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Learn7408Paper 3B · Option: ElectronicsOperational amplifiersOperational amplifiers
Operational amplifiers · Subtopic 1 of 1

Operational Amplifiers

An op-amp amplifies the difference between its two inputs with a huge open-loop gain, so on its own it acts as a comparator. Negative feedback through resistors sets a precise gain: inverting −RfRin-\frac{R_f}{R_{in}}, non-inverting 1+RfR11+\frac{R_f}{R_1}. The output can't go beyond the supply voltages (saturation), and gain × bandwidth is roughly constant.

AQA 7408 Paper 3B≈ 45 minRevision 1 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • State the properties of an ideal op-amp.
  • Use an op-amp as a comparator.
  • Calculate outputs of inverting, non-inverting and summing amplifiers.
  • Use the gain–bandwidth product.
Pause and think

An op-amp has a gain of 100 000100\,000. Why would anyone want to reduce it?

Section 2 of 14

Core idea

Start hereA huge gain, tamed

An op-amp multiplies the difference between its inputs by about a hundred thousand. Left alone, it slams to its supply voltage at the slightest nudge. Add two resistors and it becomes a precise, stable amplifier.

The big idea

Negative feedback sets the gain: inverting −RfRin-\frac{R_f}{R_{in}}, non-inverting 1+RfR11+\frac{R_f}{R_1}. Without feedback, an op-amp is a comparator.

1. The inverting amplifier

Gain from the virtual earth
  1. V−≈V+=0V_-\approx V_+=0
    Huge gain keeps the inputs almost equal: a virtual earth.
  2. I=Vin−0Rin=0−VoutRfI=\frac{V_{in}-0}{R_{in}}=\frac{0-V_{out}}{R_f}
    No current enters the op-amp, so the same current flows through both resistors.
  3. VoutVin=−RfRin\frac{V_{out}}{V_{in}}=-\frac{R_f}{R_{in}}
    Rearrange.
Worked exampleSaturation

Gain −50-50, supply ±12\pm12 V, input 0.400.40 V.

Goal
Output.
Strategy
Calculate, then check the rails.
  1. −50×0.40=−20 V-50\times0.40=-20\text{ V}
    Ideal calculation.
  2. ∣−20∣>12|{-20}|>12
    Exceeds the supply.
AnswerOutput saturates at about −12-12 V.
✓ CheckThe input needs to be below 0.240.24 V to stay linear ✓.

2. Other circuits

Worked exampleAudio mixer

Summing amplifier, all resistors 1010 kΩ, inputs 1.01.0 V and 2.02.0 V.

Goal
Output.
Strategy
Vout=−Rf∑ViRiV_{out}=-R_f\sum\frac{V_i}{R_i}.
  1. −10(1.010+2.010)-10\left(\frac{1.0}{10}+\frac{2.0}{10}\right)
    Substitute (kΩ cancel).
  2. =−3.0 V=-3.0\text{ V}
    Add.
Answer−3.0-3.0 V.
✓ CheckEqual resistors: output is minus the sum ✓.
Op-amp circuits

Choose the circuit for the job.

Key takeawayGain–bandwidth Gain × bandwidth is constant: 11 MHz GBP at gain 100100 gives 1010 kHz bandwidth.
Common misconceptionSigns Inverting and summing amplifiers give negative outputs for positive inputs.
Pause and think

Why does the non-inverting amplifier have a very high input resistance?

Summary

  • Comparator: no feedback.
  • −RfRin-\frac{R_f}{R_{in}}; 1+RfR11+\frac{R_f}{R_1}.
  • Saturation at the rails.
Key words
Negative feedback
Feeding output back to reduce and stabilise gain.
Virtual earth
Input held at 0 V by feedback.
Saturation
Output limited by the supply.
HistoryAnalogue computers. Op-amps were invented in the 1940s to do maths, adding, integrating and multiplying voltages in analogue computers that aimed anti-aircraft guns.
Fun factEverywhere. The 741 op-amp, introduced in 1968, is still sold today and appears in countless circuits.
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