PPT: Transient Analysis in AC & DC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

 Page 1


Transient 
Analysis in AC & 
DC Circuits
Page 2


Transient 
Analysis in AC & 
DC Circuits
Introduction
Servomechanisms
Systems using feedback 
principles designed so 
outputs follow inputs.
Transient Response
This part reduces to zero 
as t ³ >.
Steady-State Response
Response of the system as 
t ³ >.
Page 3


Transient 
Analysis in AC & 
DC Circuits
Introduction
Servomechanisms
Systems using feedback 
principles designed so 
outputs follow inputs.
Transient Response
This part reduces to zero 
as t ³ >.
Steady-State Response
Response of the system as 
t ³ >.
Response of the first order systems
Linear System Output
Y(s) = G(s)U(s)
Where Y(s) is Laplace transform of output, 
G(s) is transfer function, and U(s) is Laplace 
transform of input.
First-Order System
Form: ay + y = u
Transfer function shown in equation.
Page 4


Transient 
Analysis in AC & 
DC Circuits
Introduction
Servomechanisms
Systems using feedback 
principles designed so 
outputs follow inputs.
Transient Response
This part reduces to zero 
as t ³ >.
Steady-State Response
Response of the system as 
t ³ >.
Response of the first order systems
Linear System Output
Y(s) = G(s)U(s)
Where Y(s) is Laplace transform of output, 
G(s) is transfer function, and U(s) is Laplace 
transform of input.
First-Order System
Form: ay + y = u
Transfer function shown in equation.
Exponential Response Form
Time Constant
The constant 'a' is called the time constant of the 
system.
Response at t = a
When t = a, y(a) = 1 - e^-1 = 0.63.
Response Parts
Transient part e^-t/a approaches zero as t ³ >.
Steady-State
Steady-state part is 1, which is the output when t ³ 
>.
Page 5


Transient 
Analysis in AC & 
DC Circuits
Introduction
Servomechanisms
Systems using feedback 
principles designed so 
outputs follow inputs.
Transient Response
This part reduces to zero 
as t ³ >.
Steady-State Response
Response of the system as 
t ³ >.
Response of the first order systems
Linear System Output
Y(s) = G(s)U(s)
Where Y(s) is Laplace transform of output, 
G(s) is transfer function, and U(s) is Laplace 
transform of input.
First-Order System
Form: ay + y = u
Transfer function shown in equation.
Exponential Response Form
Time Constant
The constant 'a' is called the time constant of the 
system.
Response at t = a
When t = a, y(a) = 1 - e^-1 = 0.63.
Response Parts
Transient part e^-t/a approaches zero as t ³ >.
Steady-State
Steady-state part is 1, which is the output when t ³ 
>.
Transfer Function Analysis
Step Response Equation
When U(s) = 1/s, the 
equation can be written as 
shown.
Partial Fraction 
Expansion
Breaking down the 
transfer function for 
analysis.
Final Response Form
The time domain response 
after inverse Laplace 
transform.