# 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.

• 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.