Vol.29 No.6 JOURNAL OF ELECTRONICS (CHINA) November 2012

CATIA AIDED RADOME ANALYSIS USING GEOMETRIC OPTICS METHOD1

Li Gaosheng Jia Lei Ming Yongjin Cao Qunsheng (College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics,

Nanjing 210016, China)

Abstract In this paper, the Geometric Optics (GO) method using the approximate ray paths cou-pled with the Computer Aided Tri-dimensional Interface Application (CATIA) meshing modeling are implemented to analyze the performance of electric large three-dimensional dielectric radome-enclosed antenna of arbitrary contour shape. The surfaces of the radome are approximated by planar triangular patches, the influences of various number of patches on power transmission coefficient and Insertion Phase Delay (IPD) via an ogive and a conical radome are discussed by the hybrid method. The simulation results indicate that computational error from planar triangular patches can limit in one percent, meeting the engineering application requirements.

Key words Geometric Optics (GO); Computer Aided Tri-dimensional Interface Application (CATIA); Radome; Power transmission coefficient; Insertion Phase Delay (IPD)

CLC index TN82

DOI 10.1007/s11767-012-0885-9

I. Introduction Radome is defined as a housing that protects

the antenna from environmental conditions such as storm, dust, rain, lighting, static electricity, burning sun and so on. In practice, the antenna radome effects can be observed experimentally because the basic electrical properties of the ra-dome wall differ markedly from those of air. The general effects of the antenna radome for studying are involved far field pattern distortions, power transmission loss, boresight error and small sidelobe degradations[1,2].

A number of different electromagnetic analysis techniques are developed to discuss the effects of the radome, for example, Geometric Optics (GO)[2,3], Physical Optics (PO)[3,4], Plane Wave Spectra (PWS)[5], the method of moments[6], and also some hybrid techniques[7,8]. Because the GO method can produce reasonably results for ra-dome-enclosed antennas with the size about five wavelengths in diameter, and it can be easily im- 1 Manuscript received data: May 9, 2012; revised date:

August 7, 2012. Supported by the National Natural Science Foundation of China (No. 61172024). Communication author: Li Gaosheng, born in 1988, male, Master. Nanjing University of Aeronautics and Astro-nautics, Nanjing 210016, China. Email: lgs_002@163.com.

plemented on personal computer, so the method have been widely applied to antenna radome en-gineering design[3,9].

This paper aims to discuss the influences of different number of patches on power transmission coefficient and Insertion Phase Delay (IPD) via some canonical radomes modeled by the CATIA[10]. a complete three-Dimensional (3D) CAD/CAE/ CAM integrated software. In view of the CATIA, it not only supports curved surface described by Bezier, B-spline and MURBS special functions, but also has strong function to fit the surface modeling in complex radome, so it leads us using it to modeling of radome surface.

The paper is focus on electrical properties of the radome using GO method with the CATIA modeling method, the content is divided mainly into three parts. GO method is analyzed in Section II, together with validation of the developed soft-ware. The CATIA aided radome analysis using GO method is outlined in Section III, for the sake of completeness, finally, the conclusions are summa-rized in Section IV.

II. Analysis of GO Method In GO transmit mode, the antenna aperture is

considered as a collection of sources with arbitrary amplitude and phase, when a ray runs through the radome wall, each ray is modified by its amplitude

LI et al. CATIA Aided Radome Analysis Using Geometric Optics Method 563

and phase, the collection of rays defined an equivalent aperture outside of the radome which covers the effects of the radome. The Fourier transform of the equivalent aperture distribution produces far field radiation pattern of the radome- enclosed antenna, how each ray is modified is discussed in the following five steps. Step 1 To find the intercept point a ray tracing from an arbitrary point on the antenna aperture with the radome wall. Step 2 Up of the intercept point, to find unit surface normal vector and incident angle corre-sponding the incident ray. Step 3 Because the wall is assumed as locally plane at intercept point, then an arbitrarily po-larized electromagnetic wave is decomposed into two orthogonal components, for example, parallel and perpendicular wave components,

||i i

i ⊥= +E E E (1)

Step 4 On the basis of four-port network theo-ries[3], parallel and perpendicular components are obtained from complex voltage transmission coef-ficient, the parallel and perpendicular compo-nents are written as follow, respectively,

|| || ||IPDT= ∠T (2)

IPDT⊥ ⊥ ⊥= ∠T (3)

Step 5 Recompose the parallel and perpendicu-lar wave components after the ray propagating the radome wall, then the transmitted fields are ob-tained.

||t t

t ⊥= +E E E (4)

t i⊥ ⊥ ⊥= ⋅E E T (5)

|| || ||t i= ⋅E E T (6)

As our initial validation example, we choose a single-layered structure ogive radome with the vertical polarized antenna being a circular aper-ture, shown in Fig. 1, which L0 and D0 are the length and bottom diameter of the ogive radome respectively. In the ogive radome structure, the thickness of radome and relative dielectric per-mittivity are represented as d and .rε The antenna radium is Ra inside of the radome. From Fig. 1, the

radome can be described as the following equation,

Fig. 1 Geometry of ogive radome

( )2

2 2 2 2B y z x R+ + + = (7)

where 2 2

2 0 020

44

L DB

D−

= (8-1)

2 22 0 0

20

44

L DR

D+

= (8-2)

In Fig. 2, it is compared with the numerical result[3] and our result of the power transmission for an antenna enclosed in the radome with L0 = 609.6 mm, 0 0 0/2, /3, 1.27 mmaD L R L d= = = and 33.0(1 10 ),r jε −= − the azimuth and elevation observation angles both are 0°. From Fig. 2, it is found that our validation result is good agreement with that of the numerical.

