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when capacitance depends on voltage, how to calculate impedance
3

when capacitance depends on voltage, how to calculate impedance

when capacitance depends on voltage, how to calculate impedance

(OP)
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

RE: when capacitance depends on voltage, how to calculate impedance

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

RE: when capacitance depends on voltage, how to calculate impedance

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

RE: when capacitance depends on voltage, how to calculate impedance

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.

 

RE: when capacitance depends on voltage, how to calculate impedance

Quote:

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

Sometimes. But not always.
  

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

RE: when capacitance depends on voltage, how to calculate impedance

(OP)
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)?

RE: when capacitance depends on voltage, how to calculate impedance

what is your specific application or goal

RE: when capacitance depends on voltage, how to calculate impedance

(OP)
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.
 

RE: when capacitance depends on voltage, how to calculate impedance



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.

RE: when capacitance depends on voltage, how to calculate impedance

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

RE: when capacitance depends on voltage, how to calculate impedance

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

RE: when capacitance depends on voltage, how to calculate impedance

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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RE: when capacitance depends on voltage, how to calculate impedance

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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RE: when capacitance depends on voltage, how to calculate impedance

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

RE: when capacitance depends on voltage, how to calculate impedance

(OP)
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

RE: when capacitance depends on voltage, how to calculate impedance



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



 

RE: when capacitance depends on voltage, how to calculate impedance

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?

RE: when capacitance depends on voltage, how to calculate impedance

(OP)
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

RE: when capacitance depends on voltage, how to calculate impedance

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.

RE: when capacitance depends on voltage, how to calculate impedance

(OP)
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.

RE: when capacitance depends on voltage, how to calculate impedance

Not always true.  The FT is transforming a time domain into frequency, but your capacitor is actually a voltage domain device.

If your capacitance is a function of DC bias, then the FT will only be valid for that specific bias.

TTFN

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RE: when capacitance depends on voltage, how to calculate impedance

Yes. To further IRStuff's point I'll return to my previous point.  If the device adjusts it's capacitance on a time scale less than a cycle, then if you apply a sinusoidal voltage you will draw a non-sinusoidal current.

This type of linearity cannot be modeled by a single transfer fucntion - it should be obvious.  The input has only one frequency call it w0... the output has frequency components many call them w0, w1, w2, w3 (even though the fundamental frequency will remain w0).  This can't be practically addressed in the frequency domain.  

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RE: when capacitance depends on voltage, how to calculate impedance

(OP)
Thanks. we may say that the impedance I calculated in my last post is the impedance for that specific input, the pressure V(t).

RE: when capacitance depends on voltage, how to calculate impedance

I think you really really need to tell us more about what you are working on or else the thread will go around in circles forever.

What type of device do you have?

Is your system a mechanical system as might be inferred from your discussion of "For my problem, it is just a simplification of a tube with pressure inside, and so the compliance (capacitance) depends on pressure (voltage)".  

Is it a mechanical system? (yes or no).

Assuming electrical...
When you say voltage dependent... you need to tell us what you mean.

Is the applied voltage purely sinusoidal?  (yes or no?).  Is the capacitance is dependent on the magnitude of the sinusoidal voltage? (yes or no).

Is the applied voltage a sinusoidal plus dc offset bias?  (yes or no).  Is the capacitance a function of the bias voltage ?(yes or no).

Please if possible address at least each of the yes/no questions directly.

Thanks.

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RE: when capacitance depends on voltage, how to calculate impedance

(OP)
Thanks for you questions.

Yes, it is a mechanical system and I try to use circuit to simply the problem. So capacitance for example is C(V)=a*exp(-b*V)--a and b are constants. So C depends on the magnitude actually.

voltage V(t) is not purely sinusoidal, but is periodic and has complex shape, but V(t)>0 all the time.

Thanks.

RE: when capacitance depends on voltage, how to calculate impedance

the only time I've ever needed to map a mechanical system as an electrical one (or vice versa) was for homework... what advantage is it getting you to look at this system as an electrical one?

