# Exercise 7.1-2 Capacitors and Forces

# Forces in Capacitive Structures

| Let's look at the three different situations where we can produce forces electrostatically by using capacitive structures
|  | We consider one fixed plate with either a given area A or a dimension h · l (h would be the height in the z-direction in the drawing below), and a moveable plate of identical dimension to keep things easy. We also have a spring with a spring konstant k to keep the moveable plate in force equilibrium. The position xo is the equilibrium position for zero voltage. The terminals show schematically how voltage would be applied.
|  | We consider only movements in the x-direction as shown for the three configurations given (where the plates have moved some distance x from their equilibrium position (zero voltage at x = 0).
|  | The third configuration embodies one element of a comb structure that we have encountered a few times already. We assume that there is a potential differenceU between the plates of the capacitors.
| Here are the questions:
|  | 1. Find the proper relations for the forces pulling at the moveable plates for all three configurations.
|  | 2. Compare the relative strength of the first and third configuration (you may assume that y » yd)
|  | 3. Discuss the pros and cons of the two configurations for driving an actual actuator.
| Hint: Consider the work W = E needed to move a plate and remember that Force F = –dW/dx

| Solution

With frame

7.1.3 MEMS Sensors and Actuators

Solution to Exercise 7.1-2 Forces in Capacitive Structures

© H. Föll (Semiconductor Technology - Script)