Fig. 2 Power transmission and corresponding reference solution for an ogive radome

III. Radome Analysis Method Aided by CATIA

For some symmetric and simple shape radome,

564 JOURNAL OF ELECTRONICS (CHINA), Vol.29 No.6, November 2012

normally its contour, like tangent ogive, secant ogive, von karman and power series, is described by only one equation. However, for some complicated shape radome, it needs two more equations to determine whole contour. Unfortunately for some radomes, it is difficult to find the exact equations to represent the radome shape, so we need to create the model in advance using a computer aided design software. In our simulations, we choose the CATIA to create arbitrary model, and design radome structure including single-layer, A sandwich and C sandwich, etc.. The flow diagram is shown in Fig. 3, it is clear that the results of the power transmission and Insertion Phase Delay (IPD) and so on are obtained following the cal-culation processing to satisfy the requirement.

Fig. 3 Flow diagram for CATIA aided GO method

Normally when using GO method, it needs to find intercept point for a ray tracing from an ar-bitrary point on the antenna aperture patch, the planar triangular patch from the meshes created by the CATIA, the detail is discussed below.

As shown in Fig. 4, iS is the unit incident ray vector, where P0 is a point on the antenna aperture, Pj1, Pj2, and Pj3 are the vertexes of a triangular patch, jN is the unit normal vector of the tri-angular patch, Pj0 is to be solved intercept point, the unit vectors from the center point to P0 , Pj0,1,2,3, are u and 0,1,2,3,u respectively. Then we can get equations:

0P λ= +r u S (9-1)

( )11 0jjP− ⋅ =r u N (9-2)

where

j = ×N a b (10-1)

( )( )2 12 1j jP P= − −a u u (10-2)

( )( )3 23 2j jP P= − −b u u (10-3)

Then

( )( )1 01 0 jj

i j

P Pλ

− − ⋅=

⋅

u u N

S N (11)

Criterion of the true solution is,

1,2,3k j

k

S S=

=∑ (12)

where Sj is the area of the triangular patch. Because the contour surface of a radome is

generally meshed into triangular patches, then it is necessary to discuss the approximation effect of parch size. As example, the geometry of an ogive and a conical radome are shown in Fig. 1 and Fig. 5, respectively.

Fig. 4 Intercept point a ray with a triangular patch

Fig. 5 Geometry of conical radome

The parameters of the ogive and conical ra-dome are same as that of the validation example in Section II, but the structure of the ogive radome is

LI et al. CATIA Aided Radome Analysis Using Geometric Optics Method 565

replaced by A sandwich one. Tab. 1 is listed the thickness and relative permittivity of the A sandwich structure.

Tab. 1 Parameters of the ogive radome

No. εr tanδ d (mm)

1 3.30 5.0×10–4 1.27

2 1.08 1.0×10–3 2.54

3 3.30 5.0×10–4 1.27

where the parameter tanδ is loss angle tangent, d is thickness of the radome.

Fig. 6 to Fig. 9 are depicted the power trans-mission and the IPD error for given structures of ogive and conical radome, respectively, in which value of Grid is expressed the number of planar triangular patches created by the CATIA. The benchmark of the power transmission and IPD error is the result with radome shape described by equations or codes, while, validity of the method have been represented in Section II.

Fig. 6 Power transmission error of the ogive radome

Fig. 7 IPD error of the ogive radome

Fig. 8 Power transmission error of the conical radome

Fig. 9 IPD error of the conical radome

It is found from the figures that both the power transmission and the IPD error are decreased gradually with the number of patches increased, and the values two parameters are less than one percent when the number of patches is larger than 2019 for the ogive radome and 2018 for the conical radome, respectively. So it is clear validity of the correctness of the aided CATIA radome method to assess the radome performance. However, for other radomes shapes, in order to keep the precision, the number of patches to divide the radome surface is possibly larger or smaller than the numbers dis-cussed above, it is decided by the radome surface complexity, for example, a radome with the slab shape, two patches is enough, it can be obtained by the calculation of computational code coupled with radome test at the first time.

IV. Conclusions In the CATIA aided radome analysis, we use

the GO method to study in detail the influences of various number of patches of the power transmis-

566 JOURNAL OF ELECTRONICS (CHINA), Vol.29 No.6, November 2012

sion coefficient and IPD via simulation examples. The results have shown that the method could be applied to design arbitrary contour radomes. In addition, this hybrid method can be extended to other radome analysis technique, such as physical optics, hybrid Po-MoM method and so on.

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