Piezoelectric element modeling

Here is an electrical model of a power piezo transducer. I pulled the component values from the following video: https://www.youtube.com/watch?v=EAFNjyx3uX0. This matches behaviorally with what I’ve read. C3 is representative of the electrical capacitance of the piezo element and electrodes, and the series LCR circuit composed of L1, C4 and R3 is representative of the mechanical domain inertia and compressive spring forces.

An AC sweep reveals the following current response:

Note the resonance at 28kHz where current is maximized, and the anti-resonance at 34kHz where current is minimized. The goal for most ultrasonic drivers is to drive at either resonance or antiresonance, depending on application.

Drive circuit modeling

I am starting with the power driver from: http://www.imajeenyus.com/electronics/20110514_power_ultrasonic_driver/index.shtml

To increase output power I’m turning the half bridge to an H bridge, which will approximately double the drive voltage. Here is a spice model of an h-bridge driver, piezo transducer, and matching network. The H-bridge will approximately generate a square wave output voltage.

You can see the issue that is addressed at the top of the above article: namely lack of matching network. This causes huge current spikes in the mosfets on switching and poor drive voltage, as shown below:

The problem

So clearly I need some sort of matching network, or a sinusoidal driver. The major advantage of an H-bridge is that the FETs are nearly always in saturation, which greatly reduces the heat they produce. That said, I’m fairly confused about how to go about matching this. The fundamental frequency is already tuned to match the fundamental of the transducer. From playing around with spice a bit, I now suspect it has to do with matching higher-order harmonics of the drive waveform. The impedance of the transducer is inductive for anything much higher than the anti-resonant frequency. I added an LC matching network that puts a resonance at the 3rd harmonic (87kHz). Here is the full model with matching network and the current response with and without the network.

This barely shifts the primary resonance, but does substantially change the impedance to the 3rd harmonic. I would expect this to improve my current spikes, but instead, it does nothing:

Here is the network added to the total model, and the resulting current through M1:

I’m not really sure what to do from here. I’m having trouble finding useful results on google as most searches for “impedance matching” and variations thereof turn up RF matching systems. These mostly discuss matching resistive loads to the intrinsic impedance of a transmission line, not inductive loads in a lumped element system.

I’ll verify these model results with some real world devices when I have all the parts necessary. If i come up with anything, I’ll post it here. In the meantime, any ideas would be great.