# Differential equation into circuit and back - good book

I have had some electronics, but we only built our circuits and then measured the input / output signals with oscilloscopes...

Today I found an interesting question on physics stackexchange where user is trying to build an electric circuit based on the differential equation. Because I am a physicist and would like to connect my physics knowledge to electronics, am asking you:

Which book do you recommend to teach myself to think this way or vice versa - if I knew the circuit how would I write down the differential equation?

• Here, in the references section, you can find some books specializing in analog computation. Unsurprisingly, those books are from 50s and 60s and tend to be rare nowdays. Commented Sep 14, 2013 at 2:02
• Are there any newer editions to those books? So the reading is more of a pleasure :)
– 71GA
Commented Sep 14, 2013 at 9:10
• I'm not sure. I don't think that there are, because the whole field is a bit forgotten now. If you do find any, please let us know! Commented Sep 14, 2013 at 9:12
• What about theese two books? 1st & 2nd. Are this the ones i need?
– 71GA
Commented Sep 14, 2013 at 9:31
• Those are general electronics books. They'll give you the needed background to start doing any serious work and using them (or something similar to them), you may be able to implement some simpler equations using circuits. They are not however analog computing books, which is what you (may depending on how seriously you want to pursuit this area) really need. Commented Sep 14, 2013 at 20:11

Actually, try to use your basic circuit analysis methods and combine it with basic equations which you know about the components.

For example,

Current through the capacitor is:

Voltage across an inductor is:

Simply use and manipulate these two equations to get your math right. For example, look on a low-pass RC filter:

Brush up on your analysis methods and do KCL analysis... and voila! you got your diff eq. With all honesty - it always comes down to knowing the basics - and then connecting the dots.

If you know the circuit and want to write its differential equations, you can begin from any book on circuit analysis.

For turning a differential equation into a circuit, this is what analog computers were used for: by building circuits using op-amps (e.g. for differentiation, integration etc...), you could solve differential equations.

• I love the idea on the op-amps. Is there any good book to connect op-amps and differential equations?
– 71GA
Commented Sep 14, 2013 at 9:31