Laplace transformation --> Time varying capacitance

[happylex]

Hi,

I have a network with about 3 milion resistors and 1 milion load sensitive capacitors. The capacitance is directly proportional to strain, and I would like to see what happens in my system when the capacity is varying with C = C_0 + C_A*sin(omgea*t).

How do I now use Laplace transformations to analyse my circuit? Does anyone know?

Edit: I don't think it makes any difference, but all capacitors are connected to the same constant V_ref.

Thanks in advance!

[Benta]

LaPlace is normally only for time-invariant systems. You could do the analysis with different fixed capacitances and plot the result to connect the dots.

[happylex]

Thank you Benta. What you say is not correct, since varying the capacitance induces a change in voltage and current. Think about a microphone, where the voltage goes up as charge stays the same while the capacitor 'plates' come closer together.

Usually we have  C*dV/dt = I,
but in this case we have C(t)*dV/dt = I - V(t)*dC/dt

[Gibson486]

Thank you Benta. What you say is not correct, since varying the capacitance induces a change in voltage and current. Think about a microphone, where the voltage goes up as charge stays the same while the capacitor 'plates' come closer together.

Usually we have  C*dV/dt = I,
but in this case we have C(t)*dV/dt = I - V(t)*dC/dt

I am a little confused.

Are you actually pumping a a sine wave signal through?

Laplace will let you solve this equation in a linear fashion (ie with just algebra), but you may be misguided as to what you are trying to do. That being said, you do not need laplace to do it, so doing the whole transform would be a lot of work for nothing. Everything is first order.

But if you want to figure out, google first order equations and Laplace. As Benta pointed (and he is not incorrect), you will need an assumption of the initial condition.

[happylex]

Yes the only source of the sine wave is coming from the compression of the system. It is like a huge number of condensor microphones in one circuit:

http://www.learningaboutelectronics.com/Articles/Condenser-microphones

[RoGeorge]

Yes the only source of the sine wave is coming from the compression of the system. It is like a huge number of condensor microphones in one circuit:

http://www.learningaboutelectronics.com/Articles/Condenser-microphones

If you want to use an array of microphones like the one pictured in the link, please be aware that the drawing in the link might be wrong. Usually those are active microphones, not passive as drawn in the schematic, they have an internal FET transistor, and the moving plate of the sensing electret capacitor is connected to the FET's grille. That is why an external resistor connected to V+ is needed (the resistor powers the DS of the internal FET). If your microphones are active (with electret and the usual FET inside), then it outputs a voltage proportional with the pressure's variation, so no need to take into account the capacitors at all.

www.es.co.th/Schemetic/PDF/KUC.PDF
https://en.wikipedia.org/wiki/Electret_microphone