Day 11: Operational Amplifiers and Inverting Voltage Amplifier

In class today we learned about operational amplifiers and how to analyze electrical circuits in which they are present in. Under the hood an operational amplifier is very complex, with many resistors, capacitors and transistor in an interconnected network. However, we learned that we can simplify them and treat them as a very large resistor attached across the input terminals and a voltage-controlled voltage source in series with a resistor across the output terminal. The dependent voltage source relies on the voltage across the very large resistor. We then learned that we must take into account which input terminal the voltage source is connected to. If it is attached to the non-inverted terminal, we treat the voltage source as positive, and a positive gain should be obtained. If the voltage source is attached to the inverted terminal, the voltage source is treated as negative, and a negative gain is obtained. We also learned about an open loop versus a closed loop. An open loop results in no feedback between the output and input (i.e. the output and input terminals are not connected). A closed loop, as implied, has feedback between the output and input of the op amp (i.e. the input and output terminals are connected.
After, we did the lab titled "Inverting Voltage Amplifier". Once we finished the lab we then learned about ideal operational amplifiers and how so much simpler they make the circuit. An ideal amplifier has an infinite resistance for the resistor connected across the inverted and non-inverted terminals. This means that no current runs through the resistor and therefore no current through the wires attached to the terminals. No current means no voltage across the resistor; this results in the voltage-controlled voltage source providing no voltage, and therefore means no current running through the output wire of the amplifier. 

LECTURE:

This problem involved an operational amplifier with the voltage source attached to the noninverted terminal. The operational amplifier was redrawn to consist of a resistor attached to the terminals with a potentional difference Vd and on another branch a voltage source dependent on Vd with a resistor in series. The output voltage was found via node-voltage analysis, and the gain of the amplifier was also calculated. 

This problem involved an operational amplifier as well. However, the voltage source was attached to the inverted terminal, resulting in a positive output voltage. Node-voltage analysis was then used again to solve for the output voltage, the gain of the amplifier and the current running through the wire running outside of the output terminal. Again, as with all operational amplifiers, the voltage controlled voltage source is dependent on the potential across the resistor connected to the inverted and non-inverted terminals.

In this problem, the operational amplifier was treated as ideal. This really simplifies the circuit greatly; in this problem it became a simple voltage source and two resistors in series with each other and the voltage source. The current through the 20 kOhm resistor was then found, along with the gain of the amplifier.

LAB:

Inverting Voltage Amplifier:

Purpose:

The objective of this experiment was to test the gain of the operational amplifier experimentally by seeing the output voltage change when the input voltage was changed. The saturation points for the operational amplifier were also found. Because the voltage is connected to the inverted terminal, it is expected that the gain will be negative.

Prelab:

In this prelab the resistance of resistor R2 was found, and the relationship between the output and input voltages (i.e. the gain) was also found in terms of the resistors. The gain was mathematically found to be -2.

Apparatus:

The equipment used in this experiment consisted of the following pieces: an OP27 operational amplifier, an analog discovery toolbox, a laptop with Waveforms software, resistors, a breadboard, a digital multimeter, wires and alligator clips.

Procedure:

The schematic of the circuit seen in the prelab above was created, as shown in the above picture. The circuit is zoomed in to show more detail, as seen below:

In this circuit, the + 5 V and - 5 V sources (provided by the red and white wires, respectively) were attached to terminals 7 and 4 of the operational amplifier, respectively. The two resistors R1 and R2 were both attached to the second terminal on the op amp, which is the inverted input voltage terminal. In addition, the other end of resistor R2 was connected to terminal 6, or the output terminal. The waveform source (yellow wire) was attached to the end of resistor R1 to provide the varying voltages needed. A ground wire was then attached to terminal 3 of the op amp. Lastly, the DMM, acting as a voltmeter, was connected to terminal 6 in parallel with the resistor R2. The other end of the voltmeter was also attached to another ground wire. An ohmmeter was then used to measure the true resistances of the resistor, whose values are shown below:

Data Analysis:

The waveform generator was then used to apply input voltages ranging from -3 V to 4 V to the circuit, in increments of 0.5 V. The output voltages were then measured using the voltmeter and recorded. The data is seen above in the table of output vs input voltages. At -2.5 V and -3 V the op amp reached its upper saturation, and at 2 V and above it reached its lower saturation point. This data was then used to make a graph that represents the model of the op amp used. This graph is shown below:

Conclusion:

The graph obtained was the expected graph, because there were saturation points on both ends of the voltage spectrum. In addition, as seen by the data, when the input voltages were negative the output voltages were positive and vice versa. This shows that the gain of the op amp is negative, which is expected since the voltage source is attached to the inverted terminal. In addition, the output voltage was nearly the negative of the double of the input voltage at each point, with the exception of saturation points; this shows that our gain is -2. This was the calculated and expected gain, which shows that the simplification used for these operational amplifiers is true and correct. Lastly, looking back at the graph, the slope is -2; this shows that the slope is the gain value and that the relationship determined between the output and input voltages via the resistors used (and therefore gain) is accurate.