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.

 

[berkeman]

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.

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.

 

[PJC01]

I would approach this problem by first considering the fundamental principles of mechanical switches and their operation. A mechanical switch works by using a movable beam or contact to make or break an electrical connection, allowing current to flow or not. In order to determine the switching time, we need to understand the factors that affect the movement of the beam and how it relates to the voltage and spring constant.

Firstly, the voltage applied to the actuation pad will create an electric field, which will generate a force on the movable beam. This force will cause the beam to move, and the speed of this movement will depend on the strength of the electric field and the mass of the beam.

Secondly, the spring constant of the beam will also play a role in the switching time. A higher spring constant means that the beam will require more force to move, resulting in a slower switching time. On the other hand, a lower spring constant will allow for quicker movement and a faster switching time.

In addition to these factors, we must also consider the damping of the switch due to air. Damping refers to the resistance that a material or object experiences when it is in motion. In this case, the air surrounding the switch will create a resistance to the movement of the beam, slowing down the switching time.

To calculate the switching time, we can use the equation t = 2π√(m/K), where t is the time, m is the mass of the beam, and K is the spring constant. However, in order to factor in the effects of the voltage and damping, we would need to use a more complex equation that takes into account these variables.

In summary, to determine the switching time of a mechanical switch, we need to consider the voltage, spring constant, and damping of the system. By understanding these factors and using appropriate equations, we can accurately calculate the switching time and optimize the performance of the switch. I hope this helps in solving your problem. Good luck!