Radiation mechanism and polarization ... - Wiley Online Library

RADIO SCIENCE, VOL. 46, RS2009, doi:10.1029/2010RS004486, 2011

Radiation mechanism and polarization properties of leaky coaxial cables Junhong Wang,1 Yujian Li,1 Zhan Zhang,1 and Meie Chen1 Received 23 July 2010; revised 23 October 2010; accepted 10 January 2011; published 19 March 2011.

[1] Polarization properties of the leaky coaxial cables (LCXs) have significant effects on the fluctuation of the received signal. Therefore, the knowledge of the polarization state of LCXs is helpful to design LCXs with uniform radio wave coverage. In this paper, the physical understanding of the radiation from LCXs is presented first, and then a hybrid method involving finite difference time domain method and integration of equivalent electrical and magnetic currents is used to simulate and analyze the polarization properties of LCXs with circumferentially asymmetry slot. It is found that the LCXs with circumferentially asymmetry slots can excite both the circumferential and axial components of the field, and the magnitude and phase differences between them significantly depends on the structural parameters of the slot. Therefore, it is possible to design LCX with desired polarization property by properly choosing the structural parameters. Citation: Wang, J., Y. Li, Z. Zhang, and M. Chen (2011), Radiation mechanism and polarization properties of leaky coaxial cables, Radio Sci., 46, RS2009, doi:10.1029/2010RS004486.

1. Introduction [2] The applications of leaky coaxial cable (LCX) have been extended to many areas, such as, the mobile communication in buildings [Morgan, 1999], wireless LAN accessing [Nakamura et al., 2009], underground transportation [Beal et al., 1973], automated highway [Yamada et al., 1996], high‐speed railway [Haag and Lehan, 1989; Matsumoto et al., 1990], and security detection [Gagnon, 1995]. [3] In the early time, classical methods of mode matching were used in the analysis of LCX for studying the propagation modes supported by the cable conductors and environment. The cables considered are mainly the braided LCX [Wait and Hill, 1975; Seidel and Wait, 1978] and the helix shielded LCX [Hill and Wait, 1980a, 1980b]. However, these kinds of LCXs are less attractive because of the large longitudinal attenuation. Later, the radiation and transmission characteristics of the axial slotted coaxial cables were studied using mode matching method and approximate method under the certain assumption of field distribution in the slot [Hassan, 1989; Delogne and Laloux, 1980]. Now, attentions are mainly focused on 1 Institute of Lightwave Technology, Beijing Jiaotong University, Beijing, China.

Copyright 2011 by the American Geophysical Union. 0048‐6604/11/2010RS004486

the periodically slotted coaxial cables [Hill and Wait, 1980a, 1980b; Richmond et al., 1981], and a number of new methods including hybrid mode matching methods [Kim and Eom, 2007; Addamo et al., 2008], numerical methods [Kim et al., 1998; Wang and Mei, 2001a] are proposed for studying the transmission and radiation characteristics of this kind of LCXs. The periodically slotted LCXs have the advantages of controllable radiation and low longitudinal attenuation. Therefore, they are now widely used in wireless mobile communications in subway and railway. Besides the theoretical analysis, design methods and techniques for LCXs with periodic slots can also be found in [Wang and Mei, 2002]. In addition, some new kinds of LCXs for flexible radio wave coverage are proposed in [Wang and Mei, 2001b; Wang, 2008]. [4] Despite extensive studies, few of the available works have taken into account the polarization property of the LCX. However, the knowledge of the polarization property of LCX is particularly important, because the variation of polarization along and around the LCX can significantly affect the fluctuation of the received signal. In practice, LCXs, especially for those with circumferentially asymmetry slots, can radiate elliptical polarized wave, and the axial ratio of the polarization ellipse is determined by the structural parameters of the slots. Therefore, in order to achieve the maximal receiving power, the antenna is required to be oriented to the major axis of the polarization ellipse. For mobile communications where multiple and different orientations of mobile terminals exist simulta-

