Nanyang Research Programme Presentation EEE19: Beautiful Arrays Kwa - - PowerPoint PPT Presentation

Nanyang Research Programme Presentation EEE19: Beautiful Arrays

Kwa Shi Min Hwa Chong Institution (College Section)

INTRODUCTION AIMS METHODOLOGY RESULTS AND DISCUSSION CONCLUSION

Example: Satellite Communication

Satellites using same frequency bands Interference with another satellite! Target satellite Antenna with low directivity Antenna with high directivity

INTRODUCTION

INTRODUCTION

Background: Antenna Array Directivity

• Major uses in radar, sonar, wireless telecommunication, etc.
• Radiate power in a specific direction
• Single-element antenna usually limited in directivity
• Antenna array synthesis

1. Array weight - costly in implementation 2. Array geometry

• Current analytical, numerical and algorithmic approaches have yet to

reveal a general theory for non-uniform arrays

INTRODUCTION

Approach: Beautiful Antenna Array Geometry

• Implement symmetry, golden ratio (GR) and silver ratio (SR) in the

determination of inter-element spacings of non-uniform arrays

• Led to many new theories when used in other fields
• GR used implicitly before in phased arrays research – used

solely as a special logarithmic spiral array

• Not explicitly studied in the design of arrays in a general

sense

AIMS

1 2

Investigate effect of beautiful antenna array geometry on antenna array directivity Increase antenna array directivity to higher than that

• f control using beautiful antenna array geometry

METHODOLOGY

Geometry Design

• Design schemes for testing
• Adapt for linear and planar arrays
• Design tests to investigate effects

1

METHODOLOGY

Scheme 1: Scheme 2:

METHODOLOGY

Scheme 3: Scheme 4:

METHODOLOGY

Scheme 0: Linear Control Array

METHODOLOGY

Geometry Design

• Design schemes for testing
• Adapt for linear and planar arrays
• Design tests to investigate effects

1

METHODOLOGY

Planar Control Array

METHODOLOGY

METHODOLOGY

Geometry Design

• Design schemes for testing
• Adapt for linear and planar arrays
• Design tests to investigate effects

1

METHODOLOGY

Geometry Design

• Design schemes for testing
• Adapt for linear and planar arrays
• Design tests to investigate effects

1

Control parameters 1. Array weights 2. Frequency 3. Wavelength Variable 1. Element position vectors

Beampattern Generation

• Real world antenna simulated by computer-programmed isotropic elements
• Plot of array response to a plane-wave front
• with unity amplitude arriving in direction (θ, φ)
• A function of elevation angle (θ), azimuth angle (φ) &

element position vectors (r)

rn(xn, yn, zn)

xn zn yn

Direction of Source

φ θ

Plane-Wave Front

y x x(t) sampled signals at outputs of sensor elements w1 uniform weights y(t) array output

METHODOLOGY

2

x1(t) xL(t) x2(t) w1 w1 w1 y(t)

Performance Measurement

• Observe and record Main Beamwidth, Mainlobe Gain and Peak Sidelobe

Gain

• Narrow Main Beamwidth

Low Sidelobe Level (SLL) High Directivity

METHODOLOGY

3

11-Element Symmetric GR Scheme 4 Root Value 0.587 Uniform Linear Array Main Beamwidth Mainlobe Peak Sidelobe

Gain (abs) Azimuth Angle (⁰)

RESULTS AND DISCUSSION

• Length increase, main beamwidth decrease
• Coincides with general theory of uniformly-spaced linear

arrays – for the same number of elements, the larger aperture will have a smaller beamwidth

• Presence of undesirable spacings of (<0.5 or

>1 wavelength), SLL increase

• Dense regions reduce the elements contribution to the

directivity since they are too close in terms of wavelength, while empty regions increase the under-sampling

Preliminary Testing

RESULTS AND DISCUSSION (LINEAR ARRAY)

Effect of Reflection Symmetry

RESULTS AND DISCUSSION (LINEAR ARRAY)

• 20.00
• 10.00

0.00 Scheme 1 Scheme 2 Scheme 3 Scheme 4 SLL (dB) Scheme Asymmetric Symmetric

* Effect of Reflection Symmetry

RESULTS AND DISCUSSION (LINEAR ARRAY)

RESULTS AND DISCUSSION

Effect of Symmetry vs GR Schemes

RESULTS AND DISCUSSION (LINEAR ARRAY)

RESULTS AND DISCUSSION Scheme> Symmetry

Effect of Symmetry vs GR Schemes

Scheme 1 Scheme 2 Scheme 3 Scheme 4

• 20.00
• 10.00

0.00 Scheme 3 Scheme 4 Scheme 1 SLL (dB) Scheme

RESULTS AND DISCUSSION (LINEAR ARRAY)

Let the distances between origin and X number of elements in a scheme be s1, s2, …, sx. E.g. When the scheme is subjected to a root value of 0.1, the distances will become s1

0.1, s2 0.1, …, sx 0.1.

