What does mathematical operations in OpAmps mean?

[JobPositive]

Hi guys I'm learning about OpAmps. It is described as an IC that can do mathematical operations such addition, subtraction, integration, and differentiation. My question is what does addition mean here? Is it like giving two inputs lets say 1v and 2v and getting an output of 3v? or is it something else? I'm very new to electronics. Any help would be appreciated. Also, why is multiplication and division is not mentioned, can't it do those?

[CountChocula]

Op amps can be used to perform all kinds of mathematical operations, though some are easier than others, and some are really hard without purpose-built components (to wit: multiplication and division by a constant are simple, but much harder when two variable signals are involved).

Here's a great article by the inimitable Rod Elliot that gives you an idea of how each operation can be implemented.

Op amps are lots of fun to work with and learn about—just be careful to stay well within their operating parameters so that you don't get weird behaviours that can be really confusing for a beginner to understand.


—CC

[TimFox]

"Analog computers" were used years ago for solving problems, starting around WW II, including differential equations.
Multiplication and division required external analog components, and logarithms could use semiconductor diodes.
Besides addition and subtraction, the technique works well for differentiation and integration (in calculus) continuously, rather than in small finite steps.
Googling "analog computer" should give you a host of references for that topic, which is the original use for operational amplifiers, and the reason for that name.

[rstofer]

The operational amplifier (Op Amp) was designed specifically for performing mathematical operations.  They excel at showing the solution to differential equations and most of life is a differential equation.  These equations can be difficult, if not impossible, to solve but are easy to model with an op amp.

A classic problem is the Mass Spring Damper which is similar to an RLC circuit.  Derivatives are a problem because differentiator circuits generate a lot of noise.  So, we keep using integration to transform the equation to one using integration.

See https://en.wikipedia.org/wiki/Complex_harmonic_motion#:~:text=Damped%20harmonic%20motion%20is%20a,energy%20goes%20into%20thermal%20energy.

The attached schematic is from MATLAB Sumulink and it produces the characteristic waveform of Damped Harmonic Motion.

The genius of the solution is to assume we have d²y/dt² (acceleration) and integrate twice to get dy/dt (velocity) and y(t) (displacement).  Now we combine the variable and integrals to create the acceleration signal and the magic of the equal sign means we can feed the sum back as d²y/dt² to close the loop.

https://web.mit.edu/6.101/www/reference/op_amps_everyone.pdf

[dietert1]

Opamps are still used today, but not for simulating non-electrical systems.
In the context of electronics systems people do implement mathematical operations using opamps. Examples are amplifiers and filters in analog audio or voltage regulators. The precision one can reach in simple applications is about one ppm resp. 120 dB S/N - rarely even better.

Regards, Dieter

[rstofer]

For your studies, consider an integrator circuit with a time constant of 1 second (1 Mohm resistor on input and 1 ufd capacitor for feedback).  Within limitations of the amplifier, you now have a real-time analog computer.   Power supply rails +-15V and signals between -10V and +10V.  The 741 op amp excels in this application.  The ComDyna GP6 analog computer is full of them.  I have 2 of them plus a hand-built unit that is described at analogmuseum

https://analogmuseum.org/english/homebrew/vogel/

Other references:

https://www.oldcomputermuseum.com/comdyna_gp6.html

Your problem may need to be scaled in terms of time and signal voltage to fit the analog computer.

[JobPositive]

Thank you all for your detailed replies, and especially thanks for all the resources, after reading those things are making much more sense. Thanks again guys 😀🫂