theory and analysis of leaky coaxial cables with periodic slots

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 49, NO. 12, DECEMBER 2001 1723

Theory and Analysis of Leaky CoaxialCables With Periodic Slots

Jun Hong Wang, Member, IEEE,and Kenneth K. Mei, Life Fellow, IEEE

Abstract—Frequency band and coupling loss are the two im-portant parameters of leaky coaxial cables with periodic slots. fre-quency band can be predicted by analyzing the arrangement of theslots on the outer shield of the cable, but the coupling loss is not soeasy to determine by classical methods. In this paper, the finite-dif-ference time-domain (FDTD) method is used to calculate the elec-tric field distribution in the slot cut in the outer conductor of thecoaxial cable. The dyadic Green’s Function is then used to calculatethe radiation field of the equivalent surface magnetic current den-sities. By these two methods, the coupling losses of the leaky coaxialcables with different periods, sizes and shapes of the slots can beaccurately obtained. Some results in this paper were verified by theexperimental results of the leaky coaxial cables designed for railwaymobile communications with a frequency band of 100–500 MHz.

Index Terms—Dyadic Green’s function, finite-difference time-domain (FDTD) method, leaky coaxial cables, leaky wave antenna,periodic structure, slot array.

I. INTRODUCTION

L EAKY COAXIAL CABLES are known for the capabilityof distributing radio waves where discrete antennas fail.

The applications of the leaky coaxial cables have been nowextended to many places outside its original use in tunnels andmines. There are many excellent papers about leaky coaxialcables done by pioneers both in theory and application. Wait,Hill, and Seidel studied the field, propagation constant, and thesurface transfer impedance of the helical wire shielded coaxialcables [1], [2], and the series impedance and propagation modesof the braided coaxial cables within tunnels [3], [4]. These typesof cables are now less attractive because of the large longitudinalattenuation. Hassan,Delogne,and Lalouxstudied the field, prop-agationconstant,andcouplingcharacteristicof theaxiallyslottedcoaxial cables [5], [6], which are also known to have relativelylarge longitudinal attenuation but are easier to fabricate than theperiodically slotted cables. Hill and Wait, Richmond, Wang andTran studied the field, propagation constant, and the relationshipbetween the propagation constant and the transfer impedance ofthe coaxial cables with vertical periodic slots [7], [8]. Kim, Yun,Park, and Yoon studied the propagating and radiating propertiesof the coaxial cables with multiangle multislot configuration[9], [10]. These types of cables, having the advantages ofcontrollable radiation and low longitudinal attenuation, are nowbecoming the main products of numerous manufacturers.

Many application problems associated with leaky coaxial ca-bles havealso beenstudied: Forexample, the interactionbetween

Manuscript received June 29, 1999; revised January 2, 2001. This work wassupported in part under CERG Grant 9 040 201-570 of the Hong Kong Govern-ment, Hong Kong, China.

The authors are with the Department of Electronic Engineering, City Univer-sity of Hong Kong, Hong Kong, China.

Publisher Item Identifier S 0018-926X(01)10812-4.

Fig. 1. Basic configuration of the leaky coaxial cables.

the coaxial cables with short leaky sections and the tunnels [11];the techniques for accurately testing of the coupling loss of leakycoaxial cables [12]; the underground transportation system [13];the mobile communications and its application in buildings [14];[15]; the high speed railway [16]–[18]; the guided radar system;the nonintruding detection system and others [19]–[21].

Now, the development of the leaky coaxial cables is movingtoward the directions of high frequency and wide band [9], [10],[22], and [23]. However, most of these work are being doneby the classical method of mode matching at boundary or byexperiments. Reference [9] presented a combined method whichinvolved the method of moment and the conventional method ofmodematching,andobtained therelativelyaccurate resultsof thecoupling loss, but this method was complicated in the process offinding the field distribution in slot apertures. In this paper, weuse finite-difference time-domain (FDTD) method combinedwith Mei’s superabsorption method [24] to calculate the fielddistribution in the slots accurately. For far field, which is beyondthe capacity of the FDTD, we integrate the aperture electricalfield by using the dyadic Green’s function, which is presented inSection III. The analyses of the harmonic radiation and resonantpoints,whichare important indesigningthefrequencybandof theleakycoaxial cables,arepresented inSection II. InSection IV, thenumerical and experimental results are presented and discussed.

