PPT: Network Theorems | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

 Page 1


Network 
Theorems 
Page 2


Network 
Theorems 
Network Theorems
Foundation of 
Electrical Engineering
Network theorems 
build the foundation for 
Power Systems, Electric 
Machines, Control 
Systems, and more.
Essential Analysis 
Tools
These theorems 
provide crucial 
methods for simplifying 
and analyzing complex 
Electrical Networks.
Linear Networks Only
All theorems apply exclusively to Linear Networks that 
satisfy Homogeneity & Additivity conditions.
Page 3


Network 
Theorems 
Network Theorems
Foundation of 
Electrical Engineering
Network theorems 
build the foundation for 
Power Systems, Electric 
Machines, Control 
Systems, and more.
Essential Analysis 
Tools
These theorems 
provide crucial 
methods for simplifying 
and analyzing complex 
Electrical Networks.
Linear Networks Only
All theorems apply exclusively to Linear Networks that 
satisfy Homogeneity & Additivity conditions.
Linear Networks
An element is considered linear if it satisfies the homogeneity (scaling) property and additive 
(superposition) property.
Linear networks follow specific mathematical 
relationships that allow for predictable 
behavior.
These properties enable engineers to analyze 
complex circuits using simplified methods.
Page 4


Network 
Theorems 
Network Theorems
Foundation of 
Electrical Engineering
Network theorems 
build the foundation for 
Power Systems, Electric 
Machines, Control 
Systems, and more.
Essential Analysis 
Tools
These theorems 
provide crucial 
methods for simplifying 
and analyzing complex 
Electrical Networks.
Linear Networks Only
All theorems apply exclusively to Linear Networks that 
satisfy Homogeneity & Additivity conditions.
Linear Networks
An element is considered linear if it satisfies the homogeneity (scaling) property and additive 
(superposition) property.
Linear networks follow specific mathematical 
relationships that allow for predictable 
behavior.
These properties enable engineers to analyze 
complex circuits using simplified methods.
Properties of Linear Networks
Homogeneity Property
For input x and output y:
x(t) ³ y(t)
If kx(t) is applied, output must be ky(t).
kx(t) ³ ky(t)
Additivity Property
x1(t) ³ y1(t), x2(t) ³ y2(t)
If (x1(t) + x2(t)) is applied, output must be y1(t) + y2(t).
x1(t) + x2(t) ³ y1(t) + y2(t)
Page 5


Network 
Theorems 
Network Theorems
Foundation of 
Electrical Engineering
Network theorems 
build the foundation for 
Power Systems, Electric 
Machines, Control 
Systems, and more.
Essential Analysis 
Tools
These theorems 
provide crucial 
methods for simplifying 
and analyzing complex 
Electrical Networks.
Linear Networks Only
All theorems apply exclusively to Linear Networks that 
satisfy Homogeneity & Additivity conditions.
Linear Networks
An element is considered linear if it satisfies the homogeneity (scaling) property and additive 
(superposition) property.
Linear networks follow specific mathematical 
relationships that allow for predictable 
behavior.
These properties enable engineers to analyze 
complex circuits using simplified methods.
Properties of Linear Networks
Homogeneity Property
For input x and output y:
x(t) ³ y(t)
If kx(t) is applied, output must be ky(t).
kx(t) ³ ky(t)
Additivity Property
x1(t) ³ y1(t), x2(t) ³ y2(t)
If (x1(t) + x2(t)) is applied, output must be y1(t) + y2(t).
x1(t) + x2(t) ³ y1(t) + y2(t)
Superposition Theorem
Definition
In a linear network with 
multiple independent 
sources, the response equals 
the sum of responses to each 
source acting alone.
Application
Analyze complex circuits by 
breaking them down into 
simpler circuits with single 
sources.
Benefit
Simplifies analysis of circuits 
with multiple sources that 
would otherwise be difficult 
to solve.