Dan - Owner
http://www.Hi-TecDesigns.com

RE: when capacitance depends on voltage, how to calculate impedance

The fact that you're dealing with a supposed nonlinear capacitance is the precise reason for not using the electrical analog, since resorting to the electrical analog presumes constant coefficients for simplification.

 

TTFN

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RE: when capacitance depends on voltage, how to calculate impedance

Thanks for the responses.

I think analogies can in general be useful. I agree with IRstuff that an R/C analogy for a non-linear circuit loses the intuitive benefits.  More importantlyl one needs to analyse/understand the system before you can properly formulate any type of non-linear R/C analogy.

I think it is most productive if you can to describe either
1 - the physical system/problem
 or
2 -  the differential equations.

If I take a guess at the differential equations from your commments so far.
I(t) = C(V(t)) * dV(t)/dt
C(V(t))=a*exp(-b*V(t))

Combing the two equations
I(t) = a*exp(-b*V(t)) * dV(t)/dt

Does that resemble your system?  Note as I described, the instantaneous value of C depends soely on the instantaneous value of V.... is that correct?

If the problem is as described directly above, than the non-linearity precludes frequency domain analysis. You cannot characterize this as an impedance that will perform a predictable transformation on input frequency (that type of transfer function is a linear concept).  On the other hand the equation as written above should be very easy to solve in the time domain.  Input V(t). Calculate dV/dt.   Plug and chug either analytically or numerically.  

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RE: when capacitance depends on voltage, how to calculate impedance

I forgot to finish my thought.  Finish the sentence as shown in bold:

"Plug and chug either analytically or numerically to find I(t)"

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RE: when capacitance depends on voltage, how to calculate impedance

Another typo correction in bold:

Quote:

You cannot characterize this as an impedance that will perform a predictable phase and magnitudetransformation based soley on input frequency (that type of transfer function is a linear concept).  

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RE: when capacitance depends on voltage, how to calculate impedance

(OP)
Thank you a lot.

I(t)=dq/dt=d[C*V]/dt, I think we should put C(v(t)) into the derivative sign.

For non-linear capacitance (not LTI system), I didn't know we can't transform it and get the impedance. My problem is this impedance, maybe it is not correct to obtain it just like LTI system: in series or in parallel.

Yes, solving the second-order differential equation numerically is not difficult.

Thanks.
 

RE: when capacitance depends on voltage, how to calculate impedance

You are right that C should have gone inside the derivative.

In general, a non-linear system cannot be characterized by a transfer function.  Transfer functions like Impedance
Z(w) = I(w)/V(w) are an LTI concept.   

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RE: when capacitance depends on voltage, how to calculate impedance

mapi

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

Does that mean that the volume of the tube changes with pressure? If it doesn't, I would say that the "capacitance" is constant.

Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

RE: when capacitance depends on voltage, how to calculate impedance

(OP)
Skogsgurra,

   Yes, the tube is soft, not infinitely stiff. So the tube will expand as pressure increases.

RE: when capacitance depends on voltage, how to calculate impedance

OK, will it expand linearly with pressure? That would make the use of complex numbers meaningless (Z(w)=1/jWC not valid since it needs a constant C) and means that you have to apply a differential equation to describe the relation between applied pressure and "current" i.e. volume flow. For a capacitor, that would look like:

C = k*u
i = C*du/dt

Which combines to

i = k*u*du/dt

Which is the expression to use if there are no resonanses. And that is probably a valid assumption if your du/dt is small in comparison to the tube's "eigenfrequency" (if such an expression is allowed).

Does this really have any practical value? Or is it a mental excersise?



 

Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

RE: when capacitance depends on voltage, how to calculate impedance

(OP)
It is nonlinear, but we may approximate it with a linear curve, though not very good.

Thanks.

RE: when capacitance depends on voltage, how to calculate impedance

If you know the relation between pressure and volume, then use that instead of C=k*u.

It is probable that C=k*u is a very bad relation, since it means that C=0 at zero pressure. Not very likely.

C = C0 + k*u is probably better. C0 is capacitance at zero pressure.