RS2009

1 of 12

RS2009

WANG ET AL.: POLARIZATION OF LEAKY COAXIAL CABLE

RS2009

Figure 1. Schematic diagram for explaining radiation from LCX: (top) uniform axial slot, (middle) slot aperture is changed, and (bottom) periodic slot is formed. neously, LCX with smaller polarization axial ratio of the radiation field seems much more preferable. [5] This paper is devoted to the study of the polarization properties of LCXs. The structures with different circumferential asymmetry slots are the major subject of study. The paper is organized as follows. Section 2 brings a physical light on the basic theory of understanding the radiation mechanism of LCX. The methods and formulas for calculating the far field of the LCX are given in section 3. Polarization properties of LCX with circumferentially asymmetry slots, such as the inclined slots, L‐shaped slots, U‐shaped slots, and two novel kinds of slots are studied in section 4. Conclusions are given in section 5.

2. Physical Understanding of Radiation From LCX [6] For a continuous and infinite slotted cable as shown in Figure 1 (top), the far field in space can be viewed as a superposition of the radiation fields from the equivalent sources in the slot aperture. We consider two points in the aperture, marked by 1 and 1′, respectively, as shown in Figure 1 (top). The fields from these two points in the 8 direction are denoted by E1 and E′1, respectively. The magnitudes of E1 and E′1 are the same due to the uniform distribution of the slot aperture

(ignoring the longitudinal attenuation). Because the cable is infinitely long, we can always find a distance S between such two points that satisfies the following equation, S þ k0 S cos 8 ¼ ;

ð1Þ

where b and k0 are the propagation constants of the waves in cable pand ffiffiffiffiffiffi in space, respectively, and for LCXs, we have b = k0 "re > k0, where "re is the effective dielectric constant of the LCX. For most of the LCXs, "re approximates to the realistic dielectric constant "r of the isolation material in the cable. From (1), we know that E1 and E′1 will cancel each other since they have the same magnitude but opposite phases in 8 direction. For an arbitrary direction 8, it is always possible to find such a distance S that satisfies equation (1), and thereby the fields from the corresponding two points will cancel each other. Therefore, for an infinitely long LCX with uniform slot aperture, radiation field from any point in the aperture will be canceled by the field from another point. As a result, no radiation occurs. However, if we try to weaken or enhance the field from one of the two points by some means, for example, by making the width of slot aperture at point 1′ narrower, as shown in Figure 1 (middle), then the fields from points 1 and 1′ in the 8 direction cannot be canceled completely. As a result, a residual field DE1 is obtained in the 8 direction. By repeating the slot aperture width one more time, we get another pair of points denoted by 2

2 of 12

RS2009


RS2009

Figure 3. Configuration and parameters of inclined slot. [8] It should be noted that the above analysis is generally valid only for the case of b > k0 [Wang and Mei, 2001a]. Figure 2. Slots cut in the outer conductors of LCXs: (top) symmetry slot and (bottom) asymmetry slot. and 2′ as shown in Figure 1 (bottom), which have the same properties as points 1 and 1′, and another residual field DE2 is generated in 8 direction. Suppose these two pairs of points are separated by a distance of P such at P = 2S, following equation holds as combined with (1), P þ k0 P cos 8 ¼ 2:

3. Methods and Formulas 3.1. Analysis of Field Distribution in Slot [9] Although the arrangements of the slots and the environmental effect have some influences on the polari-

ð2Þ

Equation (2) indicates that in the 8 direction, DE1 and DE2 are in phase. Thus, the superposition of the residual fields reaches the maximum in the 8 direction. If the slot aperture structure is continuously repeated along the cable, and forms a periodic structure as shown in Figure 1 (bottom), the in‐phase supposition from the all residual fields can be expected in the 8 direction, and the strongest radiation will be generated in this direction. [7] Equation (2) can be written in a more general form P þ k0 P cos 8m ¼ 2m; m ¼ 1; 2; . . . :

ð3Þ

According to (3), for a fixed period P, we can find a series of discrete directions 8m in which fields from different periods of the LCX can be superposed in phase. From equation (3), we can further derive the angles for in‐phase superposition directions pffiffiffiffiffiffi 0 "re þ m 8m ¼ cos ; m ¼ 1; 2; . . . ; P 1

ð4Þ

where l0 is the wavelength in free space. Equation (4) is actually equivalent to the formulas given in the literatures for determining the propagation directions of the radiating harmonics of LCX [Wang and Mei, 2001a]. Apparently, each radiation harmonic of the LCX corresponds to an in‐phase superposition direction in which fields from different periods are superposed in phase. The amplitude of each radiation harmonic is determined by the value of the residual field in the corresponding in‐phase superposition direction.

