Electrostatic Sensing and Actuation

1
Electrostatic Sensing and Actuation

• EE485A Lecture
• 10 September 2009

2
Electrostatics Review

• Parallel Plate Capacitor Equation, again
• Use as a sensor
• Motion sensed my monitoring capacitance change
• Capacitance change is non-linear with d
• Use as an actuator
• Voltage applied to induce force
• Pull-in occurs when voltage exceeds pull-in limit
• Only motion from 2/3 gap to full gap can be
  controlled
• Larger range of motion if you control A instead
  of d

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Interdigitated Capacitors
movable plate
x0
l0
t thickness normal to image ( )
w
w
fixed plate
n fingers (here n 8)
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What they really look like
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3 Types of motion to consider
Longitudinal (most common)
Out of Plane
Transverse
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Longitudinal Sensing
keff
x0
l0y
l0 initial overlap distance y distance from
rest
Linear!
Capacitance Sensitivity (Change in Capacitance
for a Change in y)
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Longitudinal Actuation
Fmech
keff
Felec
x0
l0y
Force is constant as y changes!
No Pull-In! Can control over longer range.
Force balance yields displacement vs. voltage
relationship
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Exercise
keff
x0
l0y

• For structure shown above, x0 1 um, l0 100
  um, n 8, t 10 um
• Determine the capacitance sensitivity to
  longitudinal motion.
• What is the capacitance change associated with 10
  um of deflection?
• If the movable electrode were attached to a 1 ug
  proof mass, determine the effective spring
  constant necessary to cause a 10 um deflection in
  the presence of a 100g acceleration.

9
Exercise continued

• If this same structure (minus the proof mass) was
  then used for actuation, what voltage would be
  required to move the structure 10 um?
• Determine dimensions for the support arms that
  are consistent with your desired spring constant.

10
Out-of-Plane Motion
z
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Transverse Motion

• Usually not intentionally used
• Transverse actuators exhibit pull-in

• Comb drive supports carefully designed to prevent
  transverse motion.

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Look carefully at the suspensions
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