Many containers that infalte (a balloon, for instance) are highly non-linear and are best described by

C = C0 +k*u^m, where m depends on the container's shape. The reason is that, as pressure increases, so does the surface that pressure works on and also that the walls are getting thinner as the container expands.

Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

RE: when capacitance depends on voltage, how to calculate impedance

(This thread's been going for two weeks...)

Couldn't one just enter the basic relationship equations into a spreadsheet, structure them so they can be time-stepped, copy the cells in this first row down X thousands of rows in the time domain, and then plot the results.

Repeat the exercise with and without the C(V) relationship to highlight the difference.

An easy afternoon's work.

 

RE: when capacitance depends on voltage, how to calculate impedance

Yes, one could. Or use Matlab or just about any system.

It was only yesterday that we really got to know what it is about (pressure in a soft tube) so we could do some real work. I was, for a long time, under the impression that we were talking about a capacitance diode or a similar device and didn't think it was worthwhile to add anything to the thread.

Have you got that afternoon? My afternoon is over already smile

Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

RE: when capacitance depends on voltage, how to calculate impedance

The op did state he didn't think numerical solution would be a problem. I had the sense (rightly or wrongly) he was still looking to apply impedance

Quote (electricpete):

In general, a non-linear system cannot be characterized by a transfer function.  Transfer functions like Impedance
Z(w) = I(w)/V(w) are an LTI concept.
One exception I can think of would be so-called "small signal analsysis" that electrical types are very familiar with.

If your applied pressure is something like:
V(t) = V0 + V1*sin(w*t) where V0>>V1, the you may be able to "linearize your system" as follows:
i(t) = d/dt( C(V(t)) * v(t))
recgonizing V0>>V1, then C(V)~C(V0)  (it is an approximatin).
Then
i(t) ~ C(V0) * d/dt(V0 + V1*sin(w*t))
i(t) ~ C(V0) * d/dt(V1*sin(w*t))

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RE: when capacitance depends on voltage, how to calculate impedance

The benefit of such approach might be that the approximate solution is more intuitive.  I have to point out again (lest I be corrected) that it is an approximate solution and so of course the numerical solution using the complete function C(V(t)) is more exact.

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RE: when capacitance depends on voltage, how to calculate impedance

Time stepping all the irreducible relationships is no more an approximation than Numerical Electromagnetic Code (NEC) is an approximation of Maxwell's Equations in their raw form.

Given a non-ideal (real world) vessel, the relationship of a pressure to volume should probably include some consideration that this relationship will almost certainly roll-off at high enough frequencies. If the OP will be working with high frequency pressure waves, then this might be critical.

 

RE: when capacitance depends on voltage, how to calculate impedance

Quote:

Time stepping all the irreducible relationships is no more an approximation than...
Sounds like you are disagreeing with someone, but who it is I have no idea.

I had suggested numerical solution 3 Mar 09 22:27  and original poster agreed it would not be difficult 3 Mar 09 22:55.  The only lingering question seemed to be how the concept of impedance might be applied.  So I have mentioned the idea of linearization which might apply under certain conditions, which would be an approximate solution, as opposed to numerical solution of the complete (not linearized) problem which would be more exact.

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RE: when capacitance depends on voltage, how to calculate impedance

I was replying to something that actually isn't there.

Sorry. 'My bad.'

 

RE: when capacitance depends on voltage, how to calculate impedance

hi,
let me solve all of your problem. step by step.
1. first of all Mr mapi the thing you are interested in was discovered many years ago. so all of us can find about this issue even with the little research
2. as far as i understand to create pressure using voltage lets say input voltage does not equal to output voltage which changes by changing capacitor. so input V(t)not = output V(t). therefore C(v(t))V(t)/dt=i(t) nonsence.
3. like i said there are many applications of your resarch. so are books about it. but since you do not talk about your project exactly, for me it is just dream, i am not ganna give you sources of that project. but i will make my point
4. you must focus on C instead of Voltage. and you must focus on the what sort of gas used in the tube istead of pressure which will be solved easily.
5. in these applications you will find capacity changes with in your example pressure. so voltage sensivity (g) of the capacitor changes. g=d/E. d is the piezo electric constant of the gas. E is dielectric constant of the gas which you must know again. so the only variable is the presssure. with the pressure the output voltage will change also. there is nothing to do with the differencial in this example even if you change the pressure with the input voltage source. V=g*t*p. P is the pressure which will change with Heat or ennarrowing or voltage. t is the distance between two edges of tube which also constant. g is the voltage sensivity of the gas. it is defined by the E and d i indicated above.

