I notice that some courses at universities require high calculus as a prerequisite for circuits classes. Where is calculus used in circuits?

Thank you

 

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

 

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

 

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.

 

Anything involving AC at different frequencies, up to RF.

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

 

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.

 

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.

 

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!

 

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.

 

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.

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