Figure 4. Radiation patterns of a segment of LCX with an inclined slot cut in the middle of the outer conductor, as shown in Figure 3: (top) = 0, 180° plane (determined by cable axis and slot center) and (bottom) = 90° plane (cross section passing through z = 0).

3 of 12

RS2009


Figure 5. Electrical field distribution in the inclined slot: (top) component and (bottom) z component. zation property of a LCX, it is mainly determined by the field distribution in the slots. Figure 2 shows two kinds of slots cut in the outer conductor of the coaxial cables. The field in the slot aperture can be written in cylindrical coordinates as

RS2009

Figure 7. Phase difference of Ez, E and polarization angle around the inclined‐slot LCX, r = 2 m, z = 0.

a where Ee is the even mode component which is a is the inversely symmetry to the slot axis, whereas Eo odd mode component which is symmetry to the slot axis. For the even mode, the radiation is very weak, especially

for the case of narrow slot. For the odd mode, however, the radiation is very strong and it actually defines the radiation mode. A narrow symmetry slot like that shown in Figure 2 (top), can only excite even mode component, a . So the radiation from the component of the Ee aperture field is very small. From (5), the far field in this case is dominated by the z component of the aperture field. Therefore, the far field is mainly polarized in z direction, and a linear horizontal polarization of the far field is expected. [10] When the slot is designed to be circumferential asymmetry as illustrated in Figure 2 (bottom), the odd (radiation) mode of Ea will be generated. Therefore, the radiation field will also have component, and the polarization property of far field will depends on the ratio

Figure 6. Coupling losses around the inclined‐slot LCX calculated by E, Ez and Emax, respectively, r = 2 m, z = 0.

Figure 8. Coupling losses along the inclined‐slot LCX calculated by E, Ez and Emax, respectively, r = 2 m, = 0°.

^ a þ ^zEa : Ea ¼ E z

ð5Þ

The circumferential component Ea can be further decomposed into two parts a a þ Eo ; Ea ¼ Ee

ð6Þ

4 of 12

RS2009


RS2009

patterns in spherical coordinates are given in Figure 4. In the simulation, the radius of inner conductor and the radius of inner surface of outer conductor of the LCX are a = 8 mm and b = 20.65 mm, respectively. The dielectric constant of the isolation material between outer and inner conductors is "r = 1.26, and the dielectric constant of cable jacket is "rj = 2.3. The length of the LCX in this example is 2L = 200 mm. Parameters for the slot are l = 60 mm, d = 8 mm, and x = 24°, respectively. The operating frequency is f = 900 MHz. Results obtained by HFSS for the same structure are also given in Figure 4. The comparison of two results verifies the validity of our method. 3.3. Polarization and Coupling Loss [13] In order to analyze the polarization property, the far field is decomposed into two components Figure 9. Phase difference between Ez, E, and polarization angle along the inclined‐slot LCX, r = 2 m, = 0°.

^ þ ^zEz : E ¼ E

of magnitudes and phase difference of Eao and Eaz , so elliptical polarization can be expected. Therefore, it is possible to get different axial ratios of the polarization ellipses by choosing different aperture structures of the circumferentially asymmetry slots, and even the circular polarization wave can be realized, if properly designed.

