We then reviewed an inverting amplifier, which involves an op amp circuit with a voltage source connected to the inverting input terminal and a resistor connected across the output and inverting input terminals. The non-inverting input terminal is usually connected to ground. The inverting amplifier amplifies the input signal but also reverses its polarity.
Next, we analyzed non-inverting amplifiers. Their only difference with respect to the inverting amplifier is that the voltage source is applied to non-inverting input terminal instead of the inverting terminal. Non-inverting amplifier are used to amplify output signals without reversing their polarity; they are also used to always make larger signals, since their gain can never be less than or equal to one. If the gain does become one (i.e. by no feedback resistor or an infinite input resistance), the circuit becomes a unity gain buffer amplifier.
We then analyzed a summing amplifier. It is similar to an inverting amplifier, but now consists of voltage sources and resistors in parallel that are connected together to the inverting input terminal. The non-inverting input terminal is connected to ground and there exist a feedback resistor between the output and inverting input terminals. In this circuit the output voltage is the weighted sum of the input voltage. the output voltage is also reverse-polar to the input signal. We then did a lab on summing amplifiers.
Lastly, we spoke about difference amplifiers. They are similar to summing amplifiers but instead the input voltages are subtracted to find the output voltage. A difference amplifier amplifies the difference between two inputs and does not detect any signals shared between the two inputs.
LECTURE:
This problem involved an inverting amplifier with a time-varying input signal (a square wave). The objective was then to find the output time-varying signal. To do so the gain was found, which is just the negative of the quotient between the feedback resistor and the inverting input resistor. Then, knowing that the inverting amplifier amplifies and reverses the polarity of the signal the output signal was found. Looking at the op amp, the negative supplied voltage is zero, which limits the output signal to provide no less than 0 V. The output signal was a square wave with an amplitude of 150 mV centered at +150 mV.
This problem also involved an inverting amplifier. The objective was to find the gain of this circuit and to find the output voltage if the non-inverting input terminal had no voltage source and was just attached to ground. The gain was found to be -1/2 and the output voltage was found to be -1.64 V. This circuit was solved using nodal analysis.
The relationship between input and output voltage of a non-inverting amplifier was derived above. It was found that the gain is the quotient of the feedback and input resistors added to one. As can be seen, the gain can never be less than 1 since resistances cannot be negative.
Above is the derivation of the relationship between the output voltage and the different applied voltage to the inverting input terminal. As can be seen the output voltage is a weighted sum of the applied voltages to the input, which is weighted on the feedback resistor and the resistors in parallel to each voltage source applied to the inverting input. As can also bee seen the output voltage in this circuit had a revered polarity compared to the input voltage. This is because the applied voltages are connected in parallel to the inverting input terminal.
In the above problem the input signals across a difference amplifier were provided; the resistors in this amplifier were all assumed to be equal. The objective was to then find the output signal using these two input signals and the assumption of equal resistors. To do so, the difference between the first and second signals was found. In this problem the difference just resulted in the first input signal shifting down vertically by 1. There is Claptrap giving us a high five for our good work on finding the output signal. He is definitely very interested in this difference amplifier business.
The objective of the above problem was to construct a difference amplifier circuit that would have a gain of 2 and 10 kOhm input resistors. As seen above the circuit was constructed with the specifications. The gain was provided to be 2 by using 20k ohm resistors for the feedback and non-inverting input resistors.
Finally, this circuit was analyzed. It was found that this circuit can be treated as either a difference amplifier or a non-inverting amplifier. Our group was chosen to solve it as a difference amplifier, which allows us to skip over much of the nodal analysis. We found the gain to be 1/3, which reduces the input signal's amplitude from 5 V to 1.67 V. In addition, because the negative voltage of the op amp is connected to ground, the output signal cannot be less than 0 V, which results in a square wave centered at 0.833 with an amplitude of 0.833 V.
LAB:
Summing Amplifiers:
Purpose:
The purpose of this experiment was to design a summing amplifier circuit that would not saturate at any of the input voltages that must be provided to the operational amplifier. The objective was then to choose a gain that would not saturate the op amp in this circuit, which was adjusted via the feedback and input resistors. The circuit was then built and the needed applied voltages were applied to the input, and the output voltages were recorded and tested for accuracy based on the theoretical gain.
Apparatus:
The equipment of this experiment consisted of an OP27 operational amplifier, an analog discovery tool box, a breadboard, a laptop with "Waveforms" software, a DMM, wires and alligator clips. The only really new part of the equipment is the OP27 op amp.
Prelab:
The purpose of this prelab was to design the circuit and modify it to meet its standards before actually building and testing it. A simple summing amplifier was made, with two input voltages at the negative terminal in parallel and the positive input terminal attached to ground. The output voltage as a function of the input voltages and resistances was found for the circuit. Then resistances for the circuit were chosen. It was decided initially that all resistors be the same values of 2.2 kOhms to make the math simpler, as shown in the prelab, but that did not work because the op amp became saturated. +5 V and -5 V sources were applied to the op amp at V+ and V- inputs. Therefore, because of this, the feedback resistor R3 was dropped down to 1 kOhm, but the other two resistors were still left at 2.2 kOhms. This results in a gain of around 0.44, which prevented the op amp from saturating at the input voltages needed.
Procedure:
The difference amplifier circuit was then built and the output voltages were recorded at each input voltages necessary to be applied. The true resistances of each resistor were also measured using an ohmmeter, as seen in the prelab For the non-inverting terminal, a constant 1 V was applied. For the inverting terminal, voltages of -4 V, -2 V, -1 V, 0 V, 1 V, 2 V, 3 V and 5 V. +5 V and - 5 V were added to the + V and - V terminals. The output voltages were then measured using a voltmeter.
Data Analysis / Conclusion:
As seen above, the output voltages were recorded for each change in input voltage in the inverting terminal. As seen, there was no saturation at any of the applied voltages, which meets that requirement. In addition, the output voltages were inverted polarity-wise, which definitely also meets our requirement and shows that our circuit is set up correctly. Lastly, all of the points for output voltage followed the relationship obtained for the summing amplifier, and, as seen, the gain is roughly 0.44 for each point, which also shows that our circuit was analyzed and built correctly. Overall, our circuit was a success and a summing amplifier that met all of the requirements was created.
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