## Characteristics of a piezoelectric transducer

I study acoustics at the dept. of physics, University of Bergen. You can visit the home page here.

### Project description

Use a set of data where the conductance and susceptance is measured of a transducer, with a wide range of frequencies on an impedanceanalysator. I want to get to know this transducer so i can implement its characteristics in my work.

### Introduction

The purpose of this project is to study some typical characteristics to a piezoelectric element, with use of measurements and a simpel model based on discrete elements("BVD-model").

### Execution

The piezoelectric element was connected to take measurements of conductance G, and susceptance B. The measurements started at 100Hz and was stepped with 2kHz up near the first resonance frequency. Near the resonance there where used higher resolution to get the results more accurate. This was done equivilantly at the second resonance frequency.

### Data

My data includes frequency, conductance, susceptance, resistance and reactance in a text file. The measured values is conductance and susceptance, and the resistance and reactance has a direct link to conductance and susceptance. These convertions where done in excel before i started the project. The text file is easy to use with 5 different parameters.

### Theory

When the conductance is at maximun there is serial-resonance fs, and when resistance is at maximum there is a parallel resonance fp. The admittance Y is defines as Y = G + iB, and the impedance is defined as Z = R + iX, where G is conductance, B is susceptance, R is resistance and X is reactance. To determine values for the components in an equivilantcircuit ("BVD-model") one can use these relations:

### Some thoughts around the figures

Figure 1: Conductance. This figure is used to look at the two serial-resonances which we need in the calculations

Figure 2: Susceptance. Susceptance is the imaginary part of the admittance. We need the susceptance to see how the admittance vary with frequency.

Figure 3: Comparison of Conductance and susceptanc. This is not that useful, but it is interesting to see how they vary differently with frequency.

Figure 4: Admittance circle for the serial-resonances. This is just a comparison of the two circles you get for each serial-resonance

Figure 5: Admittance circle for the first serial-resonance. You can find the conductance value for the first serial-resonance by finding the maximum value of conductance.

Figure 6: Admittance circle for the second serial-resonance. You can find the conductance value for the second serial-resonance by finding the maximum value of conductance.

Figure 7: Resistance. This figure is used to look at the two paralell-resonances which we need in the calculations

Figure 8: Reactance. Reactance is the imaginary part of the impedance. We dont use this directly in our calculations, but is interesting to see how it is varying with frequency.

Figure 9: Comparison of resistance and reactance. This is not that useful, but it is interesting to see how they vary differently with frequency.

### Calculations

For the first resonance: Component value for the first serial-resonance is 50560Hz. To find this value you can either find the frequency value from the first peak in figure 1, or go into the text file and find where the conductance is at maximum the first time.

Ro: Resistance for the blocked part of the transducer. Basically you want to find the conductance value just before(or just after) the slope of the conductance in figure 1 changes. I have chosen the conductance value for the frequency at 2800Hz, which is 0,0032mS. You can argue that this could be done different, and that this value is not that accurate.

Co: This is the capasitance for the blocked part of the transducer. To find this read the susceptance value B for the first serial-resonance.

As mentioned before: the paralell resonance fp occurs when the resistance is at a maximum. By inspecting figure 6, and checking the text file it is around 60000Hz.

The remaining components directly calculated from these values.

For the second resonance: For the second resonance i did the exact same thing as for the first.

### Conclusion

I have used C++ and root to find out some different characteristics for a piezoelectric transducer. The results is shown in the figures. I have used the figures and my data to calculate the different parameters in the BVD-model.

### Discussion

This i basically my first time programming, and definitely the first time i used ROOT and C++. I think this project has been very interesting, and think i have learned quite alot: Not just about ROOT and C++, but also acoustics. All my calculations are done by hand which is not ideal. It would be interesting to do all the calculations in my program, and to compare my results with simulations from the BVD-model.

### Code and data

The source codes and the data files are available on the code page.