixed normalized width, the normalized length increases with the decrease in dielectric constant and for a fixed dielectric constant the 24 DUET Journal Vol. 1, Issue 3, June 2012 normalized length increases with the increase in normalized width. 3. EXPRESSIONS OF E-FIELD AND H-FIELD OF PATCH ANTENNA EФ = A e −jk o r r ejψ/2 2 cos (1 2 (k o dsinѲsinΦ + P)) (11) And the magnetic field equation becomes HѲ = {A e −jk o r r jψ e 2 2 cos (1 2 (k o dsinѲsinΦ + P))}/𝜂 (12) 4. RESULT AND DISCUSSION The electric and magnetic field radiation patterns for single element patch antenna operating at 10 GHz are plotted using MATLAB program in Fig. 6 and Fig. 7 respectively. These results are compared with the experimental results (Fig. 8 and Fig. 9). Fig. 10 shows PCCAD 5.0 software result. cos Ѳ 2 Where, k0 = phase constant = 2π/λ and 𝜂 is the intrinsic impedance For n element patch array the electric field intensity can be expressed as: Assuming, θ1 = θ2 = θ e −jk o r EФ = A{ r + e −j(k o r 1 −β ) e −j(k o r n −(n −1)β ) rn where, A = + r1 e −j(k o r 2 −2β ) r2 r 90 } × ej 270 + ⋯+ 5e-008 120 (7) 60 4e-008 3e-008 150 30 2e-008 1e-008 Finally the generalized equation becomes e −jk o r 5e-006 Fig. 6: E field radiation pattern for single element patch antenna (theoretical) jk o Im hw cosѲ sinѲ sin(k o w ) 4π 2 k w cosѲ o 2 EФ = A 300 30 (6) 240 sin Ѳ ko w 210 ) (5) 180 2 cos Ѳ 2 1e-005 cos Ѳ ko w 1.5e-005 e−jk o r sin (k o w sin Ѳ 2 150 4π𝔶o r cos Ѳ 2e-005 jk o I m hw e−jk o r sin k o w 90 HѲ = 4πr 120 jk o I m hw 60 Fig. 5 shows a rectangular patch antenna array of nelements separated from each other by a distance d. The magnetic field intensity and electric field intensity of a single element patch antenna can be expressed as EФ = 330 0 Fig. 5: Patch antenna array 180 (nψ /2) n−1 ψ/2 sin sin (ψ/2) 0 (8) where, ψ = k o dsinθsinΦ + 𝑃 (9) 210 330 P is the total phase shift between two patch elements. Hθ = EФ η = {A e −jk o r r 240 × sin (nψ /2) ej n−1 ψ/2 }/𝜂 sin (ψ/2) (10) Finally the electric field equation for two element array can be written as Dhaka University of Engineering & Technology, Gazipur 300 270 Fig. 7: H field radiation pattern for single element patch antenna (theoretical) 25 DUET Journal Vol. 1, Issue 3, June 2012 150 210 120 240 90 270 2e-006 4e-006 6e-006 8e-006 60 300 30 330 0 From the above figures, it is clear that the radiation patterns satisfy both the experimental and simulation results. 180 Fig. 8: E field radiation pattern for single element patch antenna (experimental) Fig. 11: E field radiation pattern for two element patch antenna array (Proposed) 90 1e-008 120 60 8e-009 6e-009 150 30 4e-009 2e-009 180 0 210 330 240 300 270 Fig. 9: H field radiation pattern for single element patch antenna (experimental) Fig. 12: H field radiation pattern for two element patch antenna array (Proposed) Fig. 10: E and H field radiation pattern for single element patch antenna (PCCAD 5.0) Fig. 13: E field radiation pattern for two element patch antenna array (PCCAD 5.0) Dhaka University of Engineering & Technology, Gazipur 26 Vol. 1, Issue 3, June 2012 180 150 210 120 240 90 270 2e-006 4e-006 6e-006 8e-006 60 300 30 330 0 DUET Journal Fig. 14: H field radiation pattern for two element patch antenna array (PCCAD 5.0) Fig. 17: E field radiation pattern for P=π 90 1e-008 120 60 30 330 0 8e-009 6e-009 150 30 2e-009 2e-006 4e-006 6e-006 60 300 4e-009 0 90 270 180 120 240 210 330 240 300 Fig. 18: H field radiation pattern for P=π 180 150 210 270 Fig. 15: E field radiation pattern for P=π/2 90 6e-010 120 60 Fig. 15, Fig. 16, Fig. 17 and Fig. 18 show the radiation pattern for different values of P. So, the proposed equations can be applied successfully for any difference in phase of excitation as well. 4e-010 150 30 5. CONCLUSION 2e-010 180 0 210 330 240 300 270 Fig. 16: H field radiation pattern for P=π/2 Dhaka University of Engineering & Technology, Gazipur In this paper, the effect of dielectric constant of patch element on fringing field is analyzed. Generalized equations of electric and magnetic field radiation pattern of n element patch array operating at any frequency are proposed. The radiation patterns of both single element and two element patch array, operating at 10 GHz are compared with the experimental results and PCCAD 5.0 software simulation results. The results from the proposed equations are identical to the experimental results and the PCCAD 5.0 software simulation results. The radiation patterns have been observed for different phase shift in excitation between two patch elements. All results 27 DUET Journal indicate that the proposed generalized equations can be used for any number of patch antenna array operating at any frequency. REFERENCES [1] C. A. Balanis, “Antenna theory analysis and design,” Jhon Wiley & Sons, Inc. second edition, 1996. [2] Zhang, S., Gong, S., Gong, Q., Guan, Y. and Lu, B. , “Application of the Active Element Pattern Method for Calculation of the Scattering Pattern of Large Finite Arrays,” Antennas and Wireless Propagation Letters, IEEE , vol.10, no., pp. 83-86, 2011 [3] Manik Gujral, Tao Yuan, Cheng-Wei Qui, Le-Wei Li and Ken Takei, “Bandwidth increment of microstrip patch antenna array with opposite double- E EBG structure for different feed position,” International symposium on antenna and propagation ISP-2006. [4] P. Bhartia, K. V. S. Rao, and R. S. Tomar, “Millimeter-Wave Microstrip and Printed Circuit Antennas,” ARtech House, Boston, MA, 1991. Dhaka University of Engineering & Technology, Gazipur Vol. 1, Issue 3, June 2012 [5] R. F. Harrington, “Time Harmonic Electromagnetic fields,” McGraw-Hill Book Co. p. 183, 1961. [6] E. O. Hammerstad, “Equations For Circuit Design,” Proc. Fifth European Microwave Conf., pp. 268-272, September 1975. [7] N. G. Alexopoulos and I. E. Rana, “Mutual Impedance Computation Between Printed Dipoles,” IEEE Trans. Antennas Propagate, Vol. AP-29, No. 1, pp. 106-111, January 1981. [8] D. T. Paris, W. M. Leach Jr. and E.B. Joy, “Basic theory of probe-compensated near field measurements,” IEEE Trans. Antennas Propagate., Vol. AP-26, No. 3, pp, 373-379, May, 1981. [9] J. D. Kraus. “Antennas,” McGraw-Hill, Inc, Second edition, 1988. [10] J. A. Edminister, “Electromagnaetics,” McGraw-Hill, Inc., Second edition, 2006. [11] Sergey M. Makarov, “Antenna and EM modeling with MATLAB,” Jhon Wiley & Sons, Inc., second edition, 2006. 28