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Analog8 min read
Operational Amplifiers
Learn why an op-amp tries to make its two input voltages equal and how that creates useful amplifiers.
Mental model
Think of the op-amp as an extremely sensitive controller. It watches the difference between + and − inputs, then moves its output hard enough to reduce that difference.
Vin enters the + input. Rf returns Vout to the − input, while Rg connects that node to ground. Closed-loop gain: 1 + Rf/Rg. Op-amp supply pins are omitted for clarity.Scroll sideways to view the complete circuit.UNDERSTAND THE BEHAVIOR
01
An operational amplifier starts with an enormous open-loop voltage gain. Even a tiny difference between its two inputs would command a very large output, so using it without feedback usually drives the output into saturation.
02
Negative feedback returns part of the output to the inverting input. The output then settles at the value that makes the input difference extremely small. This is the origin of the useful approximation V+ ≈ V−; it is a consequence of feedback, not a universal property.
03
Always check the non-ideal limits after calculating the ideal answer: input common-mode range, output swing, gain-bandwidth product, slew rate and output current.
Why it matters
Op-amps appear in sensor conditioning, filters, control loops, audio circuits and ADC interfaces. Understanding feedback lets you analyze many different circuits with the same two ideal rules.
Core ideas
The input current is approximately zero in an ideal op-amp.
With negative feedback, V+ ≈ V− while the output stays inside the supply rails.
The surrounding resistors—not the huge open-loop gain—set the useful closed-loop gain.
Key equationsInverting: Av = −Rf / RinNon-inverting: Av = 1 + Rf / Rg
EXAMPLE
Worked example — non-inverting amplifier
1Given: Rf = 9 kΩ, Rg = 1 kΩ and Vin = 0.20 V.
2Gain: Av = 1 + 9/1 = 10.
3Output: Vout = 10 × 0.20 = 2.0 V.
4Check: a 2.0 V output must be possible with the chosen supply voltage.
Common mistake
Do not assume V+ equals V− when there is no negative-feedback path or when the output has already saturated.
RememberThe input current is approximately zero in an ideal op-amp.
DEEPER EXPLANATION
Why does feedback make the inputs nearly equal?
An op-amp produces an output from the difference between its non-inverting (+) and inverting (−) inputs. Its open-loop gain is very high, so a tiny difference can move the output substantially. In a non-inverting amplifier, part of the output returns through Rf and Rg to the − input. If the output rises too far, the returned voltage rises too, reducing the input difference. This is negative feedback.
When the loop is stable and the amplifier is operating away from its supply limits, the − input settles close to the + input. The divider at the − input reads Vout × Rg/(Rf + Rg). Setting that approximately equal to Vin gives Vout/Vin ≈ 1 + Rf/Rg. This is a consequence of feedback, not a rule that the two pins are physically connected.
Check the datasheet before treating the output prediction as achievable. The amplifier must support the input common-mode voltage, the required output swing at the intended load, and enough bandwidth and slew rate for the signal. An ideal gain calculation cannot check those limits for you.
Walk through another example
Choose Rf = 18 kΩ and Rg = 2 kΩ. Gain = 1 + 18/2 = 10.
With Vin = 0.15 V, the ideal output is 1.5 V. The divider returns 1.5 × 2/(18 + 2) = 0.15 V to the − input.
If the device can only reach 1.2 V at this load, its output clips there and the near-equal-input approximation no longer holds.
Check your intuition
Change Rf to 8 kΩ while keeping Rg at 2 kΩ: the predicted gain falls to 5. This is an easy way to see that the resistor ratio controls the closed-loop gain.
Where this model can mislead you
A voltage follower uses 100% feedback and has gain near 1. You cannot obtain a positive gain below 1 with this simple non-inverting resistor arrangement; choose another topology if attenuation is required.
TEST YOUR UNDERSTANDING
Three quick checks
Choose one answer per question, then check your work. Each answer includes an explanation.
Practice and check your understanding
Try each question before opening the worked answer.
1. A non-inverting amplifier has Rf = 20 kΩ and Rg = 5 kΩ. What is its gain?
Show answer and reasoning
Av = 1 + Rf/Rg = 1 + 20/5 = 5 V/V. A 0.4 V input ideally produces 2 V, provided the amplifier can support that input and output range.
2. Why can you not always assume V+ = V−?
Show answer and reasoning
The approximation requires stable negative feedback and linear operation. An output at a supply limit, excessive frequency, or positive feedback breaks the assumption.