A Low-Loss, 77 GHz, 8 × 8 Microstrip Butler Matrix on a High-Purity Fused-Silica (HPFS) Glass Substrate
Abstract
:1. Introduction
2. Butler Matrix Theory and Design Challenges
2.1. Working Principle of a 4 × 4 Butler Matrix
2.2. Working Principle of an 8 × 8 Butler Matrix
3. Design and Simulation of 4 × 4 and 8 × 8 Microstrip Butler Matrices
3.1. Material Selection
3.2. 90° Hybrid Coupler
3.3. Crossover
3.3.1. Type-1 Crossover
3.3.2. Type-2 Crossover
3.4. Phase Shifters
3.5. The 4 × 4 Butler Matrix Design
3.6. The 8 × 8 Butler Matrix
- For some cases, the simulated insertion loss is 15 ± 3.5 dB.
- The insertion losses S210 (or S714), S414 (or S515), and S415 (or S514) are unexpectedly too high, most likely due to the long propagation path of the RF signal.
- The return losses for all the ports are less than 20 dB.
- The isolation between adjacent ports is below 20 dB for all the ports except S14 (or S85).
- The phase errors at the output ports are within ±15° compared to phases mentioned in Table 3.
4. Design Validation
4.1. Microstrip Patch Antenna Design
4.2. The 4 × 4 Butler Matrix with an Antenna Array of Four Elements
4.3. The 8 × 8 Butler Matrix with an Antenna Array of Eight Elements
4.4. Performance Comparison of 4 × 4 and 8 × 8 Butler Matrices at 77 GHz
5. Butler Matrix Fabrication
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Radar Type | Frequency (GHz) | Bandwidth (GHz) | Angle of Coverage | Range (m) | Resolution (m) |
---|---|---|---|---|---|
SRR | 77–81 | 4 | ±20–50° | 0.15–30 | ~0.1 |
MRR | 77–81 | 4 | ±6–10° | 0.2–100 | ~0.5 |
LRR | 76–77 | 1 | ±5–7.5° | 10–250 | ~0.5 |
Output Ports | Beam Ports | |||
---|---|---|---|---|
1L | 2R | 2L | 1R | |
A1 | −45 | −135 | −90 | −180 |
A2 | −90 | 0/360 | −225/135 | −135 |
A3 | −135 | −225/135 | 0/360 | −90 |
A4 | −180 | −90 | −135 | −45 |
Phase difference () | 45 | −135 | 135 | −45 |
Beam angle | −14.47 | 48.6 | −48.6 | 14.47 |
Beam Ports | ||||||||
---|---|---|---|---|---|---|---|---|
Output Ports | 1L | 4R | 3L | 2R | 2L | 3R | 4L | 1R |
A1 | −112.5° | 157.5° | −135° | 135° | −112.5° | 157.5° | −180° | 90° |
A2 | −135° | −45° | 112.5° | −157.5° | −180° | −90° | 22.5° | 112.5° |
A3 | −157.5° | 112.5° | 0° | −90° | 112.5° | 22.5° | −135° | 135° |
A4 | −180° | −90° | −112.5° | −22.5° | 45° | 135° | 67.5° | 157.5° |
A5 | 157.5° | 67.5° | 135° | 45° | −22.5° | −112.5° | −90° | −180° |
A6 | 135° | −135° | 22.5° | 112.5° | −90° | 0° | 112.5° | −157.5° |
A7 | 112.5° | 22.5° | −90° | −180° | −157.5° | 112.5° | −45° | −135° |
A8 | 90° | −180° | 157.5° | −112.5° | 135° | −135° | 157.5° | −112.5° |
Phase difference () | 22.5° | −157.5° | 112.5° | −67.5° | 67.5° | −112.5° | 157.5° | −22.5° |
Beam angle | −7° | 61° | −39° | 22° | −22° | 39° | −61° | 7° |
Parameter | W1 | L1 | W2 | L2 | W3 | L3 |
---|---|---|---|---|---|---|
