# A Ring-Focus Antenna with Splash Plate in Ka-Band

Authors: Laiding Zhao; Xiaodong Bai; Rui Li; Jidong Xie
Journal: International Journal of Antennas and Propagation
 (2018)

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## 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.


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## Body

## 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 throughXZ 2D section in Figure 1.Figure 1
Principle of ring-focus antenna with splash plate feed.The main reflector of such antenna is ring focus. It is produced by rotation of a parabola, whose focal length isF, away from symmetry axis a1. The main reflector equation of this antenna, whose focus is the origin, can be expressed as follows:
(1)Z=X−a124F−F.The principle of designed antenna is shown in Figure1. The feed phase center is Os. The optics ray is from Os to E, then reflects to F, and then refracts to On, where On is the ring focal of the main reflector. Om is a point of intersection by reflect line extension line and Zs axis. The vector rs is pointing from Os to E. The vector rm is pointing from E to F. The vector rn is pointing from On to F.


### 2.1. Design of Subreflector

3D description equations are required in theory derivation while 2D section is shown Figure1. Thus, assuming that ϕs is the included angle of vector rs in OsXsZs plane and OsXs axis, if fsθs,ϕs is the equation of subreflector, the vector rs can be expressed as
(2)rs=fsθs,ϕsr^s,where r^s is the unit vector. In rectangular coordinate system, r^s and r^m can be expressed as
(3)r^s=sinθscosϕsx^s+sinϕsy^s+cosθsz^s,r^m=sinθmcosϕsx^s+sinϕsy^s+cosθmz^s.To express simply, letfsθs,ϕs=fs. Then the differential coefficient is
(4)dr^sdϕs=dfsdϕssinθscosϕs−fssinθssinϕsx^s+dfsdϕssinθssinϕs+fssinθscosϕsy^s+dfsdϕscosθsz^s,dr^sdθs=dfsdθssinθscosϕs+fscosθscosϕsx^s+dfsdθssinθssinϕs+fscosθssinϕsy^s+dfsdθscosθs−fssinθsz^s.The unit normal vector of subreflector is(5)n^s=drs/dϕs×drs/dθsdrs/dϕs×drs/dθs,where “×” represents vector cross product. It can be derived from (5) that
(6)n^s=1Δdfsdθscosθs−fssinθscosϕsx^s+dfsdθscosθs−fssinθssinϕsy^s−dfsdθssinθs+fscosθsz^s,where
(7)Δ=dfsdθs2+fs2.The inner product of incident wavers’s unit vector and subreflector’s unit normal vector is
(8)−r^s⋅n^s=fsdfs/dθs2+fs2.The inner product of reflected waverm from subreflector and subreflector’s unit normal vector is
(9)r^m⋅n^s=dfs/dθssinθm−θs−fscosθm−θsdfs/dθs2+fs2.According to Snell’s law,(10)−r^s⋅n^s=r^m⋅n^s.It can be derived from (8), (9), and (10) that
(11)drsdθs=rsθscotθm−θs2.


### 2.2. Design of Dielectric Surface Forming

For simple derivation, assuming a coordinate systemOnXnZn, the dielectric surface equation is
(12)rn=fn−θn,ϕsr^n,where r^n is the unit vector and can be expressed as
(13)r^n=−sinθncosϕsx^n+sinϕsy^n+cosθnz^nin a rectangular coordinate system. For simple description, let fn−θn,ϕs be fn; the unit normal vector of the dielectric surface is
(14)n^n=drn/dϕn×drn/dθndrn/dϕn×drn/dθn.So it can be derived that(15)n^n=1Δ′dfndθncosθn+fnsinθncosϕsx^n+dfndθncosθn−fnsinθnsinϕsy^n+dfndθnsinθn−fncosθnz^n,where
(16)Δ′=dfndθn2+fn2.The inner product of incident waverm’s unit vector and dielectric surface’s unit normal vector is
(17)r^m⋅n^n=dfn/dθnsinθm+θn−fncosθm+θndfn/dθn2+fn2=cosϕ1.The inner product of refracted wavern and dielectric surface’s unit normal vector is
(18)−r^n⋅n^n=fndfn/dθn2+fn2=cosϕ2.According to Snell’s law,(19)sinϕ1sinϕ2=1n,where
(20)n=εr.It is derived from (17), (18), and (19) that
(21)dfndθn=nfnsinθm+θn1−ncosθm+θn.