II. RADIATION HARMONICS AND RESONANT POINTS OF THE

LEAKY COAXIAL CABLES

A. Radiation Harmonics

Usually, the design procedure for the leaky coaxial cableswith periodic slots includes two steps, namely, the design forthe frequency band and the design for the coupling loss. Be-cause the frequency band of the cable depends mainly on thearrangement of the slots, it is usually studied first. In this sec-tion, we briefly discuss the radiation characteristics of the leakycoaxial cables, which are the basics for frequency band design.

For a periodic structure shown in Fig. 1, the field around itcan be written by [25]

(1)

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1724 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 49, NO. 12, DECEMBER 2001

Fig. 2. Radiation frequency band of the harmonics.

where . and are the attenuation constant andpropagation constant of the basic mode of the perturbed cablerespectively, which can be expressed in terms ofand ,the attenuation constant and propagation constant of the unper-turbed cable, as and . , where

is the wave number of free space, andis the relative per-mittivity of the dielectric material in the cable.and are thefunctions of many factors, such as the slot arrangement, slot sizeand shapes, the operating frequency.

For maximizing the effective distance, the attenuations of theleaky coaxial cables are controlled to be as low as possible. Thedielectric used in the cable is usually the foamed polyethylenewith a permittivity of around 1.25, where the wave velocity inthe cable is about 88% of that in free space. So the values ofand are almost one (Ref. [9] shows thatis about 1.0002 to1.002 for different cables). In addition, becauseis very smallcomparing to , it is not so important in the harmonic analysisthat follows, so it is omitted and we let .

in (1) are the periodic functions of, and can beexpanded into Fourier series [25]

(2)

Therefore

(3)

where

(4)

is the propagation constant of theth spatial harmonic inthe direction. is the period of slots. The propagation constantof the th harmonic in the radial direction is

(5)

If , then no radiation from the th harmonic occursin the radial direction. From (5), we can find the condition forradiation from the th harmonic

(6)

where is the velocityof light in free space. The diagram for radiation frequency bandof different harmonics is illustrated in Fig. 2.

Fig. 2 indicates that if the frequency is in the region of, only the th harmonic radiates in a single direction,

as shown in Fig. 1. When the frequency increases, thethharmonic radiation will appear in the backfire direction beforethe th harmonic reaches forward endfire, and the radiationwill be bi-directional. Of course, if , then ,which means that the radiation frequency bands of theth

Fig. 3. Configurations of realistic leaky coaxial cables.

and th harmonics will not overlap each other, and thesimultaneous radiation of those two harmonics will not occur.The propagation angles are determined by

(7)

Usually, the leaky coaxial cables are designed only to allowradiation in their th harmonic, so as to avoid the large fluctu-ation caused by the radiation of high order harmonics. Equation(6) indicates that the mono-radiation frequency band ofthharmonic is very narrow, although the widest radiation bandpossible for th harmonic is . The usual way of sup-pressing the high order harmonics is to cut new slot series inaddition to the original one with the same size and shape, asshown in Fig. 3. If the small group of the new slots in each largeperiod has a period of , then the for the wholecable can be obtained by summing up the individualof each series but with a progressively phase shift of .Therefore, the total field of the cable can be written as

for vertical slot (8)

for inclined slot (9)

where

(10)

is the number of slots in the small group except the originalone . If the small group period is taken as

(11)

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WANG AND MEI: THEORY AND ANALYSIS OF LEAKY COAXIAL CABLES 1725

Fig. 4. Equivalent circuit for the leaky coaxial cable shown in Fig. 3(a).

then the equals zero and the radiation of theth higherorder harmonic is suppressed. In addition, from the equation forthe in (9) we can see that if is a negative even number,the corresponding terms in the series vanish. This means thatthe inclined slot cable naturally suppressed the radiation fromall the even order high harmonics of the . In (9), the coeffi-cients and are functions of the inclina-tion angle of the slot. If the inclined slot approaches a verticalposition, will vanish and the original slot array willbecome a new array that has a slot period only half that of theoriginal one. In this case, (9) is reduced to (8).

