Checking the resonant frequency of a piezoelectric crystal

Having failed to get a tactile response from a small piezoelectric crystal, I wanted to check that I was hitting it with the correct driving frequency. This is the frequency that makes the crystal resonate. I found a test circuit and method on this website. The schematic for the testing circuit shown below is copied from that website.

 

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

I breadboarded the circuit and used my Digilent Analog Discovery 2 as a network analyser to check on the resonant frequency. What does a network analyser do? This inputs sine waves with a range of frequencies across R1 and ground. R1 and R2 create a restor bridge, with the piezoelectric crystal (the ‘ceramic element’ in the diagram above) in parallel with R2. The output from the piezo crystal in series with resistor R3 measured for each of the input frequencies. The magnitude of the output and input waveforms and their phase difference is plotted by the network analyser module. This tool is often used with filters to characterise their behaviour. In this case I wanted to see if the output of the test circuit changed at what should be the resonant frequency of the crystal – quoted as 40 kHz by the manufacturer.

A photo of the testing circuit is shown below. This implements the schematic shown above. I used 100 Ohm resistors for R1 and R2 and a 120 Ohm resistor for R3. I did not implement R4 – the variable resistor as I am not looking to measure the equivalent resistance of the piezoelectric crystal at resonance. I am just verifying what the resonant frequency of the crystal is. The bread board circuit has the input on the right and the output on the left of the photo. Two crysals are soldered on to the green circuit board. I tested both and got similar results.

Piezoelectric crystal frequency response testing circuit

The input and output leads for the network analyser can be seen connected to the board. The test signal is input using the yellow lead on the right. The orange lead is oscilloscope channel 1 which measures the input signal. The blue lead in the middle is the second oscilloscope channel, which is used to measure the relative amplitude and phase of the output signal relative to the input signal. The three wires on the left of the photo are all connected to the circuit ground.

The output from the network analyser can be seen in the screen grab below. The amplitude of the output channel is the blue line in the top half of the screen and the phase relative to the input signal is shown in the bottom half.

Network analyser output, red cursor at 40 kHz, top amplitude, bottom phase.

We can see a hump, which using the horizontal cursor (the vertical red line) I can measure is pretty much at 40 kHz. Now you might say the hump looks small. It is roughly 10 dB in height, which is a factor of 3 in amplitude. The phase is all over the place. Naturally, I wanted to ‘scope the input signal to see what the network analyser was doing. As I was out of ‘scope channels on the Discovery 2, I hooked up a Tektronic TBS1104 ‘scope. I can see that the input signal is a sine wave. As the network analyser ramps up the input frequency, I can see the sine wave also increasing in frequency. Kind of like watching a spring compress.

The full testing rig can be seen below. The ‘scope on the left shows the input signal – a smooth sine wave. The board with the crystals is on the bottom edge of the photo at the left. You can never have too many wires on your desk.

Piezo crystal testing arrangement.

The Discovery 2 claims a resolution of 0.32mV. The input to the circuit from the network analsyser is 8 V peak to peak.

8/0.32×10-3 = 25,000 = 87.9 dB

So the amplitude measurements of -56 dB to -80 dB are within the Discovery 2’s stated resolution.

To be more thorough, I could use the amplifying circuit I designed in https://www.seismicmatt.com/200v-piezo-crystal-driver/ to generate an input of >100 V to the crystal, which should give me better resolution as the output signal would also be much higher. However, life is short and I’ve sunk enough time in this project. I was hitting the crystal with the correct signal. I just couldn’t make it vibrate enough to be tactile.