# Doubt in defining transfer function

1. Sep 12, 2010

### bharath423

why in a transfer function it is written by considering the initial condition to zero..
because if we individual write the integro-differential equation
and apply Laplace transform to them
and obtain a output/input relation,it definitely contains the initial condition terms in it also..
so removing these terms in the transfer function would definitely effect the result,but why do we not consider them while writing a transfer function??

2. Sep 13, 2010

### Naty1

Well, if there is an initial condition, then it WOULD be taken into account. Your premise IS correct.

Especially when beginning circuit analysis, I recall circuit conditions often being assumed at zero....Also the initial conditions are simply a special case of the overall transfer function analysis....after determing the circuit response as a function of time, you can always restart the analysis at some t = a time....all it does is add a constant....I don't think that would be all that interesting.

3. Sep 13, 2010

### bharath423

can u explain me with equations... i mean..take a simple RC circuit...with measuring,output voltage at the capacitor...say it has a initial voltage..
i had done it but i was not able to resolve the equation for input to output form..

4. Sep 18, 2010

### Naty1

5. Sep 19, 2010

### bharath423

thank you naty...but i came to know that transfer function is just defined like that to have zero intial conditions...so there isn't any particular reason to define it so,but they defined it only to get the ease of calculations..i think so..

6. Sep 19, 2010

### bharath423

but previously i was not asking to explain the impedance function to for capacitor..
anyway thank u for that link...
i was asking you to take two port RC network just like low pass filter..and asked for the transfer function i.e, input voltage(to RC network) to output voltage(at capacitor) with capacitor having some initial voltage..
so transfer function we will be left with a term containing initial values too..that was my problem actually..