B. Resonant Points

Another important issue of the leaky coaxial cable with peri-odic slots is to find the resonant points, at which the transmit-ting and radiating properties are degraded. In analysis, we mayreplace a single slot by a symmetry two port network with re-flection coefficient and transmission coefficient. The wholecable, shown in Fig. 3, is then equivalent to a series connectedcircuit as shown in Fig. 4.

Using the theory of small reflections [25] and neglect the mul-tireflections between the slots, we get the total reflection coef-ficient

(12)

where is the total number of the large periods. The voltagestanding wave ratio (VSWR) can be found from (12) by

. In Fig. 5(a), theVSWR of a cable with diameter of 41.3 mm (outer conductor)versus frequency is shown for . One hundred slots werecut on the cable with period of m. Each slot hasa size of 32.4 3.3 mm , and the reflection and transmissioncoefficients from it are and(these values were obtained from an approximate theoreticalanalysis at frequency of 900 MHz). In the calculation welet Np/m (corresponds to20 dB/km), and . Fig. 5(a) indicates that in themono-radiation band of th harmonic, a resonant point oc-curs at . At this frequency,the propagation angle of the th harmonic outside the cableis . This means the cable radiates in the broadsidedirection. Because large amount of the energy is reflected at thispoint, so the radiation property is also distorted. This resonantpoint can be removed by cutting another hundred slots shiftedfrom the original slots by a distance of as shown in Fig. 5(b)

. The same procedure was presented in [26]but for eliminating the rapid variation of the leakage constant inthe “stop-band” of the leaky-wave antenna. However, here we

(a)

(b)

Fig. 5. Voltage standing wave ratio of a leaky coaxial cable (a)� = 0. (b)� =1; P = P=4.

have not only removed the resonant point, but also suppressedthe radiation of the th harmonic, and extended the mono-ra-diation frequency band of the th harmonic fromto . If we wish to remove the resonant point withoutaffecting the radiation field, we could cut the nonradiation slotsinstead, i.e., the slots which do not cut the current line on thecable’s outer conductor. Sometimes, the manufactures disclosethe frequencies of the resonant in their products specification.

III. FDTD FORMULAS AND RADIATION FIELD INTEGRATION

Unlike the frequency band, the coupling loss of the leakycoaxial cables not only depends on the arrangement of the slots,but also depends on the size and shape of the slots, so it is hardto obtain its design data analytically. We decide to use FDTDmethod to calculate the field distribution in the slots, and then



Fig. 6. Configuration, coordinates and discretization of the leaky coaxial cable.

calculate the radiation field by integrating this field togetherwith the dyadic Green’s function.

A. FDTD Formulas

Fig. 6(a) and (b) show the configuration and coordinates of thecoaxial cable and the slot, whereis the outer radius of the innerconductor, is the inner radius of the outer conductor. and

are the length, width and angle of the slot respectively.isthe inclined angle of the slot. Fig. 6(c) shows the discrete meshesused in this paper. There are four regions to be considered. Forall regions, the general form of Maxwell’s curl equations is

(13)

(14)

where and are the relative permittivity and permeabilityof the corresponding region.

After expanding (13) and (14) in terms of cylindrical coordi-nates, the similar mesh nodes of Yee [27] were used to discretizethe timeandspace.The finaldiscrete forms for the fieldequationsare

(15)

(16)

(17)

(18)

(19)

(20)

whereis the spatial steps at

different places, is the wave velocity in themedium,

. If we are onlyinterested in the field amplitude, the above equations may besimplified by replacing with . For the boundarycondition, we use the superabsorption method proposed by Mei[24] combined with the Mur’s boundary condition [28].

