#### Abstract

A design for Ka-band satellite communication antenna in earth station is introduced. This kind of antenna uses splash plate feed based on ring-focus antenna. The theory of the new splash plate feed design is presented and the relative equations are derived. The measured antenna parameters, VSWR, and patterns are highly consistent with the simulated results, which demonstrates the success of the design for such kind of antenna that can be effectively used in Ka-band applications.

#### 1. Introduction

There are many kinds of Ka-band antenna, as reported in documents, including microstrip array antenna [1–3], waveguide array antenna [4–6], waveguide slot antenna [7], horn antenna [8–10], dielectric spherical lens feed antenna [11–13], and reflector antenna [14, 15]. The efficiency of Ka-band antenna is usually in the range of 50% to 60% [16].

The antenna designers always pursue high gain while using low sidelobes for the design of Ka-band antenna [17–27].

Ring-focus parabolic antenna overcomes feed shelter to realize low sidelobes and VSWR in a broad bandwidth and has been applied widely in VSAT. The antenna can enhance its efficiency by changing the shape of hat feed [28], reducing its size by using a spline-profiled smooth horn [29], and improving its performance on VSWR and cross-polarization via a small ring-shaped aperture [30]. But all the schemes above have low efficiency due to the support for subreflector.

Splash plate feed, which traces back to World War II, has not been used widely for the high VSWR [31]. Since the 1980s, antenna with splash plate feed has been researched by few papers, which present the power distribution control and equiphase on the main reflector aperture through dielectric materials and subreflector forming, while the main attention is payed on subreflector forming to improve performance [32–36]. Since the antenna with splash plate feed does not need the support for subreflector, it can gain higher efficiency. However, the problem caused by feed shelter [32–36] still exists.

In this paper, the design of a new antenna in Ka-band is introduced. This antenna adopts splash plate feed, whose main reflector is ring focus without strut and feed shelter.

In this paper, the principle of ring-focus reflector antenna with splash plate feed is introduced firstly. A group of differential equations are derived and the geometry of the antenna’s subreflector and dielectric surface is obtained by solving these differential equations. The simulated results indicate that this antenna can achieve high gain with low sidelobes. This kind of antenna has been produced based on the proposed design in this paper. The measured far-field patterns are highly consistent with the simulated results.

This product can be applied widely in Ka-band satellite communications considering its novel structure, low cost, good electrical performance, and high efficiency.

#### 2. Theoretical Analysis

The method based on geometric optics is adopted to design the ring-focus antenna with splash plate feed. This antenna consists of four parts including the main reflector, splash plate feed, media, and subreflector.

This antenna is rotational symmetric, and the principle of such design is simply described through 2D section in Figure 1.

The main reflector of such antenna is ring focus. It is produced by rotation of a parabola, whose focal length is , away from symmetry axis . The main reflector equation of this antenna, whose focus is the origin, can be expressed as follows:

The principle of designed antenna is shown in Figure 1. The feed phase center is . The optics ray is from to , then reflects to , and then refracts to , where is the ring focal of the main reflector. is a point of intersection by reflect line extension line and *Z*_{s} axis. The vector is pointing from to . The vector is pointing from to *.* The vector is pointing from to .

##### 2.1. Design of Subreflector

3D description equations are required in theory derivation while 2D section is shown Figure 1. Thus, assuming that is the included angle of vector in plane and axis, if is the equation of subreflector, the vector can be expressed as where is the unit vector. In rectangular coordinate system, and can be expressed as

To express simply, let . Then the differential coefficient is

The unit normal vector of subreflector is where “” represents vector cross product. It can be derived from (5) that where

The inner product of incident wave ’s unit vector and subreflector’s unit normal vector is

The inner product of reflected wave from subreflector and subreflector’s unit normal vector is

According to Snell’s law,

It can be derived from (8), (9), and (10) that

##### 2.2. Design of Dielectric Surface Forming

For simple derivation, assuming a coordinate system , the dielectric surface equation is
where is the unit vector and can be expressed as
in a rectangular coordinate system. For simple description, let be *f*_{n}; the unit normal vector of the dielectric surface is

So it can be derived that where

The inner product of incident wave ’s unit vector and dielectric surface’s unit normal vector is

The inner product of refracted wave and dielectric surface’s unit normal vector is

According to Snell’s law, where

It is derived from (17), (18), and (19) that

##### 2.3. Energy Conservation Equation

According to the law of energy conservation, where is the spatial angle distribution function of feed axisymmetric radiation power, is the aperture power distribution function of the antenna main paraboloid, is the radius variable of the antenna aperture, and is the proportionality coefficient.

The main reflector equation of ring-focus reflector antenna is

In logs, it can be obtained as

According to (23) and (24), then

##### 2.4. Equiphase Equation

In definition, is the maximum of , is the maximum of , is the minimum of , and is the maximum of . According to the qualification requirement, , , , , , , and can be certain firstly.