• To obtain optimized power and best scheme
• Reduce side lobe amplitudes and grating lobes

RESULTS AND DISCUSSION (LINEAR ARRAY)

Effect of GR with Change in Root Value

RESULTS AND DISCUSSION

• 10.00
• 5.00

0.00

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Root Value Scheme 0 Scheme 1 Scheme 2 Scheme 3 Scheme 4

Larger root values forces inter- element spacings to become more similar→oscillation

Effect of GR with Change in Root Value

Further test portions to 3s.f.

Consider main beamwidth when SLLs are similar SLL (dB)

RESULTS AND DISCUSSION (LINEAR ARRAY)

RESULTS AND DISCUSSION

0.00 100.00 200.00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Main Beamwidth (°) Root Value Scheme 0 Scheme 1 Scheme 2 Scheme 3 Scheme 4 .0

Effect of GR with Change in Root Value

RESULTS AND DISCUSSION (LINEAR ARRAY)

RESULTS AND DISCUSSION (LINEAR ARRAY)

Effect of GR with Change in Number of Elements

9 11

RESULTS AND DISCUSSION

+2 gradual

Effect of GR with Change in Number of Elements

• 18.00
• 13.00
• 8.00

3 5 7 9 11 13 15 17 19 SLL (dB) Number of Elements Scheme 0 Scheme 4

RESULTS AND DISCUSSION (LINEAR ARRAY)

RESULTS AND DISCUSSION

Main Beamwidth↓21% SLL↓28% Azimuth Angle (⁰)

11-Element Symmetric GR Scheme 4 Root Value 0.587 Uniform Linear Array Main Beamwidth Mainlobe Peak Sidelobe

Beampatterns of Finalised Symmetric GR Scheme vs Control

RESULTS AND DISCUSSION (LINEAR ARRAY)

Gain (abs)

Effect of Order of Rotational Symmetry

RESULTS AND DISCUSSION RESULTS AND DISCUSSION (PLANAR ARRAY)

Order 4 Order 8

Effect of Order of Rotational Symmetry

• 30.00
• 15.00

0.00 Scheme 0Scheme 2Scheme 3Scheme 4 SLL (dB) Scheme Order 4 Order 8

*

RESULTS AND DISCUSSION RESULTS AND DISCUSSION (PLANAR ARRAY)

• 30.00
• 15.00

0.00 20 30 40 50 60 70 80 90 100 SLL (dB) Number of Elements Scheme 0 Scheme 2 Scheme 3 Scheme 4

RESULTS AND DISCUSSION

but stagnates

RESULTS AND DISCUSSION (PLANAR ARRAY)

Effect of SR with Change in Number of Elements

Let the distances between origin and X number of elements in a scheme be s1, s2, …, sx.

• Eg. When the scheme is subjected to a scaling value of 1.1, the

distances will become 1.1 * s1, 1.1 * s2, …, 1.1 * sx.

• Optimize SLL and beamwidth

Effect of SR with Change in Scaling Value

RESULTS AND DISCUSSION (PLANAR ARRAY)

RESULTS AND DISCUSSION RESULTS AND DISCUSSION (PLANAR ARRAY)

Effect of SR with Change in Scaling Value

0.00 60.00 120.00 1.0 1.1 1.2 1.3 1.4 1.5 Main Beamwidth (°) Scaling Value Scaling Value (≥1)↑, Main Beamwidth↓ Control array has main beamwidth of 40.00⁰, therefore further tested to 2d.p. →1.25, 38.00⁰

RESULTS AND DISCUSSION (PLANAR ARRAY)

Effect of SR with Change in Scaling Value

Scaling Value (≥1)↑, SLL↓

• 30.00
• 15.00

0.00 1.0 1.1 1.2 1.3 1.4 1.5 SLL (dB) Scaling Value 1.25, -23.41dB

RESULTS AND DISCUSSION

Gain (dB)

RESULTS AND DISCUSSION (PLANAR ARRAY)

Cartesian Beampattern of Finalised Symmetric SR Scheme

Main Beamwidth↓5.0% SLL↓18% Elevation Angle (⁰) Gain (dB)

RESULTS AND DISCUSSION (PLANAR ARRAY)

Polar Beampattern of Finalised Symmetric SR Scheme

CONCLUSION

Novel empirical study on the effects of using symmetry, GR and SR in the design of non-uniform antenna arrays on the directivity of beampatterns

Beautiful Antenna Array Geometry: Potential Way of Increasing Antenna Array Directivity

1 2 Symmetry, GR and SR can be used to increase antenna array directivity Significant increase of antenna array directivity in comparison with control

Thank you!