Single-conductor strip leaky-wave antenna

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 7, JULY 2004 1783

Single-Conductor Strip Leaky-Wave Antenna

Wanchu Hong and Yu-De Lin

Abstract—This paper presents a leaky-wave antenna with only a single-conductor strip on a substrate without a practical ground plane. The full-wave integral equation method is used to investigate the EH₀₁ leaky mode of this single-conductor strip structure. When this single-conductor strip is on a thin substrate with a low dielectric constant, a broad-band radiation regime can exist for the EH₀₁ leaky mode. The balanced microstrip lines and the inverted balanced microstrip lines are used to excite thisEH₀₁ leaky mode. This work presents both the numerically simulated and measured data. The measured bandwidth of a voltage standing-wave ratio 2 is from 6.55–13.75 GHz (2.34:1). In this case, the normalized phase constant is very close to 1 and this results in a fixed main-beam radiation pattern in the end-fire direction. This leaky-wave antenna with only a single rectangle stripline of length 110 mm can achieve the same broad-band performance as a tapered microstrip leaky wave antenna with a length 310 mm, as previously reported by the authors.

Index Terms—Broad-band antenna, leaky-wave, microstrip line balun, single-conductor strip.

I. INTRODUCTION

T

HE EXISTENCE of the leaky modes on various open planar transmission lines such as the microstrip line, the slot line, the strip line, the coplanar waveguide and the coplanar strips, is well known and has received considerable attention [1]–[12]. This is owing to that inadvertent excitation of these leaky modes may incur undesirable radiation and crosstalk in microwave circuits. Most open transmission lines can be used as leaky-wave antennas based on the space-wave leakage of the higher order leaky modes [2]–[9]. For such planar open transmission lines, the space-wave radiation bandwidth of leaky modes is around 20% and is limited by the bandwidth of the feeding network and the dielectric constant of the substrate. For example, the center-fed aperture-coupled leaky wave microstrip antenna with a uniform strip width has a bandwidth of only 23% [6]. For wireless broad-band communication applications, a leaky-wave antenna with a wider radiation bandwidth could be useful. To enhance the bandwidth, a tapered microstrip leaky-wave antenna is developed in [7]–[9]. Because this broad bandwidth is a composition of several individual leaky-wave regimes radiated from different strip widths, the antenna length is much longer than a single uniform microstrip antenna [9].

This paper presents a novel leaky-wave broad-band antenna that has only a single conductor strip on a substrate but no ground plane. That absence of a ground plane allows both

Manuscript received October 24, 2002; revised June 9, 2003. This work was supported in part by the MOE Program for Promoting Academic Excellence of Universities under Grant 89-E-FA06-2-4 and in part by the National Science Council under Grant NSC-91-2213-E-009-130.

The authors are with the Institute of Communication Engineering, National Chiao Tung University, 300 Hsinchu, Taiwan, R.O.C.

Digital Object Identifier 10.1109/TAP.2004.829854

Fig. 1. Single-conductor strip structure. The substrate is denoted as Layer 1, while the air layers above and below the substrate are denoted as Layer 0 and Layer 2, respectively. The vertical plane denoted by dark dotted line indicates the virtual perfect electrical wall or perfect magnetic wall according to the odd or even modes analysis.

Fig. 2. Integral paths of the inverse Fourier transform on theky plane. : branch points;2: proper surface poles (TE , TM ); dashed lines: branch cuts; dashed-dotted line: path on the improper sheet.

and surface-wave modes to exist in this single-conductor strip structure, causing some interesting characteristics to be exhibited. The rest of this paper is organized as follows. Section II applies the integral equation method in the spectral

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1784 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 7, JULY 2004

Fig. 3. Normalized phase constant =k and the normalized attenuation constant 0=k of the EH leaky-wave mode of the single-conductor strip leaky-wave antenna (w = 20 mm, h = 0:508 mm, " = 2:2). Four points are indicated; the intercept point A: (=k ; freq) = (1:047; 4:0); crossing point B: (=k ; freq) = (1:000;4:5); minimum point C: (=k ; freq) = (0:9397; 6:3); end point D: (=k ; freq) = (1:000;13:7).

Fig. 4. Normalized phase constant =k and the normalized attenuation constant0=k of the first higher order leaky mode for different strip widths (h = 0:508 mm, " = 2:2).

domain and the method of moments to analyze this structure. The numerical results indicate that the leaky mode of this single-conductor strip structure on a thin substrate with a low dielectric constant has a broad-band radiation regime. Section III proposes a broad-band planar feeding structure to excite properly this leaky mode. This broad-band planar feeding structure consists of the balanced microstrip lines and the inverted balanced microstrip lines. Section IV presents the measurement results of this single-conductor strip leaky-wave antenna to verify the broad-band nature of the leaky mode.

