L2 - Electrostatic Actuators Flashcards
(18 cards)
What is the structure of a Parallel Plate Actuator?
It consists of a lower fixed plate and an upper movable plate.
Attractive force between the plates is balanced by the restoring force of the spring.
What generates the force of attraction in a Parallel Plate Capacitor?
Opposite charge on the plates.
Hence the force depends on the charge on the plates, the surface area, the medium between the plates and the distance between the plates.
State Gauss’s Law in integral form.
𝜀 ∫ E · dA = Q(enclosed)
What is the relationship between voltage (V), electric field (E), and distance (z)?
E = V/z
Electric field = Voltage / Distance
What is the relationship between voltage (V), charge (Q), and capacitance (C)?
C = Q / V
How is capacitance (C) defined in terms of ε, area (A), and distance (z)?
C = εA/z
Derived from Gauss’s Law, Electrical field formula and capacitance formula
What is the formula for work done in charging a capacitor?
U = 0.5CV²
In the parallel plate actuator. What is the expression for total energy (E) stored in the capacitor?
E = -0.5(εA/d-x)V²+0.5kx²
where d = the initial distance
x = the top plate’s displacement
C = εA/d-x
Energy in the capacitor + energy in the spring
How is the force on the movable plate obtained?
By differentiating the energy stored within the system with respect to x.
What condition is met at equilibrium in an electrostatic actuator?
The electrostatic and spring forces cancel, making F=0.
How might the displacement of a plate at equilibrium be calculated?
For a parallel plate actuator
At equilibrium the spring and electrostatic forces cancel.
The force equation F = 0.5(εA/(d-x)²)V²-kx
If F = 0 the equation can be solved for displacement (x)
What is the pull-in point?
For a parallel plate actuator
The critical instability point.
Increasing the applied voltage will increase displacement but as the field strength increases and the plates draw closer they will reach a critical Pull-in point where they will be drawn into contact.
Stiffness (the relationship between applied force and the resulting displacemnt) at the instability point = 0
solving for x yeilds x = d/3
worth practising the proof of this one
What does increasing the applied voltage cause in the electrostatic actuator?
It deflects the upper plate until x = d/3, leading to collapse onto the fixed plate.
Fill in the blank: The force between the plates in a parallel plate actuator is balanced by the _______.
restoring force of the spring.
What does the equilibrium equation allow us to calculate?
For a parallel plate actuator
The deflection x for an applied voltage U.
What is the relationship between charge (Q), capacitance (C), and voltage (V)?
Q = CV
C = Q / V
How can we calculate the pull-in voltage?
For a parallel plate actuator
The equation for force at the equillbrium = 0 and can be rearranged to find the voltage at equilibrium which can be solved by substituting x = d/3
displacement (x) at the pull-in point = d/3
worth practising the proof
Give some examples of devices which use MEMS parallel plate actuators
MEMS parallel plate actuators are used in a variety of devices due to their precision and efficiency.
MEMS Switches: These are used in RF applications for signal routing and switching.
Variable Capacitors: These are used in tunable RF circuits, such as filters and voltage-controlled oscillators.
Micro-mirrors: Utilized in optical applications like beam steering and adaptive optics.
Accelerometers: In these devices, parallel plate actuators are used to sense acceleration by measuring the displacement of a proof mass relative to fixed electrodes
Microgrippers: These are used for manipulating small objects in micro-assembly processes. The parallel plate actuators provide the necessary force to open and close the gripper arms
These devices leverage the electrostatic forces between parallel plates to achieve precise control and actuation.
