Useful Operational Amplifier Formulas and Configurations

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My friends advised me that it would be helpful to have on this site the most common operational amplifier configurations and transfer functions or formulas.  So, here they are.  This article is not just a simple collection of circuits and formulas.  It also has links to the transfer function proof for these circuits so I hope it will be very helpful.  Make sure you post a comment and let me know how I can improve this page.  This article will be updated, so do check it often.

Non-inverting Amplifier

non-inverting-amplifier-1

image0022

Note:  The proof of this transfer function can be found here:  How to Derive the Non-Inverting Amplifier Transfer Function.

Voltage Follower

voltage-follower-2

image0041

Note:  This configuration can be considered a subset of the Non-inverting Amplifier.  When Rf2 is zero and Rf1 is infinity, the Non-inverting Amplifier becomes a voltage follower.  When a resistor has an infinity value, in practice it means it is disconnected.

Inverting Amplifier

inverting-amplifier-3image0062

Note:  The proof of this transfer function can be found here:  How to Derive the Inverting Amplifier Transfer Function

Inverting Amplifier with a Finite Op Amp Gain

inverting-amplifier-3-with-finite-gain-Ainverting-amplifier-transfer-function-with-finite-op-amp-gain

where k = R2/R1

Note: The proof of this transfer function can be found here: MasteringElectronicsDesign.com:The Transfer Function of the Inverting Amplifier with a Finite Op Amp Gain

Differential Amplifier

differential-amplifier-4

image0082

Note:  The proof of this transfer function can be found here:  How to Derive the Differential Amplifier Transfer Function.

Non-inverting Summing amplifier

non-inverting-summing-amplifier-5

image0102

Note:  The proof of this transfer function can be found here:  How to Derive the Summing Amplifier Transfer Function.

Non-inverting Summing Amplifier with N Inputs

non-inverting-summing-amplifier-n-inputs-6

image0121

where n is the number of inputs.

Note:  The proof of this transfer function can be found here:  The Transfer Function of the Summing Amplifier with N Input Signals.

Inverting Summing Amplifier

inverting-summing-amplifier-7

image0141

Note:  The proof of this transfer function can be found here:  How to Derive the Transfer Function of the Inverting Summing Amplifier.

Inverting Summing Amplifier with N Inputs

inverting-summing-amplifier-n-inputs-8

image0161

where n is the number of inputs.

Note:  The proof of this transfer function can be found here:  How to Derive the Transfer Function of the Inverting Summing Amplifier.

Instrumentation Amplifier

instrumentation_amplifier_9

image018

Note:  The proof of this transfer function can be found here:  How to Derive the Instrumentation Amplifier Transfer Function.

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Are there any other Op Amp configurations you would like to see listed here?  Let me know.

5 thoughts on “Useful Operational Amplifier Formulas and Configurations

  1. Nice work, my sincerest congratulations to Adrian! … Enhorabuena!
    very nice work and very well appreciated for the effort
    I was looking for a quick refresh and found this jewel.
    Adrian, good job!

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