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 x_o 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 » y_d)

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