Values (mm) | 0.118 | 0.779 | 0.145 | 0.816 | 0.22 | 0.28 |
Parameters | W1 | L1 | W2 | L2 | W3 | L3 | W4 | L4 | W5 | L5 |
---|---|---|---|---|---|---|---|---|---|---|
Values (mm) | 0.119 | 0.834 | 0.211 | 0.29 | 0.124 | 0.855 | 0.12 | 0.825 | 0.11 | 0.912 |
Parameters | W1 | W2 | W3 | W4 | W5 | W6 |
---|---|---|---|---|---|---|
Values (mm) | 0.116 | 0.192 | 0.226 | 0.12 | 0.11 | 0.122 |
Parameters | L1 | L2 | L3 | L4 | L5 | L6 |
Values (mm) | 0.107 | 0.618 | 0.686 | 0.616 | 0.582 | 0.547 |
Parameters | |||||
---|---|---|---|---|---|
W1 | L1 | L2 | L3 | ||
Values (mm) | 22.5° | 0.119 | 0.532 | 0.0533 | 0.616 |
45° | 0.119 | 0.532 | 0.136 | 0.616 | |
67.5° | 0.119 | 0.532 | 0.2025 | 0.616 |
Parameters | W | L | a | b | c | d |
---|---|---|---|---|---|---|
Values(mm) | 0.819 | 0.9453 | 0.187 | 0.163 | 0.119 | 0.8434 |
Beam Ports | ||||
---|---|---|---|---|
Beam Angle (θp) | 1L | 2R | 2L | 1R |
Calculated | −14.47 | 48.6 | −48.6 | 14.47 |
Observed | −15 | 42 | −42 | 15 |
Error | −0.53 | −6.6 | 6.6 | 0.53 |
Parameters | 4 × 4 Butler Matrix | 8 × 8 Butler Matrix |
---|---|---|
Return loss | <−7 dB | <−9 dB |
Isolation | <−20 dB | <−20 dB |
Maximum main lobe | 10.16 dBi | 9.1 dBi |
Minimum main lobe | 9 dBi | 6.4 dBi |
Elevation angle error | ±6.6° | ±8° |
Total angular coverage | 144° | 162° |
Parameters | Reference [19] | This Work |
---|---|---|
Technology | SIW | Microstrip |
Frequency | 77 GHz | 77 GHz |
Simulation software | HFSS | ADS |
Matrix type | 4 × 4 | 4 × 4 |
Substrate | RT/Duroid 6002 | HPFS |
Thickness of substrate | 0.508 mm | 0.2 mm |
Footprint area | 31.5 × 28.5 mm2 | 9.5 × 8.3 mm2 |
Insertion loss | −6.7 ± 0.75 dB | −8 ± 2 dB |
Isolation | <−20 dB | <−20 dB |
Footprint area of antenna array | 9 × 8.4 mm2 | 2.61 × 8.994 mm2 |
Antenna type | Slot | Microstrip |
Return loss | <−10 dB | <−7 dB |
Maximum main lobe power | 12.21 dBi | 10.16 dBi |
Minimum main lobe power | 9.9 dBi | 9 dBi |
Phase error | 7° | 6.6° |
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Sakhiya, R.; Chowdhury, S. A Low-Loss, 77 GHz, 8 × 8 Microstrip Butler Matrix on a High-Purity Fused-Silica (HPFS) Glass Substrate. Sensors 2023, 23, 1418. https://doi.org/10.3390/s23031418
Sakhiya R, Chowdhury S. A Low-Loss, 77 GHz, 8 × 8 Microstrip Butler Matrix on a High-Purity Fused-Silica (HPFS) Glass Substrate. Sensors. 2023; 23(3):1418. https://doi.org/10.3390/s23031418
Chicago/Turabian StyleSakhiya, Ronak, and Sazzadur Chowdhury. 2023. "A Low-Loss, 77 GHz, 8 × 8 Microstrip Butler Matrix on a High-Purity Fused-Silica (HPFS) Glass Substrate" Sensors 23, no. 3: 1418. https://doi.org/10.3390/s23031418
APA StyleSakhiya, R., & Chowdhury, S. (2023). A Low-Loss, 77 GHz, 8 × 8 Microstrip Butler Matrix on a High-Purity Fused-Silica (HPFS) Glass Substrate. Sensors, 23(3), 1418. https://doi.org/10.3390/s23031418