Equivalent Model Analysis of Modified Satellite Antenna for Isoflux Pattern Generation
 Author: Choi EunCheol, Lee Jae Wook, Lee TaekKyung, Lee WooKyung
 Organization: Choi EunCheol; Lee Jae Wook; Lee TaekKyung; Lee WooKyung
 Publish: Journal of electromagnetic engineering and science Volume 14, Issue3, p278~283, Sep 2014

ABSTRACT
This paper presents a theoretical approach for a modified turnstile antenna suitable for satellite communication in order to investigate the current distributions of radiators and radiation characteristics with equivalent model analysis. The proposed equivalent model is composed of an ideally horizontal dipole antenna and vertically loaded tophat radiating elements. The required isoflux pattern with wide beamwidth has been achieved by attaching tophat elements to the main radiators. In addition to illustrating radiation patterns, electrical performances like current distributions have been analyzed by mathematically manipulating the equations derived from the equivalent horizontal and vertical dipole model.

KEYWORD
Circular Polarization (CP) , Dipole Antenna , Equivalent Model , Isoflux Pattern , Turnstile Antenna.

I. INTRODUCTION
In a satellite communication, Sband antenna with its functions of telemetry, tracking, and command (TT&C) is an essential and fundamental component in monitoring and controlling the normal operation of satellite [1].
In general, a relatively low gain and wide beamwidth are required because communication should be available, even in the situations of changing altitude. Researchers have suggested several candidates for TT&C satellite antennas, including the microstrip patch [2], quadrifilar helix [3], conical spiral [4], and turnstile antenna [58]. The turnstile antenna, in particular, has several advantages, such as low complexity, easy fabrication, and robust characteristics with wide beamwidth.
This paper introduces a theoretical approach with equivalent model horizontal and vertical dipole elements. We validate our analysis by conducting mathematical manipulations and fullEM simulations using farfield approximations and the commercially available software CST Microwave Studio (CST MWS; Computer Simulation Technology AG., Darmstadt, Germany). In Section II, the equivalent model of the proposed antenna is dealt with using real dipole and image sources. The analysis of current distributions verified the relationship between the bowtieshaped dipole and the wired dipole. In addition, a mathematical analysis of the modified dipole antennas is used to predict the electrical performances of the proposed antenna and compared them with the measured data of the fabricated antenna. A brief conclusion is provided in Section III.
II. EQUIVALENT MODEL OF RADIATORS
1. The Proposed Structure
Fig. 1 shows the geometry of the previously proposed antenna with structural modification and an isoflux pattern of circular polarization. As shown in Fig. 1, the radiators are composed of tophat loaded bowtieshaped dipole antennas with two feeding structures. Circular polarization with a wide beamwidth is generated by launching a Wilkinson power divider, which has a 90° phase difference and wide impedance bandwidth, below the ground plane.
The vertical tophat elements have been attached specifically to generate a radiation pattern in a direction close to the ground plane. As a candidate receiving antenna working for a TT&C satellite, it covers the frequency range from 2,025 to 2,125 MHz in the satellite communication system. The important aspects for the proposed antenna are the enhancement of the axial ratio beamwidth affected by the vertically installed tophat elements and beamwidth expansion of the isoflux pattern.
2. Equivalent Model of TopHat Loaded Antenna
For the mathematical evaluations of Efield distributions and to simplify the understanding of the radiation mechanism of the proposed antenna, the bowtieshaped dipole elements is defined and modeled as simplified crossed dipole elements.
Fig. 2 shows the equivalent model of the proposed and modified turnstile dipole radiating elements by assuming the infinite ground plane of
σ = ∞ and finite height ofh _{1}. The entire structure of the radiators consists of the horizontal dipole and vertically loaded tophat elements. The parametersl _{1} andl _{2} mean the lengths of horizontal dipole and vertical tophat elements, respectively. In addition,θ andΨ are the angles from zaxis and yaxis to the observation pointr , respectively.The current distributions on the real source dipole elements can be approximated for the evaluation of the farfield radiation patterns as following equations [9].
I _{0} andk mean the maximum current value and the wavenumber, respectively. Fig. 3 shows the surface current distributions on the bowtieshaped dipole with tophat elements and ideal dipole with vertical elements using the commercially available software CST MWS based on the finitedifference timedomain (FDTD) algorithm.Fig. 3(a) shows the surface current distributions of the bowtieshaped dipole which is a radiator in the designed turnstile antenna. As shown in Fig. 3(a), the vector current flow (real lines) can be divided into two basis components (dashed lines) relative to the main horizontal axis of bowtie radiator. The two opposite directions may cancel each other, while the other components remain and may be added positively. Consequently, the effect of actual current distribution will approach that of the ideal dipole antennas shown in Fig. 3(b).
