NDSU ECE 211 Lecture 14
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Overview
Roger Green introduces ideal operational amplifiers as powered active devices for signal operations, then derives four standard negative-feedback circuits using zero input current and equal input-terminal voltages. The results are the inverting gain of -RF/R, non-inverting gain of 1 + RF/R, unity-gain voltage follower, and summing amplifier with output -Σ(RF/Ri)Vi.
Key takeaways
- For ideal op-amp analysis under negative feedback, assume zero current into both input terminals and equal voltages at the inverting and non-inverting terminals.
- An inverting amplifier produces Vout = -(RF/R)Vin, allowing gain magnitude to be selected by the feedback-to-input resistor ratio.
- A non-inverting amplifier produces Vout = (1 + RF/R)Vin, so its gain is at least one and the output keeps the input polarity.
- A voltage follower has Vout = Vin while providing a high-impedance input and an active output that can buffer a weak source from a load.
- A summing amplifier produces Vout = -Σ(RF/Ri)Vi; equal input resistors create a uniform weighted sum, and RF = R makes the output the negative sum of all inputs.
Chapters
- The lecture shifts from Thevenin and Norton equivalents and maximum power transfer to circuits that perform useful operations.
- Op amps support applications such as sensing, filtering noise, amplifying microphone signals, comparing signals, and controlling systems.
- The discussion uses an idealized model first, leaving practical device details for later electronics study.
- The standard op-amp symbol is a triangle with two inputs and one output.
- The minus-marked terminal is the inverting input; the plus-marked terminal is the non-inverting input.
- An op amp is an active, powered device, unlike passive components such as resistors, capacitors, and inductors.
- Many op amps use positive and negative supply rails, with examples including ±12 V and ±15 V.
- Some devices use a single supply, such as ground and +5 V, though their operation may be less general.
- Practical packages can include supply connections and offset-null pins, while basic circuit diagrams often omit them.
- Ideal input terminals draw zero current, equivalent to having extremely high input impedance.
- With negative feedback, the ideal op amp maintains equal voltages at its inverting and non-inverting inputs.
- These assumptions simplify circuit analysis and are sufficiently accurate for many real applications.
- The inverting amplifier connects input voltage Vin to the minus input through resistor R and feeds output back through RF.
- The plus input is grounded, creating a virtual ground at the minus input under the ideal op-amp assumptions.
- Negative feedback is the standard configuration for these linear amplifier examples; feeding output to the plus input creates positive feedback and can destabilize operation.
- Zero input current forces the current through input resistor R to continue through feedback resistor RF.
- The virtual-ground condition gives I = Vin/R, and applying Kirchhoff's voltage law yields Vout = -(RF/R)Vin.
- Choosing RF = 2R produces an output twice the input magnitude with reversed polarity.
- The input Vin connects directly to the plus terminal, while the minus terminal sits between resistor R to ground and feedback resistor RF to Vout.
- Equal input-terminal voltages make the minus-terminal voltage equal to Vin; Kirchhoff's current law then gives Vout = (1 + RF/R)Vin.
- Because the resistor ratio is nonnegative, this configuration has gain at least one and preserves the input polarity.
- The voltage follower connects Vin to the plus input and wires Vout directly to the minus input.
- The ideal equal-voltage condition gives Vout = Vin, so the circuit has unity gain.
- Its high-impedance input draws essentially no current from the source, while the powered op amp can drive a load and isolate the source from it.
- Each input Vi connects through its own resistor Ri to a shared node at the inverting input; the non-inverting input is grounded.
- A feedback resistor RF connects the output to the shared node, forming negative feedback.
- Zero input current means the branch currents from all input sources combine and flow through RF.
- The grounded non-inverting input makes the shared inverting node a virtual ground.
- Using Ohm's law for each branch and Kirchhoff's current law gives Vout = -RF(V1/R1 + V2/R2 + ... + Vn/Rn).
- Each input receives its own negative weight, RF/Ri, so selecting different Ri values sets the inputs' relative contributions.
- When all input resistors equal R, the output becomes -(RF/R)(V1 + V2 + ... + Vn).
- Setting RF = R gives Vout = -(V1 + V2 + ... + Vn), an inverting unity-gain summer.
- A separate unity-gain inverting stage can reverse the polarity again to produce a non-inverted sum.
Transcript excerpt
0:01 Welcome to ND issue ECE21. This is lecture 14. Last time we covered the topic of thevanin and Norton equivalents. We also looked at maximum power transfer. Today we're going to switch gears um pretty significantly. Up to now I would say in the class we've really focused on basic analysis of circuits. It's certainly important. It's necessary. It forms a foundation for all the things that we do as electrical engineers. And it's also probably not the reason we became engineers. Most of us didn't sit around and join the engineering profession so we could just analyze circuits. As engineers, we really want to do stuff, right? We want to sense the world around us. Um that's a sensors type of application. We want to process signals. For example, doing filtering. Uh getting rid of noise in a
0:49 noisy environment. Uh for example, we'd like to amplify signals. Uh think about uh taking small signals and making them loud. uh making a making an amplifier, an audio amplifier so you can hear your music, comparing signals, and then maybe using those signal comparisons to control parts and systems. In the end, as engineers, we just want to get stuff done. We want to do applications. We want to do operations. All these things that we've listed here um are operations. And what I would like to do now is I'd like to introduce um our first what is called active device. And it's really made for carrying out operations. It's a fundamental um component in electrical engineering. It's used in just numerous numerous applications and it's all about getting stuff done. It's all about operations.
1:37 Because we're early in our in our progress in electrical engineering, we're going to look at this from a from a kind of a high level um idealized uh
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Related notes
Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, Roger Green.