Microstrip Antenna RCS Calculation

When using the moment method based on the hybrid potential integral equation to analyze the RCS of microstrip antennas, the two-level discrete complex image method is first used to solve the spatial Green's function, which greatly improves the calculation efficiency of the moment method. Then, the triangular mesh is used to divide the calculation target, which also makes the moment method more suitable for analyzing complex structures. The calculation results of this method are also consistent with those of related literature, which verifies the efficiency and correctness of this method.
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Keywords：MoM;discrete complex image method;microstrip antenna;RCS ?

Calculations of Microstrip Antenna RCS
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SHI Lei,DONG Xu,JIAO Yi? (Xi′an Communication Institute,Xi′an,710106,China)
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Abstract：In analyzing the RCS of microstrip antennas by MPIE-MoM,the two-level approximation discrete complex image method is applied to obtain spatial-domain Green′s function,which enhance computing efficiency.Triangular facets are used to approximate the surface of object.Hence the MoM is suitable to analyze complex structure.The result is as the same as the document given,so the method in this text is fast and right.
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Keywords：MoM;discrete complex image method;microstrip antenna;RCS
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Microstrip antenna has many advantages such as small size, light weight, low cost, easy wide-angle scanning, and can be conformal to the aircraft surface. It has broad application prospects. Therefore, research on microstrip antenna has received more and more attention. At present, one of the main methods for studying the radiation and scattering of microstrip antennas is to use the spatial moment method based on the hybrid potential integral equation. This method uses the two-level discrete complex image method [2] based on the generalized function bundle method (GPOF)?? [1] to calculate the spatial Green's function under the microstrip structure, avoiding the extraction of surface wave terms and quasi-dynamic terms, greatly improving the calculation efficiency of the moment method, and using the RWG basis [3] as the basis function of MoM, so that this method can well segment the surface of large microstrip arrays and complex scatterers. This paper will use this method to calculate the RCS of microstrip antennas and verify its correctness. ?

1 Two-level discrete complex image method?

This paper adopts the two-level DCIM method based on the GPOF method to overcome the shortcomings of the Prony method [4] that is greatly affected by noise and has poor calculation accuracy, thereby improving the exponential fitting accuracy of the DCIM method and expanding the scope of application of the DCIM method. In the application of the DCIM method, the spatial domain Green's function is first obtained by performing an inverse Hankel transform from the spectral domain Green's function:

where ?G and represent the spatial domain and spectral domain Green's functions, respectively, H(2)0 represents the second-order Hank's function, and SIP represents the Sommerfeld integral path. This paper selects a secondary integral path:

the co-function obtained by subtracting the approximate function f(kρ) from the original function (kρ) is uniformly sampled along Cap2. For Cap2, the characteristics of the co-function can be well picked up without many sampling points. Then the GPOF method is used for fitting, so there is:

2 Mixed Potential Integral Equation?

The spatial mixed potential integral equation (MPIE) is a discretization of the mixed integral equation. The key issue of this method is to transform the spectral domain Green's function into the spatial domain Green's function. Let E[WTBX]i be the incident field, then the mixed potential integral equation is:

where N is the number of basis functions on the patch, that is, the number of common edges generated when the microstrip array is segmented. The mixed integral equation is then transformed into a matrix equation:

where [WTHX]I[WTBX] is a current column vector of length N, which contains the unknown coefficient In in equation (9), [WTHX]Z[WTBX] is an N×N element impedance matrix, and [WTHX]V[WTBX] is an excitation column vector of length N. The elements in the impedance matrix [WTHX]Z[WTBX] are:

where f[WTBX]i and f[WTBX]j refer to the weight function and basis function, respectively, and Ti and T′j refer to the effective face elements of f[WTBX]i and f[WTBX]j, respectively. The surface current J[WTBX] can be obtained by the Gaussian integral formula, and the far-field directivity pattern can be obtained by the reciprocity theorem.

3 Calculation results and analysis

The radar cross section of a single microstrip antenna is calculated using the proposed method. Assume that the baseband thickness is h = 158 mm, the dielectric constant is εr = 217, and the patch size is L = 366 mm and W = 26 mm in the x and y directions, respectively. The trend of the RCS of a single station with respect to frequency is calculated when the frequency range is f = 2~5 GHz and the incident angle is θi = 60°, φi = 45°, as shown in Figure 1.
The result is compared with the result in the literature [5], as shown in Figure 2. It can be found that the trend of the RCS of a single station with respect to frequency calculated in this paper is consistent with the result in the literature when the frequency is 2~5 GHz, which proves the correctness of the proposed method. ?

参考文献?
［1］Hua Y,Sarkar T K.Generalized Pencil-of-Function Method for Extracting Poles of an EM System from Its Transient Response[J].IEEE Trans.on AP,1989,37:229-234.
［2］Chow YL,Yang JJ,Fang DG,?et al?.A Closed-form Spatial Green′s Function for Thick Microship Substrate[J].IEEE Trans.Microwave Theory Tec.,1991,39(3):588-592.
［3］Rao SM,Wilton D R.Glisson A W.Electromagnetic Scattering by Surfaces of Arbitrary Shape[J].Acoustics,Speech& Signal Processing,1990,38(5):814-824.
［4］Van Blaricum ML,Mittra RA Technique for Extracting the Poles and Residues of a System Directly from its Transient Response[J].IEEE Trans.on AP,1975,23:777-781.
［5］Wang CF,Ling F,Jin J MA Fast Full-wave Analysis of Scattering and Radiation from Large Finite Arrays of Microstrip Antennas[J].IEEE Trans.on AP,1998,46:1 467-1 474.
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About the Author Shi Lei, male, born in 1981, graduated from Xi'an Communication Institute with a major in telecommunication switching in 2003 and stayed on to teach at the institute. He is currently a communications staff officer of the Military Affairs Department of Xi'an Communication Institute. He is mainly engaged in research on telecommunication switching, optical fiber communication, and wireless communication.