| Activity/Tremor Detector | EEE 4202C-Medical Instrumentation Design | Exercise 1Group #6 | Group Members:
Diego RamirezKarina AlonsoEric GundersonWilliam NoundouAlejandro BuitragoRaidel Martinez | 3/7/2012 |
Table of Contents
Abstract……………………………………………………………………………………………3
Steps Taken………………………………………………………………………………………..3
Data Recorded...………………………………………………………………………………...4-5
Data Tables………………………………………………………………………………………..6
Observations………………………………………………………………………………………7
Answered Questions………………………………………………………………………………7
Lessons Learned…………….……………………………………………………………………..8
Appendix…………………………………………………………………………………………..9
|

Abstract
The purpose of this exercise is to analyze some parameters of the piezoelectric transducer in order to better understand its characteristics and know which way to use it in this project.
The piezoelectric firm transducer has a mass attached on the end of an elastic film. As an input the system response has the movement of the electrode end, and as the output it has the flexure of the firm which causes a voltage displacement used for analysis.
This 2nd order high pass function is calculated and analyzed in this experiment by taking into account the mass, spring constant of the film and the friction due to air and plastic viscosity in the firm. For this reason the weight added to the transducer during the procedure was measured to be taken into consideration for the calculations. The ultimate goal is to calculate the resonant frequency as well as the damping ratio and create a Bode plot to show the behavior of the signal.

Steps Taken

1. Piezoelectric transducer set up and measurement with a normal and extra mass added 1. 1 The piezoelectric film transducer was connected to the breadboard and jumper cables connected to each lead of the film.(Shown in Figure 1) 1. 2 The jumper cables were connected to the oscilloscope in order to monitor the signal. 1. 3 The transducer was moved to produce a response and the results displayed in the oscilloscope were recorded. (Shown in Figure 2) 1. 4 After the measurements all the data was recorded to our tables (Figure 7&8). 1. 5 This process should be repeated for the transducers with extra mass attached to it (As shown in figure 4) in order to provide a differing signal response (as shown in Figure 5). 1. 6 With all the measurements taken and calculations done, the Bode Plot was created (Shown in figure 3,6)

Data Recorded

Figure 1. No Mass Piezoelectric transducer connected to oscilloscope. (1.1-1.3)

Figure 2. No Mass Transducer oscilloscope signal. (Step 1.3)

Figure 3. Massless Transducer Bode Plot and Phase Diagram. (Step 1.4)

Figure 4. 2.2g Mass Attached Piezoelectric Transducer connected to oscilloscope. (Steps 1.1- 1.3)

Figure 5. 2.2g Mass attached transducer oscilloscope signal. (Step 1.3)

Figure 6. 2.2 g Mass Attached Transducer Bode Plot and Phase Diagram. (Step 1.4)

Data Tables
Figure 7: Quantifies the output attained from the oscilloscope in Figure 2 & 5 and lists parameters used to calculate the transfer functions in Table 2. Refer to appendix for functions. Transducer | Piezo-electric (Standard Mass) | Piezo-electric(Massless) | Piezo-Electric--Calculated--(Target Mass) | Mass Aggregate (g) | 0.75g | 0g | 8.66g | Voltage Amplitude at Peak 1 | 165mV | 395mV | N/A | Voltage Amplitude at Peak 2 | 100mV | 340mV | N/A | P-P Time Period | 45ms | 5.8ms | N/A | Logarithmic Decrement(Λ) | 0. 4947 | 0.1643 | N/A | Slope(k) | 6.54*10-5 | 10.6*10-7 | 6.54*10-5 | Ks | 15297.5 | 944465.96 | 15297.5 | Natural Frequency (ωn) | 142.82 | 1122.18 | 43.9822 | Damping Ratio(ζ) | 0.07849 | 0.02614 | 0.024165 | Static Sensitivity(K) | 1.3334 | 1.3336 | 1.3336 |

Figure 8: Shows the transfer function for each Pizo-electric transducer mass. Transducer | Pizo-electric (Standard Mass) | Pizo-electric(Massless) | Pizo-Electric(Target Mass) | Mass (g) | 0.75g | 0g | 8.66g | Transfer Function | 1.3336s2+58.7s+1.259*106 | 1.3334s2+22.42s+24,000 | 1.3336s2+2.13s+1,934 |

Observations In our experiment we carried out three different tests using three different masses on a piezoelectric transducer. First we used a 0 mass piezoelectric transducer and we discovered that it does not provide a uniform response over the 3-7 Hz frequency range. Additionally, the peak to peak voltage is rather high at 395-340 mV. Then we increased the mass of the piezoelectric transducer to approximately 0.75 g (1.8g total with wires) and we discovered that the amplitude response is acceptable over the specified tremor frequency range with a variation of 0.8 dB with a peak to peak voltage of 165-100 mV. We did further testing with a mass of 2.2 g total and the results are shown in figure 4-6.

Answered Questions
1. Will the mechanical response of this transducer provide uniform amplitude response over this tremor frequency range?
The piezoelectric transducer without a mass does not provide a good response over the 3 to 7 Hz range with 0dB variation of the frequency range of the bode plot. However, the mechanical response of the transducer with mass does provide a uniform amplitude response over the tremor frequency range with a sensitivity variation of about 0.8dB.
2. Given that the original mass is 0.75 grams, how much mass would have to be added to make the resonant frequency suitable for tremor detection?
To make the resonant frequency suitable for tremor detection, 7.908g should be added.

3. Consider the response of this modified transducer to a single jerk of the hand of the subject. What effect might this have on using the modified transducer to monitor tremors?
This modified transducer with mass could detect the tremor of a single jerk of the hand within the tremor frequency range better than without mass. The complete oscillations would not be recorded in a transducer without mass, since the resonant frequency would be outside the frequency range.
4. Would it be practical to further modify this transducer to increase the damping factor while keeping the resonant frequency at this value?
It would not be practical to further modify this transducer to increase the damping factor while keeping the resonant frequency at this value. Increasing the damping factor or adding more mass would shift the resonant peak, which would result in the transducer not picking up the tremor frequency range.

Lessons Learned Based on our observations, we can safely say that both the 0 g and the 8.66 g (resonant frequency ideal weight) piezoelectric transducers are not suitable for detecting tremors. The 0 g piezoelectric transducer is practically massless and it does not properly register the tremors as an electric signal, in other words it’s too sensitive and might detect tremors where there are none. On the other hand, the 8.66 g piezoelectric transducer is too heavy and does not detect tremors at all. Based on the above statement, we chose the 2.2g piezoelectric transducer as having the ideal mass for this project. Not only does it provide a stable response over the required frequency range, but we also get a sensible variation of 0.8 dB along with an acceptable peak-to-peak voltage for the signal. If need be, the signal can be further amplified by using a properly configured op amp circuit to guarantee detection of even the slightest of tremors.

Appendix: Transfer Function | Slope | ks | K(sωn)2+2ζsωn+1 | K=1ks | ks=ωn2*mass | Natural Frequency | Damping Ratio | Logarithmic Decrement | ωn=2πTn | ζ=(Λ4π)2+Λ2 | Λ= Ln(YnYn+1) |