Linear Dielectric Resonator Antenna Array Fed by Dielectric Image Line Asem Al-Zoubi*, Ahmed Kishk, and Allen W. Glisson Department of Electrical Engineering, Center for Applied Electromagnetic Systems Research, University of Mississippi, University, MS 38677
[email protected],
[email protected],
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1. Introduction An array of DRAs must have a specific phase and amplitude distribution in order to maximize the gain or reduce the sidelobe levels. Several types of feeding have been used to feed a linear array of DRAs to achieve these objectives, such as microstrip lines [1], coplanar waveguide [2], slotted waveguide [3], and dielectric image line [4]. Since microstrip feed lines have high conductive losses, and surface modes could be excited that affect the gain of the antenna at high frequencies, dielectric image lines (DILs) can be used to avoid these losses. This paper presents a linear dielectric resonator antenna array fed by dielectric image line. The effective dielectric constant (EDC) [5-6] is used to approximate the coupling between the DIL and the DRAs. A Dolph-Chebyshev amplitude distribution is used to control the sidelobe level of the array radiation pattern. From the amplitude coefficients the separation between the DIL and each DRA is obtained. The cross polarization is suppressed using two methods: by inserting a metal sheet [7] at the center of the DRA normal to the propagation direction of the wave in the DIL, or by wrapping a conducting strip around the DRA at the center. The cross polarization in this case is suppressed without affecting the co-polarized radiation pattern. 2. Configuration of the DIL Feed line The dielectric image line of Fig. 1 has dimensions ad = 0.9 mm, bd = 5 mm, and εr2 = 10.2. In order to excite the DIL, the DIL is tapered and connected to the rectangular waveguide as shown in Fig. 1. The dimensions used are given in the caption of Fig. 1. The total length of the DIL is about 16 wavelengths. The transmission coefficient and return loss for the DIL side are shown in Fig. 2. From the figure it can be seen that the system with that transitions and a DIL 16 wavelengths long at 10 GHz has a total insertion loss of about 1.43 dB and the return loss is below the 10 dB level. 3. Coupling between the DRAs and the DIL The array is designed to operate at 10 GHz. 15 DRA elements with the same dimensions are used. The separation between elements is 23.5 mm. The parameters of the DRA are: LDRA = 11 mm, a = 0.9 mm, b = 5 mm, and εr1 = 10.2. The effective dielectric constant (EDC) method can be used to obtain the coupling between two identical DILs as shown in Fig. 3. Applying the boundary conditions we obtain the following set of equations:
bd k z =
nπ − tan −1 {k z ε r 2 k z 0 } , with k z20 = k02 [ε r 2 − 1] − k z2 and k x2 = β 2 = ε r 2 k02 − k z2 − k y2 , 2
978-1-4244-2042-1/08/$25.00 ©2008 IEEE
2 2 2 ad k y = ( mπ 2 ) − (1 2 ) tan −1 {k y k y 0 } + tan −1 {Dk y k y 0 } , with k y 0 = k0 [ε rez − 1] − k y ,
{
(
)
(
)
}
and D = tanh ck y 0 for odd modes and coth ck y 0 for even modes , where kz, ky, kz0, and ky0 are transverse propagation constants inside and outside the guide, respectively. The length Lc for complete transfer of power from one guide to the other is Lc = 2 ( βe − βo ) = 2 ( kxe − k xo ) . If the second DIL (in our case this is a DRA with the same height and width as the DIL) has a length LDRA, then the power coupled to the DRA is given by N PDRA PDIG ≈ sin 2 (π LDRA 2 Lc ) and PDRAn Pin = (1 − [ Pout Pin ]) An2 ∑ Am2 m =1 where Pin is the input power in the DIL and Pout is the remaining power transmitted in the DIL at the end of the DRA array [7]. Table 1 displays the coefficients An obtained by Dolph-Chebyshev amplitude distribution for a sidelobe level of 40 dB, the power Pn which is a fraction of the power coupled from the DIL into the DRA, and the required spacing S = 2(c+a) between the DRAs and the DIL. 4. Results and Discussion The geometry shown in Fig. 4(a) is simulated using HFSS commercial software [8]. The return loss is shown in Fig. 4(b). It can be seen that the return loss is below 10 dB. The E-plane and H-plane radiation patterns for this array are shown in Fig. 5. The cross polarization is