192 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 5, 2006 This method can be applied to all kinds of antennas in any environment and it becomes

Size: px

Start display at page:

Download "192 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 5, 2006 This method can be applied to all kinds of antennas in any environment and it becomes"

态从雍
6 years ago
Views:

1 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 5, Calculation of Small Antennas Quality Factor Using FDTD Method S. Collardey, A. Sharaiha, Member, IEEE, and K. Mahdjoubi, Member, IEEE Abstract The complexity in the evaluation of the radiation quality factor Q of small antenna lies in the calculation of the stored energy. Previous authors proposed several analytical expressions for simple antennas to obtain the Q, which is of practical importance because of its relationship to the antenna bandwidth. This letter presents a general numerical method to calculate the Q using finite-difference time-domain (FDTD) method giving us accurate results and can be applied to complex antennas. Examples of a linear dipole antenna, a loop antenna and an inverted L-shaped antenna along with their results are presented and compared to analytical results of the literature. Index Terms Electrically small antennas, quality factor. I. INTRODUCTION THE performance properties of small antennas include the antenna s resonant frequency, resonant radiation resistance, efficiency and the quality factor Q. The quality factor is of practical interest when designing small antennas because of its relation to the antenna bandwidth. Previous works done by several authors [1] [6] starting from Chu [2] predict a lower bound on the radiation Q of small antennas enclosed in the smallest circumscribing sphere (as defined by Wheeler [1]). This lower bound of Q defined by previous authors is usually too low since it doesn t take into account the energy stored inside the sphere. We can see this in Fig. 1 where we present the Q calculated by McLean [6] versus of an electrically small dipole antenna enclosed in a sphere of radius a where is the wave number defined by where is the wavelength. Recently, Thiele et al. [7] have used the far field approach to obtain a more realistic bound of Q as well as McLean using an oblate spheroidal volume [8]. And Geyi [9] has also proposed analytical formulas for simple antennas taking into account the energy stored in all the space. We note that Geyi s [9] formulas give more exact value of Q as shown in Fig. 1. More recently, another approach exists based on the derivative of the antenna input impedance developed by Yaghjian [10], to obtain the Q and the bandwidth. In all these analytical studies except for the one done by Yaghjian, the authors assume that the antenna will be resonated with a lossless matching circuit so as to obtain a real input Fig. 1. Comparison between the quality factors calculated by McLean, Thiele and Geyi. (Note: a is the Wheeler sphere radius and k is the wave number wave.) impedance. Therefore, the quality factor Q can be given by this definition where is either the time average stored electric or the magnetic one and is the average radiated power and is the radian frequency. In this letter, we propose a simple technique to compute numerically the lower bound of the antenna radiation Q using the finite-difference time-domain (FDTD) method. The FDTD software based on a numerical method allows to take taking into account all the energy that can be stored by the antenna into the smallest sphere and consequently to obtain a realistic value of the Q based on the following fundamental definition [11]: (1) (2) Manuscript received December 16, 2005 revised February 3, S. Collardey is with the IETR (Institut d Electronique et de Télécommunications de Rennes, UMR CNRS 6164), IUT Saint-Malo, Rennes, France ( sylvain.collardey@univ-rennes1.fr). A. Sharaiha and K. Mahdjoubi are with the IETR, University of Rennes 1, Rennes, France. Digital Object Identifier /LAWP where is the time average energy stored in the system (3) (4) /$ IEEE

