Transfer Function.

[lord loh.]

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.

 

[Optikon]

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.

You can think of H(s) like gain in many cases. However, H(s) is general and may take on any form such as N degree polynomial for numerator, M degree polynomial for denominator. It could also include non-linear terms and trancendental functions.... so whether you call it "gain" or not it is what it is... gain is an arbitrary term.

By the way, H(s) doesnt have to be Volts/volts. It could be Amps / volts, watts/coulombs or even [number of people with red hair] / [number of people with black hair] it depends on your system and models and is not at all specific to electical engineering nor electronics. You can theoretically write a "transfer function, H" for ANY system.


Laplace is a mathematical tool that helps simplify analysis in the frequency domain. Time domain operations have a clearer physical meaning associated with them. Since no information is lost in the time domain - frequency domain transformations, the physical meanings carry over but tend to be much harder to visualize in the frequency domain.

 

[dknguyen]

s for Laplace transforms is a complex number. So s = r + jw, j is the imaginary number sqrt(-1). w is frequency in radians per second. For real frequencies you set r to 0 so s = jw. The transfer function is actually H(jw) or H(jf) rather than H(f). The j is always there and takes care of phase shifts as well as magnitude, so it's not quite H(w) or H(f). The j is there in the actual equation somewhere. The addition of the real part r let's you deal with decaying sinusoidal frequency components of the signal, rather than just constant amplitude sinusoid frequency components (it's the way the math is if you work it out).

You know about the Fourier transform right? It works on the variable jw. The Laplace transform is the same thing except generalized to work in the entire complex plane r +jw rather than just the "complex number line". If you set s = r +jw =0+jw, that is you let r = 0 and for the Laplace transform, you get the Fourier transform. THe Laplace transform kind of let's you deal with decaying sinusoidal frequency components in addition to constant amplitude frequency components, while Fourier only lets you deal with the latter.