Op-Amp Amplifier Gain
Lesson notes
Overview
A feedback resistor ratio sets the gain of an inverting amplifier precisely. This topic is rated advanced and is number 39 of 93 in Engineering. Deeper models, formal results and harder reasoning.
What you are seeing
The panel above shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.
In depth
An operational amplifier has very high open-loop gain, so negative feedback sets the gain of the circuit by external resistors. In the inverting configuration, the gain is A = −R_f/R_in, so the output is the input multiplied by the ratio of the feedback resistor to the input resistor and inverted. The precision depends on the resistors, not on the op-amp itself. The same chip can be used as an amplifier, filter, integrator or comparator.
Reading the relationship
The expression "A = −R_f/R_in" is a compact summary of the idea. It uses the symbols A, R_f, R_in; name what each one stands for before you start. Notice that it contains a ratio, so increasing the denominator makes the result smaller. Then use the sliders to see how changing one quantity changes the others.
A guided exploration
1. Set every slider to its middle value and note the shape of the curve. 2. Move one slider at a time and describe whether the curve shifts, stretches or turns. 3. Find the value where the behaviour changes sharply, then connect it to the formula.
Try this
Try to explain why the pattern holds, not just what it is. Look for limiting cases and what happens at the edges.
Common pitfalls
Always ask what the safety margin is and which assumption would break the design first. Idealised models hide losses, noise and limits.
How it connects
It builds on “The Diode I–V Curve”, the topic before it in Engineering. Once you are comfortable, continue with “The Transistor as a Switch”.
Why it matters
Engineers use this idea to design structures, machines and systems that are safe, efficient and reliable.
Where you might use it
- Revising “Op-Amp Amplifier Gain” before a class, exam or certification
- Designing safe structures, machines and control systems that must work reliably
- Diagnosing faults in electrical, mechanical or signal-processing equipment
- Checking that a design meets safety margins before it is built or deployed
Frequently asked questions
What is Op-Amp Amplifier Gain?
A feedback resistor ratio sets the gain of an inverting amplifier precisely. It is an advanced topic in Engineering.
How do I use the Op-Amp Amplifier Gain simulation?
The panel at the top shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression A = −R_f/R_in packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.
Who is this topic for?
Deeper models, formal results and harder reasoning. If the quiz feels hard, reread the lesson notes and try the previous topic first.
What should I learn before this?
Start with “The Diode I–V Curve”, the previous topic in Engineering. Each topic in a subject builds on the ones before it.
How do I track my progress?
Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.
Quick quiz
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