Basic Operational Amplifiers
Analog Integrated Circuits
Don’t just sit there! Build something!! 
Learning to mathematically analyze circuits requires much study and practice. Typically, students practice by working through lots of sample problems and checking their answers against those provided by the textbook or the instructor. While this is good, there is a much better way.
You will learn much more by actually building and analyzing real circuits, letting your test equipment provide the änswers” instead of a book or another person. For successful circuitbuilding exercises, follow these steps:
 1.
 Carefully measure and record all component values prior to circuit construction.
 2.
 Draw the schematic diagram for the circuit to be analyzed.
 3.
 Carefully build this circuit on a breadboard or other convenient medium.
 4.
 Check the accuracy of the circuit’s construction, following each wire to each connection point, and verifying these elements onebyone on the diagram.
 5.
 Mathematically analyze the circuit, solving for all voltage and current values.
 6.
 Carefully measure all voltages and currents, to verify the accuracy of your analysis.
 7.
 If there are any substantial errors (greater than a few percent), carefully check your circuit’s construction against the diagram, then carefully recalculate the values and remeasure.
Avoid using the model 741 opamp, unless you want to challenge your circuit design skills. There are more versatile opamp models commonly available for the beginner. I recommend the LM324 for DC and lowfrequency AC circuits, and the TL082 for AC projects involving audio or higher frequencies.
As usual, avoid very high and very low resistor values, to avoid measurement errors caused by meter “loading”. I recommend resistor values between 1 kΩ and 100 kΩ.
One way you can save time and reduce the possibility of error is to begin with a very simple circuit and incrementally add components to increase its complexity after each analysis, rather than building a whole new circuit for each practice problem. Another timesaving technique is to reuse the same components in a variety of different circuit configurations. This way, you won’t have to measure any component’s value more than once.
An operational amplifier is a particular type of differential amplifier. Most opamps receive two input voltage signals and output one voltage signal:

Here is a single opamp, shown under two different conditions (different input voltages). Determine the voltage gain of this opamp, given the conditions shown:


Also, write a mathematical formula solving for differential voltage gain (A_{V}) in terms of an opamp’s input and output voltages.
The 8pin DualInlinePackage (DIP) is a common format in which single and dual operational amplifiers are housed. Shown here are the case outlines for two 8pin DIPs. Draw the internal opamp connections for a single opamp unit, and for a dual opamp unit:

You will need to research some opamp datasheets to find this information. Examples of single opamp chips include the LM741, CA3130, and TL081. Examples of dual opamp chips include the LM1458 and TL082.
Shown here is a simplified schematic diagram of one of the operational amplifiers inside a TL08x (TL081, TL082, or TL084) opamp integrated circuit:

Qualitatively determine what will happen to the output voltage (V_{out}) if the voltage on the noninverting input (V_{in+}) increases, and the voltage on the inverting input (V_{in−}) remains the same (all voltages are positive quantities, referenced to V). Explain what happens at every stage of the opamp circuit (voltages increasing or decreasing, currents increasing or decreasing) with this change in input voltage.
Shown here is a simplified schematic diagram of one of the operational amplifiers inside an LM324 quad opamp integrated circuit:

Qualitatively determine what will happen to the output voltage (V_{out}) if the voltage on the inverting input (V_{in−}) increases, and the voltage on the noninverting input (V_{in+}) remains the same (all voltages are positive quantities, referenced to ground). Explain what happens at every stage of the opamp circuit (voltages increasing or decreasing, currents increasing or decreasing) with this change in input voltage.
One of the first popular operational amplifiers was manufactured by Philbrick Researches, and it was called the K2W. Built with two dualtriode vacuum tubes, its original schematic diagram looked like this:

To make this opamp circuit easier for modern students to understand, I’ll substitute equivalent solidstate components for all tubes in the original design:

Explain the configuration (commonsource, commondrain, or commongate) of each transistor in the modernized schematic, identifying the function of each in the operational amplifier circuit.
Predict how the operation of this operational amplifier circuit will be affected as a result of the following faults. Specifically, identify whether the output voltage (V_{out}) will move in a positive direction (closer to the +V rail) or in a negative direction (closer to ground). Consider each fault independently (i.e. one at a time, no multiple faults):

 •
 Transistor Q_{5} fails shorted (collectortoemitter):
 •
 Transistor Q_{6} fails shorted (collectortoemitter):
 •
 Resistor R_{1} fails open:
 •
 Current source I_{2} fails shorted:
For each of these conditions, explain why the resulting effects will occur.
Predict how the operation of this operational amplifier circuit will be affected as a result of the following faults. Specifically, identify whether the output voltage (V_{out}) will move in a positive direction (closer to the +V rail) or in a negative direction (closer to the V rail). Consider each fault independently (i.e. one at a time, no multiple faults):

 •
 Diode D_{1} fails open:
 •
 Resistor R_{1} fails shorted:
 •
 Transistor Q_{2} fails shorted (draintosource):
 •
 Transistor Q_{5} fails shorted (collectortoemitter):
 •
 Resistor R_{2} fails open:
 •
 Current source I_{2} fails open:
For each of these conditions, explain why the resulting effects will occur.
A helpful model for understanding opamp function is one where the output of an opamp is thought of as being the wiper of a potentiometer, the wiper position automatically adjusted according to the difference in voltage measured between the two inputs:

To elaborate further, imagine an extremely sensitive, analog, zerocenter voltmeter inside the opamp, where the movingcoil mechanism of the voltmeter mechanically drives the potentiometer wiper. The wiper’s position would then be proportional to both the magnitude and polarity of the difference in voltage between the two input terminals.
Realistically, building such a voltmeter/potentiometer mechanism with the same sensitivity and dynamic performance as a solidstate opamp circuit would be impossible, but the point here is to model the opamp in terms of components that we are already very familiar with, not to suggest an alternative construction for real opamps.
Describe how this model helps to explain the output voltage limits of an opamp, and also where the opamp sources or sinks load current from.
Ideally, when the two input terminals of an opamp are shorted together (creating a condition of zero differential voltage), and those two inputs are connected directly to ground (creating a condition of zero commonmode voltage), what should this opamp’s output voltage be?

In reality, the output voltage of an opamp under these conditions is not the same as what would be ideally predicted. Identify the fundamental problem in real opamps, and also identify the best solution.
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