when capacitance depends on voltage, how to calculate impedance 3

[mapi]

For a simple circuit with only one capacitor C, when C is constant, the impedance is Z(w)=1/jWC. But when C is dependent of the voltage, C(V), then what is the impedance?

Thanks,

Mapi

 

[ScottyUK]

Just substitute the equation for the voltage-dependent capacitance into the standard capacitive impedance equation. You will end up with a V term somewhere in the equation plus whatever other constants and operators (ln, e, etc) are needed.


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[hacksaw]

the usual case is that C is a function of the bias voltage (mostly) so you have c=c(Vdc) and model the circuit in the usual way

 

[jimmyinct]

capacitance does not depend on voltage
voltage depends on capicatance
capacitance is fixed in value

voltage over the capactior is a function of both time and frequency of which are recripocal in nature. You can ball park the voltage in the time domain by the time constant. In the frequency domain, use the voltage divider rule to get voltage.

 

[ScottyUK]

capacitance does not depend on voltage
voltage depends on capicatance
capacitance is fixed in value

Sometimes. But not always.


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If we learn from our mistakes I'm getting a great education!

 

[mapi]

If just substitute equation of C into Z(w)=1/jWC, then Z(w) will be time-dependent, which seems not correct?

In my case, capacitance is indeed dependent of voltage.

When calculating impedance, do we do that in time domain or frequency domain? Complex V(t)/I(t) or V(w)/I(w)?

 

[jimmyinct]

what is your specific application or goal

 

[mapi]

It is an analog: simply my current situation under study with a circuit. Then I need to calculate the impedance from circuit and fit it to the experimental data.

 

[hacksaw]

a lot of circuits use electrically "tunable" capacitors, i.e. non-linear element, if you are confined to nice linear elements then C is a constant unless it goes bad.

 

[mapi]

Unfortunately I do need this non-linear circuit, and try to see if such nonlinear circuit is better than linear circuit.

 

[geekEE]

jimmyinct, check out the voltage coefficients for Y5V and X5R capacitors for some huge drops in capacitance at increasing voltage. And these are certainly very commonly used caps.

Glenn

 

[electricpete]

Draw two curves of V vs C.

First curve represents the capacitor characteristic (what is C for a given V)

Second curve represents the system characteristic (what voltage is created accross the element for a given C).

The intersection of the two curves gives the effective C.

The same thing might be accomplishable using equations.

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[electricpete]

I guess there is also a question of the time frame over which the capacitance response to voltage. If it is much more than a cycle, then approach as above and we have an effective value of C. If it is much less than a cycle, then when we apply sinusoidal ac voltage (I assume that from your post), the current will be non-sinusoidal. This latter behavior cannot be represented by a single value of capacitance.

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[Bronzeado]

mapi,

This problem seems to be very similar to that on how to calculate the impedance of a winding with a ferromagnetic core, where the impedance change with the saturation stage of the core.

This has been normally solved by using methods such those in EMTP-Like software.

Regards,

H. Bronzeado

 

[mapi]

Bronzeado,

Could you please give me the paper information if you know?

Now I am concerned with the definition of impedance: voltage(t)/current(t) in time domain. If we want the impedance in the frequency domain, two methods: 1) FFT of voltage and current, then impedance is V(w)/I(w); 2): FFT of V(t)/I(t). Which is the correct definition?

Thanks,

Mapi

 

[jimmyinct]

there is a section on how to determine the frequency responce in A RLC circuit below. It can be used as template.

http://en.wikipedia.org/wiki/RLC_circuit

 

[BobM3]

Impedance is a function of frequency (for reactive elements)and therefore is a frequency domain problem. It's often times calculated in the time domain at a particular frequency. So, for instance, you might say "the impedance of the circuit at 10 hertz is 100 ohms".

Just curious, what element are you modeling where the capacitance is a function of the voltage?

 

[mapi]

BobM3,
I asked some people in EE, they didn't say time-dependent impedance was wrong.

For my problem, it is just a simplification of a tube with pressure inside, and so the compliance (capacitance) depends on pressure (voltage).

Mapi

 

[hacksaw]

If you are really modelling a pneumatic system, then post it more appropriately.

Impedence in the electrical field is a frequency domain parameter. If you claim time domain variation of the impedence then you have a much more compllex problem that the level of your questions suggest. Perhaps a bit more clarity on your part would make it possible for the forum contributors to help you more effectively.

 

[mapi]

Thank you all for your help.

I think we may do it as:

Given a voltage V(t), we can calculate the current through C(V).dV(t)/dt=I(t), then get the Fourier transform (FT) of V(t) and I(t), respectively. Now we calculate the impedance as: Z(w)=V(w)/I(W).

Please correct me if there is any.

Thanks.