Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27 30,

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1 Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27 30, Transient Electromagnetic Response of a Coaxial Feeding Monopole Antenna Mounted on a Rectangular Metallic Enclosure Illuminated by Electromagnetic Pulses (EMP) Qingqing Zhang 1, Jian Wang 1, and Wen-Yan Yin 1, 2 1 Center for Microwave and RF Technologies Key Lab of Ministry of Education of EMC and High-Speed Electronic Systems Shanghai Jiao Tong University, Shanghai , China 2 Center for Optical and EM Research (COER), State Key Lab of MOI Zhejiang University, Hangzhou , China Abstract As we all know, coaxial cables are often used in the feed network of various antennas. In this paper, the terminal electromagnetic interference (EMI) responses of coaxial cables as a feed network of monopole antenna are studied, which is placed in an enclosure with a window on its wall and illuminated by an external pulse. The mathematical treatment is based on the finite-difference time-domain (FDTD) method combined with equivalent feed model method, Node s thin wire method, and two-step coupling method. The results obtained by our coupling method are compared with the direct telegraph equation coupling method, with good agreement achieved. Further, the proposed method is used to perform EMI transient analysis of the practical enclosure model illuminated by external pulses with different incident and polarization directions. 1. INTRODUCTION It is well known that feed networks of antennas in most information systems can be interfered by external electromagnetic pulses (EMP), and under such circumstances, source integrity problem will be caused and the system performance will be degraded [1]. Therefore, in order to protect them from the intentional interference, certain metallic enclosure or cabin will be employed as plotted in Fig. 1, with the feed network often enclosed. However, the external electromagnetic pulses in the environment will produce induced current on the antenna and it couples into the coaxial feeding cable through the interaction at the connection point between the coaxial cable and the monopole antenna [2, 3]. In the other hand, FDTD Feeding models of coaxial cables for antennas have been studied extensively in the past a few years [4, 5]. [5] proposed an equivalent feed model, which captures the equivalent connection port voltage and current of transmission lines as the source for the antenna.in this paper, a hybrid method, based on FDTD method, combined with thin wire antenna model, an equivalent feed model, and telegraph equations, is integrated for computing the EMI responses of the coaxial cable in an enclosure as shown in Fig. 1, which is illuminated by external pulses with different incident and polarization directions. 2. HYBRID FDTD METHOD 2.1. FDTD Formulas of Thin-wire Antenna For the thin wire antenna, as shown in Fig. 1, there are several methods to model it in FDTD, such as Taflove s model [6] and Noda s model [7]. When the wire radius is very thin, the latter is more accurate. In Noda s method, applied in this paper, both adjacent electric and magnetic fields are modified by changing the relative permeability and the relative permittivity of the thin wire s adjacent cells. The modified relative permeability and the modified relative permittivity are described as µ r = µ r /m, ε r = mε r (1) ( ) ( ) δ δ m = ln / ln, a 0 = 0.230δ (2) a a 0 where µ r and ε r are the relative permeability and permittivity of the original medium surrounding the wire, δ is the spatial cell size of the FDTD method, a 0 is the equivalent radius represented by forcing the tangential components of electric field along the wire axis to be zero, and a is the real

2 1136 PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27 30, 2012 Figure 1: Geometry of a coaxial feeding monopole antenna mounted on a rectangular enclosure with a window illuminated by external EMP. Figure 2: The original adjacent field configuration; the modified adjacent field configuration. radius of thin wire. The original and modified configurations of the adjacent electric and magnetic fields of thin wire are shown in Figs. 2 and, respectively. Then the adjacent electric and magnetic fields can be calculated by using the relative permeability µ r and the relative permittivity ε r instead of the original µ r and ε r. The calculation of other field components is kept same as the original method Coaxial Cable Feed Model An equivalent feed model for the FDTD analysis of an antenna excited by a coaxial line is proposed in [5], which is simple and accurate. In this paper, its mathematical equations are further modified for the purpose of applying it in the Cartesian coordinate system. The coaxial aperture is represented as an equivalent magnetic-frill current through the quasi-static approximation, as show in Fig. 3. The equivalent magnetic-frill current, including the effect of TEM mode, is described as M (x, y, z) = 2V inc (t) + Z 0 I (t) a ln (b/a) (3) where M is magnetic-frill current, V inc is the incident voltage, I(t) is the feed current, Z 0 is the characteristic impedance of coaxial line, a is the inner conductor radius, and b is the outer conductor radius.