From electromagnetic theory, we can get the maximum and minimum of the electrical field, that is, the major and minor axes of the polarization ellipse pffiffiffi 2E Ez sin Emax ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi; min 2 E2 þ Ez2 Ez2 E2 þ 4E2 Ez2 cos2

3.2. Calculation of Radiation Field [11] In the calculation, the LCX is enclosed by a cylindrical mathematical surface, as shown in Figure 3. The mathematical surface is involved into the FDTD meshes that are discretized in cylindrical coordinates. For the formulas and applications of FDTD in cylindrical coordinates, please refer to the literatures [He and Liu, 1999; Teixeira and Chew, 2000; Wang and Mei, 2001a; Dib and Omar, 2002; Lee and Teixeira, 2007]. After the iterative computation of FDTD, the field distribution and the corresponding equivalent electric and magnetic currents on the mathematical surface can be obtained. The far field is then obtained by integrating the electrical and magnetic currents. [12] In order to examine the efficiency of the method, one section of LCX with an inclined slot located in the center, as shown in Figure 3, is simulated. The far field

ð7Þ

ð8Þ where d is the phase difference of Ez and E. The axial ratio of the polarization ellipse, AR, is represented by AR ¼

Emax : Emin

ð9Þ

In this paper, the polarization angle a is defined as the included angle between the major axis of the polarization ellipse and the z (cable) axis. 1 2E Ez cos : ¼ tan1 2 Ez2 E2

ð10Þ

[14] It should be noted that radial component of field also exists on the surface of LCX. However, it decays

Figure 10. Configuration and parameters of a U‐shaped slot. 5 of 12

RS2009


Figure 11. Electrical field distribution in a L‐shaped slot: (top) component and (bottom) z component. exponentially in the radial direction. Therefore, and z components turns to be the dominant components, and we only consider them here. In addition, the coupling loss is another important parameter of LCX. It is defined by Ac = −10 log(Pr /Pt), where Pr is the received power of a standard half‐wavelength dipole antenna located 2 m away from the cable axis, and is evaluated by 0.13l2 · ∣Eq∣2/120p where Eq represents E, Ez or Emax. Pt is the power transmitted in the cable.

4. Polarization Properties of LCX With Circumferentially Asymmetry Slots 4.1. Inclined Slot [15] An inclined slot can excite both the and z components of electrical field in the slot, as shown in Figure 5, therefore the radiation field will also have two components. Figure 6 gives the coupling losses around an

Figure 12. Electrical field distribution in a U‐shaped slot: (top) component and (bottom) z component.

RS2009

Figure 13. Coupling losses calculated by E, Ez and Emax around the L‐slot LCX, r = 2 m, z = 0. inclined‐slot LCX calculated by E, Ez and Emax at r = 2 m, z = 0, respectively, and Figure 7 gives the phase difference of Ez, E and the angle of polarization ellipse. In calculation, the cable length is 2L = 100 m (the FDTD can only simulate several meters of LCX, the whole radiation field of the 100 m long LCX is obtained by the superposition principle [Wang and Mei, 2001a, 2001b]), period of slots is P = 200 mm, other cable parameters are the same as those in Figure 4. The slot parameters are l = 86 mm, d = 4.8 mm, respectively, and the inclined angle of the slot is x = 12.7°, all the slots are arranged in the same orientation. The operating frequency is f = 900 MHz. Due to the phase difference of Ez and E changes with observation angle as shown in Figure 7, the axial ratio

Figure 14. Phase differences of Ez, E and polarization angles around the L‐slot LCX and the U‐slot LCX, r = 2 m, z = 0.

6 of 12

RS2009


RS2009

Figure 15. Coupling losses calculated by E, Ez and Emax along the L‐slot LCX, r = 2 m, = 0°.

Figure 17. Coupling losses calculated by E, Ez and Emax around the U‐slot LCX, r = 2 m, z = 0.

and orientation of major axis of polarization ellipse constructed by Ez and E also vary with the observation angle, as seen from Figures 6 and 7. The maximum value of field in this case cannot be derived directly from Ez and E as in the case of linear polarization. It is actually the major axis of the polarization ellipse and can be calculated by formula (8). It must be noted that because the inclined slot edges are simulated using the staircase FDTD method, the field distributions in the slot aperture also exhibit in the shape of staircase, as shown in Figure 5. The maximum values of Ez and E components in the slot aperture are 32.3 and 56.7 V/m, respectively (voltage applied to cable is 1 V).

