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What is the transfer function and laplace transform?

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Lord Loh.

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Transfer Function.

What is transfer function?

Some references I saw over google, said H=Vout/Vin

So how is this different from Gain?

Wikipedia says

H=V(s)out/V(s)in

So can I call the transfer function as a gain of the Laplace transforms of i/p and o/p ?

And what is the physical meaning of Laplace Transform?
A search across wikipedia, makes it sound as it converts x(t) into (f) i.e. time domain to frequency domain. but the output of a Laplace transform of an x(t) is always an x(s)....

Please clarify my misconceptions....

Thank you.
 

Re: Transfer Function.

Transfer function is equivalent to input frequency gain.
Substitute s=jw in laplace eqn. It will give gain(both magnitude and phase being a complex function) in terms of input frequency 'w'.

''Automatic Control Systems" by B.C. Kuo will be useful
 

Re: Transfer Function.

The transfer function is really the ratio of the Laplace transfor of the output to the Laplace transform of the input. Therefore, it is not the gain that you would measure in the time domain.

The Laplace transform becomes a tool that allows you to more easily solve differential equations. You transform all quantities involved, do the calculations, which thanks to the Laplace transform only involve simple arithmetic, and then transform the result back to the time domain. The transformations are relatively easy to do, thanks to tables of Laplace transforms.

The Laplace transform actually transforms the time domain into the complex domain, more than just frequency. That allows you to also use it for transient responses, that is, non-periodic signals.

You do not have to worry too much about its physical meaning, consider it just a mathematical tool.
Perhaps an analogy would be the old slide rule: it allows(ed) you to do multiplications and divisions, simply by addition/ subtraction. Of course, it has to use logarithms to achieve that, but in the end, you do not care about the logarithms the slide rule is based on, you just care(d) about the ease of doing a relatively complicated operation, such as division, by simply subtracting two quantities. In a way, you "transformed" the inputs to their logs, added/ subtracted these "transforms" and finally read the result, "converting" it back to a humanly-understandable number. The "transformations" were transparent, of course, but they existed, they were embedded in the non-linear divisions of the slide rule.

The above is not meant to belittle Laplace's contribution to science. I tip my hat to the great man.
 

Re: Transfer Function.

Transfer function is the actual behavior of the whole system.once u culculate the transfer function then u can find ur system response with any input.
 

Transfer Function.

A transfer function is a mathematical representation of the relation between the input and output of a system.
 

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