Q. Illustrate about Transfer Functions?

The transfer function is a means by which the dynamic characteristics of devices or systems are described. The transfer function is a mathematical formulation that relates the output variable of a device to the input variable. For linear devices, the transfer function is independent of the input quantity and solely dependent on the parameters of the device togetherwith any operations of time, such as differentiation and integration, that it may possess. To obtain the transfer function, one usually goes through three steps: (i) determining the governing equation for the device, expressed in terms of the output and input variables, (ii) Laplace transforming the governing equation, assuming all initial conditions to be zero, and (iii) rearranging the equation to yield the ratio of the output to input variable. The properties of transfer functions are summarized as follows.

• A transfer function is defined only for a linear time-invariant system. It is meaningless for nonlinear systems.

• The transfer function between an input variable and an output variable of a systemis defined as the ratio of the Laplace transform of the output to the Laplace transform of the input, or as the Laplace transform of the impulse response. The impulse response of a linear system is defined as the output response of the system when the input is a unit impulse function.

• All initial conditions of the system are assumed to be zero.

• The transfer function is independent of the input.