### 2.3. Energy Conservation Equation

According to the law of energy conservation,(22)Pθssinθsdθs=−IXmXmdXmA,where Pθs is the spatial angle distribution function of feed axisymmetric radiation power, IXm is the aperture power distribution function of the antenna main paraboloid, Xm is the radius variable of the antenna aperture, and A is the proportionality coefficient.The main reflector equation of ring-focus reflector antenna is(23)Xm=2Ftanθn2+a1.In logs, it can be obtained as(24)dXmdθn=Fsec2θn2.According to (23) and (24), then
(25)dθndθs=−APθssinθscos2θn/2FIXmXm.


### 2.4. Equiphase Equation

In definition,θsmax is the maximum of θs, fsmax is the maximum of fs, θnmin is the minimum of θs, and fnmax is the maximum of fn. According to the qualification requirement, Pθs, IXm, a1, a2, θsmax, fsmax, and F can be certain firstly.Whenθs=θsmax and fs=fsmax, boundary condition can be obtained according to the following geometrical relationship:
(26)θnmin=arctanfsmaxcosθsmax+a2a1−fsmaxsinθsmax,fnmax=fsmaxcosθsmax+a22+fsmaxsinθsmax−a12.In a dielectric material, the optical length that an electromagnetic wave radiates from primary feedOs and refract to the air after being reflected by subreflector to the main reflector’s focus is equal. Namely,
(27)nfs+nfm+fn=K,fsmax+fnmax=K.


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

According to the geometric relationship in Figure1, it can be obtained that
(28)fssinθs+fmsinπ−θm+fnsinθn=a1,fscosθs+a2=fmcosπ−θm+fncosθn.Whenθs is certain, θm, θn, fs, fm, and fn can be solved according to (11), (21), (23), (25), and (28).InOsXsZs plane, subreflector equations are
(29)X=fssinθs,Z=fscosθs.Dielectric surface equations are(30)X=α1−fnsinθn,Z=fncosθn−α2.Thus, the shapes of subsurface and dielectric surface can be obtained.


## 2.1. Design of Subreflector

3D description equations are required in theory derivation while 2D section is shown Figure1. Thus, assuming that ϕs is the included angle of vector rs in OsXsZs plane and OsXs axis, if fsθs,ϕs is the equation of subreflector, the vector rs can be expressed as
(2)rs=fsθs,ϕsr^s,where r^s is the unit vector. In rectangular coordinate system, r^s and r^m can be expressed as
(3)r^s=sinθscosϕsx^s+sinϕsy^s+cosθsz^s,r^m=sinθmcosϕsx^s+sinϕsy^s+cosθmz^s.To express simply, letfsθs,ϕs=fs. Then the differential coefficient is
(4)dr^sdϕs=dfsdϕssinθscosϕs−fssinθssinϕsx^s+dfsdϕssinθssinϕs+fssinθscosϕsy^s+dfsdϕscosθsz^s,dr^sdθs=dfsdθssinθscosϕs+fscosθscosϕsx^s+dfsdθssinθssinϕs+fscosθssinϕsy^s+dfsdθscosθs−fssinθsz^s.The unit normal vector of subreflector is(5)n^s=drs/dϕs×drs/dθsdrs/dϕs×drs/dθs,where “×” represents vector cross product. It can be derived from (5) that
(6)n^s=1Δdfsdθscosθs−fssinθscosϕsx^s+dfsdθscosθs−fssinθssinϕsy^s−dfsdθssinθs+fscosθsz^s,where
(7)Δ=dfsdθs2+fs2.The inner product of incident wavers’s unit vector and subreflector’s unit normal vector is
(8)−r^s⋅n^s=fsdfs/dθs2+fs2.The inner product of reflected waverm from subreflector and subreflector’s unit normal vector is
(9)r^m⋅n^s=dfs/dθssinθm−θs−fscosθm−θsdfs/dθs2+fs2.According to Snell’s law,(10)−r^s⋅n^s=r^m⋅n^s.It can be derived from (8), (9), and (10) that
(11)drsdθs=rsθscotθm−θs2.


