# Transfer Function

Transfer Function is the ratio of Laplace transform of the output to the Laplace transform of the input, assuming all initial conditions zero.

• In general
• Where x is the input of the system and y is the output of the system.
• When order of the denominator polynomial is greater than the numerator polynomial the transfer function is said to be ‘proper’. Otherwise it is ‘improper’.

## Properties of Transfer Function

Transfer function can be used to check

• The stability of the system from characteristic equation.
• Time domain and frequency domain characteristics of the system.
• Output of the system for any given input.
• Poles/zeros of the system.

## Advantages of Transfer Function

• It gives the gain of the given system.
• Integral and differential equations can be converted into simple algebraic equations.
• Once the transfer function is known the output of the system can be determined for any input.
• Poles and zeros can be found out by transfer function and they play important role in response of the system.

## Disadvantages of Transfer Function

• Transfer function is valid only for Linear Time Invariant (LTI) systems.
• In transfer function initial conditions are neglected hence initial conditions loose their importance.
• It does not give any idea how the present output is progressing.