Piezoelectric Element Impedance Question

[Evan.Cornell]

Does a piezoelectric element's impedance change with applied amplitude?

I'm wondering if, all other factors being equal, a larger or smaller applied signal amplitude will cause resonant/anti-resonant frequencies to shift around, or the absolute impedance value to shift up or down.

[Conrad Hoffman]

Yes, the materials are usually far from ideal. The harder materials (type 4 and 8 ) will do better. Also consider the fact that a pure reactance can't dissipate any power. If the PZT is going to do any work, there will have to be a loss component. That loss component will change with the mechanical loading. IOW, the dissipation factor will rise.

[Evan.Cornell]

So is it any use using a standard bench RLC/impedance meter to get impedance curve with a 0.5Vrms-2Vrms range of signal, when the final application will have orders of magnitude higher excitation voltage?

Or do I need to do a more manual impedance measurement using scope probe and current probe at the excitation signal level I need?

[Conrad Hoffman]

It depends on how good an answer you need and the type of material. If you're going to be running under power at resonance, you'll need to measure at the actual signal levels. If you're just roughly characterizing the material, a low voltage measurement might be good enough. Need more info.

[ejeffrey]

Capacitance usually goes down at high voltage much like a high-k ceramic capacitor.  They are frequently made of the same materials.  A low voltage measurement with an LCR meter will give you a worst case load if you want to know how beefy of a driver you need.  But it depends on how accurate of an answer you need.

[John Heath]

You can change the natural resonance of piezoelectric devises by added or taking away mass. A quarts crystal at 1 MHz can be moved up to 1.1 MHz by filing bits off the edge of it. I use to do this for non critical pinballs for TV IF alignment. Those crystals frequencies were had to find so just file down a crystal that is close. You want to make real sure you do not file too much off as it is hard to go back , ha. I have a piezoelectric devise on my bench the resonates at 60 Hz. You hear me right 60 Hz! It was done by adding a sheet of fiberglass increasing its mass. The reason was to have a really quiet fan that is very reliable. I have a picture of it. It is hard to tell from the picture but if you look close you can make out the two fiber sheets waving back and forth at 60 Hz. It runs off 120 volts AC house wall plug with a 10 K resistor is series.

[Evan.Cornell]

I'd be running high power, but not necessarily at the resonance point. There are LC components upstream of the piezo (think class-D amplifier filter), and I need to be able to simulate all the complex impedance interactions accurately. I need to know the impedance that the amplifier sees to ensure I don't present too low (in ohms) of an impedance that will cause over-currenting, and too high of an impedance that won't allow me to get the desired power output.

[dmills]

I used to work in sonar, where the standard approach even for materials run at kV levels was just to use an HP 4192A to plot a G/B curve via GPIB, this was usually close enough.

Temperature and voltage matter to a degree, but voltage tends to make the things non linear on a cycle by cycle basis, so you get intermod and harmonics, generally not a problem (Most of the time!).

What we did find is that making sure the transducer face has fully wetted out is important before making these measurements, a handful of bubbles on the front face can cause chaos when trying to measure the admittance.

In terms of matching, a tuned transformer can be your friend (Make the secondary inductance resonate the fixed capacitance of the transducer), and drive the primary (wound to have a sane voltage and magnetising inductance) with a RLC matching network (The R extends the bandwidth and mostly dissipates power near the band edges). Because of the resonant secondary, this is more of a coupled choke sort of situation so you often find you need a gap, and the driver has to  work into a very low impedance at the start of a pulse until the resonant current builds in the secondary circuit.

For sonar, a simple bridge drive with active clamp gets it done often as not.

Regards, Dan.

[Evan.Cornell]

Dan,

That was a very helpful response. Here's a few more questions.

• Wetting during impedance measurement - does it matter if the transducer is in little bucket of water vs. "infinite" bucket? Effect of reflections on the impedance measurement?
• Matching - I don't necessarily want to operate at resonant point, so how would you suggest handling the matching in this case?
• Modeling - is the C in parallel with series RLC model of piezo that I see only applicable around the resonance point?

[John Heath]

Dan,

That was a very helpful response. Here's a few more questions.