2 192 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 5, 2006 This method can be applied to all kinds of antennas in any environment and it becomes useful when one calculates or designs antennas of certain complexity (noncanonical). In the Section II, we present the computation of Q using the FDTD method. In Section III, we compare our new approach with the analytical results obtained previously by McLean [6] and Geyi [9] for an electrically small dipole antenna, an inverted L-shaped antenna as well as a loop antenna. II. CALCULATION OF Q USING THE FDTD METHOD The FDTD method consists in the numerical computing of the electric and magnetic field components in every cell of a discretised volume at every moment of the discretised time. The FDTD computational volume is discretised into elementary cubic cells called Yee cells. The maximum values of fields components and are computed in each cell [12]. To evaluate the radiation Q, we first calculate the average total electric and magnetic energies using these following wellknown formulas: (5) Fig. 2. Dipole antenna considered in the FDTD method. where is the volume of the unit cell and is equal to. We also calculate the average radiated electric and magnetic energies by the following expressions: (6) (7) Fig. 3. Method of calculation. (8) where and are the radiated far fields. The average stored energy is then obtained by subtracting the total radiated field energy away from the total energy. Hence, the expression used to calculate Q here is (9) Knowing the radiated power in the far field, we can easily calculate the quality factor. III. RESULTS As an example, we consider a small dipole of size that fits a cubic volume of radius (see Fig. 2). The dipole antenna has a length of 27 mm and a radius equal to 0.1 mm. The antenna is fed by a voltage source with 50 impedance. The FDTD spatial steps are equal to 1 mm and the total cube dimension is equal to 92 mm. The nonpropagating energy is plotted to estimate the quantity stored in the near field of the antenna. The total and radiated energies are determined for each discrete volume (see Fig. 3). Fig. 4. Variations of stored energy when ka is equal to Then, we compute the nonpropagating energy in. The plotted value denotes the supplementary stored energy when the dimension volume increases from 0 to 92 mm. In Fig. 4, the variations of the average stored electric and magnetic energies are plotted versus the distance for. We can see that the nonpropagating energy is mainly stored in the near field of the antenna and tends to vanish for. Consequently, the quality factor value calculated previously by Chu [2], McLean [6] and others will surely be too low since the main stored energy is not taken into account.

3 COLLARDEY et al.: CALCULATION OF SMALL ANTENNAS QUALITY FACTOR USING FDTD METHOD 193 Fig. 7. Current distributions versus distance. Fig. 5. Q of dipole antenna. Fig. 8. method. Inverted L-shaped antenna characteristics considered in the FDTD angular, as Geyi has supposed in his Q computation. However, if is greater than, the current distribution becomes sinusoidal. The two previous remarks explain why the Q obtained by Geyi becomes slightly different to the one calculated by the FDTD method when increases. In another example, we consider a small inverted L-shaped antenna shown in Fig. 8, which has also been studied by Geyi [9] and proposed the following analytical expression of Q: (10) Fig. 6. Difference between stored and total energy. The Q calculated using the FDTD method and based on the (9) is greater than the Q obtained by McLean and almost equivalent to the one obtained by Geyi [9], as shown in Fig. 5. The difference between the two curves is due to the fact that in Geyi s analysis he neglects the radiated energy and his formula based on a triangular current distribution is more accurate when. To confirm this, we plot the total electric energy in the volume as well as the total radiated energy versus (Fig. 6). We can notice that for small antennas with, the value of the total radiated energy is too small and can actually be neglected. Furthermore, as shown in Fig. 7, the current distribution on the antenna dipole depends on the frequency of interest. In this figure, the current distribution is plotted versus the distance from the antenna center, for different values of. We can notice that if remains lower than, the current distribution is nearly tri- where is the radius of the antenna, is the length of the vertical part of the antenna and is the length of the horizontal section. The FDTD spatial steps are equal to 1 mm and the cubic volume dimension is equal to 92 mm. Here again the Q calculated by FDTD is similar to the one calculated by Geyi. The difference is due to the same reasons indicated above (see Fig. 9). Finally, as a last example, we take a small loop antenna, which was also examined by Geyi. The analytical expression in this case is (11) where is the radius of the loop and is the radius of the wire. The quality factor computed by the FDTD method is close to the one obtained by Geyi (see Fig. 10).