II. ANALYSIS ANDNUMERICALRESULTS

Fig. 1 shows the structure of the single-conductor strip leaky-wave antenna. Only one perfect conducting strip of width is located at the interface between a semi-infinite air layer and an isotropic lossless substrate, with a dielectric constant of and a thickness of . In this structure, the strip is uniform

Fig. 5. Normalized propagation constant of the structure with" = 2:2 for different strip widths and substrate thicknesses. (a) The normalized phase constant (b) the normalized attenuation constant.

along the longitudinal directoin and no practical ground metal plane is placed on the substrate. This single-conductor strip structure is analyzed based on the integral equation formulation and the dyadic Green’s function in the spectral domain [4], [5]. A. Integral Equation Formulation

To simplify the analysis, the structure is assumed to be infi-nite in both the and directions, and the conducting strip is assumed to be infinitesimally thin, such that the surface current density on the strip has components in the and directions only. The structural symmetry is such that a wave’s propagation along such a structure can be expressed as even or odd modes corresponding to even or odd symmetry about the plane that can be replaced by a perfect magnetic or electric wall in the center of the conducting strip for the purpose of analysis. Hence, the lon-gitudinal currents on this strip are forced to be evenly or oddly symmetric according to which mode is under consideration.

For fields that propagate in the positive direction, the sur-face current can be expressed as

(1) where and represent the -directed and -directed currents, respectively. The complex propagation constant is

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HONG AND LIN: SINGLE-CONDUCTOR STRIP LEAKY-WAVE ANTENNA 1785

Fig. 6. Normalized propagation constant of the structure withw = 20 mm for different dielectric thicknesses and dielectric constants. (a) The normalized phase constant (b) the normalized attenuation constant.

, where is the phase constant and is the atten-uation constant. The terms and can be expanded approximately as linear combinations of known basis functions

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where and are unknown current coefficients. The choice of the expansion functions should correspond to the odd or even symmetry of the currents for the mode of interest. The electric field can be represented by a dyadic Green’s function and the surface current density on the strip as [4], [5]

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Fig. 7. Normalized propagation constants of the structure with the dielectric thicknessh = 0:508 mm for different strip widths and dielectric constants (a) the normalized phase constant (b) the normalized attenuation constant.

For this single-conductor strip structure, the dyadic Green’s function can be expressed as

(4) (5) (6) where is the wavenumber in free-space and is the wavenumber associated with the surface wave mode of the dielectric slab structure and and indicate the and directions, respectively. The Appendix lists the dyadic Green functions for . The other the dyadic Green functions are presented in . The complex propagation constant along the uniform strip can be determined by solving the determinant equation derived from the Galerkin moment method, under the boundary condition of a zero tangential electric field on the strip.

The choice of the integration path used to determine the com-plex propagation constant, , depends on the physical interpre-tation of the integration path since the path of integration is an

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Fig. 8. Current distributions of the first higher order mode at 10 GHz: (a) the longitudinal currents (b) the transverse currents (w = 20 mm, h = 0:508 mm, " = 2:2).

open contour in the plane from to [4], [5]. Both the and the surface wave modes exist for a dielectric slab structure, so two proper surface-wave poles of are present in the plane. As present in Fig. 2, the path is used to de-termine the solution for the leaky-wave mode that energy leaks into both the space wave and the surface wave [4], [5]. This path lies partly on the improper sheet of the plane in the region between the branch cuts and includes both proper surface-wave poles for the and the modes.

B. Numerical Results

Consider the single-conductor strip structure in Fig. 1, with a strip width of , a substrate of dielectric constant

of and a thickness of . Fig. 3 plots

the normalized phase constant and the normalized attenu-ation constant against the frequency of the leaky mode. As shown in the figure, the normalized phase constant declines from 1.22 at 3.0 GHz to a minimum of 0.9397 at 6.3 GHz, and then increases very slowly to 1 at 13.7 GHz. In the microstrip line structure, the leaky wave radiation begins at the frequency at which the real propagated power starts to ex-ceed the imaginary propagated power, and ends when

