# Highly Sensitive Capacitive Pressure Sensors

```Joe Ridgeway
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Relevant Capacitor Equations
Current Capacitive Pressure Sensors
Initial Proposed Sensor Concept
 Theory
 Results
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Revised Sensor
 Results
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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 QA 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)
Low Temperature Hysteresis
Low Pressure Hysteresis
Low Power Consumption
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) -&gt; Displacement -&gt; Radius -&gt; Wetting Area -&gt; 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)
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) -&gt; Displacement -&gt; Radius -&gt; Wetting Area -&gt; 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
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
 3T
A
A is the Original Wetting Area
ΔA is the Change in Wetting Area
λ is the Expansion Coefficient (Mercury – 9.1x10-5&deg;C-1)
ΔT is the Change in Temperature
Figure 11: Error in Pressure from +10&deg;C to +40&deg;C
Figure 12: Temperature Hysteresis at 3kPa
Figure 13: Pressure Hysteresis at -10&deg;C
Maximum error &lt; &plusmn;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
Dynamic Range: ~6&micro;F
Figure 15: Diagram of Inductive Pressure Sensor [8]
Figure 16: Components of Inductive Sensor
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[1] Bakhoum, E.G.; Cheng, M.H.M.; , &quot;Novel Capacitive Pressure Sensor,&quot; Microelectromechanical
Systems, Journal of , vol.19, no.3, pp.443-450, June 2010
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[2] Bakhoum, E.G.; Cheng, M.H.M.; , &quot;Capacitive Pressure Sensor With Very Large Dynamic Range,&quot;
Components and Packaging Technologies, IEEE Transactions on , vol.33, no.1, pp.79-83, March 2010
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[3] W.H. Hayt and J.A. Buck, Engineering Electromagnetics. New York: McGraw-Hill, 2006.
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[4] http://www.instrumentationguide.com/utilities/pressfund/press_sen_tech1.htm
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