Switching time of a mechanical switch - capacitive model

msandeep92

Hi,

I am trying to solve a problem, where i need to find the switching time of a mechanical switch.

A voltage of V is applied to an acutation pad, and the movable beam is assumed to have a spring constant of K.

I have attached the photo for better clarity.

Please help me out. Consider the damping of the switch due to air also.

Thanks,
Sandeep.

Attached Thumbnails

 

berkeman

Welcome to the PF.

What is the context of your question? Is this for a school research project? Why are you using a capacitive switch instead of inductive? Is this for a nano-scale structure? Why would you still have air in the assembly? What have you done so far on this problem?

msandeep92

Yes. This is a part of my research project.

This is a nano scale structure. This is a capactive switch being used in RF MEMS - one of the latest emerging fields which is hoped to replace the semiconductor switches for RF applications. Semiconductor switches have very high capacticances turning up at high frequencies. So, we use these switches as a replacement, which provide lower capacitance and hence higher isolation.

We are deivcing a new model of the switch for higher switching speed. So, in this regard i need this calculation.

What i have done so far on the beam is:

Electrostatic force Fe = εA(V^2 )/(2*(d-x)^2);

Froce due to spiring Fk = -K*x;

Force due to damping Fd = - b*(dx/dt)

Using conservation of energy:

.5*m*(v^2) = ∫Fdx

F = Fe + Fk + Fd

Neglect the damping as of now.

If i go on integrating Fe and Fd, i get:

dx/dt = √[(εA(V^2)x/m(d-x)d) - k(x^2)/2] = p

From here, i get time by t = ∫(dx/p).

I am struck in this integration, Please help me.

I am not able to understand how to integrate the damping term also.

Thanks,

Sandeep.

msandeep92

You can see this paper(attached) for better understanding.

Attached Files

Closed form expressions for RF MEMS.pdf (105.3 KB, 2 views)