Synthesis of a Travelling Wave Slotted Substrate Integrated Waveguide (SIW) Array with Dual-Circular Polarization

Songnan Yang1, Aly E. Fathy1 and Shady Suleiman2

1EECS department, University of Tennessee, Knoxville; 2Winegard Company, Burlington Iowa

Abstract— SIW slot array antennas fed by emulated waveguide feed structure have lower insertion loss when compared to planar printed antennas. They are easy to manufacture, have light weight, and their use should lead to a lower cost fabrication as well. A synthesis procedure for the SIW antenna design is introduced, where the optimum slot parameters and the number of slots per radiating SIW can be optimized for a given beam tilt angle. Slots are designed to provide specific coupling factors that are determined numerically using an approximate step-by-step design recipe. The coupling is a function of slots dimensions, slots spacing, and beam tilt angle. A full array prototype with 32 radiating SIW guides with 13 "X" shaped slots, and a folded feed network have been developed. The feed network of this multi-layer slot array has been tapered to maximize the antenna efficiency and lower the side lobe level.

Index Terms — SIW, Travelling wave antenna, Slot array

I. INTRODUCTION

Travelling wave slot array antennas’ main beam radiation is off-broadside and can be designed for circular polarization with relatively low axial ratio [1]. For a specific tilt angle, the slots’ spacing and aperture distribution can be tailored to achieve a desirable balance between antenna gain and side lobe level. In this paper, optimum slot length and spacing for a given number of slots per radiating SIW and tilt angle are derived numerically using an approximate design recipe. A design example following these design steps is developed, where given a fixed array size and the beam tilt angle; an optimum slot length, spacing, and number of slots are selected. A tapering of the slots is implemented to control the coupling factors to the slots to achieve a low side lobe level while maintaining almost the same gain. A 32 element SIW slot array has been developed and its radiation pattern is measured using near field measurement setup and will be presented.

II. DUAL CIRCULAR POLARIZATION DESIGN

The developed slot array has "X" shaped slots that are densely arranged on the broad wall of the radiating guides. For low cost implementation, SIW is utilized where slots are accurately defined using chemical etching to form a leaky waveguide that radiates a circular polarization at the main beam with a large tilt angle that can be controlled. The radiated beam for the dielectric loaded waveguide slot antenna is backward as shown in Fig. 2 (b) (i.e. obtuse angle to the direction of traveling wave), and would provide a dual circular polarization depending on the port of excitation. Our SIW

design is based on analyzing an equivalent conventional dielectric loaded rectangular waveguide of the SIW guide.

Fig.1 Photo of 32x13 elements dual-circular slotted SIW array

III. ANALYSIS OF TRAVELLING WAVE SLOTTED SIW ARRAY

A. Single element design

The pair of the X-slots on the broad wall of the rectangular guide would produce orthogonal currents with the same magnitude and quadrature phase if placed at specific off-axis locations and can produce circularly polarized radiation [2]. The length of these slots can be used to control the amount of radiated power. Such slot pairs can have any orientation. But, it is more convenient to rotate them by 45º degrees in order to allow defining relatively long slots.

Fig. 2 (a) Single element Design Parameters (b) Array configuration and LHCP and RHCP beam tilt angle vs. feed port

In our implementation, a 3.175mm (125mil) thick Rogers RT/Duroid 5880 substrate is used and gold-platted via holes are utilized to emulate the SIW structure. Fig. 2(a) shows the radiating element dimensions, where the width of the SIW “L3“ is 14.2 mm, its vias have a diameter of 1.27mm and 2.54mm spacing, which surmount to an equivalent waveguide width "aeq" of 13.5 mm according to [3]. The offset of the slots

(a)

� �

LHCP from Port 1

RHCP from Port 2

Port 2

Rotating Direction

Port 1

(b)

L

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from the SIW axis OO' is S1 = 2.29 mm to obtain circular polarization radiation. The slot width was fixed at S2=1.27mm, but the total length of each unit cell (also known as the element spacing between slots) is “L “, and its length lneed to be determined.

B. Beam Tilt Angle Control

It is well known that for an infinite leaky wave array (with low leakage factor per radiating element), the beam tilt angle can be directly calculated from the ratio of free space wave number (k0) and guided wave number (�z) [4]. However, in our case, each of these slots need to radiate a large fraction of the power passing by it, or in other words, having a relatively strong leakage/coupling coefficient [5]. Such coupling disturbs the fields’ distribution of the wave traveling inside the waveguide, and introduces sudden jumps of the phase to both the radiated wave (Pr) outside the waveguide and the travelling wave (Pt) inside the waveguide.

Fig. 3 Phase diagram to determine beam tilt angle θ

As depicted in Fig. 3, for a backward radiating travelling wave array, the differential phase difference between the radiated fields from adjacent radiating elements is 2�. In this case, at the center frequency, the tilt angle (as shown in Fig. 2(b)) relationship can be simplified as:

21sin 1

2 2t

rP

L aλ λθ ε

π� � � �= − − − � �� �

� �� � (1)

where � indicates free space wavelength and �r represents the dielectric constant of the filling dielectric, i.e. the substrate, Prand Pt represents the phase change of the radiated and travelling waves caused by these slots respectively. Obviously, the beam tilt angle θ is a function of the operating frequency and at higher frequencies, it decreases (moving toward zenith) and vice versa.

