Simulating transient charging current for a capacitor

[Conrad Hoffman]

The common series and parallel models for a capacitor are useful for a single frequency and with sine waves. AFAIK, they're fairly useless for simulating current during a step voltage change, which is anything but single frequency. The parallel model is especially useless because there's nothing at all limiting the instantaneous current. My application is piezoelectric devices where the impedance differs quite a bit from what would be seen with a quality film or other "decent" capacitor. How might one approach the modeling for this using LTSpice or similar?

[Marco]

Do you have a LRC meter?

The parameters for the standard Piezo model, with LCR in parallel to C, isn't too difficult to extract. Though I'd have to look up the formulas (Cp is easy, just measure capacitance away from resonance, then R can be determined at series resonance and Lm/Cm can be determined through the difference between parallel and series resonance). You have to measure them while the Piezo is realistically loaded of course.

[Conrad Hoffman]

Yes, I have the formulas and have created the standard model, but like the capacitor models, it's only useful over a narrow range and doesn't predict transient response. The model is similar to a crystal model, for which there's much documentation, but I think it needs some additional loss terms to be realistic.

[T3sl4co1l]

Most of the time, a first order RLC model gets close enough, and ratings can be respected by following voltage and current limits.

What cap are you looking at, and what waveform?

Tim

[mag_therm]

Recently did a common mode filter which sounds something like your description at RLC component level.
I've added a transient solution to the AC solution:

AC cct and solution:
https://app.box.com/s/0ecw5ibwiorna5hhykwsetenu6l9jvqb
https://app.box.com/s/h9diqtx4k38otk6ceu1ld368peo1ai7q

Transient cct and solution:
https://app.box.com/s/mix9rwwftjxsymhwvn6hcbjj66cw37y5
https://app.box.com/s/pk9pe4682w96s86yiaamlofnkuvwggy8

For the transient, it is necessary to include  capacitor and inductor  ESR and provide realistic rise and fall times along with very small time steps.
( In qucs, a MinStep can be added at which the solution will fail. I used 1 ps although it did not need that low )

[Marco]

Yes, I have the formulas and have created the standard model, but like the capacitor models, it's only useful over a narrow range and doesn't predict transient response. The model is similar to a crystal model, for which there's much documentation, but I think it needs some additional loss terms to be realistic.

Why? The parallel capacitance really only has parasitic inductance and resistance, very little. Trying to apply a fast rising voltage to a piezo crystal isn't much difference than a normal capacitor, except that it rings afterwards.

[Conrad Hoffman]

Thanks! That's pretty much what I'm doing, but you've got a series term in the bulk capacitance that I need to add. The value is frequency dependent, but something close is better than nothing!

@Marco - No, when used as an actuator the Q gets squashed. It's like a bell, but with your hand on it! Hint- a pure reactance can't dissipate any power and therefore can't do any work. To do work you have to dissipate power, so a loss term has to exist.

[Marco]

@Marco - No, when used as an actuator the Q gets squashed. It's like a bell, but with your hand on it! Hint- a pure reactance can't dissipate any power and therefore can't do any work. To do work you have to dissipate power, so a loss term has to exist.

When applying a faster risetime transient, more power will be dissipated in the parasitic resistance of the connections to the Piezo.

That's not part of the standard model, because it's generally not all that important. Why would you drive it in a way which wastes most of the power?

[JohnG]

Some time and jobs ago, I worked on a model for a type of piezo-electric actuator. One issue was that the capacitance was a strong function of voltage, so we measured a Q-V curve. LTspice (and some others) allow you to make a capacitor where you can specify Q as a function of V. You can even use a table if you don't have a nice curve fit. In our case, it was a resonant actuator (piezo air mover), and the losses varied non-linearly with amplitude. We used a low frequency NA (HP3577) and an amplifier to gather data, and made a curve to try and capture this. It worked ok, and was good enough for electrical design.

I'm not sure what kind of actuator you are looking at. If you have a force versus voltage curve, you should be able to do something similar. In fact, you can use Spice to model lumped electro-mechanical systems quite well using B-sources. The challenge is coming up with the model and the parameters.

Hope this is somewhat useful,
John

[Terry Bites]

I've seen equivalent models for piezo transducers; a cap in parallel with a series LCR to simulate the mechanical properties. It going to be very similar or the same to the model for a quartz crystal.
I'd be looking at a crystal macro.

[T3sl4co1l]

Some time and jobs ago, I worked on a model for a type of piezo-electric actuator. One issue was that the capacitance was a strong function of voltage, so we measured a Q-V curve. LTspice (and some others) allow you to make a capacitor where you can specify Q as a function of V. You can even use a table if you don't have a nice curve fit. In our case, it was a resonant actuator (piezo air mover), and the losses varied non-linearly with amplitude. We used a low frequency NA (HP3577) and an amplifier to gather data, and made a curve to try and capture this. It worked ok, and was good enough for electrical design.

As I recall, charge drive is good for these, particularly for avoiding hysteresis (which manifests in voltage as well).  For general purpose actuators that is.  (I think it was AoE3 that mentions this..?)

Tim

[Conrad Hoffman]

Not much freedom on drive. These are very tiny self-contained devices, so boxed in by size, current capacity, voltage rating and speed.

[JohnG]

As I recall, charge drive is good for these, particularly for avoiding hysteresis (which manifests in voltage as well).  For general purpose actuators that is.  (I think it was AoE3 that mentions this..?)

Tim

In my particular case, we were also highly size and cost constrained, especially cost. The modeling was to test the circuit because the transducer (a sort of piezo fan) needed to run at or just above the primary electro-mechanical resonance and I was using a primitive phase feedback to do this.

In the end, the phase feedback was not necessary because the Q dropped like a rock when the air started moving, and this was not well captured by the model.

This is probably not relevant to Conrad's original posting, though.

John

[Conrad Hoffman]

Actually, it's very relevant! These actuators have multiple PZTs and 2-phase drive. Resonance is about 175 kHz and they're heavily loaded, so low Q.