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Operations Using Operational Amplifiers

Benjamin Sepe & TJ RumbaughConducted: 2/12/13Submitted: 2/19/13

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OBJECTIVES

The purpose of this lab was to gain familiarity with the operational amplifier(OP AMP). We will be able to understand the relationships between theory,equations, and real life experiments on the OP AMP after the completion of lab five.

EXPERIMENTAL

Experiment 1. Measurement of DC Integrator Drift

The first thing that we did in order to prepare for this lab was to obtain allthe required components. The components that we would be using that we notalready in our toolbox were: (1) 741 Op Amp, (1) 0.1 F capacitor , (104) (1) 0.47 Fcapacitor, ( 1) 1 M resistor , (1) 10 k resistor , (1) 120 k resistor , (1) 3.9 kresistor, and ( 1) 200 resistor . The nominal and actual values of the resistors aredescribed below in Table 1. Additionally, we were carful to properly label each

component used in this lab so to easily keep track of each circuit element.

Resistor Nominal Value Resistor Actual Value1 M 0.982 M 10 k 9.877 k

120 k 119.3 k 3.9 k 3.824 k 200 196.73

Table 1 . Resistor Nominal v. Actual

Following Figure 1, provided in the lab manual, we used the requiredelements to construct the Integrator. We used R1 = 0.982 M and C = 0.47F . Ajumper wire was used as the switch in this case.

Figure 1. DC Integrator

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After successfully completing the construction of the DC Integrator, weopened the switch and recorded the time it took for Vo to reach a predeterminedvoltage. For this lab, we chose to find the time it took Vo to reach 0.5 V. The resultsof this experiment are tabulated below in Table 2. The current through the 0.47 F capacitor was then computed using Equation 1.

ic = C *( dV / dt )Equation 1. Current through a Capacitor

Voltage Change 0.5 VTime Required 16.9 seconds

Calculated Bias Current (EQN 1) 1.39e-8 ampsTable 2 . Results of Experiment 1

Experiment 2. Integration of Square, Sine, and Triangle Waveforms by an ACIntegrator

In the second part of this lab, we changed the construction of our circuit tomodel an AC Integrator. This was used with the help of Figure 2. We then used thefunction generator to provide various Vin functions, and record the input andoutput using BioComm Software. The total combinations for Vin include:

Square wave, 4 Vpp, 200 Hz, Vin-ave = 0 Sine wave, 4 Vpp, 200 Hz, Vin-ave = 0 Sine wave, 4 Vpp, 400 Hz, Vin-ave = 0 Triangle wave, 4 Vpp, 200 Hz, Vin-ave = 0

Figure 2. AC Integrator

The waveforms are presented in the results section of this lab report.

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Experiment 3 . Uncompensated Differentiator, Tested with Sine, Square, and TriangleWaveforms

Using Figure 3 as a guide, we constructed the Uncompensated Differentiatoron our breadboard. We implemented C = 0.1 F , and R = 3.824 k for this

experiment. Letting Vawg be 1 Vpp and 400 Hz, we tested the Differentiator for Sine,Square and Triangle Waves. We then returned to a Sine wave and varied thefrequency input from 200 Hz to 2 kHz. We used frequencies of 200 Hz, 500 Hz, 1000Hz, 1500 Hz, and 2000 Hz. The results of these waveforms are presented in theresults section of the lab report.

Figure 3 . Uncompensated Differentiator

ANALYSIS

In Experiment 1, the current through the capacitor was calculated to be1.39e-8 amps. This was done by using equation 1 and a timed voltage change. The

nature of the integrator in this lab was utilization under DC voltage sources. Thismeans that when the switch was open, the capacitor existed in the negativefeedback loop of the OP AMP, and would function until it had saturated. TJ and Inoticed the saturating nature of the capacitor as the voltage across it roseincreasingly slower as we approached 0.5 V.

In Experiment 2, we recorded the input vs. output waveforms for the ACIntegrator. In the lab experimental it asked what the Vo waveform was for Vin as atriangle wave. The results for each experiment are on the next pages, however forthis specific question I will comment that for a Triangle Wave Input, Vo was a SineWave. Figure 7 represents this. It is also notable that the same sinusoidal output isobserved in Figure 5 for a sine input.

The results for experiment 2 indicate that the amplitude of the output isbased on frequency. This is because the transfer function for an AC Integrator hasone frequency term, and it is in the denominator. When we double the frequency we expect to see a halving of the amplitude. This is apparent in Figure 6. Theamplitude is roughly half of the input (out = ~2 & in = ~ 0.9)

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Results EXP. 2

FIG. 4 Square wave - 4 Vpp - 200 Hz - Vin-ave = 0

FIG 5. Sine wave - 4 Vpp - 200 Hz - Vin-ave = 0 .

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In Experiment 3, we used an experimental differentiator and with a constantinput voltage and various waveforms. Then, using that same input voltage and asinusoidal waveform we altered the frequency from 200 to 2,000 Hz. The results

are presented in Figures 8 through 15. I believe that the best-inverted derivativewas that of the Sine Wave in Figure 8. The reason for this assessment is the Outputin Channel 2 is smooth and there is no obvious jumps or fluctuations. Perhaps mostimportantly, the output is indeed indicative of the inverted derivative of the Input.The worst inverted derivative that we took was likely the square wave. Representedin Figure 10, the square wave has tremendous fluctuations that occur during thesignal alternating between -500 and 500. While a true inverted derivative would notrecognize these near-instantaneous fluctuations, the signal here is more like an EKGsignal than the theoretical straight line.

FIG. 8 Sine Wave

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FIG. 9 Triangle Wave

FIG. 10 Square Wave

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FIG. 12. F = 500 Hz

FIG. 13. F = 1000 Hz

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FIG. 14. F = 1500 Hz

FIG 15 . F = 2000 Hz

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FIG 16. Output Variance with Constant Input Voltage

CONCLUSION

In this lab we used Operation Amplifiers in conjunction with a few commonsetups to practice the basics of Integrators and Differentiators. These setups areuseful in many bioengineering applications, and knowledge of their basics is vital inmany professions that this degree may lead to. In experiment 1, we saw thesaturating nature of capacitors in these loops. This was important to see so that wemay understand the use of large load resistors as a means of discharging thecapacitors in real like functions. In experiment 2, we used the AC integrator toperform waveform permutations and calculations based on the integrators transferfunction. Similar steps were repeated in experiment 3, though the frequency wasvaried. By that means we learned that the output may be varied linearly withincreasing frequency and a constant input.

APPENDIX

R = 0.9969

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0 500 1000 1500 2000 2500

O u t p u t

V

Frequency Hz

Output Peak-to-Peak w/ 1 V Input(V)