3 Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27 30, According to Ampere s law, the feed current I(t) can be calculated by [ I (t = n t) I n = y Hy (i n feed + 12 ) Hy (i n feed 12 )] [ ( x Hx n i feed, j feed + 1 ) ( 2, k feed Hx n i feed, j feed 1 )] 2, k feed (4) where i feed, j feed, and k feed are the spatial indexes of the feed cell in x-, y-, and z-direction, respectively, and t is the discrete time step. The update equation of the magnetic field in y direction is expressed as follow: H n+ 1 2 y ( t µ 0 z) E n x = H n 1 2 y +( t/(µ 0 x)) (ln ( x/a)) Ez n (i feed + 1, j feed, k feed ) ( t/(µ 0 z)) ( 2V inc + Z 0 I n ) / ( x/2) ln ( x/a) (5) The update equation of the magnetic field in x-direction can be obtained as the same way. According to transmission line theory, the total voltage at the aperture V ab and the reflected voltage V ref can be obtained by V ab = 2V inc Z 0 I n (6) V ref = V inc Z 0 I n (7) So, when needed to calculate the terminal end response of the coaxial cable, the connection port voltage V ab between antenna and coaxial line when the system is illuminated by external pulse is calculated by setting the inner source zero. Then, the terminal voltage response V load can be obtained through transmission line model. This is our two-step coupling calculation method. In the other hand, another coaxial cable feed model is direct telegraph equation model as proposed in [4], which modify the magnetic field around the connection port using the transmission line voltage according to Faraday s Law. 3. NUMERICAL RESULT AND DISCUSSION At first, the inner feed model for thin wire antenna in semi-space is considered as described in [4, 5] and the incident source is Gauss pulse described as follow: U i (t) = U 0 e t 2 2τp 2 (8) The outer-to-inner radius ratio b/a of an air-filled coaxial line filled with 50 Ω is about 2.3 and the inner radius a is 1 mm. The length-to-radius ratio h/a of the monopole antenna is 100. The Gauss pulse wave form with unit amplitude and τ p /τ a = 0.16 is used as an excited voltage, where τ a = h/c and c is the velocity of light. U 0 is set to be 50 V/m. The CPML is used as a boundary condition in our simulation. The calculated reflected voltage on the coaxial line and the input impedance of the antenna as a function of time are presented in Fig. 3 and Fig. 4, which have good agreement with the results presented in [5]. It is observed that there is certain time delay in Fig. 3, as different locations of the reflected voltages are selected. Then, we further investigated the connection port voltage responses when the thin wire antenna connected with coaxial line enclosed in a enclosure is illuminated by an external pulse, without inner source. The geometry of coaxial line and antenna doesn t change here and the geometry of the cabin is set as Fig. 1, with L = W = 30 cm, H = 20 cm, a = 15 cm, b = 10 cm, L 1 = 5 cm, and L 2 = 10 cm. The coaxial line is loaded by Zl = 50 Ω and the incident EMP is also Gauss pulse as described before. The voltage data obtained by our two-step coupling model and telegraph equation model is shown in Fig. 4 and they have good agreement. Next, we keep the geometry of the practical model as shown in Fig. 1 not changed and consider the terminal responses of the coaxial cable in enclosure. The computational domain is discretized with the cubic cells of x = y = z = 5 mm and the time step is t = x/(2c). The sixside walls of the enclosure are set as perfectly conducting planes except the windows. The CPML

