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LNGR SPKRHIFI. TWO WAYS. HANDCRAFTED.
Knowledge / Understand components
LNGR · Learning workshop

The operational amplifier

Feedback turns enormous internal gain into a predictable amplifier. Its supply still sets limits.

Try the experiment ↓

Example package · not a pinout diagram

Start without prior knowledgeUnderstand the model limitsDE / EN
01

The mental picture

A controller compares target and actual values, correcting until the difference is small. A feedback op amp compares part of its output with its input. This works only while the amplifier is fast enough and its output can reach the required value.

02

The principle

The inputs are non-inverting (+) and inverting (−); they are not power-supply pins. In a non-inverting amplifier, a feedback resistor divider sets gain. Supply range, input common-mode range and output swing remain component-dependent.

03

Try it yourself

Interactive experiment

The operational amplifier

Increase gain until the output becomes flat at its top and bottom. Then reduce input amplitude. Clipping depends on signal, gain and available headroom together.

Model limits: Ideal amplifier with hard clipping 1 V inside each supply rail. Required slew rate is calculated but slew distortion is not simulated.

04

A worked example

A gain of 5 turns a 0.5 V input peak into an ideal 2.5 V output peak. With ±5 V supplies and an assumed 1 V margin to each rail, this model clips at ±4 V.

A closer look · equations and assumptions
Formula notes
A=1+\frac{R_f}{R_g}
U_{\mathrm{out}}=A U_{\mathrm{in}}
\mathrm{SR}_{\mathrm{required}}=2\pi f\hat U_{\mathrm{out}}

For a dominant-pole op amp, small-signal bandwidth is approximately GBW/A when that model and stability conditions apply. Slew rate additionally limits voltage change per unit time. An op amp can therefore distort large high-frequency signals despite adequate supply voltage.

A common pitfall. “Rail-to-rail” does not mean exactly reaching both rails under every load. Input and output specifications are separate.

05

Workshop takeaway

Write down gain, maximum signal amplitude, supply and load before choosing an op amp. Then consider the finer noise and distortion specifications.

Sources & transparency

Original illustrations and educational calculations. No measurements of a specific product. Edited 11 October 2026.

Work it out · answers unfold

Write down your prediction first, then your calculation. Open the answer only when you are ready to compare.

14 · Divider: R1 = 2 kΩ upper, R2 = 3 kΩ lower, input 10 V. Unloaded output across R2. Find output.

Show worked answer
  1. Total resistance: 5 kΩ.
  2. Current: 2 mA.
  3. Voltage across R2: 6 V.
Calculation
U_o=10\frac{3}{2+3}=6\,V

15 · Load the divider in task 14 with 3 kΩ across R2. Find the new output.

Show worked answer
  1. R2 parallel load = 1.5 kΩ.
  2. Total resistance: 3.5 kΩ.
  3. Output = 10 · 1.5/3.5 = 4.286 V.
Calculation
U_o=10\frac{1.5}{2+1.5}\approx4.286\,V

16 · An unloaded divider should turn 12 V into 3 V. Choose R2 = 1 kΩ. Find R1.

Show worked answer
  1. Output is one quarter of input.
  2. Total resistance must be four times R2.
  3. R1 = 4 kΩ - 1 kΩ = 3 kΩ.
Calculation
R_1=R_2\left(\frac{U_i}{U_o}-1\right)=3\,k\Omega

19 · How do you connect ideal ammeter and voltmeter to a resistor? Explain the short-circuit mistake.

Show worked answer
  1. Ammeter in series with the current path.
  2. Voltmeter in parallel across the resistor.
  3. An ammeter across the source nearly shorts it.

All new learning modules →

20 exercises · PDF ↓Teacher solutions · PDF ↓