B. Radiation Field Integration

The radiation field can be solved by integrating the equivalentmagneticcurrent togetherwithdyadicGreen’s function. Itshouldbe noted that although the leaky coaxial cable is assumed to be in-finitely long, the FDTD, can only solve the field distributions ofseveral slots. However, we shall see late in this paper, that if theslots are separated far enough, the effect of interference between



theslotson theaperture fielddistribution isnegligible.Therefore,the only parameters in the aperturedistributionsare the phaseandthe amplitude of the distribution, which can be predicted by the-oretical analysis. The whole cable can be considered as a phasedslot array with the same field distribution in each slot.

The radiating electrical field from the leaky coaxial cable canbe expressed by [29]

(21)

where

(22)

and

(23)

is the equivalent surface magnetic current density, whichhas two components and . They should not be confusedwith the which denotes the vector wave functions.is the electric field in the slot aperture,is the normal directionof the aperture pointing outward. We only need to use the evenmodes and of the vector wave function owing tothe coordinates we have chosen in Fig. 6. Using the expressionsof and and the relationship between them [29] wecan finally expand (21) as follows:

(24)

(25)

(26)

where

(27)

(28)

(29)

The integrals in (29) include a series of slots with larger groupperiod and small group period as shown in Fig. 3. The finalresults are

(30)



Fig. 7. Distributions ofE in the aperture of the vertical slot (exciting voltagein cable is 0.707 V,f = 900 MHz, a = 8 mm, b = 20:65 mm, " =

1:26; w = 2:53 mm).

where and . is the total number ofslots, and

(31)

(32)

Equation (31) is for the case of inclined slots, for vertical slotscase, just remove the terms and in(31). is determined by the formula . shouldnot be less than the standard length of 70 m (or 100 m), whichis demanded by the experiment. For and , just replaceparameter in (31), (32) with .

The integration limits and the summation limits mustbe tested carefully in calculating (24)–(26). The kernel willbecome singular when . In this case, we set a small devi-ation to the integral limits as . Bycomputation and comparison, we have found that ifand , the errors due to the deviation of the limits arenegligible. The series summation appears to have converged for

. Actually, if becomes larger, the second integrationsin (24)–(26) become smaller as expected, andcan be choseneven smaller.

IV. NUMERICAL AND EXPERIMENTAL RESULTS

A. Field Distribution in Slots

Fig. 7 shows the influences of the cable jacket and the neigh-boring slot on the aperture field distribution of a slot. The cableis designed to have a characteristic impedance of 50, its struc-tural parameters are mm, mm, the relative per-mittivity of the dielectric is , the thickness of the cablejacket is about 2.5 mm with . This cable is consistentwith the standard– " leaky coaxial cables of several manu-facturers. The exciting voltage in cable is 0.707 V at frequency

(a)

(b)

Fig. 8. Distributions of electrical field in the apertures of the inclined slots(exciting voltage in cable is 0.707 V,a = 4:15 mm, b = 16 mm," = 1:23;

l = 61 mm,w = 5:3 mm). (a)E . (b) E .

of 900 MHz. The distance between the two slots is 5 cm. Thelength of the slots is 32.44 mm corresponding to , andthe width of each slot is 2.5 mm. From Fig. 7 we can see that theinfluences from the jacket and neighboring slot are very smalland can be neglected.

Fig. 8 shows the aperture field distributions of the slots withinclined angle of 14.2, 9 , and 5 . The cable’s parameters are

mm, mm, , with a characteristicimpedance of 75 . The slot length and width are 122 mm and5.3 mm respectively. As expected, the slots with larger inclinedangle excited larger aperture field. Fig. 9 illustrates the wave-forms of and , both in the middle of the slot with an



Fig. 9. Waveforms ofE andE in the middle of the inclined slots (excitingvoltage in cable is 0.707 V,a = 4:15 mm, b = 16 mm, " = 1:23; l =

61 mm,w = 5:3 mm,� = 14:2 ).

