On Analysis of Planar Antennas Using FDTD Method

Transcription

1 PIERS ONLINE, VOL. 3, NO. 7, 7 9 On Analysis of Planar Antennas Using FDTD Method K. Niikura, R. Kokubo, K. Southisombath, H. Matsui, and T. akabayashi 3 Graduate School of Engineering, Tokai University, Japan Faculty of Engineering, National University of Laos, Lao PDR, Laos 3 School of Information Science and Engineering, Tokai University, Japan Abstract The FDTD method is a powerful method for analysis of electromagnetic fields in microwave circuits and devices, antennas, optical devices and transmission lines. In this paper, numerical conditions in analysis of planar antennas using the FDTD method are considered and found for a planar dipole antenna. The obtained results are compared with other and experimental results. DOI:.59/PIERS6344. INTRODUCTION The planar antennas that are useful for mobile communications have been developed for many researchers. The FDTD method is a powerful method for analysis of planar antennas that are defined as antennas that have planar shapes. e have analyzed several kinds of planar antennas for mobile communications. In this paper, numerical conditions in analysis of planar antennas using the FDTD method [3] are considered and found for a planar dipole antenna. In order to use the method, it is important to decide the number of layers of the PML and the distance between the antenna and the wall of the analytical area. If they are decided appropriately, the computational time and memories are saved. Therefore, the relation between them is discussed precisely. The FDTD method which used their numerical values are applied to several planar antennas [, ]. The obtained results are compared with other and experimental results.. FDTD METHOD Figure shows an analytical area in the FDTD method. The cell size is assumed to be dx = dy = dz = mm. The PML that has M layers is assumed as the absorbing boundary. The time step dt is decided by the following Courant stability condition, where c is the velocity of light in the free space. dt ( c dx ) ( + dy ) ( ) () + dz The Gaussian pulse is used as an input pulse to analyze. The feeding method is cell delta gap feed. The distance D between the antenna and the wall of analytical area is assumed in each direction as shown in Fig.. In Fig., D includes the number of layers M of the PML. x z D y Figure : Analytical area.

2 PIERS ONLINE, VOL. 3, NO. 7, 7 3. ANALYTICAL PARAMETERS OF THE FDTD METHOD Let s consider a planar dipole antenna in free space as shown in Fig. as an example of consideration of analytical parameters of the FDTD method. An element of planar dipole antenna (PDA) is assumed to be L mm in length, mm in width and infinitesimal thin. L Figure : Structure of planar dipole antenna. The element is also assumed to be a lossless conductor. The PDA is placed in the analytical area to analyze as shown in Fig.. In this case, the PML as the absorbing boundary is included in the D. Since it is seemed that the accuracy of the numerical result depends on the distance D and the operating wavelength of the PDA, the numerical analysis is implemented for several lengths of antenna elements. e select that = mm, L = 9 mm, and is infinitesimal small as a numerical example. The design frequency of PDA is.833 GHz. Fig. 3 shows the convergence of first resonance as a function of the number of layers (M) with the numerical parameter D. The parameter D is the same distance along the three axes x, y, z. From Fig. 3, the first resonance frequency converges with increasing M, even if D is any kind of value more than. And when D = and D =, the first resonance frequency converges even if M is any kind of value more than 8. Table shows an illustration of the rate of convergence for the resonance frequency. hen D = and D = the convergent frequency is.784 GHz. From the above results, it is clear that D = is the satisfied distance even if M is more than 8. hen =.5 mm, the first resonance frequency is.8 GHz. This frequency is close to.833 GHz. Figure 4 shows return loss of PDA for M = 8 and D =. It has three resonance frequencies between GHz and 5 GHz. The current distributions of each resonance frequencies are shown in Fig. 5. It is shown that the resonance points exist at.5λ,.5λ and.5λ in length of PDA. Fig. 6 shows the radiation patterns at the resonance frequencies. The radiation patterns analyzed by our D= cells ( =mm) D=3 cells ( =mm) D=5 cells ( =mm) D= cells ( =mm) D= cells ( =.5mm) Number of Layers (M) Figure 3: Convergence of the first resonance frequency Figure 4: Characteristic of return loss. Table : An illustration of the rate of convergence for the resonant frequency. [mm] M [Layers] D [cells]

