Transfer function and Characteristic Equation

Transfer Function:

Mathematically Transfer Function  is defined as the ratio of Laplace transform of output of the system to the Laplace transform of input under the assumption that all initial conditions are zero.
Symbolically system can be given as below and its transfer function of system can be shown as given below,

G(s) = Laplace transform of output/ Laplace transform of input

= C(s) / R(s) = L[ c(t)] /  L[r(t)]

By taking Laplace transform of the differential equations for nth order system,

Characteristic Equation of a transfer function:

Characteristic Equation of a linear system is obtained by equating the denominator polynomial of the transfer function to zero. Thus the Characteristic Equation is,

$\\a_{ n }s^{ n }+a_{ n-1 }s^{ n-1 }+…..a_{ 1 }s+a_{ 0 } = {0} \$
• Single Phase Full Wave Controlled Rectifier
• Single Phase Half Wave Controlled Rectifier
• Three Phase Full Wave Controlled Rectifier
• Three phase Half controlled rectifier
• Amplifier
• Arduino Projects
• Combinational Logic Circuits
• Control Systems
• DC circuits
• DC-DC converter (chopper)
• DC-TO-AC INVERTER
• Digital Logic Gatesa>
• Digital Logic Gates
• Electronic Components
• Electronic Devices
• Electronic Instruments
• Electronic Systems
• MATLAB Projects
• Number Systems
• Programmable Logic Devices
• Quiz
• Semiconductors
• Sequential Logic Circuits