Question

Using any transfer function as an example (e.g. a linear transfer function), explain why for a sensor, the higher the sensitivity, the better.

Write your answers and graphs of transfer functions.

Answer 1

What is the transfer function:

In physics, the transfer function may be defined as mathematical representation (in terms of frequency) of interrelation between input and output in linear time uninterrupted systems with zero pint equilibrium and zero initial conditions. If talking particularly about control systems then it can be defined as the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable, with all zero initial conditions.
A transfer function is a function of complex variables. The transfer function can be obtained by simple algebraic jugglery of differential equations that illustrates the system. A transfer function can represent higher-order systems also, even infinite dimensionless systems which regulate on partial differential equations.
For sensors higher sensitivity is better because the sensors are fully based on sensing its environment. So more the sensitivity of a sensor more will be the accurate results that it can give. This leads the sensor better for future implementation also.

Transfer Function of a Linear System: The Transfer Function An input-output description of a system is essentially a table of all possible input-output pairs. For linear systems, the table can be characterized by one input pair only, for example, the impulse response or the step response. In this section, we will consider another interesting pair of signals.

Consider the linear input-output system, the differential equation (1) that express it will be:

Where u is the input and y is the output the differential equation is completely described by two polynomials:

The characteristic polynomial of the system is polynomial a(s). Taking u (t) = est as input to find transfer function so the output will also be an exponential function that will be y (t) = y0 est. Inserting signals in equation (1), we get:

If a, , it will give,

The transfer function of this linear system thus will be a rational function,

Note that, a(s) and b(s) are given above as polynomial of system.

The graphical representation of Transfer Function of a Linear System,