• Wetting during impedance measurement - does it matter if the transducer is in little bucket of water vs. "infinite" bucket? Effect of reflections on the impedance measurement?
• Matching - I don't necessarily want to operate at resonant point, so how would you suggest handling the matching in this case?
• Modeling - is the C in parallel with series RLC model of piezo that I see only applicable around the resonance point?

Matching. By their nature they are high voltage low current. I would run with an flyback transformer from an old TV and use the high voltage business end of it to drive the piezoelectric. With both the piezo and transformer off resonance you could drive it with a function generator to get a feel of what you need for a driver. With a little luck it could be as easy as a off the self audio amp, nice and cheap.

[dmills]

Little buckets don't work at all well, you need to be at least out into the far field, which for a large transducer at high frequency can be a LONG way (Think 10m or so), for smaller things that are less directional you need less distance, for some measurements (particularly things like beam patterns) temporal gating on the analyser is your friend.
Some companies offer test cells with absorptive foam lining that claim to emulate a large body of water, but I have no experience with these.
To get the transducers to wet out, spray with a dilute solution of washing up liquid before dropping it into the water.

RX off resonance is not a problem, just use a high impedance preamp close to the transducer, but I wish you luck getting much power into the thing more then about an octave off resonance, that is quite the trick (Note that many transducers have two usable resonances, sometimes with very different radiation patterns (Ring transducers with both hoop and thickness modes, looking at you). The acoustic matching between the ceramic and the water is often a 1/4 wave impedance match done with something like a carefully chosen thickness of FR4 in a simple device, or either a 1-3 piezo composite or something like a Tonpills element in low frequency devices. 

Matching is matching, the standard RF methods apply, and usually you are trying to get a flatish response between the two usable resonances and maybe just a bit outside them.

There are two capacitors in the standard model of such things, the series one (Motional capacitance) and the parallel one at the input of the network (The 'Fixed' capacitance, which as its name suggests does not much change ,well apart from temperature and ageing).

They are actually not all that low current, you can have 10A circulating at resonance with a kV across the thing, hence the gapped core in the shunt inductor.

Regards, Dan.

[Evan.Cornell]

If my amplifier can drive the element off-resonance (whatever voltage is required at that particular impedance level to achieve the desired power numbers), will the piezo actually vibrate? Or is there something about needing to have the piezo present as a resistive load rather than reactive?

[dmills]

Have a look at the GB curve for your transducer, you will find that producing any real level in the water off resonance requires the sort of voltages (And thus currents in the fixed C) that make it ah, "difficult").

Can it be done? Sure, if you only want tiny levels in the water, but you would find it difficult if you were after the sort of 200dB SPL (Ref 1uPa, standard for underwater work) that is considered normal for a sonar transmitter.

Note that not only is the electrical match difficult off resonance, but there will be significant losses in any acoustic matching layer which will now be the wrong thickness to produce the desired transformation.

Usually you can manage a sort of flatish octave of bandwidth on transmit without the efficiency going too horrible, more is a big ask.

Regards, Dan.

[Evan.Cornell]

Dan,

Understood. Just to clarify, by GB curve, do you mean impedance vs. frequency, or perhaps you mean SPL(in the water) vs. frequency?

[dmills]

GB is Conductance (G) and Susceptance (B) vs frequency, for various reasons this is generally used for sonar transducers instead of a complex impedance, (which is clearly just the reciprocal of G+jB.

Regards, Dan.

[John Heath]

If my amplifier can drive the element off-resonance (whatever voltage is required at that particular impedance level to achieve the desired power numbers), will the piezo actually vibrate? Or is there something about needing to have the piezo present as a resistive load rather than reactive?

A off the shelf amp and possibly a step up transformer to match the impedance.

I was stewing on your problem at work today. You indicated an interest in Knowing L R C properties of the piezoelectric while it was running dynamically. This brings to mind a dirty trick HP used a long ago to quickly test components on a PC board. They would send out an sine wave  impedance 0 then monitor current at - 90  , 0 , + 90 degrees chopped up clean with a square wave to FET switches.  By measuring AC at -90 , 0 and + 90 degrees you have the C R L impedance in one shot without fancy calculations for a given frequency. As luck would have it all computers and lap tops have the required test equipment in them in the sound card standard. 2 function generators with FM AM and most importantly in this case phase change between function 1 and function generator 2.  In short you will only have to sort out the software details as the hardware is already there in any computer for C R L details of the piezoelectric unit while it is running.

