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Active circuits: �Op amps & �Voltage buffers

TENSS 2026

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Resistance when V is constant

Resistance which changes when V changes

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Impedance

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Impedance

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Impedance

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Tomorrow

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Why amplify?

  • Make it larger

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  • Make it stronger

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Why amplify?

  • Make it larger

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  • Make it stronger

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Impedance transformation

Input impedance: very high�

Driven with weak current sources (like neurons)

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Output impedance: very low�

Drive cabling and digitizers without interference

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How much should I amplify?

  • Is that big enough:

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  • Should we aim for that instead?

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How much should I amplify?

  • Is that big enough:

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  • Should we aim for that instead?

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How much should I amplify?

  • Match digitizer dynamic range

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How do we amplify?

  • With a magic triangle

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Ideal opamp: voltage-dependent voltage source

  • Inputs draw no current1

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  • Very large differential gain, K 2

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  • Zero output resistance

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1 Input resistance can be Gigaohms.�2 Typically K ~ 1E6 or higher

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Ideal opamp: voltage-dependent voltage source

  • What will happen to a sine wave?

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Saturation

  • What will happen to a sine-wave input?

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Negative feedback

  • Weird idea: connect the output to the negative input

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Negative feedback

  • Weird idea: connect the output to the negative input
  • Use a pulse instead of a sign wave

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Negative feedback

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Ideal opamp: voltage-dependent voltage source

  • Inputs draw no current

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  • Very large differential gain, K

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  • Zero output resistance

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  • , when there is feedback

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A non-amplifying amplifier

Is it useful to have an amplifier with a unity gain?

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Very useful

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Negative feedback

  • Connect some of the input to the output

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Negative feedback

  • Connect some of the input to the output

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Negative feedback

  • Connect some of the input to the output

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Negative feedback

  • Connect some of the input to the output

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Negative feedback

  • Connect some of the input to the output

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Negative feedback

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Negative feedback

  • Now Vout has to change twice as much to get input terminals to be equal!
  • V- = V+ when Vout = 2 * V+

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Closed-loop gain, in general

  • Gain: Determined by voltage divider

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Intuition

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Intuition

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Closed-loop gain, in general

  • Gain: Determined by voltage divider

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Closed-loop gain, in general

  • Gain: Determined by voltage divider

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PRACTICALS