Gain & Transfer Function - Difference?

[dominicfhk]

I know the transfer function = Laplace{output}/Laplace{input}, while gain = output/input, but why is that matter? The ratio will still be the same (or is it?).

And if there is a distinct different, is the result of the mason's formula using signal-flow graph a gain or a transfer function? Wiki says it is a gain but my teacher did an example on the board and got a transfer function at the end.

Thank you so much!

 

[rude man]

I know the transfer function = Laplace{output}/Laplace{input}, while gain = output/input, but why is that matter? The ratio will still be the same (or is it?).

And if there is a distinct different, is the result of the mason's formula using signal-flow graph a gain or a transfer function? Wiki says it is a gain but my teacher did an example on the board and got a transfer function at the end.

Thank you so much!

Gain and tranfer function as you have stated them are the same thing. Except that a transfer function is capable of handling a large number of different inputs besides sine functions. "Gain" usually implies either dc or a sine wave input, but can also refer to a Laplace transfer function. The Laplace transfer function with s replaced by jω gives the sine gain, including phase.

I am not familiar with signal flow diagrams and in fact have studiously avoided them as the source of unnecessary irritation and complication.