[james_s]

I remember seeing ads for those piezoelectric fans, thought they seemed cool but I never had one. I've never seen one in any kind of equipment either, I wonder if they ever achieved any degree of commercial success?

[John Heath]

I remember seeing ads for those piezoelectric fans, thought they seemed cool but I never had one. I've never seen one in any kind of equipment either, I wonder if they ever achieved any degree of commercial success?

I think I found it in a junk electronic shop. Being unusual I had to have it. I tested it's natural resonance by driving it directly with a function generator. It turned out to be surprisingly high Q only operating from 58 to 61 Hz. Off frequency is only 1/3 the movement. The nice thing about this fan is there are no bearings to dry out. To this day I do not know how the fan was used nor have I seen it in any electronic equipment. It's a mystery.

[Conrad Hoffman]

Running off-resonance is no problem, it can just take a lot of voltage to accomplish anything. Look at the D31 and D33 constants for the material to get an idea of the sensitivity. We used to tune optics with stacks of disks, usually about 0.05" thick, running at 1 kV. Motion was a few to a few dozen micrometers at low frequencies. Arcing was sometimes an issue. 

[dmills]

Yup, sounds about right, you quickly learn a lot about the virtues of Kapton tape and vacuum degassing of potting compounds when playing with that stuff.

DC for micropositioners is a rather different problem to driving power into an acoustic load of course.

Regards, Dan.

[Conrad Hoffman]

True. Of course off-resonance not only do you not get much motion output, but you still have to drive the bulk capacitance at possibly a high frequency and high voltage. You can resonate it with a low loss inductor, but the circulating currents can still be surprising. Inductor losses become an interesting topic, depending what frequency is chosen. I once worked on a system that had to run at 1 kHz and a very high power level (100W+). The customer just didn't believe the acoustic output would be a problem. Even with hearing protection it was hard to be in the same room with it!

[dmills]

I did a kW over ~2-4kHz for a marine mammal deterrent system, that thing was pigging loud even above the water, I would have hated to be a diver anywhere in the area. Incidentally, you know you have too much Q when the free flooded ring about a foot across keeps failing due to internal arcing. 

The fixed cap does tend to make for large currents in that loop, the saving grace for sonar is that you usually run **WAY** less then 1% duty cycle.

Regards, Dan.

[Evan.Cornell]

So I'm running into an issue where I can easily get a couple hundred volts peak-to-peak and an amp or two peak-to-peak into the piezo element, but it's below resonance, and current is close to 90deg (maybe 77-85deg) out of phase with voltage. Obviously, voltage * current = power, and so even my peak power is rather lower than I'd like. Does this mean I'm not actually doing work (i.e. converting signal to sound) in the piezo element?

Do I need to have matching network to make the impedance mostly real in the frequency range of interest, in order to actually get mechanical output for all my voltage?

Thanks!

[John Heath]

So I'm running into an issue where I can easily get a couple hundred volts peak-to-peak and an amp or two peak-to-peak into the piezo element, but it's below resonance, and current is close to 90deg (maybe 77-85deg) out of phase with voltage. Obviously, voltage * current = power, and so even my peak power is rather lower than I'd like. Does this mean I'm not actually doing work (i.e. converting signal to sound) in the piezo element?

Do I need to have matching network to make the impedance mostly real in the frequency range of interest, in order to actually get mechanical output for all my voltage?

Thanks!

Quote

Do I need to have matching network to make the impedance mostly real in the frequency range of interest, in order to actually get mechanical output for all my voltage?

End quote

Wow that was a lot of information in a succinct intuitive way that does not need a calculator to understand and act on . Nicely done. Have not heard it put that way but I know exactly what you mean. Matched impedance is the max energy transfer point with 50 percent efficiency and 100 percent real power.

 

[T3sl4co1l]

You don't need a matching network, if your amplifier can supply all the reactive power that must come with the desired output power.

Acoustic as well as electrical matching would seem to be desirable here!

Tim