FULL-WAVE ANALYSIS OF SCATTERING FROM A STUB-LOADED
MICROSTRIP PATCH ANTENNA
Sachendra N. Sinha
Department of Electronics & Computer Engg.
Indian Institute of Technology, Roorkee-247667
INDIA
Pujara Dhaval Kumar
Department of Electronics & Communication Engg.
Nirma Institute of Technology, Ahmedabad-382481
INDIA
Abstract: -The design of a microstrip reflectarray requires precise prediction of the phase and amplitude of the field scattered by either an unloaded patch or a stub-loaded patch. In this paper, we present a full-wave formulation, using sub-domain expansion functions and spectral-domain Green’s functions, for a rectangular patch loaded with a T-shaped stub. The formulation is general in the sense that it can be used to analyze an unloaded patch and a patch loaded with either a linear or L-shaped or T-shaped stub. Numerical results on the radar cross-section (RCS) are presented for various geometries as a function of frequency and angles of incidence. The effect of various parameters, such as, dielectric constant, substrate thickness, on the scattering properties of the patch is also discussed.
Key-Words: - Microstrip reflectarray, Microstrip antennas, Stub-loaded patch antennas
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1.Introduction
The increasing demands of satellite and space communication systems and the approaching maturity in the field of microstrip antenna design, has given rise to a novel antenna concept known as microstrip reflectarray [1]-[3]. This antenna combines some of the best features of the reflector antennas and the phased arrays and is specially attractive for space applications, in view of its light weight and easy deployment mechanism. It consists of a flat array of microstrip patches, illuminated by a primary feed, giving rise to a flat reflector surface in which the feed system losses of a conventional array are eliminated. A planar phase front in front of the aperture is obtained by adjusting the phase of the field scattered by the individual patches of the array. Two methods are generally used to control the phase of the scattered field. One method is to utilize linear or L-shaped stubs of variable lengths and the second is to utilize patches of variable size. Thus, an inherent requirement for microstrip reflectarray synthesis is the accurate knowledge of the scattering properties of a patch with and without stubs. However, very little or no data is available in the open literature on the scattering properties of a stub-loaded patch.
In this paper, we present a full-wave analysis of a rectangular patch antenna loaded with a T-shaped stub. The formulation is general in the sense that it can be used to analyze an unloaded patch, patch with a linear stub, patch with an L-shaped stub and the patch with a T-shaped stub.
2. Problem Formulation
The top view of the geometry of the problem considered is shown in Fig.1. Here we have chosen the microstrip antenna, loaded with a ‘T’ shaped stub Thus, the same antenna structure can be used to find scattering from a linear-stub loaded microstrip patch, ‘L’ shaped stub loaded microstrip patch, and the patch with a T-shaped stub, just by changing the size of different arms of the ‘T’ shaped stub. The entire structure can be divided in to three parts, namely, the surface S1 of the patch, the surface S2 of the linear stub attached to a radiating edge, and a surface S3 representing the T-arm of the stub. The surface S2 includes the attachment regions, shown by dotted lines, where the linear stub is connected with the patch and the T-arm. These attachment regions have been shown to extend into the surfaces S1 and S3 and have been included to enforce current continuity at the two junctions. The reason for adding attachment regions is to maintain the current continuity at the junction points.
Attachment regions
T-shaped stub
patch
(Surface S1)Surface S3
Surface
S2 Surface S2
T-shaped
y Stub
x (Surface S3)
Fig. 1 Problem Geometry
The entire stub loaded microstrip patch is assumed to be excited by an incident plane wave of unit amplitude. All fields and currents are time harmonic with the ejwt time dependence suppressed. The total fields on the whole antenna structure (are the vector sum of the incident fields (and the scattered fields due to current on S1,on S2, and on S3. The following equations may thus be written:
(1)
(2)
Enforcing the boundary condition that the tangential component of the total electric field be zero on the conductor, we obtain the operator equation
(3)
over S, where S S1, S2, S3
Following the moment procedure, (3) can be reduced to matrix form
(4)
where the matrix [Zpq] represents the coupling between regions Sp to Sq, p,q = 1,2,3.
Computation of various elements of the submatrices in (4) has been carried out using rooftop functions and the spectral domain dyadic Green’s function for an electric current element located on a grounded dielectric slab [2].
