Solving Basic Circuit with Fourier Transforms

[FunkyDwarf]

Hey guys

Im doing a small signals and noise course this year as part of physics and I am trying to wrap my head around a few things, namely in what way to actually use Fourier transforms.

Say i have (sorry about the lack of pictorial aids but its pretty easy to picture) a voltage/current source which is connected in series to a resistor then a capacitor. I then take two leads, one on either end of the cap so it becomes a voltage divider.

Say for example we had to find the norton/thevenin equivalent of this circuit. Now i know in DC you'd use ohms law to get current through the circuit, then voltage over the resistor in the place of a cap and then get the resistance and you're done. What i don't get with AC is when and where to apply the Fourier transform? Do i apply it to the voltage function and the impedance of the cap and then fiddle in Fourier space and come back?

Cheers
-Graeme

EDIT: Just realized (duh) that cap impedance is a function of f already, i need not apply the transform then?

 

[antoker]

Usually when doing a AC analysis, you write a complete equation in terms of laplace that describes your circuit, for instance, a High-Pass circuit:$$V_{s} = I\cdot( R+\frac{1}{s\cdot C})$$
$$V_{o} = I\cdot \frac{1}{s\cdot C}$$

Devide $$V_{o}$$ by $$V_{s}$$

Then you'll get something that is called a transfer (gain function) function in s-domain:

Now, replace the s in your transfer function with $$j\omega$$ and you're in frequency domain, ready to analyze the frequency response of your function.

 

[FunkyDwarf]

you'll have to forgive me, I am not an electrical engineer. whilst I am vaugely aware that Fourier transforms are related or a specific case of laplace transforms, and have dealt with laplace transforms in maths courses, I am a physics student and have no idea how they relate to circuitry :P So basically you're saying write out my ohmic equation assuming were in Fourier space then proceed?

 

[antoker]

you'll have to forgive me, I am not an electrical engineer. whilst I am vaugely aware that Fourier transforms are related or a specific case of laplace transforms, and have dealt with laplace transforms in maths courses, I am a physics student and have no idea how they relate to circuitry :P So basically you're saying write out my ohmic equation assuming were in Fourier space then proceed?

You're forgiven and your assumption is correct, here are some things that you should remember:

Capacitor in S/jw domain is : $$\frac{1}{sC} = \frac{1}{j\omega C}$$
Inductor in S/jw domain is : $$sL = j\omega L$$

Be sure to write a complete equation that describes the circuit, like a transfer function which is composed of output divided by input:

Matlab has a tons of functions related to analysis of transfer functions, take a look in help files.

 

[FunkyDwarf]

Sweet cheers. yeh i know the basics of resonance and LCR circuits and stuff from first year courses but some of this is new and what isn't is buried beneath lots of beer coated braincells :)

 

[antoker]

Hehe. I hope it will work out for you, just PM me if you run into any trouble.

 

[kendr_pind]

hi funky...these LCR circuits are an ocean in itself...one can go on and on abt it...literally every branch of calculus puts its fingers in this...as if this were not enuf, thre are imaginary numbers like sqrt(-1) i.e. 'j' thrown in abundance...but basically the objective behind doing this is to find out the response of these circuits to a particular stimulus which gives valuable insights into its beaviour, i.e stability aspects, characteristics etc., so it can be used when a particular behavior is needed. the example has been already mentioned above...ie in high pass ckt. so this 'high pass' , 'low pass' etc. are ckts that have a particular characteristic curve in the frequency domain...i guess u get a brief picture of this..y I am telling this is that it is better to know the story behind things so u'll solve it faster...



PS: sorry for the sermonising :-))