Understanding Op Amps (publ. 2025-07-28)

I've been trying to better understand if/how electronic analog models are affected by amplitude dampening or growth effects that are not explicitly part of the model. E.g., the differential equation y'' = - y, should give you a stable sinusoid. But when implemented on an electronic analog computer, the wave will either grow or diminish in amplitude. On my system, it seems that with the larger feedback capacitors, such as 1uF, the signal will rapidly diminish. But with the smaller ones, such as 10nF, the signal will rapidly grow.

Incidentally, y'' = -y is called the "circle test" because, if you use the output signals of both integrators in XY mode, then this produces a circle, or rather a spiral, as the signals grow or diminish. The test is to see how rapidly your system diverges from the ideal circle.

I've been researching into this, and asking about it on the sci.electronics.design usenet challenge, but much is unclear to me. Something that has been helpful, or at least very interesting, is working through the book "Operational Amplifiers: Theory and Practice" by Roberge. I am still on the first chapter, mind you, but working through the explanations and equations regarding gain and feedback and such has been stimulating.

The copy I have been working through is scan of the 1975 book, but it appears that there is an updated 2nd edition available here:

Copyright

This work © 2025 by Christopher Howard is licensed under Attribution-ShareAlike 4.0 International.