[16] Figure 8 gives the coupling losses along the LCX calculated by E, Ez and Emax at r = 2 m, = 0°, respectively, the axial ratio of the polarization ellipse is also given. The variations of phase difference between Ez, E and angle of polarization ellipse along the cable are given in Figure 9. From Figures 8 and 9, we can conclude that for the LCX with inclined slots in the same orientation, the variation of phase difference between E and Ez along the cable is very small, which verifies that the polarization ellipse keeps stable along the cable. [17] In this paper, the plane of z = 0 is defined by a cross section which is passing through the center of the central slot on the cable, and plane of = 0° is defined by the cable axis and centers of slots.

Figure 16. Phase differences between Ez, E and polarization angles along the L‐slot LCX and U‐slot LCX, r = 2 m, = 0°.

Figure 18. Coupling losses calculated by E, Ez and Emax along the U‐slot LCX, r = 2 m, = 0°.

7 of 12

RS2009


RS2009

Figure 19. LCX with slots shaped by horizontal diamonds: (top) slots arranged on cable and (bottom) slot shape and size. 4.2. L‐ and U‐Shaped Slots [18] Figure 10 shows the configuration of the U‐shaped slot. By removing one of the two short vertical slots from the U‐shaped slot, we get an L‐shaped slot. If without the asymmetry parts (short vertical slots), the horizontal part will only excite the even mode of Ea in the slot, and the radiation from the slots is very weak, while with one or two asymmetry parts, the slot will excite the odd mode of Ea as well, and the vertical polarization component of radiation field can be observed. [19] Figures 11 and 12 give the field distributions in the L‐shaped slot and U‐shaped slot on LCXs, respectively, the maximum values of Ez and E components in the aperture are 22.14 and 12.13 V/m, respectively, for L‐shaped slot, and are 40.54 and 21.09 V/m, respectively, for U‐shaped slot (voltage applied to cable is 1 V).

The cable parameters used in calculation are the same as those in Figure 5. The cable length is 2L = 100 m, and P = 200 mm. The slot parameters are w = 73 mm, h = 16.2 mm, t = 7 mm, d = 7 mm, respectively, for the L‐slot LCX, and are w = 73 mm, h = 21.6, t = 7 mm, d = 7 mm, respectively, for the U‐slot LCX. f = 900 MHz. From Figures 11 and 12, it can be observed that a strong odd mode of Ea is generated. [20] Figure 13 gives the variations of the coupling losses around the L‐slot LCX, calculated by E, Ez and Emax at r = 2 m, z = 0, respectively. Meanwhile, the axial ratio of the polarization ellipse is also given. The variations of phase difference of Ez, E and the polarization angle around the cable are given in Figure 14. Figures 13 and 14 show that the axial ratio and the angle of major axis of polarization ellipse change with circumferential

Figure 20. Coupling losses calculated by E, Ez and Emax around the LCX with horizontal diamond slots, r = 2 m, z = 0.

Figure 21. Coupling losses calculated by E, Ez and Emax along the LCX with horizontal diamond slots, r = 2 m, = 0°.

8 of 12

RS2009


RS2009

Figure 22. Coupling losses calculated by E, Ez around the LCX with horizontal diamond slots as function of frequency, r = 2 m, z = 0.

Figure 23. Axial ratio of the polarization ellipse of the radiation field around the LCX with horizontal diamond slots as function of frequency, r = 2 m, z = 0.

angle significantly. The reason is the rapid change of the magnitude difference and the phase difference of E and Ez. Figure 13 indicates that an L‐slot LCX may have more than 10 dB variance in coupling loss around the cable. For the cable considered here, the radiation field is mainly polarized in horizontal within 2 [−60°, 150°], and is mainly polarized in vertical within 2 [150°, 300°]. This can also be seen from the curve of polarization angle a as shown in Figure 14. [21] Figure 15 gives the coupling losses and axial ratio of polarization ellipse along the L‐slot LCX, calculated, respectively, by E, Ez and Emax at r = 2 m, = 0°. The variations of the phase difference of Ez, E and polarization angle along the cable are given in Figure 16. From Figure 15, it can be observed that the coupling losses calculated by Ez and E are relatively smoother, while the coupling loss calculated by Emax exhibits an variation around 1.3 dB along the cable. This is different from the case of inclined‐slot LCX, as shown in Figure 8. The reason is that in this case, the L‐shaped slots are arranged in an interlaced manner, which results in a linearly increase of the phase difference of Ez and E along the cable, as shown in Figure 16. Therefore, the polarization state of the radiation field, especially for the axial ratio and polarization angle of the polarization ellipse, changes between the circular and linear polarizations periodically, as been seen from the curves in Figures 15 and 16. [22] The coupling losses and axial ratios for the U‐slot LCX are given in Figures 17 and 18. The variations of phase differences between Ez, E and polarization angles around and along the cable are also given in Figures 14 and 16 for comparing with those of the L‐slot LCX. By comparison, we find that the U‐slot LCX gives a

