Lab 1

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University of Michigan, Dearborn *

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ECE 311

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`ECE 311: Electronic Circuits 1 (Fall 2017) Lab 1 : Op-Amps By Kayleigh James (UMID: 81519321) September 27th, 2017 Fall 2017 Honor Code: I have neither given nor received unauthorized assistance on this graded report. X_____________________________________________________________________

Abstract In this lab we confirmed the characteristic behavior of three different operational amplifier configurations that we learned in lecture. We worked with non-inverting, inverting, and voltage follower op-amp configurations. We confirmed the characteristics taught in class by building these circuits with hardware and by simulating them using PSpice. Introduction and Background In class we learned that for inverting op-amps the voltage can be found by finding -R2/R1. For the non-inverting configuration, voltage gain is calculated by finding 1+R2/R1. Finally, for the voltage follower the gain should be 1. This mean Vin = Vout. We derived all three of these characteristics using KCL and KVL. In this lab, we aim to validate these derivations using simulation and hardware. Pre-Lab Questions and Answers 1. Draw and label the pin out of the Op-Amp IC 741. 2. Op-Amp 741 Datasheet: ● Supply Voltage: ±22 V (maximum)

● Power Consumption: 50 mW ● Input Resistance: 2 MΩ ● Input Offset Voltage: 1mV ● Input Offset Current: 20 nA ● Output Resistance: 75 Ω ● Voltage Gain Min: 200 V/mV ● Bandwidth Min: 1.5 MHz 3. When referring to op-amps, what is clipping and when does it occur? Op-Amps have a minimum and maximum voltage they can produce. If you input enough voltage to exceed this range, the op-amp will be unable to apply the gain to the input voltage to produce a high enough (or low enough) voltage. This results in a distorted waveform which we say has been “clipped”, i.e. the waveform will have its voltage minimums and maximums chopped off. 4. Describe the difference between open loop gain and closed loop gain. Closed loop gain is measured by dividing the output voltage by the input voltage when the output of the op-amp is fed back into the input terminal of the op-amp, this “closes” the loop. Open loop gain is measured when there is no feedback loop. This open loop gain is very high and in ideal op-amps is infinite. This is why in practice we use negative feedback and closed loop gain (in order to produce stability). 5. Define negative feedback and explain why it is essential for op-amps. Without feedback, the gain of an op-amp is very large and in ideal op-amps the gain is infinite. Feedback allows us to control the gain and it stabilizes the circuit. Without feedback, small disturbances such as differences in temperature can cause the op-amp to behave unpredictably. 6.

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7. 8.

Simulation Part 1 - Inverting Op-Amp: Theoretical Gain is: V out /V in = -R 2 /R 1 = -20kΩ/5kΩ = -4 Image 1: Part 1 Schematic

Image 2: Part 1 Waveform Image 3: Part 1 Bonus Waveform, 1V DC Offset. Part 2 - Non-Inverting Op-Amp: Theoretical Gain: V out /V in = 1+(R 2 /R 1 ) = 1+ (10kΩ/1kΩ) = 11

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Image 4: Part 2 Schematic Image 5: Part 2 Waveform

Image 6: Part 2 Bonus Part A Waveform Image 7: Part 2 Bonus Part B Waveform Part 3: Voltage Follower Op-Amp: Theoretical Gain: V out /V in = 1 Image 8: Part 3 Schematic

Image 9: Part 3 Waveform Image 10: Part 3 Bonus Waveform with Resistor 2 Removed Hardware Experiment Part 1: Inverting Op-Amp R 1 = 4.586 kΩ, R 2 = 21.897 kΩ, So gain = -4.775

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Image 11: Part 1 of Hardware Waveforms, 1V Amplitude for V in Measured Gain = -4.68/1.00 = -4.68 V/V Image 12: Part 1 of Hardware Waveforms, 3V Amplitude for V in Measured Gain = -14.0/3.04 = -4.61 V/V Part 2: Non-Inverting Op-Amp

