Can I increase the inductive component stored-energy of a Piezo Buzzer?

Question

In this example of a model for a piezo element, there is an inductive component (I think this is a quartz crystal model -- it should not matter for the question. This graphic was also used here and here):

As the piezo vibrates, there are two forms of energy storage going on... capacitive, and inductive (or something like inductive). I believe that the inductive component comes from the piezoelectric effect, which relates electric field across the ceramic to its expansion on one side, and contraction on the other side. But there is also a mass-related momentum storage-of-energy involved, which means that we can increase the amount of energy that can be stored (at a particular voltage, 50% duty cycle, square waveform, lower frequency). Can I add a small weight to the vibrating mass, thereby increasing the stored "inductive" energy? (or what I'm hoping is the inductive component). And are there any other ways to do this, like adding stiffness (a little), springs on both sides, or connection to a tuning fork tine?

Answer 1

Piezos are electromechanical transducers. That means that they are literally a bridge between the electrical and mechanical worlds. The series LCR circuit in your diagram is the electrical incarnation of the mechanical part of your piezo system. The 'm' subscripts in your diagram stands for 'mechanical' and the values of Lm, Cm, and Rm will change depending on the mechanical system that the piezo is attached to. Co is just the bulk capacitance of the piezo.

Commonly, the values of the mechanical terms are useful when performing modeling (i.e. Spice.) Specifically, the mechanical resonant frequency (and Q) is the same as the electrical resonant frequency of the mechanical branch of the model:

There are direct analogs between the electrical terms and mechanical properties: L is related to mass, C is related to elasticity, and R is related to damping. In fact, the equations of motion for a driven LCR circuit and a driven damped harmonic oscillator have exactly the same form. (I looked for an online reference, but was unsuccessful in finding one suitably simple.)

So, the answer to your question is, yes, you can increase the apparent Lm by increasing the mechanical inertia. That might be done by adding mass.

Answer 2

Ceramic Resonators have the same model as Quartz Resonators and MEMS with big differences , chemistry domain wall angle cut, and RLCC values for chossing either parallel mode or series mode.

For XO low power oscillators parallel mode is better for < 20MHz fundamental and series mode for more stable higher frequency and lower phase noise.

Piezo PZT Xtals are used for buzzers and ultrasonic cleaners and welders can withstand much higher power. The tricky part never discussed is why 10 to 50uW is a common low power for XTals. This is actually because the motional capacitance which is in femtofarads for RF and picofarads for larger power devices, is the vibrational or motional capacitance that actually has thousands of voltages across very pure insulator crystal domain walls that resonate.

I can tune your model for high voltage amplification or make it high current in series for vibration and ultrasonic welding of metal without heat.

• here I show a plot selector for voltage on the mode for each node with an added current sense resistor. and 3 position switch for driver impedance with a low RdsOn driver, a resonant inductor or step-up transformer and a capacitor.

Although my coil is finely-tuned to double resonance with 3 L's {coarse medium and fine}, you would normally use 0 deg. phase-feedback in a self-resonant amplifier to avoid tuning the L and then choose rated power for short bursts or derate for reliability.

You can simply use a step-up axial autotransformer style (single winding with tap) around ferrite core to boost the low voltage over 100V for a really loud buzzer from a 1" diaphram, (120 dB at arm's length) We used to make these for a personal security company in Montreal. I also fixed their design bugs.

Driving with a series C is not used much but shown.

The equations are well-published and even the series resistance can tune the vector impedance and frequency in an oscillator, so it's not quite a simple LC resonator but a dual series / parallel resonator with separate frequencies.