smoother circumferential distribution of E than that of the L‐slot LCX, and the E becomes the dominant component. Therefore, the polarization of the field is mainly in vertical, as the curve of a shown in Figure 14. Meanwhile, due to the phase difference between Ez and E around the cable is smoother than that of the L‐slot LCX as shown in Figure 14, the variation of coupling loss calculated by Emax in circumferential direction is smaller than that of the L‐slot LCX. [23] For coupling loss along the cable, as shown in Figure 18, a larger fluctuation of about 2.5 dB can be observed. The reason for this phenomena is similar to that of the L‐slot LCX, but the difference is that the

Figure 24. Coupling losses calculated by Emax along the LCX with horizontal diamond slots as function of frequency, r = 2 m, = 0°.

9 of 12

RS2009


RS2009

Figure 25. LCX with slots shaped by modified horizontal diamonds: (top) slots arranged on cable and (bottom) slot shape and size. magnitudes of Ez and E in = 0° direction are close to each other in this case. As we know, for two orthogonal field components with almost the same magnitude, the maximum variation of the major axis of polarization ellipse can be up to 3 dB when the phase difference between two components changes linearly.

polarization ellipse are in big fluctuation. Figure 24 gives the coupling losses along the cable for different frequencies. It can be seen that the coupling loss at frequency of 1100 MHz fluctuates very much, and this means that the LCX already enters the state of multispatial harmonic radiation [Wang and Mei, 2001a].

4.3. Horizontal Diamond‐Shaped Slots [24] The configuration of LCX with horizontal diamond‐shaped slots is shown in Figure 19. The cable parameters are the same as those in the above sections. As shown in Figure 19 (top), the slots in the outer conductor are arranged in an interlaced manner with P = 200 mm and f = 900 MHz. After a lot of tries, a set of optimum parameters for the horizontal diamond slot is obtained, that is, w = 54.06 mm, h = 10.8 mm. In this case, the maximum values of Ez and E components in the slot aperture are 19.8 and 14.01 V/m, respectively (voltage applied to cable is 1 V). [25] The coupling losses around the cable calculated by E, Ez and Emax, respectively, at r = 2 m, z = 0 are given in Figure 20. As been shown therein, the angular range for fluctuation lower than 3 dB can reach 200° ( 2 [−40°, 160°]). Figure 20 also depicts the phase difference of Ez and E around the cable; it indicates that the cable radiates an elliptical polarized wave. The corresponding axial ratio of the polarization ellipse is given in Figure 23. Figure 21 gives the variations of coupling loss and axial ratio of the polarization ellipse along the cable, which shows that the fluctuation of coupling loss at 900 MHz is no more than 2 dB along the cable, and the wave is mainly polarized in vertical. [26] Figure 22 gives the coupling losses calculated by E, Ez around the cable for different frequencies; the corresponding axial ratios of the polarization ellipse are shown in Figure 23. It can be seen from Figures 22 and 23 that the fluctuations of coupling losses are relatively smoother for frequencies of 850, 900, 950, 1000 and 1100 MHz, but for 950 and 1100 MHz, the axial ratios of

4.4. Modified Horizontal Diamond‐Shaped Slots [27] The modified horizontal diamond‐shaped slots is shown in Figure 25 (bottom). The cable parameters and the period of slots are the same as those for horizontal diamond slot LCX, and f = 900 MHz. The slots are also arranged in an interlaced manner. The slot parameters are w = 54.06 mm, h = 10.8 mm, t = 4.1 mm, a = 63.43°, respectively. [28] The coupling losses around the cable calculated by E, Ez and Emax, respectively, at r = 2 m and z = 0 are

Figure 26. Coupling losses calculated by E, Ez and Emax around the LCX with modified horizontal diamond slots, r = 2 m, z = 0.

