Inverting Differentiator Lab

Objective:
We covered integrators and differentiator op amps which involve resistors and capacitors In order to create an ideal integrator, we replace the resistor feedback with a capacitor for an inverting amplifier. We can find the current  through nodal analysis at the negative terminal which has a voltage of 0v and can calculate an equation based on the voltage input and output (Vout(t) -V(0) =-1/RC int(Vin(t)dt). To create an differentiator, we can replace the input resistor with a capacitor in an inverting amplifier. the equation calculated is Vout = -RCdvi/dt. Differentiators are unstable and rarely used because of exaggerated noise. We also covered the idea of switching functions and others. In the end, we covered step response of RC and RL circuits.

Group Practice:
1. We are required to find the voltage by using the equation as seen in figure 1. In order to acquire the voltage, we will integrate the current. The voltage graph is then plotted.

Figure 1. Finding the voltage given a current impulse

Inverting Differentiator Lab Procedures and Results:
1. For pre lab, we are required to find an equation of an output voltage as a function of input voltage based on the differentiator op amp. The final equation can be seen in figure 2. We are required to find the frequency needed in the experiment by having the voltage gain Vout/Vin = 1. Therefore, we acquire a frequency of f =2344Hz as long as A = 1, R = 680ohms, and C = 1microfarad.

Figure 2. Calculations for the frequency. 

2. Before, the circuit built, we first measure the actual capacitance of the capacitor and the resistance of the resistor. The resistor has a resistance of R=680 +/-.005 ohms and capacitor of capacitance of C= .945+/-.0005 microfarad. The final build op amp differentiator can be seen in figure 3 & 4. We make sure that we create a voltage sine input with frequencies of 100Hz, 250Hz, 500Hz and measure the voltage output with oscilloscope.

Figure 3. Over all set of op amp differentiator.

Figure 4. Close visual of op amp differentiator.

5. We measured the voltage output when the voltage input with a frequency of 100 Hz was set as seen in figure 5. The voltage output at 250 Hz can be seen in figure 6 and 500 Hz in figure 7.

Figure 5. Voltage output at 100Hz

Figure 6. Voltage output at 250 Hz

Figure 7. Voltage output at 500 Hz

6. We then calculate the theoretical voltage output which can be seen in figure 8 and compare them to our experimental voltage output measurements by looking at the amplitude of the sin wave. We can that they close to each other with percent error less that 3%. We also notice that fussiness throughout the curves.

Figure 8. Comparison of theoretical and experimental voltage outputs for a differentiator op amp. 

Summary of Inverting Differentiator Lab and Learning Outcome:
The lab required us to calculate or find the voltage output as a function of the input voltage in the form of a sinusoid. Since we are dealing with an inverting differentiator, we use the applicable equation derived from earlier in class. We are looking for gain of or Vout/Vin = 1. As a result we can find the frequency in which we can acquire this gain. The frequency we calculated is f = 234 Hz. We also noted that the amplitude of the sinusoidal input will be 1 V and an offset of 0. The measurements of resistor and capacitor are R=680 +/-.005 ohms and C= .945+/-.0005 microfarad. The frequency that we will use to will fall within our frequency of f =234Hz. The frequencies used in the experiment are 100Hz, 250 Hz,  and 500 Hz. From this we noticed that our amplitude increased which means that our voltage output is just proportional to the frequency. We do notice some fussiness in our measurements. Overall when we compared our theoretical and experimental measurements, we see that there is 1.09% error at 100Hz,  2.99% at 250Hz, and 1.69% at 500Hz. The equation for an inverting differentiator hold true since the percent error is relatively low.