# Calculus and circuits

#### jaygatsby

Joined Nov 23, 2011
182
I notice that some courses at universities require high calculus as a prerequisite for circuits classes. Where is calculus used in circuits?

Thank you

#### rstevenson

Joined Apr 5, 2011
20
capacitors, inductors you name it. like current through a capacitor is i = C * dv/dt. There are lots of other examples too

#### jaygatsby

Joined Nov 23, 2011
182
capacitors, inductors you name it. like current through a capacitor is i = C * dv/dt. There are lots of other examples too
I do remember reading that formula in the all about circuits AC volume. And there was a similar formula for inductors. But this is all I've seen so far. Not enough to warrant calc I, calc II, and then diff. eq + linear algebra! Is there anything else?

Thanks

#### steveb

Joined Jul 3, 2008
2,436
I notice that some courses at universities require high calculus as a prerequisite for circuits classes. Where is calculus used in circuits?

Thank you
Analyzing linear AC circuits with coils and capacitors requires solving differential equations, making integral based transforms (Laplace and Fourier) to the frequency domain and calculation of convolution integrals in the time domain.

Nonlinear circuits using transistors, diodes, opamps etc, are sometimes linearized, which requires calculation of partial derivatives to make an effective linear small signal AC model.

Some circuits (for example analog computers, or control feedback compensators) are designed to actually do calculus calculations such as integrals and derivatives.

The modeling of DC/DC converters, which utilize high speed switching, can be simplified by making an average model, by integrating to find the averages of relevant circuit variables.

• jaygatsby

#### thatoneguy

Joined Feb 19, 2009
6,359
Anything involving AC at different frequencies, up to RF.

You end up having imaginary power used, and need to describe how.

• jaygatsby

#### crutschow

Joined Mar 14, 2008
23,508
The calculations involving electric and magnetic fields including electromagnetic wave transmission through space, wave-guides, transmission lines, and antennas all use calculus. Take a look at Maxwell's Equations sometime. #### Wendy

Joined Mar 24, 2008
21,906
Then there is the analog computers made with op amps. You can wire calculus equations directly as a circuit, extremely complicated equations with very simple circuits.. Something similar to this was used for WWII bombers, they were classed top secret at the time.

#### Geoffr67

Joined Dec 5, 2011
69
Then there is the analog computers made with op amps. You can wire calculus equations directly as a circuit, extremely complicated equations with very simple circuits.. Something similar to this was used for WWII bombers, they were classed top secret at the time.
Very cool! do you have any interesting resources regarding this? id love to read about it!

#### Blofeld

Joined Feb 21, 2010
83
Very cool! do you have any interesting resources regarding this? id love to read about it!
You might be interested in a similar development: The M9 gun director, used for anti aircraft artillery.

Some historical information:
http://www.antiaircraft.org/M9.htm

A discussion of a very early operational amplifier that was used as part of this system can be found in chapter H, p. 15 of
http://www.analog.com/library/analogdialogue/archives/39-05/Op_Amp_Applications.zip
(Op Amp Applications by Walt Jung, 16.8 MB zip file)

Generally speaking, I think that during WWII there existed a mix of mechanical analog computers (like the famous Norden bombsight) and electronic analog computers. The principle is the same - as Bill Marsden has explained, it is all about solving complicated differential equations.

#### hgmjr

Joined Jan 28, 2005
9,029
Very cool! do you have any interesting resources regarding this? id love to read about it!
Search on the topic "norden bomb sight".

Here is just one sample.

hgmjr