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GOVERNMENT COLLEGE OF ENGINEERING,KALAHANDI




DEPARTMENT OF ELECTRICAL ENGINEERING



Lecture notes on Network Theory
Submitted By
Soudamini Behera

, BEES2211 Network Theory


MODULE- I
1. NETWORK TOPOLOGY: Graph of a network, Concept of tree, Incidence matrix,
Tie-set matrix, Cut-set matrix, Formulation and solution of network equilibrium
equations on loop and node basis.
2. NETWORK THEOREMS & COUPLED CIRCUITS: Substitution theorem,
Reciprocity theorem, Maximum power transfer theorem, Tellegen’s theorem,
Millman’s theorem, Compensation theorem, Coupled Circuits, Dot Convention for
representing coupled circuits, Coefficient of coupling, Band Width and Q-factor for
series and parallel resonant circuits.

MODULE- II
3. LAPLACE TRANSFORM & ITS APPLICATION: Introduction to Laplace
Transform, Laplace transform of some basic functions, Laplace transform of periodic
functions, Inverse Laplace transform, Application of Laplace transform: Circuit
Analysis (Steady State and Transient).
4. TWO PORT NETWORK FUNCTIONS & RESPONSES
: z, y, ABCD and h-parameters, Reciprocity and Symmetry, Interrelation of two-port
parameters, Interconnection of two-port networks, Network Functions, Significance
of Poles and Zeros, Restriction on location of Poles and Zeros, Time domain
behaviour from PoleZero plots.


MODULE- III
5. FOURIER SERIES & ITS APPLICATION: Fourier series, Fourier analysis and
evaluation of coefficients, Steady state response of network to periodic signals,
Fourier transform and convergence, Fourier transform of some functions, Brief idea
about network filters (Low pass, High pass, Band pass and Band elimination) and
their frequency response.
6. NETWORK SYNTHESIS
: Hurwitz polynomial, Properties of Hurwitz polynomial, Positive real functions and
their properties, Concepts of network synthesis, Realization of simple R-L, R-C and
L-C functions in Cauer-I,Cauer-II, Foster-I and Foster-II forms.

, -: NETWORK THEORY:-

Any branch in a network may be substituted by a different branch without
disturbing the voltage and current in the entire network provided the new
branch has same set of terminal voltage and current as the original branch.
This theorem states that components can be interchanged as long as the
terminal voltage and current are maintained.
NOTE.
This theorem is a general theorem and is applicable for any network. the
modified network must be a unique solution. This theorem is very important in
circuit analysis of network having non-linear elements.
PROOF.
In a network ‘N’ let no of branches is ‘b’. The branchy method requires
the solution of ‘2b’ equations. Now after substitution 2b-2 or 2 (b-1) branch
equations remain unaltered. However as a branch voltage and current remain
same in it. This means that the set of 2b equation will be satisfied with the
same current and voltage as before.
EXPLANATION
Let’s take an example of a simple networkwhere we see the branch equivalent
of the load resistance.
It is observed that a known potential difference and current in a branch can be
replaced by an ideal current and voltage source respectively.




LIMITATION

, The theorem can’t be used to solve the network containing two or more
sources that are not in series or parallel.
- First obtain the concerned branch voltage and through current given by
Vxy Ixy
- The branch may be substituted by independent voltage source or
current source shown in fig.respectively.
RECIPROCTY THEORUM
In a linear bilateral network if current flowing through any branch is I
due to voltage source E, then the same current will flow when the
position of voltage and ammeter are interchanged.in other case E and I
are mutually transferable.
Now transfer resistance =E/I




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