Doubt in defining transfer function

AI Thread Summary
The discussion centers on the definition of transfer functions, particularly why initial conditions are often assumed to be zero. It is noted that while initial conditions can affect the output/input relationship derived from integro-differential equations, they are typically excluded for simplicity in transfer function analysis. Participants mention that initial conditions can be considered later in the analysis, as they only add a constant to the response. A specific example involving an RC circuit is referenced, highlighting the challenge of incorporating initial voltage into the transfer function. Overall, the consensus is that transfer functions are defined this way for ease of calculations, despite the potential impact of initial conditions.
bharath423
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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??
 
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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.
 
Naty1 said:
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.

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..
 
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..
 
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..
:smile:
 

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