For the validation of the assumed current distributions, the normalized current distributions obtained from mathematical representations in this work and CST MWS have been compared in Fig. 4 and show good agreement with a small discrepancy. As shown in Fig. 4, some discrepancies are evident in the results at dipole lengths of less than 30 mm, around 70 mm, and more than 110 mm. It can be expected that the reason is due to the feeding point for horizontal dipole and discontinuities in the connections between vertical and horizontal elements. However, all three results using mathematical representations and CST simulation for two kinds of dipoles are nearly the same.
First of all, all the current distributions on the radiating elements without/with tophat elements are assumed to be sinusoidal. The total radiated electric field can be obtained from the six components consisting of real source and image source effects (see Appendix).
Eqs. (3) and (4) show the farzone radiated field of horizontal dipoles without/with tophat elements, respectively.
Fig. 5 shows the normalized radiation pattern when an ideal dipole without/with tophat loaded elements are considered. As predicted from Fig. 5(a) and (b), the entire radiation pattern becomes broader, which means that radiation in the direction of 90° can be generated as the additionally vertical elements is attached. Hence, the enhancement of beamwidth can be accomplished because of the effects of the attached vertical dipoles.
In order to analytically investigate the change of the radiation pattern according to the length of tophat loaded radiating elements and isoflux radiation pattern for covering all the target area uniformly, the proposed antenna is assumed to be installed on the PEC ground with an ideally infinite area. As shown in Fig. 6, it can be estimated from the mathematical representations using equivalent model and commercially available software based on EM full simulation that the radiation pattern could be changed by adjusting the height and the length of the tophat radiating elements.
Fig. 6(a) and (b) show that the usage of a quarter wavelength in the distance between the ground plane and horizontal dipole elements results in the pattern of broadside direction perpendicular to the horizontal dipole elements. However, as the height increases, the gain in the broadside direction parallel to
θ = 0° decreases. For example, it can be seen that no radiation occurs in the broadside direction if the height approaches a half wavelength. In addition, Fig. 6(c) and (d) delineate the effects according to the variations of parameterl _{2}, which is the length of tophat loaded vertical elements.For the gain and axial ratios of the proposed and modified turnstile antenna, simulations and measurements were carried out with the parameter values of
h _{1} = 61 mm andl _{2} = 31 mm to determine the gain and axial ratios of the proposed and modified turnstile antenna, as shown in Fig. 7. By considering the mathematically equivalent model analysis, it can be ensured that the effect of the antenna height,h _{1}, and the length of tophat radiating element,l _{2}, on the radiation pattern and axial ratio is remarkably important relative to the other parameters.Ⅲ. CONCLUSION
An equivalent model of a tophat loaded turnstile antenna has been developed by applying an image method and investigating current distributions on the radiating elements. The ideal dipole antennas and the proposed antenna were compared using the radiation pattern. A wide AR beamwidth was achieved with an isoflux pattern. It is ensured that the proposed equivalent model analysis can be effective for rapid design in terms of the radiation pattern and axial ratio in satellite communication.

[Fig. 1.] The radiator part of Sband turnstile antenna [8].

[Fig. 2.] Equivalent sources of horizontal dipole with tophat elements.

[Fig. 3.] The current distributions on the tophat radiating elements. (a) Bowtieshaped dipole and (b) ideal dipole with vertical elements.

[Fig. 4.] The magnitude of normalized current on the horizontal dipole elements with tophat loaded radiators.

[Fig. 5.] The radiation pattern of dipole elements: (a) dipole without vertically loaded tophat elements and (b) dipole with vertically loaded tophat elements.

[Fig. 6.] The predicted radiation pattern using equivalent model of tophat loaded antenna. (a) Mathematical results according to the variation of height h1 when l2 = 31 mm, (b) simulation results according to the variation of height h1 when l2 = 31 mm, (c) mathematical results according to the variation of length l2 when h1 = 61 mm, and (d) simulation results according to the variation of length l2 when h1 = 61 mm.

[Fig. 7.] Gain and axial ratio of the proposed antenna according to variation of h1 and l2 at ？ = 2,075 MHz: (a) right hand circular polarization (RHCP) gain and (b) axial ratios.