How do you integrate a square wave?

[Evilinside]

I'm doing homework where i have to find a function representation of the output signal from a simple op amp integrator circuit with a 4.7k resistor and a .01uf capacitor. I know I'm supposed to use the equation -1/rc * int vin(t) but the input is a square wave signal. I never learned how to integrate that. Can i anyone help me out? Do i have to use something called a Fourier series or Fourier transform?

 

[gnurf]

This quote from wikipedia also applies to a square wave:

A definite integral of a function can be represented as the signed area of the region bounded by its graph.
http://upload.wikimedia.org/wikipedia/commons/9/9f/Integral_example.svg
Does that help?

 

[DragonPetter]

This is a discontinuous function, so it is easier to integrate in sections. You need to do integrals over specifc intervals and you need to account for the initial conditions at each interval.

 

[Bob S]

As pointed out above, you have to integrate each half cycle of the input square wave in sections. The basic form of the integration is

V_{out}(t)=\frac{-1}{RC}\int_t V_{in}(t) dt

Each segment is a straight line. The line is continuous, but its derivative is not. The output of the square wave is a triangle wave.

Bob S

 

[Evilinside]

Yes I finally got the answer i think. I set the square wave input to 2V peak and i got an answer of (-4Vp/.000047)*t and since the frequency of the input square wave is 2000khz, the period is 500us. so (-4v/.00047)*t should be the graph of a triangle wave for the an interval of 0-500us and repeat itself every period after that. I think that's the answer anyway. Oh well whether I'm wrong or right, thanks for help.