Opto-Mechanical accelerometer sensor (FBG)
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This document discusses the design and testing of an optomechanical fiber Bragg grating (FBG) sensor for measuring acceleration. It presents two approaches to modeling the sensor as a multi-degree of freedom system and analyzing its dynamic response. The first approach models it as two uncoupled single-degree of freedom systems, determining the natural frequencies and mode shapes. The second approach models it as a rigid body with one rotational and one translational degree of freedom. Both approaches show the sensor has a linear response and is dynamically stable over time.
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Lecture Notes: EEEE6490345 RF and Microwave Electronics - Transmission Line
Lecture Notes: EEEE6490345 RF and Microwave Electronics - Transmission Line
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A supplementary document explaining the details is available among my uploads.
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Lecture Notes: EEEC6440315 Communication Systems - Spectral Analysis
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Other RLC resonant circuits and Bode Plots 2024.pptx
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EE402B Radio Systems and Personal Communication Networks-Formula sheet
Programmes in which available:
Masters of Engineering - Electrical and Electronic
Engineering. Masters of Engineering - Electronic
Engineering and Computer Science. Master of Science -
Communication Systems and Wireless Networking.
Master of Science - Smart Telecom and Sensing
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My Online Courses: https://www.byparams.com/courses
From Basics to RF Transceivers
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Opto-Mechanical accelerometer sensor (FBG)
- 5. Problem Need light propagation is changed (modulated) by a mechanical variable Opto-mechanical sensors Optomechanical advantages • Non-contact sensors • High precision • Limited sensitivity/ bandwidth due to thermal and electrical noise • Immunity to electromagnetic interference • Wide dynamic range • Reliable operation
- 9. Strain is used to measure Acceleration ε= ( 𝑴 𝑬𝑨 ) × 𝒂Linear Relation K= 𝑬𝑨 𝑳 Stiffness of FBG 𝑴 𝒙 𝒚 λ 𝐵 = 2𝑛 𝑒𝑓𝑓Λ ∆λ 𝐵=λ 𝐵 1 − 𝜌 𝑎 ∆𝜀 + (𝛼 + ζ)∆𝑇 T.F = 𝑍(𝑠) 𝐴(𝑠) = − 𝑚 𝑚𝑠2+𝑘 𝑚 𝑧 + 𝑘𝑧 = −𝑚𝑎 No damping!! 2nd Order system FBG Small light range (150 nm -248 nm No effect of ∆𝑇 on ∆λ Constant 𝑇 𝑛 𝑒𝑓𝑓 Input Acceleration (𝑎) Output Change in wavelength (∆λ)
- 12. Sensitivity = 𝟎. 𝟐 𝒏𝒎 𝒎 𝒔 𝟐 compared to 10 v/g which resolution of electric accelerometers! No hysteresis due to absence of damping. Dynamic Error: Bandwidth Analysis: y = 2E-10x + 1E-11 0 5E-10 1E-09 1.5E-09 2E-09 2.5E-09 3E-09 3.5E-09 4E-09 4.5E-09 5E-09 0 5 10 15 20 25 30 deltalamda(nm) -Acceleration(m/s^2) Calibration Curve 𝝎 𝒏 = 𝒌 𝒎 = 𝟐𝟗𝟎. 𝟗 𝒓𝒂𝒅𝒔−𝟏 1.85 𝒎 𝒔 𝟐 𝒏𝒎 Resolution: 𝑑𝑒 = 𝑦 𝑘𝑥 𝑠 − 1 Linearity
