# How to measure resonant frequency of piezoelectric material

I just want to know the resonant frequency of piezoelectric material. We can determine by using the equation which is related to the dimension of the material. But i want to confirm it by applying AC voltage source in the sample.

So basically when you apply voltage the piezoelectric material vibrates and using oscilloscope you can determine the frequency. My problem was if AC voltage is your source then you can adjust the frequency but the frequency that you set is also the frequency the will be detected by the oscilloscope? How can i set the frequency of the AC voltage and differentiate the resonant frequency that will be detected by the oscilloscope?

It depends a bit on the equipment you have, and the desired accuracy.

You say you have an oscilloscope. I would start by wiring the crystal to the scope and giving a sharp tap. The response of the crystal (which has a high Q) will be a decaying waveform, whose frequency you can determine.

To get more accurate you want to apply a voltage and measure the current - that is, the voltage across the crystal and the voltage across a resistor in series with the crystal. The phase relationship between these varies rapidly as you cross the resonance - so even if your frequency steps are too coarse to see the (narrow) resonance you would be able to tell that you passed the point because of the phase shift.

At the exact point of resonance there is a 90 degree phase shift between driving force and response amplitude. This makes it an easy measurement to do accurately - more accurate than measuring the response amplitude.

If you look at the thread posted at this site you will see that measurements of the real impedance of a transducer show one or more characteristic dips - each of which corresponds to a characteristic (resonant) frequency. Of course there is a direct relationship between phase shift and real part of impedance... so if you have a network analyzer, it will give you a more direct determination than the method I sketched above.

• So basically what are your trying to say is, i will vary frequency in the pulse generator (keeping the amplitude voltage constant) and then i will measure the voltage across the a resistor with crystal? and the frequency the gives me the highest voltage is the resonant frequency? – Raldenors Sep 1 '16 at 16:41
• Yes, that should work. Note that if the Q is very high, the peak may be very sharp and you might "miss it". This is where looking at the phase of response can help - if you went past the resonance, the phase would shift: this helps you figure out the direction in which you need to move your frequency. – Floris Sep 1 '16 at 16:52
• What is Q sir? and how can i determine the phase shift? is it the values of voltages? – Raldenors Sep 1 '16 at 17:22
• Q is a measure of the width of the resonance: $Q=\frac{\omega}{\Delta \omega}$. The higher Q is, the narrower the range where the amplitude increases significantly. The phase shift is best seen by displaying the wave form of input voltage and response on an oscilloscope. – Floris Sep 1 '16 at 17:44
• Or, is the phase shift the difference between the voltage across the crystal and the voltage across the resistor with the crystal? or the vice versa? – Raldenors Sep 1 '16 at 17:54

As with all resonance experiments, you apply a fixed amplitude voltage at a variable driving frequency, and measure how much current is transmitted. At the resonant frequency the current is maximum.

https://www.americanpiezo.com/knowledge-center/piezo-theory/determining-resonance-frequency.html

• so its a current vs frequency?... actually i'm trying to plot the voltage vs. frequency by applying different voltages – Raldenors Aug 19 '16 at 3:48
• As Floris says, you can use voltage across a fixed resistor in series with the PZT. – sammy gerbil Aug 19 '16 at 4:17