The change of the Pt phase due to the pair of slots, with certain slot length l and spacing L, is estimated using (2) by calculating an average of the phase advances for each unit cell using HFSS along the shown d-lines in Fig. 4, where �zl is the loaded guided wave number.

( )1

1

1, arg argn n

N

zl t zn d d

L P l L L E dy E dyN

β β+

=

� � � � � �⋅ = + ⋅ = ⋅ − ⋅� � � �� � � � �� � � ��

� � ��� �� (2)

Fig. 4. Simulation setup for determining the phase change

The simulated results of the beam tilt angle � of the slotted SIW array with the current design parameters are shown in Fig 5, where the contours of the constant beam tilt angle values are depicted against various elements spacing L and slot length l.

40

40

45

45

45

50

50

50

55

55

Slot Length l (mils)275 280 285 290 295 300 305 310

Elem

ent S

paci

ng L

(mils

)

435

440

445

450

455

460

465

470

475Beam Tilt Angles θ

Fig. 5 Constant beam tilt angle contours of travelling wave slotted SIW array with various slot length and spacing combinations

C. Evaluation of the coupling factor and Slot Design

0.0

0.1

0.2

0.3

0.4

0.5

282288

294300

306312

2 4 6 8 10 12

Cou

plin

g Fa

ctor

α(n

)

Slot Lengthl (m

ils)

Slot Number

0.1 0.2 0.3 0.4 0.5

Fig. 6 Variation of the calculated slot coupling factor for a traveling wave slot array with uniform slot length

To design the slots, the coupling factors for a wide range of slot dimensions were calculated numerically using HFSS through the evaluation of the aperture field intensity in a traveling wave array. Simulation results of the power coupling

Incident Wave

Slot spacing L Pt1 Pt2

Pr1 Pr2

Beam Direction �

L·sin�

Free Space

SIW

k0

�z

2�/k0

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factor of a thirteen element slot array are plotted in Fig. 6. For constant coupling, the slot dimensions are different along the array.

Meanwhile, to achieve maximum antenna efficiency, a specific coupling factor is required for each slot element. The contour of constant slot coupling factor is plotted in Fig. 7, optimum combination of the slot length and the element spacing can be found in the close neighborhood of the intersection between the constant 45° beam tilt (from Fig. 5) and the constant coupling factor contours as shown in Fig. 7.

Fig. 7 Overlay of constant beam tilt angle and constant slot coupling factor contours for optimum performance.

IV. Design Example

According to Fig. 7, the configuration with 13 radiating slots gives an overall length close to our design height goal of 6 inch. So for the folded feed network design (as shown in Fig. 1), a slotted SIW radiating element with 13 "X" shaped slots is selected. Similarly, the average slot length of 297mil is depicted from Fig. 7.

A tapering of the slot length is also applied to the design such that the overall radiation pattern has low side lobe in the elevation cut. The optimized slot length selection for the design is shown in Table 1.

TABLE I OPTIMIZED SLOT LENGTH DISTRIBUTION Slot

Numbers 1,13 2,12 3,11 4,10 5,9 6,8 7

Slot Length (mil) 276 279.5 287.5 298 302.5 299.5 297

The radiation patterns of the fabricated array (shown in Fig. 1) have been measured over the 12.2 GHz-12.7 GHz using near-field measurements and its performance at 12.45 GHz is shown in Fig. 8. The side lobe levels in the elevation cuts have been maintained at levels better than 17dB down from the peak radiation which is a result of the slot length tapering. Due to the relatively highly efficient feed network, the gain of the LHCP radiation is 26.1, 26.5 and 26.4dBi for 12.2, 12.45, and 12.7 GHz respectively.

Fig. 8 Radiation patterns in the EL and AZ planes.

V. Conclusion

A synthesis procedure for travelling wave slotted SIW array design is introduced, where the optimum slot parameter combination and number of slots per radiating SIW can be numerically derived for a given beam tilt angle and slot coupling factor using a step-by-step approximate recipe. Slot lengths tapered with optimum distribution can provide almost the same gain and significant improvement in side lobe levels as compared to the uniform slot array.

REFERENCES

[1] W. J. Getsingger,”Elliptically Polarized Leaky-Wave Array” March 1962, IRE Trans. Antennas and Propagat, pp. 165-171.

[2] A. J. Simmons, “Circularly Polarized Slot Radiators,” IRE Trans. Antennas and Propagat, pp. 31-36, Jan. 1957.

[3] S. Yang and A.E. Fathy, “Synthesis of an Arbitrary Power Split Ratio Divider Using Substrate Integrated Waveguide,” in Proc. IEEE MTT-S Int. Microwave Symp., Jun. 2007, pp. 427-430

[4] R. S. Elliot, H. L. Krauss, Antenna Theory and Design (Revised Edition) s.l., New York: J. Wiley & Sons, 2003.

[5] K. Sakakibara, Y. Kimura, J. Hirokawa, M. Ando, N. Goto. “A Two-Beam Slotted Leaky Waveguide Array for Mobile Reception of Dual-Polarization DBS.” IEEE Trans. Vehicular Tech., Vol. 48.January 1999

978-1-4673-2141-9/13/$31.00 ©2013 IEEE