to summarize you can convert output voltage to any bigness such as power, soudnd, light. lets say output bigness is voltage V=g*t*p t=d/E. in this application you have to bulit your system according to gas so define this gas's characteristics first.
this application i mean variable capacite have very large use in very large areas. to give example i am the avionics so i find many pratics of this in aircrafts.
  

RE: when capacitance depends on voltage, how to calculate impedance

Let put this thread once and for all... Impedance DOES NOT NOT NOT NOT depend on Voltage.. The steady state time domain impedance equation (Z(w)=1/jWC) said that Impedance depends on Frequency(W) and Capacitance (C) for a Capacitor. So if we have 0hz frequency (DC current) then Impdeance is Infinite.. because 1/j*0*C = infinity and if we have a high frequency signal such a 1Ghz, then the impdence is LOWER. Thus, this equation verify the fact that if we connect a Capacitor to a voltage source, its Steady state current flow will be ZERO, however, initially, there will be current flow until the Capacitor is charged (or reach its steady state) then there will be NO current flow...then from this point on... the Impedance of the capacitor is INFINITE for a DC voltate.. just like what the equation predicted.

If you connect this capacitor across a HIGH frequency sources, then there will be current flow at steady state, and as you increase the frequency of this sources, the impdedance will keep dropping.. So if the same capacitor is now connect to a 1Ghz voltage source, it's impdedance will be lower and thus current is flowing across the capacitor at steady state.

So again..Impedance does NOT NOT NOT NOT NOT NOT NOT NOT NOT NOT NOT NOT NOT NOT NOT NOT NOT NOT depend on Voltage... it depends only on FREQUENCY and CAPACITANCE of the device under analysis.

 

RE: when capacitance depends on voltage, how to calculate impedance

2
I thought this thread was put to rest 9 days ago...

You can have a voltage dependent capacitor (C vs V) - it is called a reverse biased diode (varactor).  

The RF guys use them all the time to tune circuits.  This effect is really useful when you want it to happen, and a real pain when you don't want to happen (like a DC offset signal having different delays depending upon the amplitude).  

Good night,

Z
 

RE: when capacitance depends on voltage, how to calculate impedance

lest we for get the original poster is modelling a pneumatic circuit.

try finding a radio or modern TV that does not use varactors.

so I guess capacitance can depend on voltage after all

good morning
 

RE: when capacitance depends on voltage, how to calculate impedance

Hiya,

I couldnt help post on this long dead forum.

If C is related to V
I=C V`(t) no longer holds

Because V = q(t) / C

So V`(t) = q`(t) * 1/C`(t) - C`(t)/(C(t)^2) (Quotient Rule)

Substituting C = ae^-bV(t) gives

I = -bV`(t) * ae^-bV(t) + C`(V(t)*V`(t))/C(V(t))

I = V`(t) ( ae^-bV(t) - bae^-b(V(t) / (ae-bV(t) )

I = V'(t) * (ae^-bV(t) - b)

you can plot this parametrically to get a hysterisis type loop.

Punch this into wolframalpha:

parametric plot (Sin(t) , (cos(t)*(e^-0.5*sin(t))-0.5)),t=-100...100

Just my thoughts.

Thanks,
Andrew

 

RE: when capacitance depends on voltage, how to calculate impedance

Sorry got the plot wrong

parametric plot (Sin(t) , (cos(t)*((e^-0.5*sin(t))-0.5))),t=-100...100

Thanks,
Andrew
 

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