4 194 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 5, 2006 IV. CONCLUSION In this letter, a new and simple method is presented to calculate numerically the antenna radiation Q by using the FDTD method. The results obtained for different kind of antennas shows a good agreement between FDTD and the analytical approaches proposed by Geyi. The main advantage for using FDTD is that we can obtain more accurate results of Q factor for small antennas and can be easily used to characterize more complex structures. REFERENCES Fig. 9. Inverted L-shaped antenna Q. Fig. 10. Loop antenna Q. [1] H. A. Wheeler, Fundamental limitations of small antennas, Proc. IRE, vol. 35, pp , Dec [2] L. J. Chu, Physical limitations on omni-directional antennas, J. Appl. Phys., vol. 19, pp , Dec [3] R. E. Collin and S. Rothschild, Evaluation of antenna Q, IEEE Trans. Antennas Propagat., vol. AP-12, pp , Jan [4] R. L. Fante, Quality factor of general idea antennas, IEEE Trans. Antennas Propagat., vol. AP-17, pp , Mar [5] R. C. Hansen, Fundamental limitations in antennas, Proc. IEEE, vol. 69, pp , Feb [6] J. S. McLean, A re-examination of the fundamental limits on the radiation Q of electrically small antennas, IEEE Trans. Antennas Propagat., vol. 44, pp , May [7] G. A. Thiele, P. L. Detweiler, and R. P. Penno, On the lower bound of the radiation Q for electrically small antennas, IEEE Trans. Antennas Propagat., vol. 51, pp , Jun [8] H. D. Holtz and J. S. McLean, Limits on the radiation Q of electrically small antennas restricted to oblong bounding regions, in Proc. IEEE Antennas Propagat. Int. Symp., vol. 4, Jul , 1999, pp [9] W. Geyi, A method for the evaluation of small antenna Q, IEEE Trans. Antennas Propagat., vol. 51, pp , Aug [10] A. D. Yaghjian and S. R. Best, Impedance, bandwidth, and Q of antennas, IEEE Trans. Antennas Propagat., vol. 53, pp , Apr [11] H. G. Booker, Energy in Electromagnetism, ser. IEE Electromagnetic Wave Series 13. Stevenage, U.K.: Peter Peregrinus, [12] S. Collardey, A. Sharaiha, and K. Mahdjoubi, Evaluation of antenna radiation Q using FDTD method, Electron. Lett., vol. 41, no. 12, Jun

易迪拓培训专注于微波射频天线设计人才的培养网址 :http://www.edatop.com 射频和天线设计培训课程推荐易迪拓培训 (www.edatop.com) 由数名来自于研发第一线的资深工程师发起成立, 致力并专注于微波射频天线设计研发人才的培养 ; 我们于 2006 年整合合并微波 EDA 网 (www.mweda.

永业科技全一电子等多家台湾地区企业易迪拓培训课程列表 :http://www.edatop.com/peixun/rfe/129.

