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Negative Feedback OpAmp Circuits
21 questions By Tony R. Kuphaldt
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Question 7 of 21
Write the transfer function (input/output equation) for an operational amplifier with an open-loop voltage gain of 100,000, and the inverting input connected directly to its output terminal. In other words, write an equation describing the output voltage of this op-amp (Vout) for any given input voltage at the non-inverting input (Vin(+)):
Then, once you have an equation written, solve for the over-all voltage gain \((A_v = \frac{V_{out}}{V_{in(+)}})\) of this amplifier circuit, and calculate the output voltage for a non-inverting input voltage of 6 volts.
Reveal answerVout = 100,000(Vin(+) − Vout) (I’ve left it up to you to perform the algebraic simplification here!)
AV = 100,000 100,001= 0.99999 For an input voltage of 6 volts, the output voltage will be 5.99994 volts.
Notes:The significant point of this question is that students see the over-all voltage gain of the opamp radically attenuated from 100,000 to approximately 1. What is not so evident is just how stable this new voltage gain is, which is one of the purposes for employing negative feedback.
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Question 8 of 21
How much effect will a change in the op-amp’s open-loop voltage gain have on the overall voltage gain of a negative-feedback circuit such as this?
If the open-loop gain of this operational amplifier were to change from 100,000 to 200,000, for example, how big of an effect would it have on the voltage gain as measured from the non-inverting input to the output?
Reveal answerThe different in overall voltage gain will be trivial.
Follow-up question: what advantage is there in building voltage amplifier circuits in this manner, applying negative feedback to a “core” amplifier with very high intrinsic gain?
Notes:Work with your students to calculate a few example scenarios, with the old open-loop gain versus the new open-loop gain. Have the students validate their conclusions with numbers!
Negative feedback is an extremely useful engineering principle, and one that allows us to build very precise amplifiers using imprecise components. Credit for this idea goes to Harold Black, an electrical engineer, in 1920’s. Mr. Black was looking for a way to improve the linearity and stability of amplifiers in telephone systems, and (as legend has it) the idea came to him in a flash of insight as he was commuting on a ferry boat.
An interesting historical side-note is that Black’s 1928 patent application was initially rejected on the grounds that he was trying to submit a perpetual motion device! The concept of negative feedback in an amplifier circuit was so contrary to established engineering thought at the time, that Black experienced significant resistance to the idea within the engineering community. The United States patent office, on the other hand, was inundated with fraudulent “perpetual motion” claims, and so dismissed Black’s invention at first sight.
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Question 9 of 21
Complete the table of voltages for this opamp “voltage follower” circuit:
Vin Vout
0 volts 0 volts
5 volts
10 volts
15 volts
20 volts
-5 volts
-10 volts
-15 volts
-20 volts
Reveal answer
Vin Vout
0 volts 0 volts
5 volts 5 volts
10 volts 10 volts
15 volts 15 volts
20 volts 15 volts
-5 volts -5 volts
-10 volts -10 volts
-15 volts -15 volts
-20 volts -15 volts
Follow-up question: the output voltage values given in this table are ideal. A real opamp would probably not be able to achieve even what is shown here, due to idiosyncrasies of these amplifier circuits. Explain what would probably be different in a real opamp circuit from what is shown here.Notes:A common mistake I see students new to opamps make is assuming that the output voltage will magically attain whatever value the gain equation predicts, with no regard for power supply rail voltage limits.
Another good follow-up question to ask your students is this: “How much voltage is there between the two input terminals in each of the situations described in the table?” They will find that the “golden rule” of closed-loop opamp circuits can be violated!
If students have difficulty answering the follow-up question, drop these two hints: (1) Rail-to-rail output swing and (2) Latch-up.
