# Abstract

We conducted this experiment to get a better understanding of how an oscillator works and how we can use the data that it gives us to make the information more usefull. We also used our knowledge of resistors to set up the curciut and used bayesian update to predict how many time we would have an amount of failures within a time period.

# Description

In part A we found that that V+ was equal to around .819 V in our curciut and we predicted that our output voltage was 1.003 and .6342. In part 2 the data was ploltted on a graph in blue dot in comparisonm to the theoretical curve. In exercise 1 we proved that the amount of times a falure would happen in 10minutes in an 8 hour shift was 11.491. In exercise 2 we used calculus to prove that the V+ was .819V and in exercise 3 we proved the gain.

# Part A

(/work/instrumentation-projects/proj3/Part A schematic.JPG)

(/Part A Average Line.JPG)

1] The expected value for V$_+$ is calcualted using the voltage divider equation as follows:

$$V_+ = \frac{V + R_B}{R_1 + R_2} = \frac{3.3V + 330\Omega}{1000\Omega + 330\Omega }$$ = .819V

By looking at the average of the square wave function in Figure 2 above you can confirm that expected value is close to what is shown on the oscilliscope.

2] The output is a square wave function as we expected. Using $$ V*{\rm out} = V*+ - R*F C*{\rm in} \frac{dV*{\rm in}}{dt}$$ we can calculate what the $$V*{out}$$ was supposed to be and then compare it to what is shown on the oscilliscope. The values calculated for $$V*{out}$$ are 1.0038V and .6342V using the equation with a V$*+$ of .819V, R$*F$ is 1000$\Omega$, C$*{in}$ is .22$\mu$F, and $$\frac{dV_{\rm in}}{dt}$$ equals $$\frac{.84V}{.001s}$$. The work for the calculations are shown below in exercise 2.

# Part B

Our Data

Explain why we chose each component

R2 and R3 were 1k resistors to obtain the gain of two at low frequency, as proen by Project 2's equation

C1 was chosen to be 0.22 microfarad and R1 was chosen to be 1k by solving for R with your know capicators of 0.22 mricofarad and 1 microfarad $$ f_c = \frac{1}{2\pi RC}$$ and solving for R.

$$ R = \frac{1}{2\pi f_c C}$$ = 723.43 ohm = 1k ohm

# Exercise 1

Estimated 11.491 times you would see 3 or more defects in 10 minutes over an 8 hour shift.

# Exercise 2

$$ I = C*{\rm in}\frac{dV*{\rm in}}{dt}$$

$$ I = .00000022 *\frac{.84}{.001} $$

$$ I = .0001848 A$$

$$V_+ = \frac{V_s * R_2}{R_1+R_2}$$

$$V_+ = \frac{3.3V + 330\Omega}{1000\Omega + 330\Omega }$$

$$V_+ = \frac{1089}{1330}$$

$$V_+ = 0.818797 V $$

$$ V*{\rm out} = V*+ - R*F C*{\rm in} \frac{dV_{\rm in}}{dt}$$

$$ V*{\rm out} = V*+ - R_F I$$

$$ V_{\rm out} = 0.819 - 1000\Omega * .0001848$$

$$ V_{\rm out} = .6342 $$

$$ V_{\rm out} = 0.819 + 1000\Omega * .0001848$$

$$ V_{\rm out} = 1.0038 $$

In the picture Figure 2 of our oscilliscope, the upper value appeared to be around 1 V and the lower to be around 0.6 V, with an average around 0.8 V. Unfortunatly, we did not zoom all th way in using the oscilliscope so these numbers are close estimates using the tick marks on the ocsicllscope, knowing that each box was 1 V.

# Exercise 3

$$I =\frac{V_{in}}{R + R_2}$$

$$I =\frac{3.3}{1000 + 1000}$$

$$I = .00165 $$

$$V*2 = R_2 I = R_2 \frac{V*{in}}{R + R_2}$$

$$V_2 = 1000 * .00165 $$

$$V_2 = 1.65 $$

$$X_C = \frac{1}{\omega C}$$

$$\omega = 2 \pi f_c$$

$$f_c = 1000 hz$$

$$\omega = 2000 \pi $$

$$\omega = 6283.185 $$

$$X_C = \frac{1}{6283.185 * .00000022}$$

$$ Z = \sqrt{R^2 + X_C^2} $$

$$ Z = \sqrt{1000^2 + 723.43^2 } $$

$$ I = V_{in}/Z $$

$$ I = 3.3/1234.24 $$

$$ I = .00267 $$

$$V*C = X_C I = X_C \frac{V*{in}}{Z}$$

$$V_C = 723.43*.00267 $$

$$V_C = 1.93156 $$

$$G = 2*\frac{V C}{V{in}} = 2*\frac{X_C}{Z}$$

$$G = 2*\frac{1.93156}{3.3} = 2*\frac{723.43}{1234.24}$$

$$G = 1.17246 = 1.17226 $$

Value from data is equal to 1.17226862

# Conclusion

In conclusion the data that we presented was very close to what it theoretically should have been. With uncontrolable factors we cant be perfect but of data is close enough to say that it was good data that we got from our oscilloscope.