3 PIERS ONLINE, VOL. 3, NO. 7, 7 (a) (b) (c) Figure 5: Current distributions at each wavelength. (a).5λ (.784 GHz), (b).5λ (.49 GHz), (c).5λ (4.4 GHz). (a) (b) Figure 6: Characteristics of radiation patterns at each wavelength. (a).5λ (.784 GHz), (b).5λ (.49 GHz). method are compared with the radiation patterns obtained by assuming an ideal sinusoidal current distribution with zero current at the end points of the dipole antenna [4]. Those results are in good agreement. 4. NUMERICUL APPLICATIONS AND EXPERIMENTS Numerical applications are described for several planar antennas. Their experimental results are shown in figures. 4.. Planar Dipole Antenna (PDA) on the Dielectric Substrate Figure 7 is the structure of the planar dipole antenna on the dielectric substrate (L d = 5 mm, d = 7. mm, h = 3 mm, ε r = 6.68). Fig. 8 shows return loss for a planar dipole antenna that is printed on the dielectric substrate. In this figure, three resonance frequencies are shown in L d d L h Figure 7: Structure of PDA on the dielectric substrate Antenna Element L [mm] first resonance frequency (analytical value) second resonance frequency (analytical value) third resonance frequency (analytical value) first resonance frequency (experimental value) second resonance frequency (experimental value) third resonance frequency (experimental value) Figure 8: Analytical and experimental results of resonance frequency.

4 PIERS ONLINE, VOL. 3, NO. 7, 7 three kinds of lines, respectively and their experimental results are plotted. Analytical results are coincident with experimental results. 7mm mm 3mm x z mm mm 3mm y Figure 9: Structure of DMA on the dielectric substrate. 4.. Planar Monopole Antenna (PMA) on the Dielectric Substrate Figure 9 shows a structure of a planar monopole antenna, which consists of a monopole element and ground plane (7. mm 3. mm) on the dielectric substrate (49. mm 3. mm, h = 3 mm, ε r = 6.68). An illustration of the rate of convergence of the first resonance frequency is shown as a function of the number of layers M in Fig.. The return loss of the first resonance frequency is shown in Fig. and also compared with experimental result D= cells D=3 cells D=4 cells D=5 cells D= cells analytical value experimental value Number of Layers (M) Figure : Convergence of the first resonance frequency Figure : Characteristics return loss of PMA on the dielectric substrate. Ground conductor A Antenna element Antenna element 3 Antenna element L H L L 3 B Dielectric substrate Figure : Structure of BEPA Basic E-type Planar Antenna (BEPA) A structure of a basic E-type planar antenna (BEPA) is shown in Fig.. In Fig., the BEPA has three antenna elements and the ground conductor that are printed on dielectric substrate (A B).

5 PIERS ONLINE, VOL. 3, NO. 7, 7 3 Table : Numerical examples of parameters. Parameter [mm] Parameter [mm] L 9., 3., 7. H 3. L 67.5 A B 86.5 ε r Their antenna element i (i = 3) has a length L i (i = 3) and a width i (i = 3), respectively. The ground conductor has a width and a length A. Characteristics return loss of the BEPA that are shown in Fig. 3 as parameter of L. Resonance frequencies f B, f B3, and f B4 are constant for different values of L (Fig. 3). However, resonance frequency f B changes according to the length of the antenna element L. Fig. 4 shows the analytical and experimental results. Both of them are in good agreement. - f B3 f B4 L =9[mm] - f B L =3[mm] L =7[mm] f B Figure 3: Return loss of BEPA for parameter L. - analytical value experimental value Figure 4: Analytical and experimental results. 5. CONCLUSIONS Parameters in analysis of planar antennas using the FDTD method are considered. From analytical results, the value of the distance D between the antenna and the wall of analytical area and the number of layers M were found for the cell size. By using them we could obtain reasonable results for several applications. Their results agreed with experimental results. In future our analytical method using the FDTD method will be applied for many applications. REFERENCES. akabayashi, T., K. Southisombath, et al., Miniaturization and broadband characteristics of E-type planar antennas for mobile communications, EAS Trans. on Communications, Vol. 5, Issue 9, Sep. 6.. Kokubo, R., et al., Consideration of analytical parameters in FDTD method for planar antenna analysis, KJJC6, Vol. EMT4-, 47 4, Sep Uno, T., Finite Difference Time Domain Method for Electromagnetic Field and Antennas, Corona Publishing, Balanis, C. A., Antenna Theory, John iley & Sons Inc, 98.