Study of feed horn solutions for IrbeneRT-32 radio telescope

Marcis Bleiders

Ventspils International Radio Astronomy Center of Ventspils University College

BAASP 2019 – 6th International Scientific Conference

Ventspils, Latvia

Contents of presentation

• Main requirements for RT-32 geometry

• Employed analysis and optimization techniques

• Investigation of varous feed horns –profiles and far field performance

• Performance comparison and conclusions

2

Secondary focus feed horn for RT-32

• Main requirements:

Secondary mirror subtended angle 21°

Equivalent f/D ratio 2.7

Aplitude taper at secondary mirror edge 13 dB

Feed apperture phase error ≈1.3 rad (0.1…0.3 𝜆)

Main lobe full bandwidth 10.6° @ -3dB, 21° @ 10…13 dB

Directivity 25 dBi

Maximum cross-polarization level <-20 dB (𝑒𝑓𝑓𝑝𝑜𝑙>0.99)

Sidelobe level & co-polar beam <-25 dB with good E/H plane symmetry

Input return loss <-25 dB

Bandwidth >50 % (octave is 67 % fractional BW)

Other Easy to manufacture, compact size

3

Initial estimation of feed dimensions

• Estimation is carried using Gaussian beam technique [P. F. Goldsmith, QuasiopticalSystems, 1998]

• Radius of beam waist:

𝑊0 = 0.216 |𝑇(𝑑𝐵)|𝑓

𝐷, where 𝑇 is edge taper

• Aperture radius and slant length, which maximizes coupling to fundamental Gaussian beam mode:

𝑎𝑎𝑝𝑝 = 𝑊01+0.172𝛽2

0.644, 𝐿 =

𝜋𝑎𝑎𝑝𝑝2

𝜆𝛽, where 𝛽 is aperture phase error

• Using previously shown parameters for RT-32 (𝑓

𝐷= 2.7, T = 13 dB, 𝛽 = 1.3 rad) :

𝒂𝒂𝒑𝒑 ≈ 𝟑. 𝟑𝝀 , L ≈ 𝟐𝟐…𝟐𝟓𝝀

• Optimum radius of input waveguide (above TE11 and below TM11 cutoff):

𝒂𝒊𝒏 = 𝟎. 𝟒𝟖𝝀4

𝝀 = 𝟏𝟖 𝒄𝒎

𝝀 = 𝟑. 𝟓 𝒄𝒎

[Wylde et al. 1984]

Beam at RT-32 secondary focus

Ideal Gaussian beam pattern for RT-32

5

Edge taper: 13 dB

Current RT-32 C-X band horn

6

• Length: 102 cm (23 𝜆 @ 6.7 GHz )• Radius of aperture: 24 cm (5.3 𝜆 @ 6.7 GHz )

4.5 GHz, 𝜑 = 0˚

4.5 GHz, 𝜑 = 90˚ 6.7 GHz, 𝜑 = 90˚

6.7 GHz, 𝜑 = 0˚ 8.8 GHz, 𝜑 = 0˚

8.8 GHz, 𝜑 = 90˚

Actual measurements

Investigated feed horns

1. Classical dual-mode conical Potter horn

2. Smooth discrete section shaped horn

3. Classical conical corrugated horn

4. Compact profiled corrugated horn

7

Analysis method – Mode matching

[L]

[S]𝒃𝒊𝑳

𝒃𝒋𝑺

𝒂𝒊𝑳

𝒂𝒋𝑺

ො𝒛

𝐸𝑡𝐿,𝑆 =

𝑖=1

𝑁𝐿,𝑆

(𝑎𝑖𝐿,𝑆 + 𝑏𝑖

𝐿,𝑆)𝒆𝒊𝑳,𝑺

𝐻𝑡𝐿,𝑆 =

𝑖=1

𝑁𝐿,𝑆

(𝑎𝑖𝐿,𝑆 − 𝑏𝑖

𝐿,𝑆)𝒉𝒊𝑳,𝑺

𝑩𝑳

𝑩𝑺= 𝑺

𝑨𝑳𝑨𝑺

𝑒−𝛾𝑛𝑙𝑺𝒏 𝑺𝒏+𝟏

𝑬(𝐑, 𝜽, 𝝋) =𝒋𝒌𝒆−𝒋𝒌𝑹

4𝝅𝑹(1 + 𝐜𝐨𝐬 𝜽 )𝒂2න

0

1

න0

2𝝅

𝑬𝒂(𝒓, 𝝋′)𝒆𝒋𝒌𝒂𝒓𝒔𝒊𝒏 𝜽 𝐜𝐨 𝐬 𝝋−𝝋′

𝒓𝒅𝒓𝒅𝝋′

𝑬𝒂(𝒓,𝝋′)

𝑬(𝐑, 𝜽, 𝝋)

𝑇𝐸11 𝑧

𝑟

Field matching on waveguide interface and scattering matrix calculation: Complex device approximation by cascading multiple waveguide steps:

Far field calculation from obtained aperture field distribution:Comparison of MATLAB implementation against CST MWS:

8

Optimization method – Genetic Algorithm (GA)

• GA searches for parameters which gives minimum of fitness (objective)function.