Fig. 10. E distribution along a cable with two vertical slots 5 cm departurefrom each other (exciting voltage in cable is 0.707 V,f = 900MHz,a = 8mm,b = 20:65 mm," = 1:26;w = 2:53 mm,� = 45 ).

inclined angle of 14.2. The difference of their phase is about139 .

B. Radiation Field From the Slots on the Coaxial Cable

It must be pointed out that the influence of the cable jacketwas neglected in the derivation of the formulas in Section III forthe radiation field. When the jacket thickness is less than ,the error due to it is of no significance. Fig. 10 gives the radi-ation field distribution along the cable with two vertical slots,the field points were located in the front of the slots, and werekept 5 cm away from the cable. Fig. 11 shows the field distribu-tion around a cable with single vertical slot only, the field pointswere also kept 5 cm away from the cable. The curves with dotsin both figures were directly obtained from FDTD calculationswhich have considered the influence of the cable jacket. Thesolid lines represent the results from the integration after theelectrical field in the slot have been computed by FDTD. Theseagreements in results also demonstrate the integrity of the com-plicated integrations involved in the dyadic Green’s function. Inthe following sections, the electric fields used in the computa-tion all come from the magnetic current integrations.

Fig. 11. E distribution around a cable with a single vertical slot (excitingvoltage in cable is 0.707 V,f = 900 MHz, a = 8 mm, b = 20:65 mm," = 1:26;w = 2:53mm,� = 45 , field point located 5 cm from the cable).

Fig. 12. Coupling losses of the leaky coaxial cables with different slot periodsat 900 MHz (a = 8 mm, b = 20:65 mm, " = 1:26;w = 2:53 mm,� =

45 ).

C. Harmonic Effects on Coupling Loss

Coupling loss is the only parameter which distinguishes theleaky cable and the normal RF cable. It’s defined as

(33)

where is the received power of a standard half-wave-length dipole antenna, and is evaluated in this paper by

. This corresponds to the multiplication ofthe Poynting vector with the effective area of the half-wave-length dipole. In the case of surface wave mode, this formulacan also indicate the variation of the electric field. is thepower transmitted in the cable. The coupling loss varies alongthe cable, and therefore it is called local coupling loss. For awhole cable, the coupling loss is defined in a statistical way. Ifthere are 50of the tested points at which the local coupling lossis less than a certain value, then this value is called the couplingloss of the cable with probability . The same definition can



Fig. 13. Coupling losses of the leaky coaxial cables with and without the radiation of high order harmonics (f = 900 MHz, a = 8 mm, b = 20:65 mm," = 1:26; P = 0:4 m, P = 0:1 m,w = 2:53 mm,� = 45 ).

Fig. 14. Coupling losses computed from theE of the leaky coaxial cables with different inclined slots (f = 456 MHz, a = 4:15 mm, b = 16 mm, " =

1:23; P = 24 mm, l = 61 mm,w = 5:3 mm).

be made for . The distance between the tested point andthe cable also affects the coupling loss, so usually, the standarddistance is defined as 1.5 m, 2 m, or even 6 m. In this paper, weadopt the standard of 1.5 m and 2 m. Incidentally, different typeof cables needs different orientations of the dipole when testing.It must be emphasized that in our computation of electric field

from (24) to (26), we let and . The value ofwas obtained from some manufacture’s specification. The

effect of these approximations on the numerical results is verysmall, because the leaky coaxial cables are usually designedmore like transmission lines. The value ofis dominated bythe materials constructing the cable.

