# The transfer function is applicable to which of the following?

#### SOLUTION

The transfer function of a linear, time-invariant system is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input with all initial conditions being zero. **The transfer function is applicable to linear and time-invariant systems.**

The transfer function is a frequency-domain concept that is used to calculate the output of the linear system to any input.

$TF = \frac{{C\left( s \right)}}{{R\left( s \right)}}$

**A transfer function may only be defined for a linear, time-invariant (constant parameter) single-input-single-output system.** The transfer function is an input-output description of the behavior of a system where the information about the initial conditions is lost. Thus, the transfer function description does not include any information concerning the internal structure of the system and its behavior.

**Properties of Transfer function**

- The transfer function of a system is the Laplace transform of its impulse response.
**The transfer function concept is applicable only to linear, time-invariant systems.**- The transfer function does not take care of the initial conditions of the system. This is the greatest disadvantage.
- The transfer function is applicable to single-input-single-output systems, though for multivariable systems, the transfer matrix can be obtained by using the principle of superposition.
- The degree of the denominator polynomial of the transfer function is the order of the system. The denominator polynomial gives the poles and the numerator polynomial gives the zeros.