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Analog design

Operational Amplifiers

Why an op amp can satisfy the equation on the schematic and still give the wrong answer on the bench, and which of its limits decided that.

  • Intermediate
  • 10 lessons

About this course

An operational amplifier is the component most likely to be used without being understood, because the equations are easy and they are usually right. A gain of 119 needs two resistors and no thought.

The trouble starts when a circuit obeys its schematic and still fails. The gain is correct at DC and wrong at 10 kHz. The output sits in the middle of its range and reads two per cent high. A buffer that worked on the bench rings when the cable is fitted. None of those are mistakes in the arithmetic. They are limits of the part that the arithmetic never mentioned.

This course takes each of those limits in turn, explains the mechanism rather than the symptom, and works the numbers in front of you. A single front end runs through most of the lessons: a sensor producing a few tens of millivolts, amplified on a single 3.3 V supply, read by a 12-bit converter. The same circuit is examined from a different direction each time, and each time it is a different parameter that decides whether it works.

Course contents

In order. Each lesson assumes the one before it.

  1. How an Operational Amplifier Actually Works

    The two inputs are not equal. They are driven close together, and five things can stop that happening.

  2. Inverting vs Non-Inverting Op Amps: What Actually Changes

    Same two resistors, two circuits, and three differences the gain equations never show.

  3. Gain-Bandwidth Product: Why Op-Amp Gain Falls with Frequency

    A gain of 119 from a 1 MHz part leaves you 8.4 kHz, and nothing on the schematic says so.

  4. Slew Rate: The Op-Amp Limit That Gain-Bandwidth Does Not Explain

    The same amplifier is good to 1 MHz with a small signal and to 40 kHz with a large one.

  5. Input Offset Voltage: How Small Errors Become Large Output Errors

    150 microvolts at the input is 22 converter codes at the output, and calibration only removes part of it.

  6. Input Bias Current: When Nanoamps Matter

    Ten nanoamps into a one-megohm source is ten millivolts of error, nearly seventy times the offset.

  7. Common-Mode Input Range: Why an Op Amp Can Fail Before It Saturates

    The output is nowhere near a rail, the arithmetic is right, and the reading is still wrong.

  8. Rail-to-Rail Op Amps: What Rail-to-Rail Actually Means

    Two separate claims, neither of which promises the rail, and both of which depend on the load.

  9. Why Op Amps Oscillate with Capacitive Loads

    One nanofarad is fine and ten is not, and the arithmetic says why to the degree.

  10. How to Choose an Op Amp for a Real Circuit

    Start from what the circuit has to do, not from a parametric search sorted by price.

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