Fig. 12 illustrates the local coupling loss as a function ofwith period of 0.155 m, 0.157 m, 0.31 m, and 0.32 m, the op-erating frequency is 900 MHz, the distance between dipole andcable is 2 m, the dipole orientation is in thedirection. From theanalysis of Section II we know, m corresponds to thecase of surface wave mode, m and m cor-respond to the case of mono-harmonic radiation mode, while

m corresponds to the case of multi-harmonic radi-

ation mode. From Fig. 12 we find that the fluctuation is verysmall when the cable is working in the mono-harmonic radiationband. If high-order harmonics exist, the fluctuation becomesvery large. But if we use the method discussed in Section II tosuppress the radiation from higher order harmonics, the fluctu-ation will be reduced again as shown in Fig. 13. Fig. 12 alsoshows that although the fluctuation of the surface wave mode issmall, the coupling loss, however, is larger than the others. Thisis due to the fact that most of the energy coupled from the cableis involved in surface wave mode and is bounded near the cable,so the attenuation in radial direction is larger.

Fig. 14 gives the computed coupling losses of three typesof leaky coaxial cables with inclined angles of , 9and 5 respectively, which correspond to the realistic leakycoaxial cables designed previously for a frequency band of100–500 MHz. The configuration of these cables are similar tothat shown in Fig. 3(b), but with and . Theparameters of the cable and slots are mm,mm, m, mm, mm,

mm. This configuration ensures the suppression of



Fig. 15. Experimental coupling losses of the inclined slot cables corresponding to Fig. 14.

Fig. 16. Sampled coupling losses from Fig. 14 with a sample step of 0.4 m as in Fig. 15.

the radiation from higher order harmonics within the frequencyband. Here, the coupling loss is only computed fromwhich corresponds to the vertical orientation of the dipole. Theoperating frequency is MHz. As expected, the slotswith larger inclined angle will couple more energy into thespace from the cable, so the corresponding cable has a lowercoupling loss.

D. Experimental Results and Comparison

The types of the cables described in Fig. 14 have been man-ufactured and tested previously [30]. The cables are all 200 mlong, and were hung 3.5 m high along a road. The cables wereconnected to a source with frequency of 456 MHz, and were ter-minated at the other ends by standard terminating loads. Whentesting, the receiving dipole was placed vertically to the cableaxis in the front of the slots, and 1.5 m away from the cables, soonly was received. The spatial sampling step is 0.4 m alongthe cables. Other parameters concern about the cables are thesame as in Fig. 14. The tested results are given in Fig. 15 and inTable I. For comparison, we made the same sampling procedureas the experiment from Fig. 14, the sampling results are shownin Fig. 16 and also in Table I.

From Table I we can see that the two statistical results arein good agreement, the main difference is in the distributionsof the local coupling losses. This is due to the disagreement innumerical calculation and experiment. The formula for inSection IV-C implies that the coupling losses in Figs. 14 and 16

TABLE ICOUPLING LOSSESDEFINED BY 50% PROBABILITY (D = 1:5 m)

are actually calculated at the discrete points under the assump-tion of an ideal plane wave incidence. But in experiment, thingswere more complicated, the field received by the realistic dipolewas affected by the environment.

V. CONCLUSION

In this paper, the electrical field in the aperture of the slotcut in the outer conductor of the coaxial cable is calculated byFDTD method, the radiation field from the slots is then ob-tained by integrating the equivalent magnetic current togetherwith the dyadic Green’s function. By these methods, the rela-tionship between the coupling losses and the configurations ofthe cables and the slots can be accurately determined, whichare important issues in the design of the leaky coaxial cables.The results of this paper show that for the same structure of theslots, the leaky coaxial cables working in the surface-wave modewill have larger coupling losses than that working in radiation



mode. If radiation of higher order harmonics occurs, then thefield along the cable will fluctuate very sharply. In order to ex-tend the frequency band of monoharmonic, radiation from highorder harmonics should be suppressed by cutting one or morenew series of slots in addition to the original one with the samesize and shape.

REFERENCES

[1] J. R. Wait and D. A. Hill, “Propagation along a braided coaxial cable ina circular tunnel,”IEEE Trans. Microwave Theory Tech, vol. MTT-23,pp. 401–405, May 1975.

[2] D. B. Seidel and J. R. Wait, “Transmission modes in a braided coaxialcable and coupling to a tunnel environment,”IEEE Trans. MicrowaveTheory Tech., vol. MTT-26, pp. 494–405, July 1978.