3.Computation of Radar Cross-section
The scattering behaviour of a stub-loaded microstrip patch is described in terms of its Radar Cross Section (RCS). It is defined as [4]
(5)
(6)
Where are the -polarized and -polarized scattered fields. In (5) and (6), the scattered field can be calculated by a summation of the radiated field from each mode on the antenna structure. Mathematically this can be written as,
(7)
Where En is the field from the nth expansion mode
In is the nth current co-efficient.
4. Results and Discussion
Using the formulation presented in the previous sections, a detailed numerical study has been carried out on unloaded and stub-loaded patch antennas. Radar cross-section(RCS) has been computed as a function of angle of incidence, relative dielectric constant, and substrate thickness. In this section, we present some typical results, which establish the accuracy of the present method. All results have been obtained by selecting suitable number of expansion function required to achieve convergence.
Fig. 2 shows the variation of RCS of an unloaded rectangular patch as a function of frequency. The parameters of patch were: L = W = 1.5 cm, substrate thickness d = 0.787 mm, r = 2.33, tan = 0.001, angle of incidence (, ) = (60, 180). The peak value of RCS is seen to occur at 6.4 GHz and 12.6 GHz, which correspond to the first and second resonance of the patch.
Also shown in the figure are the computed and measured results by Shivley and Bailey [5]. A good agreement can be observed.
Next, we have studied the variation of RCS with the angles of incidence and . Fig. 3 and 4, respectively, show and as a function of for various values of . For this study, the antenna parameters used are: L= 2.6 cm, W = 3.66 cm, d = 0.158 cm, r = 2.17 = 60, and = 45. These figures show that the RCS is a very strong function of angles of incidence. Therefore, in the design of a reflectarray using patches of variable size, the effect of feed location will greatly influence the patch design.
The effect of substrate thickness and r has also been studied for various patch sizes and angles of incidence. The detailed results can be found elsewhere [6].
A comprehensive study has been carried out on a stub-loaded antenna and the results are available in [6]. Here we present only some typical results for a patch antenna loaded with a linear stub on one of its non-radiating edges. Figs. 5-6 present the RCS of a rectangular patch antenna for different stub lengths. The patch used is same as that used in the study presented in Figs.3-4.
In Fig. 6, we have included the data of Metzler and Schaubert [7] for comparison. These authors have used entire-domain basis functions to analyze the problem. It is found that their results show a false peak around a frequency of 2.8 GHz, which should not have been there. It clearly shows a limitation of their method. Since the sub-sectional domain basis functions used by us can represent the patch current more accurately, this type of false peak does not appear in our results.
5. Conclusion
A comprehensive investigation on an unloaded and a stub-loaded patch antenna has been carried out using a full-wave technique. Rooftop functions have been used, which can represent the patch current with a high degree of accuracy. This analysis can be used to generate the scattering data required in the design of microstrip reflectarrays.
References:
[1]S.D. Targonski and D.M. Pozar, Analysis and design of a microstrip reflectarray using patches of variable size, Digest ofIEEE Symposium on Antennas and Propagat., vol. 3, 1994, pp. 1820-1823.
[2]R.D. Javor, X.D. Wu, and K. Chang, Design and performance of a microstrip reflectarray antenna, IEEE Transac. on Antennas and Propagat., vol. AP-43, 1995, pp. 932-938.
[3]J. Huang and R.J. Pogarzelski, A Ka band microstrip reflectarray with elements having variable rotation angles, IEEE Transac. on Antennas and Propagat., vol. AP-46, 1998, pp. 650-656
[4]D. G. Shivley and M.D. Deshpande, Scattering from arbitrarily shaped microstrip patch antennas, Electromagnetics, vol. 14, 1984, pp. 1-18.
[5]D.G. Shiveley and M.C. Bailey, Analysis of microstrip patch antennas with nonzero surface resistance, NASA Technical Paper, No. 220733, 1993.
[6]Pujara Dhaval Kumar, Scattering from a stub-loaded microstrip patch antenna, M.Tech. Dissertation, 2003.
[7]T. Metzler and D. Schaubert, Scattering from a stub-loaded microstrip antenna, Digest of IEEE Internat. Symp. on Antennas & Propagat., vol.1, 1989, pp. 446-449.
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