Crapacitors

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much

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tants

want

caps?

And unlike you he stood up and admitted it.

?-)

Got anything interesting to say about capacitors?

I think the definition JL uses, is standard - i.e. that a capacitor as a default has a linear charge-voltage relationship, and the constant of proportionality is C, the capacitance.

This relates to the large subset of more general electric circuits, namely *linear* circuits, which are much simpler to treat mathematically than general circuits. For instance, the superposition principle applies, which is one consequence of the fact that network equations can be Laplace transformed into s-domain without invoking convolutions and other mathematical nastieties.

In order a network to be linear one, its circuit elements must be linear elements, i.e. resistors with the linear I-V relation, capacitors with the linear Q-V relation, inductors with the linear phi-I relation, and so on [*].

It is unfortunate that the constant of proportionality, C, is called "capacitance" because it sounds so similar to "capacitor" that one might indeed think that it is the linear C-to-something (maybe voltage) relation which defines the the linear capacitor. However, it is the linear Q-V relationship which ties the capacitor to the family of linear circuit elements, which we know and love, not the linear C-V relationship.

What JF wants to call the linear capacitor, might in general usage be called a linear *varactor*, obeying the linear relation C = C0 + k_C * V, which would imply Q = C0*V + 1/2*k_C*V^2 . But then there is a risk someone begins to call the constant of proportionality k_C the varactance, which sounds a lot like "varactor"...

There are two possible definitions one might use, when moving outside the realm where the C was originally defined (the linear circuit theory): Fields uses the definition C = Q / V, whereas Larkin seems to use C = dQ / dV . In the linear case the two coincide. If someone continues to use the linear theory concept of "capacitance" in the nonlinear case, this suggests that he/she may want to linearize the nonlinear circuit for small signals at some dc setpoint. If so, Larkin's definition is the correct one to use.

Regards, Mikko

Nice, I might have written that with a minus sign, C = C0 - k_C * V,

Interesting.. so I wonder which definition the manufacturers use? Differential or do they measure how much charge it takes to get to some voltage?

If I had some of these crapacitors I could try a measurement.

George H.

Just plotting numbers from some of the previously posted data sheets. It looks like it has to be the differential definition. (otherwise I get C*V products that are constant or even decreasing as the voltage is increased.)

George H.

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I've got a few reels, but I can't remember where!

The mfrs.clearly use C=dQ/dV. Capacitance meters do too.

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rkin

Yeah don't bother with any measurment. The link from JL (other thread) to clifton labs also shows that it's dQ/dV.

George H.

capacitor's

capacitor's

Good c-meters apply a small ac voltage, millivolts, and measure the small resulting ac current. They put DC bias on top of that.

Of course, people can choose to define C = Q/V like they choose to define R = E/I and always be right.

I did use c and C somewhere above, as the incremental and gross capacitances.

The Boonton 72 series are great c-meters, available used fairly cheap.

You are very reactive, just like a good capacitor.

?-)

I'll take that for a "no."

--

John Larkin Highland Technology Inc

Precision electronic instrumentation Picosecond-resolution Digital Delay and Pulse generators Custom timing and laser controllers Photonics and fiberoptic TTL data links VME analog, thermocouple, LVDT, synchro, tachometer Multichannel arbitrary waveform generators

Better C meters have variable ac voltage.

Modeling nonlinear capacitors is fairly trivial. I know of several ways of doing it. Most are irritatingly slow.

However, they don't adequately model the behavior of a Y5V ceramic. I did some detailed measurements recently. Small signal AC capacitance versus DC bias can be accurately modeled with a 5th order polynomial. However, stored charge versus applied DC, measured with an electrometer, follows a totally different curve, almost linear, nearly the nominal capacitance.

Put another way, we have a "slow" capacitance, and a "fast" one, which are quite different. I need to investigate C versus f, next.

LTspice's nonlinear capacitance model (Q=f(V)) doesn't appear to work with polynomials, at least in .ac analyses BTW.

Pspice capacitance model has quadratic voltage coefficients, which LTspice barfs at.

It

better.

barely

My first two ideas didn't work out.

?-(

Thank you for trying. I believe simple non-linearity is not enough. A region of negative differential impedance is probably necessary, or some sort of storage effect. Either way, one needs a bifurcation in its phase space trajectory somewhere. Sinple non-linearity doesn't do that.

I don't know what to make of John's results then. I should look into this in some more detail. So many projects, so little time...

Jeroen Belleman