5 易迪拓培训专注于微波射频天线设计人才的培养网址 : 射频和天线设计培训课程推荐易迪拓培训 ( 由数名来自于研发第一线的资深工程师发起成立, 致力并专注于微波射频天线设计研发人才的培养 ; 我们于 2006 年整合合并微波 EDA 网 ( 现已发展成为国内最大的微波射频和天线设计人才培养基地, 成功推出多套微波射频以及天线设计经典培训课程和 ADS HFSS 等专业软件使用培训课程, 广受客户好评 ; 并先后与人民邮电出版社电子工业出版社合作出版了多本专业图书, 帮助数万名工程师提升了专业技术能力客户遍布中兴通讯研通高频埃威航电国人通信等多家国内知名公司, 以及台湾工业技术研究院永业科技全一电子等多家台湾地区企业易迪拓培训课程列表 : 射频工程师养成培训课程套装该套装精选了射频专业基础培训课程射频仿真设计培训课程和射频电路测量培训课程三个类别共 30 门视频培训课程和 3 本图书教材 ; 旨在引领学员全面学习一个射频工程师需要熟悉理解和掌握的专业知识和研发设计能力通过套装的学习, 能够让学员完全达到和胜任一个合格的射频工程师的要求课程网址 : ADS 学习培训课程套装该套装是迄今国内最全面最权威的 ADS 培训教程, 共包含 10 门 ADS 学习培训课程课程是由具有多年 ADS 使用经验的微波射频与通信系统设计领域资深专家讲解, 并多结合设计实例, 由浅入深详细而又全面地讲解了 ADS 在微波射频电路设计通信系统设计和电磁仿真设计方面的内容能让您在最短的时间内学会使用 ADS, 迅速提升个人技术能力, 把 ADS 真正应用到实际研发工作中去, 成为 ADS 设计专家... 课程网址 : HFSS 学习培训课程套装该套课程套装包含了本站全部 HFSS 培训课程, 是迄今国内最全面最专业的 HFSS 培训教程套装, 可以帮助您从零开始, 全面深入学习 HFSS 的各项功能和在多个方面的工程应用购买套装, 更可超值赠送 3 个月免费学习答疑, 随时解答您学习过程中遇到的棘手问题, 让您的 HFSS 学习更加轻松顺畅课程网址 : `

易迪拓培训专注于微波射频天线设计人才的培养网址 :http://www.edatop.

6 易迪拓培训专注于微波射频天线设计人才的培养网址 : CST 学习培训课程套装该培训套装由易迪拓培训联合微波 EDA 网共同推出, 是最全面系统专业的 CST 微波工作室培训课程套装, 所有课程都由经验丰富的专家授课, 视频教学, 可以帮助您从零开始, 全面系统地学习 CST 微波工作的各项功能及其在微波射频天线设计等领域的设计应用且购买该套装, 还可超值赠送 3 个月免费学习答疑课程网址 : HFSS 天线设计培训课程套装套装包含 6 门视频课程和 1 本图书, 课程从基础讲起, 内容由浅入深, 理论介绍和实际操作讲解相结合, 全面系统的讲解了 HFSS 天线设计的全过程是国内最全面最专业的 HFSS 天线设计课程, 可以帮助您快速学习掌握如何使用 HFSS 设计天线, 让天线设计不再难课程网址 : MHz NFC/RFID 线圈天线设计培训课程套装套装包含 4 门视频培训课程, 培训将 13.56MHz 线圈天线设计原理和仿真设计实践相结合, 全面系统地讲解了 13.56MHz 线圈天线的工作原理设计方法设计考量以及使用 HFSS 和 CST 仿真分析线圈天线的具体操作, 同时还介绍了 13.56MHz 线圈天线匹配电路的设计和调试通过该套课程的学习, 可以帮助您快速学习掌握 13.56MHz 线圈天线及其匹配电路的原理设计和调试详情浏览 : 我们的课程优势 : 成立于 2004 年,10 多年丰富的行业经验, 一直致力并专注于微波射频和天线设计工程师的培养, 更了解该行业对人才的要求经验丰富的一线资深工程师讲授, 结合实际工程案例, 直观实用易学联系我们 : 易迪拓培训官网 : 微波 EDA 网 : 官方淘宝店 : 专注于微波射频天线设计人才的培养易迪拓培训官方网址 : 淘宝网店 :

ANSYS 在航空航天器电磁兼容、电磁干扰分析中的应

ANSYS 在航空航天器电磁兼容、电磁干扰分析中的应易迪拓培训专注于微波射频天线设计人才的培养网址 :http://www.edatop.com 射频和天线设计培训课程推荐易迪拓培训 (www.edatop.com) 由数名来自于研发第一线的资深工程师发起成立, 致力并专注于微波射频天线设计研发人才的培养 ; 我们于 2006 年整合合并微波 EDA 网 (www.mweda.com), 现已发展成为国内最大的微波射频和天线设计人才培养基地,