[3] J. R. Wait, “Electromagnetic theory of the loosely braided coaxialcable: Part I,”IEEE Trans. Microwave Theory Tech., vol. MTT-24, pp.547–553, Sept. 1976.

[4] D. A. Hill and J. R. Wait, “Propagation along a coaxial cable with ahelical shield,”IEEE Trans. Microwave Theory Tech., vol. MTT-28, pp.84–89, Feb. 1980.

[5] E. E. Hassan, “Field solution and propagation characteristics ofmonofilar-bifilar modes of axially slotted coaxial cable,”IEEE Trans.Microwave Theory Tech., vol. 37, pp. 553–557, Mar. 1989.

[6] P. P. Delogne and A. A. Laloux, “Theory of the slotted coaxial cable,”IEEE Trans. Microwave Theory Tech., vol. MTT-28, pp. 1102–1107,Oct. 1980.

[7] D. A. Hill and J. R. Wait, “Electromagnetic characteristics of a coaxialcable with periodic slots,”IEEE Trans. Electromagn. Compat., vol.EMC-22, pp. 303–307, Nov. 1980.

[8] J. H. Richmond, N. N. Wang, and H. B. Tran, “Propagation of surfacewaves on a buried coaxial cable with periodic slots,”IEEE Trans. Elec-tromagn. Compat., vol. EMC-23, pp. 139–146, Aug. 1981.

[9] S. T. Kim, G. H. Yun, and H. K. Park, “Numerical analysis of thepropagation characteristics of multiangle multislot coaxial cable usingmoment method,”IEEE Trans. Microwave Theory Tech., vol. 46, pp.269–279, Mar. 1998.

[10] S. T. Kim, K. J. Kim, Y. J. Yoon, and H. K. Park, “New design techniquefor 22 mm ultra-wideband LCX,” inProc. Asia Pacific Microwave Conf.,1995, pp. 514–516.

[11] P. P. Delogne and L. Deryck, “Underground use of a coaxial cablewith leaky sections,”IEEE Trans. Antennas Propagat., vol. AP-28, pp.875–883, Nov. 1980.

[12] D. J. Gale and J. C. Beal, “Comparative testing of leaky coaxial cablesfor communications and guided radar,”IEEE Trans. Microwave TheoryTech., vol. MTT-28, pp. 1006–1013, Sept. 1980.

[13] J. C. Beal, J. M. Josiak, and V. Rawat, “Continuous-access guided com-munication (GAGC) for ground-transportation systems,”PIEEE, vol.61, pp. 562–568, 1973.

[14] K. J. Bye, “Leaky-feeder for cordless communication in the office.EUROCON88: 8th European Conference on Electrotechnics,” inProc.Conf. Area Commun., June 1988, pp. 387–390. (Cat. no. 88ch2607-0).

[15] H. G. Haag, “Leaky coaxial cable for mobile communication,” inProc.38th Int. Wire Cable Symp., 1989, pp. 286–294.

[16] H. G. Haag and K. Lehan, “Leaky coaxial cable systems for high speedtrains in tunnels and other environmental conditions-theory and experi-ence,” inProc. 39th Int. Wire Cable Symp., 1990, pp. 71–79.

[17] K. Matsumoto, Y. Yokoyama, S. Matsumoto, S. Arimura, and S. Fu-jita, “A new communications network for the Todaido Shnkansen,”Mit-subishi Denki Giho, vol. 64, pp. 11–17, 1990.

[18] K. Matsumoto, Y. Yokoyama, M. Hanafusa, and T. Nakamura, “A newtrain radio-telephone system for the Tokaido Shinkansen,”MitsubishiDendi Giho, vol. 63, pp. 64–69, 1989.

[19] S. F. Smith and R. I. Crutcher, Leaky Coaxial Cable Signal Transmissionfor Remote Facilities. DE93 007 916 CONF-930 403-20.

