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Joe Ridgeway Relevant Capacitor Equations Current Capacitive Pressure Sensors Initial Proposed Sensor Concept Theory Results Revised Sensor Results Conclusion Plate Area (A) Deriving Capacitance Equation [7] Dielectric thickness (d) d d 0 0 V Edz Plate Area (A) Figure 1: Parallel Plate Capacitor C is Capacitance Q is Charge Q QA A V is Voltage C (2) V Qd d ε is Permittivity of the Dielectric D is Separation Distance A is Plate Area d Qd dz A V is Voltage E is the Electric Field ε is Permittivity of the Dielectric ρ is the Charge Density Q is the Charge A is Plate Area d is Separation Distance (1) Advantages: Low Temperature Hysteresis Low Pressure Hysteresis Low Power Consumption Disadvantages: Poor Resolution Figure 2: Typical Capacitive Pressure Sensor [4] A golf ball striking steel at 150 mph [5] Figure 4: Components of Sensor Figure 3: Diagram of Proposed Pressure Sensor [2] Input(Pressure) -> Displacement -> Radius -> Wetting Area -> Output(Capacitance) Figure 6: Simplified Diagram of Mercury Figure 5: Pressure vs Displacement for Test Diaphragm Pint Patm 2 R (3) Pint is Internal Pressure Patm is Atmospheric Pressure γ is Surface Tension (Mercury – 487 dyn/cm) R is Radius of Drop Relating Applied Pressure to Change in Internal Pressure P Pint Pint 0 (4) Replacing Pint with (3) P Patm 1 1 2 2 Patm 2 (5) R R0 R R0 Input(Pressure) -> Displacement -> Radius -> Wetting Area -> Output(Capacitance) Parallel Plate Capacitor Equation Wetting Area Equation [2] R 2R A R 3R 4 16 2 3 0 A is Wetting Area R is Radius of Deformed Mercury R0 is Initial Radius of Mercury 2 C is Capacitance ε is Permittivity of the Dielectric A is Plate Area d is Separation Distance Low Pressures: Excellent Agreement High Pressures(7-10kPa): up to a 7% difference Dynamic Range: 2500pF High Sensitivity: 250pF/kPa Figure 7: Sensor Capacitance vs Pressure Significant Differences: Dielectric Thickness: 2mm to 1μm Constant: 1,200 to 12,000 Mercury – Drops: 2 to 1 Drop Diameter: 5mm to 3mm Figure 8: Revised Pressure Sensor Diagram Figure 9: Revised Pressure Sensor Physical Assembly Low Pressures: Excellent Agreement High Pressures(2-3kPa): about 3% difference Revised Sensor: High Dynamic Range!: 6μF High Sensitivity: 2.24 μF/kPa First Sensor: Dynamic Range: 2500pF High Sensitivity: 250pF/kPa Figure 10: Capacitance vs Pressure Equation for Thermal Expansion of Mercury A 3T A A is the Original Wetting Area ΔA is the Change in Wetting Area λ is the Expansion Coefficient (Mercury – 9.1x10-5°C-1) ΔT is the Change in Temperature Figure 11: Error in Pressure from +10°C to +40°C Figure 12: Temperature Hysteresis at 3kPa Varies about 1.5% Figure 13: Pressure Hysteresis at -10°C Maximum error < ±0.05% Max ~50ms Significantly Less as Pressure Increases Figure 14: Recovery Time vs Applied Pressure Table 1: Comparison of New Sensor to Existing Pressure Sensors Additional Notes: Dynamic Range: ~6µF Figure 15: Diagram of Inductive Pressure Sensor [8] Figure 16: Components of Inductive Sensor [1] Bakhoum, E.G.; Cheng, M.H.M.; , "Novel Capacitive Pressure Sensor," Microelectromechanical Systems, Journal of , vol.19, no.3, pp.443-450, June 2010 [2] Bakhoum, E.G.; Cheng, M.H.M.; , "Capacitive Pressure Sensor With Very Large Dynamic Range," Components and Packaging Technologies, IEEE Transactions on , vol.33, no.1, pp.79-83, March 2010 [3] W.H. Hayt and J.A. Buck, Engineering Electromagnetics. New York: McGraw-Hill, 2006. [4] http://www.instrumentationguide.com/utilities/pressfund/press_sen_tech1.htm [5] British Broadcasting Corporation [6] Liu Shuangfeng, Ma Tiehua, Hou Wen, Design and fabrication of a new miniaturized capacitive accelerometer, Sensors and Actuators A: Physical, Volume 147, Issue 1, 15 September 2008, Pages 70-74 [7] http://hyperphysics.phy-astr.gsu.edu/hbase/electric/pplate.html#c2 [8] Bakhoum, E. G.; Cheng, M. H. M.; , "High-Sensitivity Inductive Pressure Sensor," Instrumentation and Measurement, IEEE Transactions on , vol.PP, no.99, pp.1-7, March 2011