10 of 12

RS2009


RS2009

Figure 27. Coupling losses calculated by E, Ez and Emax along the LCX with modified horizontal diamond slots, r = 2 m, = 0°.

given in Figure 26. From that, it can be seen that the angular range for fluctuation lower than 3 dB can reach 210° ( 2 [−60°, 150°]). The phase difference of Ez and E are also given in Figure 26; it indicates that the cable also radiates the elliptical polarized wave. Figure 27 reflects the variations of coupling loss and axial radio of polarization ellipse along the cable calculated by E, Ez and Emax, respectively, at r = 2 m and = 0°. It shows that the fluctuation of coupling loss is smaller than 2 dB, and the wave is mainly polarized in circumferential direction. For the frequency property, the LCX with modified diamond slots is similar to the LCX with diamond slots.

5. Conclusion [29] In this paper, the physical understanding of the radiation from LCX is presented first, and then the method for calculating the far field of the LCX is given and verified. By this method, the polarization properties of several LCXs with different circumferentially asymmetry slots are simulated and analyzed. By the analysis and results we can conclude that there are certain directions for a radiating LCX in which the fields from different periods of slots on the LCX can be superposed in phase, which corresponds to the radiation harmonics of the LCX. In this paper, it is found that the LCX with circumferentially asymmetry slot can excite both the circumferential and axial components of the field, and the magnitude and phase differences between these two components change significantly with the structural parameters of the asymmetry slot, therefore, it is pos-

sible to find some slot structures that can make the LCX radiating the desired polarization wave.

[30] Acknowledgments. This work was supported by NSFC project under grant 60825101, National High‐Tech R&D Program of China (863) under grant 2008AA01Z224, and PCSIRT, MOE, China, under grant IRT0707.

References Addamo, G., R. Orta, and R. Tascone (2008), Bloch wave analysis of long leaky coaxial cables, IEEE Trans. Antennas Propag., 56(6), 1548–1554, doi:10.1109/TAP.2008.923346. Beal, J. C., J. M. Josiak, S. F. Mahmoud, and V. Rawat (1973), Continuous‐access guided communication (GAGC) for ground‐transportation systems, Proc. IEEE, 61(5), 562–568, doi:10.1109/PROC.1973.9112. Delogne, P. P., and A. A. Laloux (1980), Theory of the slotted coaxial cable, IEEE Trans. Microwave Theory Tech., 28(10), 1102–1107, doi:10.1109/TMTT.1980.1130232. Dib, N., and A. Omar (2002), Dispersion analysis of multilayer cylindrical transmission lines containing magnetized ferrite substrates, IEEE Trans. Microwave Theory Tech., 50(7), 1730–1736, doi:10.1109/TMTT.2002.800423. Gagnon, A. (1995), A new invisible volumetric sensor for solid wall applications, paper presented at IEEE Annual International Carnahan Conference on Security Technology, Inst. of Electr. and Electron. Eng., Sanderstead, U. K. Haag, H. G., and K. Lehan (1989), Leaky coaxial cable systems for high speed trains in tunnels and other environmental conditions‐theory and experience, paper presented at

