# transfer functions

Discussion in 'Math' started by suzuki, Apr 1, 2012.

1. ### suzuki Thread Starter Member

Aug 10, 2011
119
0
I think this should be the correct place to post this.

I am wondering about deriving transfer functions. Let's say typically, we have a basic circuit with a source and two series resistors. We can do a voltage division to find the relationship between Vo/Vin.

Would this be the same as calculating the output voltage, and then dividing both sides by Vin? For example, lets say I know the output voltage is equal to v(t) = 5cos(wt). Does that mean Vo/Vin = 5cos(wt) / Vin? Would this outcome be the same as the scenario as described above?

Hope that makes sense.

tia

2. ### panic mode Senior Member

Oct 10, 2011
1,641
456
if you know exact function (and phase) yes, you just divide the two.

suzuki likes this.
3. ### suzuki Thread Starter Member

Aug 10, 2011
119
0
hi,

thank you for confirming that. it seems obvious, but i just wasn't sure as that is not the normal "approach".

I have another question, which i thought would just add here instead of creating a new thread. Here goes...

Usually, when we have a transfer function, it is a function of 's'. i.e. H(s) = s^2 / s+1

we also know that s = jw.

Something strange I have recently come across, which i have not really seen before is the following

H(s) = 1/w *(s^2 / s+1).

i can't quite seem to wrap my head around what seems to be pretty trivial problem. according to the equation, we want the equation to be a function of 's', so 1/w should be constant. But as stated before, s= jw, and it is the 'w' value that is varied in the frequency response for example. Does this imply that 1/w should also be changing along with the value of s?

thanks again for all replies.

4. ### panic mode Senior Member

Oct 10, 2011
1,641
456
can't tell without seeing entire question but

if you know that s=jω

then ω=s/j or ω=-js

5. ### suzuki Thread Starter Member

Aug 10, 2011
119
0
hmm that is a good point.

so as an example, if we had

H(s) = w*(s/(s+1))

we could actually rewrite this as

H(s) = -js*(s/(s+1))

which gives an equation as a function of 's'?