When and , boundary condition can be obtained according to the following geometrical relationship:

In a dielectric material, the optical length that an electromagnetic wave radiates from primary feed and refract to the air after being reflected by subreflector to the main reflector’s focus is equal. Namely,

##### 2.5. Calculation of Subreflector Equation and Dielectric Surface 2D Equation

According to the geometric relationship in Figure 1, it can be obtained that

When is certain, , , , , and can be solved according to (11), (21), (23), (25), and (28).

In plane, subreflector equations are

Dielectric surface equations are

Thus, the shapes of subsurface and dielectric surface can be obtained.

#### 3. Structure of Antenna

The main reflector, whose material is carbon fiber, is a rotationally symmetric paraboloid. The surface of the reflector should be processed by metallization, and the accuracy should be controlled within 0.3 mm (r.m.s.). In the processing, a carbon fiber reflector and a copper sheet are made out of molds. Then they are bonded together with glue. The accuracy of the molds ensures the accuracy of the reflector. The structures of the main reflector and subreflector and dielectric are shown in Figure 2.

The exploded view of the feed structure is shown in Figure 3, where the green and yellow parts are dielectric material REXOLITE1422 and aluminum material, respectively. After programming according to the designed data, the subreflector and dielectric can be processed by high precision CNC (computer numerical control) machines. Ultraviolet (UV) glue is adopted here to bond the subreflector and the dielectric. Since the dielectric is transparent, the glue between subreflector and dielectric will cure after UV radiates for a period of time.

Let 15 mm *≤ |X| ≤* 525 mm, mm, mm*.* After fabrication of the subreflector and dielectric materials, the assembled antenna is shown in Figures 4 and 5.

#### 4. Simulation and Measurement on VSWR

This antenna adopts circular polarization. It uses 27.5~30.0 GHz as transmitting frequency and 17.7~20.2 GHz as receiving frequency. Physical optics (PO) method and finite element method (FEM) are combined in the simulation by FEKO, where PO method is used for the main reflector and FEM for the feed (subreflector and dielectric). The simulation defines “mesh” as 1/6 wavelength. The computer has an 8-core CPU and 128 GB RAM.

The curves of VSWR are obtained through the simulation of FEKO, and the simulated results are shown as red continuous lines in Figures 6 and 7.

The VSWR is measured with Agilent Vector Network Analyzer N5230C in microwave anechoic chamber. After the measurement on antenna transmitting and receiving VSWR, the relative results are shown as blue chain lines in Figures 6 and 7.

As shown in Figure 6, antenna transmitting VSWR is below 1.24. As shown in Figure 7, antenna receiving VSWR is below 1.73.

#### 5. Simulation and Measurement on Antenna Patterns

This design adopts arbitrary phase and amplitude feed power pattern as the feed model. Antenna patterns are simulated and analyzed by FEKO, and the curves obtained are shown with red continuous lines in Figure 8.

**(a) 27.5 GHz**

**(b) 28.75 GHz**

**(c) 30.0 GHz**

**(d) 17.7 GHz**

**(e) 18.95 GHz**

**(f) 20.2 GHz**

The far-field patterns are then measured, and the measured patterns obtained from data are shown as blue chain lines in Figure 8.

The distance between the transmitting and receiving antennas should satisfy the far-field test distance condition, namely,
where *R* is the distance between the source antenna and the antenna under test. is the aperture of the antenna under test, and is the wavelength. According to (31), it is possible to calculate the minimum distance between the transmitting and receiving antennas in the far-field test. The highest frequency of the Ka-band antenna is 30 GHz, and mm, so m. The actual distance is about 282 m.

The sidelobes meet the envelope of 29–25log *θ* dBi. The measurement and related calculation of the antenna gain adopt comparison method. Acquired gain and first sidelobe are listed in Tables 1 and 2.

As shown in Figure 8, considering dielectric loss, splash plate scattering, cross-polarization efficiency, main reflector toleration, and other efficiency, simulated results of the antenna are highly consistent with the measured results, which demonstrates the success of such design. The measured antenna efficiency is about 65.6%, while the efficiency of the existing antenna in Ka-band is below 60% [16].

#### 6. Conclusion

This paper introduces a ring-focus antenna based on splash plate feed. The prototype of this antenna has been produced based on the proposed design. The measured results verify that this antenna can achieve efficiency of over 65% and can satisfy the regulations of Rec. ITU-R S.580-6 in receiving band on antenna sidelobe. The measured results of the antenna are highly consistent with the simulated results, which proves the high engineering value of the proposed method.

#### Conflicts of Interest

The authors declare that there is no conflicts of interest regarding the publication of this paper.

#### Acknowledgments

This work was jointly sponsored by scientific research foundation NUPTSF (Grant nos. NY-214144 and NY-215073) and NSFC (Grant no. 61701260).