[5]. In this single-conductor strip structure, the intercept point

of is at 4.0 GHz, but at this

fre-quency, the normalized phase constant (and the attenua-tion constant ) exceeds not only unity one but also those of both the surface mode (1.0003) and the surface mode (1.0001). The space-wave radiation regime of this leaky-wave mode under the condition of is from 4.5 GHz to 13.8 GHz. Fig. 4 plots the normalized propagation constants of the leaky mode against frequency for strips of various widths. Because of the resonance of the transverse cur-rents, the leaky regime obviously shifts to a higher frequency for a narrower strip. Also, a narrower strip increases of the

attenu-Fig. 9. Diagram of the broad-band balun structure used to excite the first higher order leaky mode of the single-conductor strip antenna. This balun structure consists of a closed loop that connects back to the original ground plane (h = 0:508 mm, " = 2:2). This feeding structure consists of (i) a conventional microstrip line; (ii) a microstrip-to-balanced-microstrip-line transition; (iii) a balanced-microstrip-line T-junction power divider; (iv) one set of the balanced microstrip lines is changed to form the inverted balanced microstrip lines and returned back to the original ground plane of the microstrip line; (v) single-strip antenna. (a) On the upper substrate; (b) on the lower substrate side.

Fig. 10. Inverted balanced microstrip line. The length of the bent stubs:l = 1:60 mm and l = 2:75 mm; the gap width: l = 0:15 mm; the radius of vias is 0.3 mm; the slanted angle is 45 degrees. The black circles: the vias; the solid lines: the strips on the upper substrate side; dashed lines: the strips on the lower substrate side.

ation constant. When the thickness of the substrate increases, as in Figs. 5 and 6, the normalized phase constant in-creases, since the effective strip width is reduced by the fringing

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Fig. 11. Two pairs of the broad-band planar baluns on the upper and lower substrate sides, respectively.

Fig. 12. Measured return loss. Solid line: the back-to back feeding structure; dashed line: the inverted balanced microstrip line.

effect. As shown in Figs. 6 and 7, a substrate with a high dielec-tric constant will rapidly increase the normalized phase con-stant. If the normalized phase constant always exceeds unity one, the leaky wave radiation may not occur. Most of the en-ergy is focused under the strip when the dielectric constant is high or the substrate is thick. The energy leaks out to the air much more easily if the thickness or the dielectric constant of the substrate is lower or smaller. Increasing the dielectric con-stant of the substrate also increase the attenuation concon-stant. The attenuation constant of a thin substrate is less than that of a thick substrate but the difference is small. Fig. 8 plots the longitudinal and transverse current distributions of the leaky mode. On the conductor strip, the distributions of the longitudinal currents are in the opposite direction and those of transverse currents are in the same directions. These current distributions confirm that the mode is the mode, and help in designing an appro-priate feeding structure for this mode.

III. BROAD-BANDFEEDINGSTRUCTURE

A broad-band planar feeding structure based on the balanced microstrip lines and the inverted balanced microstrip lines is de-veloped to feed this single-conductor strip and thus excite the leaky mode. As shown in Fig. 9, gradually tapering the

Fig. 13. Measured return loss of the single-conductor strip antenna.

ground plane to a width equal to the strip width makes con-ventional microstrip line a balanced microstrip line, with a strip of positive voltage on the upper side of the substrate and a strip of negative voltage on the lower side of the substrate [8], [11]. The position of the positive strip on the upper side of the sub-strate of the inverted balanced microstrip line structure is ex-changed with that of the negative strip on the lower side of the substrate after a microstrip phase inverter illustrated in Fig. 10. Each of these positive and negative strips is terminated with a chamfered right-angled bend in an opposite direction. The sub-sequent strip is also headed with a chamfered right-angled bend but in the other direction. A slanted gap separates two strips on the same side of the substrate. The positive strip on the upper substrate side is connected vertically through a cylindrical via to the subsequent strip on the lower side of the substrate. The negative strip on the lower side is similarly connected to the subsequent strip on the upper side. Hence, the positions of the positive and negative strips alternate. The bent stubs , and on the upper and lower sides of the substrate, respectively, can be used to compensate for the reactance induced by the via holes and the slanted gaps, and may have different lengths. The details of the design method for such an microstrip phase in-verter structure are presented in [8]. Using a T-junction bal-anced-microstrip-line power divider with inverted balanced mi-crostrip lines substituted for balanced mimi-crostrip lines in one of the two output ports, two pairs of broad-band planar baluns can be formed as shown in Fig. 11. No background metal plane is located beneath the single-conductor strip, so the balun on the lower substrate side may be floating, resulting in a disturbed radiation pattern. Fig. 9 depicts a method for preventing such disturbed radiation. The strips of the balun on the lower side of the substrate are connected to each other and returned back to the original ground plane of the microstrip line. Hence, only the balun on the upper side of the substrate feeds the single-con-ductor strip and a closed metal loop is formed on the lower side of the substrate. On this closed metal loop, two semicir-cles beneath the two feeding strips are etched out with diam-eters equal to the widths of the feeding strips, respectively, to enhance the electrical field transition from feeding points to the single-conductor strip. Fig. 12 indicates that the back-to-back measured bandwidth of this feeding structure exceeds 6:1 from 2.5–15.2 GHz for a voltage standing-wave ratio (VSWR) .