## 2.2. Design of Dielectric Surface Forming

For simple derivation, assuming a coordinate systemOnXnZn, the dielectric surface equation is
(12)rn=fn−θn,ϕsr^n,where r^n is the unit vector and can be expressed as
(13)r^n=−sinθncosϕsx^n+sinϕsy^n+cosθnz^nin a rectangular coordinate system. For simple description, let fn−θn,ϕs be fn; the unit normal vector of the dielectric surface is
(14)n^n=drn/dϕn×drn/dθndrn/dϕn×drn/dθn.So it can be derived that(15)n^n=1Δ′dfndθncosθn+fnsinθncosϕsx^n+dfndθncosθn−fnsinθnsinϕsy^n+dfndθnsinθn−fncosθnz^n,where
(16)Δ′=dfndθn2+fn2.The inner product of incident waverm’s unit vector and dielectric surface’s unit normal vector is
(17)r^m⋅n^n=dfn/dθnsinθm+θn−fncosθm+θndfn/dθn2+fn2=cosϕ1.The inner product of refracted wavern and dielectric surface’s unit normal vector is
(18)−r^n⋅n^n=fndfn/dθn2+fn2=cosϕ2.According to Snell’s law,(19)sinϕ1sinϕ2=1n,where
(20)n=εr.It is derived from (17), (18), and (19) that
(21)dfndθn=nfnsinθm+θn1−ncosθm+θn.


## 2.3. Energy Conservation Equation

According to the law of energy conservation,(22)Pθssinθsdθs=−IXmXmdXmA,where Pθs is the spatial angle distribution function of feed axisymmetric radiation power, IXm is the aperture power distribution function of the antenna main paraboloid, Xm is the radius variable of the antenna aperture, and A is the proportionality coefficient.The main reflector equation of ring-focus reflector antenna is(23)Xm=2Ftanθn2+a1.In logs, it can be obtained as(24)dXmdθn=Fsec2θn2.According to (23) and (24), then
(25)dθndθs=−APθssinθscos2θn/2FIXmXm.


## 2.4. Equiphase Equation

In definition,θsmax is the maximum of θs, fsmax is the maximum of fs, θnmin is the minimum of θs, and fnmax is the maximum of fn. According to the qualification requirement, Pθs, IXm, a1, a2, θsmax, fsmax, and F can be certain firstly.Whenθs=θsmax and fs=fsmax, boundary condition can be obtained according to the following geometrical relationship:
(26)θnmin=arctanfsmaxcosθsmax+a2a1−fsmaxsinθsmax,fnmax=fsmaxcosθsmax+a22+fsmaxsinθsmax−a12.In a dielectric material, the optical length that an electromagnetic wave radiates from primary feedOs and refract to the air after being reflected by subreflector to the main reflector’s focus is equal. Namely,
(27)nfs+nfm+fn=K,fsmax+fnmax=K.


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

According to the geometric relationship in Figure1, it can be obtained that
(28)fssinθs+fmsinπ−θm+fnsinθn=a1,fscosθs+a2=fmcosπ−θm+fncosθn.Whenθs is certain, θm, θn, fs, fm, and fn can be solved according to (11), (21), (23), (25), and (28).InOsXsZs plane, subreflector equations are
(29)X=fssinθs,Z=fscosθs.Dielectric surface equations are(30)X=α1−fnsinθn,Z=fncosθn−α2.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 Figure2.Figure 2
Structure of the main and side reflector.The exploded view of the feed structure is shown in Figure3, 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.Figure 3
Exploded view of the feed structure.Let 15 mm≤ |X| ≤ 525 mm, F=420 mm, a1=15 mm. After fabrication of the subreflector and dielectric materials, the assembled antenna is shown in Figures 4 and 5.Figure 4
Antenna front view.Figure 5
Antenna lateral view.


## 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 Figures6 and 7.Figure 6
Curves of transmitting VSWR.Figure 7
Curve of receiving VSWR.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 Figures6 and 7.As shown in Figure6, 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 patternPθs 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.Figure 8
Antenna pattern.
(a)
27.5 GHz
(b)
28.75 GHz
(c)
30.0 GHz
(d)
17.7 GHz
(e)
18.95 GHz
(f)
20.2 GHzThe far-field patterns are then measured, and the measured patterns obtained from data are shown as blue chain lines in Figure8.The distance between the transmitting and receiving antennas should satisfy the far-field test distance condition, namely,(31)R≥2D2λ,where R is the distance between the source antenna and the antenna under test. D is the aperture of the antenna under test, and λ 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 D=1020 mm, so R≥200 m. The actual distance is about 282 m.The sidelobes meet the envelope of 29–25logθ 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.Table 1
Measured data of antenna transmitting patterns.
27.5 GHz
28.75 GHz
30 GHz
Gain (dBi)
47.57
47.92
48.63
First sidelobe (dB)
−20.04
−22.65
−21.66Table 2
Measured data of antenna receiving patterns.
17.7 GHz
18.95 GHz
20.2 GHz
Gain (dBi)
43.79
44.27
44.89
First sidelobe (dB)
−22.4
−22.28
−24.31As shown in Figure8, 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.



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*Source: 9790143-2018-03-18.xml*