why is the transfer function considered as the ratio of laplace transform of output to input. why not z-transform??

 

why is the transfer function considered as the ratio of laplace transform of output to input. why not z-transform??

Because it is the appropriate form for systems that operate in continuous time. Nothing else does what it does, it is unique in that regard.

The z-transform is for sampled data systems that operate in discrete time. Again nothing else does what it does either.

 

With S tranfer functions, you can immediately see the effect on the output.
With Z transforms you cannot until the next sample of the signal.