very high in this case because of the hybrid nature of the fields inside the DIL, so other modes are excited in the DRA. Two methods can be used to eliminate these additional modes in which the cross polarization is reduced without changing the copolarization patterns. The first method is by inserting a metal sheet at the center of the DRA perpendicular to the x-axis as shown in Fig. 6(a). The resulting cross polarization patterns are shown in Fig. 6(b). The reduction in cross polarization is about 25 dB. The practical problem with this method is the difficulty of inserting the sheet inside the DRA. The second method, which is easier to implement, is to wrap a conducting strip around the DRA at the center as shown in Fig. 7(a). The cross polarization level is reduced about 20 dB in this case as shown in Fig. 7(b). 5. Conclusions A linear dielectric resonator antenna array fed by dielectric image line is presented. The effective dielectric constant method is used to approximate the coupling between the DIL and the DRAs. A Dolph-Chebyshev amplitude distribution was used to control the sidelobe level of the array radiation pattern. The cross polarization is suppressed by inserting a metal sheet at the center of the DRA or by inserting a microstrip line around the DRA at the center. References [1] A. Petosa, A. Ittipiboon, M. Cuhaci and R. Larose, “Bandwidth improvement for a microstrip-fed series array of dielectric resonator antennas,” Electronics Letters, Vol. 32, No. 7, Mar. 1996, pp. 608 – 609. [2] R. Q. Lee and R. N. Simons, “Bandwidth enhancement of dielectric resonator antennas,” IEEE Antennas and Propagation Society International Symposium, vol. 3,
July 1993, pp. 1500-1503. [3] I. A. Eshrah, A. A. Kishk, A. B. Yakovlev, A. W. Glisson, “Theory and implementation of dielectric resonator antenna excited by a waveguide slot ,” IEEE Transaction on Antennas and Propagation, Vol. 44, No. 53, Jan. 2005, pp. 483-494. [4] A. S. Al-Zoubi, A. A. Kishk, and A. W. Glisson, “Analysis and Design of A Rectangular Dielectric Resonator Antenna Fed by Dielectric Image Line Through Narrow Slots, ” Progress In Electromag. Research , PIER 77, pp.379-390, 2007. [5] P. Bhartia and I. Bahl, Millimeter-Wave Engineering and Application, Wiley, 1984. [6] R. M. Knox and P. P. Toulios, “ Integrated circuits for the millimeter through optical frequency range,” Proc. Symp. Submillimeter Waves, 1970, pp. 497-516. [7] M. W. Wyville, A Petosa, and J. S. Wight, “DIG Feed for DRA Arrays,” IEEE Antennas and Propagation Society International Symp., pp. 176 – 179, July 2005. [8] HFSS: High Frequency Structure Simulator Based on Finite Element Method, v.10.0, Ansoft Corporation, 2005.
εr2
A
2ad
B
εr2
bd
L L1 Top view side view (a) DIL excited by a waveguide (b) transition from waveguide to DIL Fig. 1. Geometry of the DIL and the transition from rectangular waveguide to DIL with A = 22.86 mm, B = 10.16 mm, L1 = 27.5 mm, and L = 24.5 mm. 0
0
-2
-10
S
S
21
11
-4
-20
-6
-30
-8 with dielectric loss without dielectric loss -10 8.5
9
9.5
10 10.5 Frequency (GHz)
11
-40 8.5
11.5
9
9.5 10 10.5 Frequency (GHz)
11
11.5
(a) (b) Fig. 2. (a) Transmission coefficient and (b) return loss of the DIL excited by rectangular waveguide. n 1 2 3 4 5 6 7 8
An 0.112 0.205 0.353 0.526 0.703 0.857 0.962 1.000
PDRA/Pin
0.162 0.542 1.602 3.560 6.358 9.448 11.90 12.84
Pn % S(mm) 0.163 13.0 0.547 12.5 1.634 11.6 3.706 10.0 6.902 8.85 11.06 7.97 15.74 7.31 20.24 6.84
n 9 10 11 12 13 14 15
An 0.962 0.857 0.703 0.526 0.353 0.205 0.112
PDRA/Pin
11.90 6.448 6.358 3.560 1.602 0.542 0.162
Pn % 23.62 24.64 22.10 15.95 8.580 3.187 0.989
Table 1: Required amplitude and power distribution for 15-element Array.
S(mm) 6.55 6.47 6.68 7.28 8.44 10.3 12.0
2ad bd
+
Z 2c
2ad ¯
Z 2c
2ad Y
bd
+
(a) Fig. 3. Coupler configuration for (a) odd and (b) even modes.
2ad Y
+ (b)
0
S11
-10
-20
-30
-40 8.5
9
9.5 10 10.5 Frequency (GHz)
11
11.5
(a) (b) Fig. 4. (a) Geometry of the 15 elements DRA fed by DIL and (b) simulated return loss.
(a) Co-polar (b) Cross-polar Fig. 5. Radiation patterns of the 15 elements DRA at 10 GHz.
(a) (b) Fig. 6. (a) DRAs with shorting plates (b) cross polarization pattern.
(a) (b) Fig. 7. (a) DRAs with microstrip lines wrapped around them (b) cross polarization pattern.