4 1138 PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27 30, 2012 Figure 3: Equivalent representation of the coaxial aperture; reflected voltage on the coaxial line calculated by two feed models. Figure 4: The input impedance of monopole antenna calculated by two feed models; the connection port voltage calculated by two methods when the inner source is set zero. absorbing boundary is employed to truncate the computational domain. The incident EMP used in our simulation is described by a double-exponential function shown as follows: ( E = E 0 k e βt e αt) (9) where the values of the parameters are slow with k = 1.036, α = and β = , medium with k = 1.052, α = and β = , and fast with k = 1.3, α = and β = , which includes three kind of pulses. E 0 is set to be 50 V/m. The terminal voltage responses when the system is illuminated by three different EMP are shown in Figs. 5 and. In these two cases, the incident wave propagates along y- and z-directions, respectively. The results presented in Fig. 5 show that there is only a little EM energy of the whole input energy coupling into the terminal end of the coaxial cable, so as to Fig. 5. We also can see that the energy of fast pulse coupling into the coaxial line is the most from Fig. 5. In Fig. 5, the terminal voltage polarity changes because of the changes of the polarization and the propagation directions of input pulses. However, the fast pulse which contains more high frequency components, couples most energy into the coaxial line. This tells us that the system may be damaged more seriously when external intentional EMI is at a high frequency and we should be careful in the high frequency design about EMC of information systems.

5 Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27 30, Figure 5: The terminal voltage responses of the coaxial line: when the external pulse propagates in y direction with z direction polarization; and when the external pulse propagates in z direction with x direction polarization. 4. CONCLUSIONS In the paper, we present a hybrid methodology that combines thin wire FDTD methods, feed model, telegraph equations, and windows model together. Further, we have predicted the terminal voltage responses of the end of the transmission line when the system is illuminated by external pulses. The main advantage of our method is that external field full-wave simulation just needs to be carried out one time, and then we just need to solve the telegraph equation to obtain the terminal response of the coaxial cable. From results presented, we can conclude that different polarity direction and propagation external pulses have different interferences on the coaxial line feed network and high frequency pulses couple into it with more EM energy. ACKNOWLEDGMENT The authors acknowledge the financial support by the National Natural Science Fund Grant of China. REFERENCES 1. Georgakopoulos, S. V., C. R. Birtcher, C. A. Balanis, and R. A. Renaut, HIRF penetration and PDE coupling analysis for scaled fuselage models using a hybrid subgrid FDTD(2, 2)/FDTD(2, 4) method, IEEE Trans. Electromagn. Compat., Vol. 45, No. 2, , May Liu, Q. F. and W. Y. Yin, Time-domain investigation on cable-induced transient coupling into metallic enclosures, IEEE Trans. Electromagn. Compat., Vol. 51, No. 4, , Nov Wang, J., W. Y. Yin, J. P. Fang, and Q. F. Liu, Transient analysis of transmission lines under external field coupling into an electrically large scale cabin with thin-slots, Progress In Electromagnetics Research, Vol. 106, 1 16, Maloney, J. G., K. L. Shlager, and G. S. Smith, A simple FDTD model for transient excitation of antennas by transmission lines, IEEE Trans. Antennas Propagat., Vol. 42, No. 2, , Feb Hyun, S.-Y., S.-Y. Kim, and Y.-S. Kim, An equivalent feed model for the FDTD analysis of antennas driven through a ground plane by coaxial lines, IEEE Trans. Antennas Propagat., Vol. 57, No. 1, , Jan Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-difference Timedomain Method, 2nd Edtion, Artech House, Norwood, MA, Node, T. and S. Yokoyama, Thin wire representation in finite difference time domain surge simulation, IEEE Trans. Power Delivery, Vol. 17, No. 3, , Jul

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