R 1 = 0.987 kΩ, R 2 = 9.969 kΩ, So gain = 11.1 Image 13: Part 2 of Hardware Waveforms with V in at an amplitude of about 1V Measured Gain = 10.2/0.96 = 10.625V/V

Image 14: Part 2 of Hardware Waveforms with V in at an amplitude of about 2V (did 2V instead of 3V) Measured Gain = 18.0/1.80 = 10.0V/V Discussion of Results 1. Quantitatively Discuss the waveforms. Simulation: For the inverting configuration, we see that where V in has peaks, V out has troughs. This is because the gain is negative as we expected from our calculations. We calculated from R 2 and R 1 that the gain should be -4, which is what the waveforms show. When V in is 0.4V, V out is -1.6V which demonstrates that the circuit simulation validates our derivation for voltage gain. For the bonus question, we added a 1V DC offset to the schematic and re-did the simulation. This caused V in to shift upwards and have its inflection point on the 1V line (as opposed to having an

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inflection point on the X-axis without the DC offset). This does not affect the gain though, so the V out line shifts down in order to center itself on the -4V line to match the new behavior of V in . For the non-inverting configuration, we see that where V in has peaks, V out has peaks as well. This is consistent with the positive gain we calculated before running the simulation. We calculated that gain should be +11, if you look at the waveform, when V in is 0.4V, V out is 4.4V. This validates our derivation for how to calculate voltage gain for non-inverting circuits using R 2 and R 1 . For the first part of the bonus question a 1V DC offset was once again added to the circuit. Once again, V in shifts up to center itself at 1V. Unlike in the inverting configuration though, V out does not center itself at 11V, it instead orients itself around 9.5V. I think this is due to the op-amp itself having a voltage limit. For the second part of the bonus question, a -0.5V DC offset was placed into the circuit. This causes V in to shift down and center itself on -0.5V. This time V out cannot extend down past around -9.5V. This is probably due to limitations in the design of the 741 op-amp. For the voltage follower configuration the waveforms do validate the gain of 1 we derived. The V in and V out waveforms are right on top of eachother. This was dependent on where we placed the volt meters in simulation though; when we viewed the voltage source as V in the gain was more than 1. Based on discussion in class we knew this was wrong since the gain of a voltage follower should be 1, so we moved the voltage meter to the terminal of the op-amp which resulted in the expected waveforms. Hardware: For the inverting configuration, we calculated gain to be -4.775, in practice we got our gains to be -4.61 and -4.68. This is very close to our predicted value and the slight differences can be attributed to internal resistances of the wires and instrumentation. For the non-inverting configuration, we calculated gain to be 11.1, when we measured the gain using the oscilloscope, however, we got 10.625 and 10.0 for our voltages. These values are also very close to the predicted value and can once again be attributed to the internal resistances in the wires and instrumentation. 3. Is it possible to get a gain of less than 1 using a non-inverting amplifier? Explain.

It is not possible to get a gain of less than 1 using a non-inverting amplifier. We derived the gain of a non-inverting op-amp to be 1 + R 2 /R 1 so if we have non resistance (i.e. just wires instead of resistors) the gain would still be 1. The only way to get less than 1 would be for the value of R 2 /R 1 to be negative. Resistance cannot be negative, thus there is no way to get a gain of less than 1 when using the non-inverting configuration. To get a gain of less than 1, the inverting configuration would have to be used. Conclusion In this lab, we have learned and validated characteristics of three op-amp configurations: inverting, non-inverting, and voltage following. Through the simulation portion of the lab we saw the theoretical behavior of these devices along with their limits through the bonus questions. When building the circuits with hardware we were able to prove that our derivations and simulations hold true in practice. In the hardware experiment we were also able to see how to wire an op-amp and better use an oscilloscope. References 1. http://www.ti.com/lit/ds/symlink/lm741.pdf 2. https://www.allaboutcircuits.com/textbook/semiconductors/chpt-8/introduction- operational-amplifiers/