11 of 12

RS2009


39th International Wire and Cable Symposium, Int. Wire and Cable Symp., Inc., Atlanta, Ga. Hassan, E. E. (1989), Field solution and propagation characteristics of monofilar‐bifilar modes of axially slotted coaxial cable, IEEE Trans. Microwave Theory Tech., 37(3), 553–557, doi:10.1109/22.21627. He, J.‐Q., and Q. H. Liu (1999), A nonuniform cylindrical FDTD algorithm with improved PML and quasi‐PML absorbing boundary conditions, IEEE Trans. Geosci. Remote Sens., 37(2), 1066–1072, doi:10.1109/36.752224. Hill, D. A., and J. R. Wait (1980a), Electromagnetic characteristics of a coaxial cable with periodic slots, IEEE Trans. Electromagn. Compat., 22(11), 303–307. Hill, D. A., and J. R. Wait (1980b), Propagation along a coaxial cable with a helical shield, IEEE Trans. Microwave Theory Tech., 28(2), 84–89, doi:10.1109/TMTT.1980.1130014. Kim, D. H., and H. J. Eom (2007), Radiation of a leaky coaxial cable with narrow transverse slots, IEEE Trans. Antennas Propag., 55(1), 107–110, doi:10.1109/TAP.2006.888414. Kim, S.‐T., G. H. Yun, and H.‐K. Park (1998), Numerical analysis of the propagation characteristics of multiangle multislot coaxial cable using moment method, IEEE Trans. Microwave Theory Tech., 46(3), 269–279, doi:10.1109/22.661714. Lee, H. O., and F. L. Teixeira (2007), Cylindrical FDTD analysis of LWD tools through anisotropic dipping‐layered earth media, IEEE Trans. Geosci. Remote Sens., 45(2), 383–388, doi:10.1109/TGRS.2006.888139. Matsumoto, K., Y. Yokoyama, S. Matsumoto, S. Arimura, and S. Fujita (1990), A new communications network for the Tokaido Shinkansen, Mitsubishi Denki Giho, 64, 11–17. Morgan, S. P. (1999), Prediction of indoor wireless coverage by leaky coaxial cable using ray tracing, IEEE Trans. Vehicular Tech., 48(6), 2005–2014, doi:10.1109/25.806793. Nakamura, M., H. Takagi, K. Einaga, T. Nishikawa, N. Moriyama, and K. Wasaki (2009), Evaluation of a dual‐band long leaky coaxial cable in the 2.4 and 5 GHz frequency bands for wireless network access, paper presented at IEEE Radio and

RS2009

Wireless Symposium, Inst. of Electr. and Electron. Eng. Comput. Soc., San Diego, Calif. Richmond, J. H., N. N. Wang, and H. B. Tran (1981), Propagation of surface waves on a buried coaxial cable with periodic slots, IEEE Trans. Electromagn. Compat., 23(3), 139–146, doi:10.1109/TEMC.1981.303954. Seidel, D. B., and J. R. Wait (1978), Transmission modes in a braided coaxial cable and coupling to a tunnel environment, IEEE Trans. Microwave Theory Tech., 26(7), 494–499, doi:10.1109/TMTT.1978.1129421. Teixeira, F. L., and W. C. Chew (2000), Finite difference computation of transient electromagnetics waves for cylindrical geometries in complex media, IEEE Trans. Geosci. Remote Sens., 38(4), 1530–1543, doi:10.1109/36.851953. Wait, J. R., and D. A. Hill (1975), Propagation along a braided coaxial cable in a circular tunnel, IEEE Trans. Microwave Theory Tech., 23(5), 401–405, doi:10.1109/TMTT.1975.1128580. Wang, J. H. (2008), Research on the radiation characteristics of patched leaky coaxial cable by FDTD method and mode expansion method, IEEE Trans. Vehicular Tech., 57(1), 90–96, doi:10.1109/TVT.2007.905250. Wang, J. H., and K. K. Mei (2001a), Theory and analysis of leaky coaxial cables with periodic slots, IEEE Trans. Antennas Propag., 49(12), 1723–1732, doi:10.1109/8.982452. Wang, J. H., and K. K. Mei (2001b), Design and calculation of the directional leaky coaxial cables, Radio Sci., 36(4), 551–558, doi:10.1029/2000RS002344. Wang, J. H., and K. K. Mei (2002), Design of the leaky coaxial cables with periodic slots, Radio Sci., 37(5), 1069, doi:10.1029/2000RS002534. Yamada, Y., M. Arizumi, and S. Sato (1996), Automated highway system and longitudinal/lateral control system, paper presented at IEEE Intelligent Vehicles Symposium, Inst. of Electr. and Electron. Eng., Tokyo. M. Chen, Y. Li, J. Wang, and Z. Zhang, Institute of Lightwave Technology, Beijing Jiaotong University, Beijing 100044, China. ([email protected])

12 of 12