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Fig. 14. Measured copolarization and cross-polarization radiation patterns of (a) H plane (x 0 z plane) and (b) E plane (x 0 y plane) E fields at 11 GHz.

IV. PERFORMANCE OFANTENNA

Careful attention is paid to the feeding points on the edge of strip to exploit the leaky-wave bandwidth as much as possible. As shown in Fig. 9, the feeding points are offset from the edges by 3.485 mm. Fig. 13 presents the return loss of a single-conductor strip leaky-wave antenna with a strip width of

and a length of 110 mm, on a substrate with a dielectric

constant of and a thickness of . This

antenna has a from 6.55–13.75 GHz, yielding a relative bandwidth of 2.1:1, more than an octave. This measured data justifies the classification of this antenna as a broad-band antenna [12]. Fig. 14 presents the measured copolarization and cross-polarization radiation patterns of the H plane ( plane) and the E plane ( plane) fields at 11 GHz. The

Fig. 15. Measured copolarization patterns of (a) H plane (x 0 z plane) and (b) E plane (x 0 y plane) E fields at 9 and 12.4 GHz.

cross-polarization level of the E plane radiation pattern is relatively large compared to that of the H plane radiation pattern. The copolarization patterns of the H plane ( plane) and the E plane ( plane) fields at 9 and 12.4 GHz, as shown in Fig. 15, have peak gains of 9.03 and 8.22 dBi, respectively. According to Fig. 3, the value of the normalized phase constant ranges from 0.94–1.0 in the space-wave leaky regime; the radiation pattern is almost in the endfire direction and has a fixed mainbeam in the far-field region. For the same radiation bandwidth, this single-conductor strip leaky-wave antenna, with a length of 110 mm, is much shorter than the broad-band tapered microstrip leaky-wave antenna, which is 310 mm long [9].

V. CONCLUSION

This paper describes the basic characteristics of the leaky-wave mode of the single-conductor strip structure. Both

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surface wave modes and exist in the single-con-ductor strip structure, so the behavior of the space-wave and surface-wave modes differs from that of open transmission lines covered with ground planes, and so needs further investigation. A broad-band feeding structure is developed and a feeding method is also proposed to excite this leaky mode. The measured results of return loss and radiation patterns reveal the broad-band characteristics of the structure.

APPENDIX

The dyadic Green functions of the single-conductor strip structure for are listed as follows:

(A-1) (A-2) (A-3) (A-4) (A-5) (A-6) (A-7) (A-8) (A-9) (A-10) (A-11) (A-12) (A-13) (A-14) (A-15) (A-16) ACKNOWLEDGMENT

The authors would like to thank Dr. T.-L. Chen and Dr J.-W. Sheen for their valuable discussions.

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Passive Structure. New York: Wiley, 1989, ch. 3 and 5.

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Wanchu Hong received the B.S. degree in electrical

engineering from Feng Chia University, Taiwan, R.O.C., in 1992 and the M.S. degree in electronic engineering and the Ph.D. degree in communication engineering from the National Chiao Tung Univer-sity, Hsinchu, Taiwan, R.O.C., in 1994 and 2002, respectively.

From 1994 to 1996, he was a Second Lieutenant in the Army. In 1996, he joined the TECOM Com-pany where he was involved in RF circuit design. His research interests include computational electromag-netics, antenna theory and communication circuit design.

Yu-De Lin received the B.S. degree in electrical

engineering from National Taiwan University, R.O.C., in 1985, and the M.S. and Ph.D. degrees from the University of Texas at Austin, in 1987 and 1990, respectively.

In 1990, he joined the faculty of the Department of Communication Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C., where he is cur-rently a Professor. His current research interests in-clude characterization and design of microwave and millimeter-wave circuits and analysis and design of microwave and millimeter-wave antennas.