[20] S. Rampalli and H. R. Nudd, “Recent advances in the designs of radi-ating (leaky) coaxial cables,” inProc. 40th Int. Wire Cable Symp., 1991,pp. 67–77.

[21] “Radiating coaxial cable aids RF communications,”Australian Electron.Eng., vol. 23, pp. 30–32, 1990. .

[22] K. Aihara, “Ultra-high-bandwidth heat-resistant leaky coaxial cable,” inProc. Int. Wire Cable Symp., 1992, p. 41.

[23] M. S. Leong, P. S. Kooi, T. S. Yeo, and X. G. Liu, “Higher perturbedmodes excited by 1.8 GHz leaky cable located in a circular tunnel,” inAsia Pacific Microwave Conf., 1995, pp. 163–165.

[24] K. K. Mei and J. Fang, “Superabsorption—A method to improve ab-sorbing boundary conditions,”IEEE Trans. Antennas Propagat., vol. 40,pp. 1001–1010, Sept. 1992.

[25] R. E. Collin,Foundations for Microwave Engineering. New York: Mc-Graw-Hill, 1992, ch. 5 and 8.

[26] M. Guglielmi and D. R. Jackson, “Broadside radiation from periodicleaky-wave antennas,”IEEE Trans. Antennas Propagat., vol. 41, pp.31–37, Jan. 1993.

[27] K. S. Yee, “Numerical solution of initial boundary value problems in-volving Maxwell equations in isotropic media,”IEEE Trans. AntennasPropagat., vol. AP-14, pp. 302–307, May 1966.

[28] G. Mur, “Absorbing boundary conditions for the finite-difference ap-proximation of the time-domain electromagnetic-field equations,”IEEETrans. Electromagn. Compat., vol. EMC-23, pp. 377–382, Nov. 1981.

[29] C. T. Tai, Dyadic Green Function in ElectromagneticTheory. Piscataway, NJ: IEEE , 1994, ch. 7.

[30] J. H. Wang, “Theory and Design of the Synthesizing Leaky Coaxial-Op-tical Cables,” Northern Jiaotong University, Beijing, China, Tech. Rep.Postdoctoral Works, 1996.

Jun Hong Wang (M’02) was born in Jiangsu, China,in 1965. He received the B.S. degree and the M.S. de-gree, from the University of Electronic Science andTechnology of China, Chengdu, and the Ph.D. de-gree, from Southwest Jiaotong University, Chengdu,China, all in electrical engineering, in 1988, 1991,and 1994, respectively.

Since 1999, he has been a Professor with theInstitute of Lightwave Technology, NorthernJiaotong University, Beijing, China. From January1999 to June 2000, he was a Research Associate in

the Department of Electronic Engineering, with the City University of HongKong, Hong Kong, China. His research interests include numerical methods,numerical simulation of microwave circuit components, antennas, scattering,and leaky wave structures.

Kenneth K. Mei (S’61–M’63–SM’76–F’79–LF’98)received the B.S.E.E., M.S. and Ph.D. degreesin electrical engineering from the University ofWisconsin, Madison, in 1959, 1960, and 1962,respectively.

In 1962, he joined the Department of ElectricalEngineering and Computer Sciences University ofCalifornia, Berkeley, where he became a Professorin 1972. In 1992, he also became a Professor ofBuddhist Study at Berkeley. He is now an EmeritusProfessor with the University of California at

Berkeley. Since 1994, he has been a Professor the with the Department ofElectronic Engineering of the City University of Hong Kong. Since 1998, hehas been the Director of the Wireless Communication Research Center of theCity University of Hong Kong and began his research in electromagneticsin the area of computation, which includes, the method of moments, finiteelement/difference, hybrid methods, time domain methods and most recently,the measured equation of invariance.

Dr. Mei received the Best Paper Award in 1967 and Honorable Mention ofthe Best Paper Award in 1974 from the IEEE Antennas and Propagation Society.He is a member of URSI/USNC.


theory and analysis of leaky coaxial cables with periodic slots

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