• Already available in MATLAB

• In this work, optimization for best cross polarization is carried out.

9

Genetic Algorithm

Horn Profile generation

Mode Matching

Far field calculation

Y = Goal -Result

Profile parameters Y

Fitness function

Antenna #1 – Potter dual-mode horn

+ =

TE11 (P≈ 𝟖𝟒%) TM11 (P≈ 𝟏𝟔%)

10

3.3𝜆

22𝜆

0.64𝜆0.48𝜆 0.56𝜆

2 x 0.045𝜆

[P.D. Potter, A new horn antenna with suppressed sidelobes and equal beamwidths, 1976]

Antenna #1 Far field patterns

Antenna #2 – Smooth discrete section shaped horn

12

• Optimized for best average cross-polarization at multiple normalized frequencies. Fitness function:𝑌 = 𝐺𝑋𝑝𝑜𝑙 − 𝐴𝑉𝐺([𝑓𝑠𝑡𝑎𝑟𝑡 …𝑓𝑠𝑡𝑜𝑝])

Resulting profile

22𝜆

0.48𝜆

3.3𝜆

11.64𝜆1.75𝜆

6.61𝜆1.54𝜆

3.75𝜆

13

Antenna #2 Far field patterns

Antenna #3 – conical corrugated horn

3.52𝜆 18.48𝜆

3.3𝜆

0.47𝜆

≈ 0.25𝜆

3 corrugations per 𝝀

• Optimized for best cross-polarization at center frequency

0.48𝜆

14

R

Antenna #3 Far field patterns

15

16

Antenna #4 – Compact profiled corrugated horn• Optimized for best average cross-polarization with reduced spread at multiple normalized frequencies.

Beamwidth optimization added. Fitness function:𝑌 = 𝐺𝑋𝑝𝑜𝑙 − 𝐴𝑉𝐺𝑋𝑝𝑜𝑙 ([𝑓𝑠𝑡𝑎𝑟𝑡 …𝑓𝑠𝑡𝑜𝑝]) + 𝑆𝑇𝐷𝑋𝑝𝑜𝑙([𝑓𝑠𝑡𝑎𝑟𝑡 …𝑓𝑠𝑡𝑜𝑝]) + 3 ∗ |𝐺𝐵𝑊 − 𝐴𝑉𝐺𝐵𝑊([𝑓𝑠𝑡𝑎𝑟𝑡 …𝑓𝑠𝑡𝑜𝑝])|

Resulting profile

2.84𝜆 2.91𝜆 7.72𝜆 1.53𝜆

3.3𝜆3.24𝜆

1.67𝜆0.8𝜆

4 corrugations per 𝝀

T𝐨𝐭𝐚𝐥 𝐥𝐞𝐧𝐠𝐭𝐡: 𝐨𝐧𝐥𝐲 𝟏𝟓𝝀

17

Antenna #4 Far field patterns

Antenna #4 MM vs. CST MWS

18

CST Time Domain

CST Frequency Domain

Profile summary

19

#1 #2 #3 #4

Performance summary

20

Phase center position

21

• Following phase center definition is used – point in horn which gives minimum phase deviation withinilluminated reflector (secondary mirror in this case) subtended angle. This point should be positioned in focus.

Feed efficiencies

22

Antenna #2

Antenna #3 Antenna #4

Antenna #1

Conclusions1. Dual-mode conical Potter horn

Advantages: Simplest to make and lightweight. Suitable for very low or very high frequencies

Disadvantages: Very narrowband.

2. Smooth discrete section shaped horn:

Advantages: Improved bandwidth, and overall performance. Lightweight. Length potentially could be reduced with more optimization and different profile options. Good candidate for RT-32 L/S band feed horn

Disadvantages: Must maintain sharp and accurate flare steps and angles.

3. Conical corrugated horn:

Advantages: Great performance, cross polarization >25 dB, low sidelobes and equal E/H plane beam widths over almost octave bandwidth.

Disadvantages: Expensive to make, Heavy.

4. Compact discrete profiled corrugated horn

Advantages: 30 % smaller length, but similar performance to corrugated horn antenna #3.

Disadvantages: High fabrication accuracy must be maintained

23

Thank You for the attention! Any questions?

24