- 13. t(s) A(𝑚𝑠−2 ) Harmonic input Ramp Input Step input Calibration curve Under effect of different inputs
- 14. Harmonic inputRamp inputStep input A(𝑚𝑠−2 ) t(s)t(s)t(s) A(𝑚𝑠−2 ) A(𝑚𝑠−2 )
- 16. 1st approach
- 17. 𝐿 = 𝑇 + 𝑉 𝑑 𝑑𝑡 𝜕𝑇 𝜕 𝑞 𝑗 − 𝜕𝑇 𝜕𝑞 𝑗 + 𝜕𝐷 𝜕 𝑞 𝑗 + 𝜕𝑉 𝜕𝑞 𝑗 = 𝑄𝑗 𝑑 𝑑𝑡 𝜕𝐿 𝜕 𝑥𝑗 − 𝜕𝐿 𝜕𝑥𝑗 = 0 𝑇 = 1 2 m1z1 . 2 + 1 2 m2z2 . 2 𝑉 = 1 2 [z1 2(k1+k2)−2k2z1z2+z2 2(k2+k3)] 𝑚 𝑞 + 𝑘 𝑞 = 𝑄 𝑚 2 0 0 𝑚 2 𝑧1 .. 𝑧2 .. + 5𝑘 12 − 𝑘 6 − 𝑘 6 5𝑘 12 𝑧1 𝑧2 = 1 2 𝑚 𝑦 .. 𝑦 .. 𝑴 𝟏 𝑴 𝟐 𝒙 𝟏 𝒙 𝟐 𝒌 𝟑 = 𝟏 𝟐 𝑲𝒌 𝟏 = 𝟏 𝟐 𝑲 𝒌 𝟐=1000 K 𝒌 & 𝒎 are Real Positive definite Using System is Dynamically uncoupled System is Statically coupled Stable 𝒚 Using Single Degree system as Multi degree system
- 18. 1st Approach
- 19. 𝑘 − 𝜔2 𝑚 𝑋 = 0 𝑘 − 𝜔2 𝑚 = 0 Natural Frequencies Mode shapes 𝜔1 = 290.991 𝑟𝑎𝑑𝑠−1 𝜔2 = 18406.191𝑟𝑎𝑑𝑠−1 Fundamental 𝑋1 = 1 1 𝑋2 = 1 −1 𝑋 1 𝑇 𝑚 𝑋 2 = 0 𝑋 1 𝑇 𝑘 𝑋 2 = 0 𝑋 1 𝑇 𝑚 𝑋 1 ≠ 0 𝑋 1 𝑇 𝑘 𝑋 1 ≠ 0 𝑋 2 𝑇 𝑚 𝑋 2 ≠ 0 𝑋 2 𝑇 𝑘 𝑋 2 ≠ 0 Orthogonal Stable all over time ! Mode 1 Mode 2 𝑈 = 1 1 1 −1 𝑢1 = x1 + 𝑥2 2 , 𝑢2 = x1 − 𝑥2 2 Principal Coordinates
- 20. Approach 1.A F= 𝟏 𝟐 𝒎 𝒚 .. 𝒚 .. Bode plot of X1 and X2 𝜔1 A(𝑚𝑠−2) 𝜔( rad s )
- 21. Approach 1.B F= 𝒎𝒚 .. 𝟎 Bode plot of X1 𝜔1A(𝑚𝑠−2 ) 𝜔( rad s )
- 22. Approach 1.B Cont’d 𝛺 = 0 𝑡𝑜 𝛺 = 300 𝛺 = 300 𝑡𝑜 𝛺 = 20000 𝛺 = 20000 𝑡𝑜 𝛺 = 30000 Bode plot of X2 t(s) A(𝑚𝑠−2 )
- 23. Auto Correlation = 𝟎. 𝟎𝟎𝟓𝟔𝟐𝟔𝟒𝟗𝟑𝟖𝟑𝟕𝟖𝟐𝟓𝟕𝟏𝟔𝟔 Auto Correlation = 𝟎. 𝟎𝟏𝟐𝟕𝟒𝟔𝟏𝟒𝟖𝟖𝟔𝟑𝟖𝟖𝟎𝟓𝟓𝟑 Approach 1 Using Mathematica 𝑞1 (m) t(s) 𝑞2(𝑚) t(s)
- 25. M R r 𝑚1 0 0 𝐽1 𝑥 𝜃 + 𝑘1 −𝑘1 𝑅 −𝑘1 𝑅 𝑘1 𝑅2 + 𝑘3 𝑟2 𝑥 𝜃 = 𝐹(𝑡) 𝑇(𝑡) 𝜔1 = 1.717 𝑟𝑎𝑑𝑠−1 𝜔2 = 290.991𝑟𝑎𝑑𝑠−1 Fundamental 𝑋1 = 1 1333.43 𝑋2 = 1 0.00976 Real Positive definite System is Dynamically uncoupled System is Statically coupled Stable Orthogonal 𝑈 = 1 1 1 −1 𝑢1 = 2y − 𝜃 1333.42 , 𝑢2 = θ 1333.42 − 𝑦 Using single degree of freedom as a building block Principal Coordinates
- 26. Approach 2.A F= 𝟏𝟎 𝟎 (N) Bode plot of X1 t(s) A(𝑚𝑠−2 )
- 27. Approach 2.B Cont’d Bode plot of X2 F= 𝟏𝟎 𝟎 (N) t(s) A(𝑚𝑠−2)
- 28. Auto Correlation = 𝟎. 𝟎𝟎𝟏𝟖 Auto Correlation = 𝟎. 𝟎𝟎𝟏𝟖 Approach 2 t(s) t(s) A(𝑚𝑠−2) A(𝑚𝑠−2)
- 30. • C.Baldwin, J.Niemczuk, J.Kiddy, and T.Salter. "Review of fiber optic accelerometers." 2005.. • A.Bertholds, and R.Dandliker. "Determination of the individual strain-optic coefficients in single-mode optical fibres." Journal of lightwave technology 6, no. 1 (1988): 17-20. • R.E.Blake. "Basic vibration theory." Shock and vibration handbook 1 (1961): 2-8. • T.Li, Y.Tan, X.Han, K.Zheng, and Zude Zhou. "Diaphragm based fiber bragg grating acceleration sensor with temperature compensation." Sensors 17, no. 1 (2017): 218. • P.Antunes, F.Domingues, M.Granada, and P. André. "Mechanical properties of optical fibers." In Selected Topics on Optical Fiber Technology. InTech, 2012.
- 31. Any Questions?