Unit 1: Basic Concepts Practical sources, Source transformations, Network reduction using Star – Delta

transformation, Loop and node analysis With linearly dependent and independent

sources for DC and AC networks, Concepts of super node and super mesh.

Basic Concepts

Node: It's a point in an electrical circuit, for which two elements are connected

Principal Node: It’s the node in an electrical circuit, for which two or more elements

are connected

Reference Node: It’s the node in an electrical circuit, with the zero potential

Branch: It's a line segment, which represents a network element or a combination of

elements connected between two nodes

Path: It's set of braches, traversed in the form that no node is passed through again

Loop: It's an electric circuit’s closed path. Loop can has other loops within it

Mesh: It's an independent loop in an electric circuit, which doesn't contain any other

loops within it. All meshes are loops but all loops are not meshes

Planar circuit: It's a circuit drawn on a plane surface, such that no branch passes over or

under any other branch

Non-planar circuit: It's the circuit which can't be drawn without passing over or under

any other branch

Independent and Dependent Sources

Independent Source: It's the source in which the voltage source is completely

independent of the current and the current source is completely independent of the

voltage

Symbol: Circle symbol is used to represent the independent sources

Dependent Source: It's the source in which the voltage or current depends upon the

current and voltage elsewhere in the circuit

Symbol: Diamond symbol is used to represent the dependent sources

Types of Network Elements

1. Bilateral and Unilateral Element

Bilateral Element: It's the source, in which the current-voltage relationship remains

same for either direction of the current flow

Example: Voltage Source, Current Source, Resistance, Inductor, Capacitor and etc.,

Bilateral Circuit: It's the circuit containing the bilateral elements

Unilateral Element: It's the element, in which the current-voltage relationship doesn't

remains same for the either direction of the current flow

Example: Vacuum diode, Silicon diode, Selenium rectifier and etc.,

Unilateral Element: It's the circuit containing the unilateral elements

2. Distributed and Lumped Elements

Distributed Element: It's an element which is considered to be uniformly distributed

throughout the length of the line and is not concentrated at any particular point

Lumped Element: It's an element which is considered to be lumped at any particular

point over the line

3. Linear and Non-linear Elements

Linear Element: It's a passive element, which has the linear voltage-current relationship

Non-linear Element: It’s the element, which has the non-linear voltage-current

relationship

4. Ideal Element and Practical Element

Ideal Element: It’s the element, whose internal resistance is zero

Practical Element: It’s the element, whose internal resistance is not zero

Ideal Source

It’s the source, in which the internal resistance is zero

Types:

1. Active Ideal Source

2, Passive Ideal Source

E

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SourcesPractical SourcesIdeal Sources

DC Sources AC Sources DC Sources AC SourcesVoltage Current Voltage Current Voltage Current Voltage Current

E +

1. Active Ideal Source

It's the ideal source which possess energy of its own and imparts it to the other elements

of the circuit

Types:

1. Active Ideal Voltage Sources

2. Active Ideal Current Sources

1. Active Ideal Voltage Sources

It's the active ideal source, which delivers energy to the load with constant terminal

voltage, irrespective of the current drawn by the load

2. Active Ideal Current Source

It's the active ideal current source, which delivers energy with the constant current to the

load, irrespective of terminal voltage across the load

2. Passive Ideal Sources

It's the ideal source, which doesn’t possess energy of it’s own and depends on the sources

elsewhere in the circuit

Types:

1. Passive Ideal Voltage Sources

2. Passive Ideal Current Sources

1. Passive Ideal Voltage Sources

It’s the passive ideal source, which delivers energy to the load with constant terminal

voltage, irrespective of the current drawn by the load

2. Passive Ideal Current Source

It’s the passive ideal source, which delivers energy to the load with constant terminal

voltage, irrespective of the current drawn by the load

Practical Sources

It’s the source, in which the internal resistance is not zero.

Types:

1. Active Practical Sources

2. Passive Practical Sources

1. Active Practical Sources

It's the practical source circuit possess energy of its own imparts it to the other elements

of the circuit

Types:

1. Active Practical Voltage Source

2. Active Practical Current Source

1. Active Practical Voltage Source

It's the active practical source, which delivers energy to the load with constant terminal

voltage, irrespective of the current drawn by the load

2. Active Practical Current Source

It's the active Practical current source, which delivers energy with the constant current to

the load, irrespective of terminal voltage across the load

2. Passive Practical Sources

It's the practical source which doesn’t possess energy of it’s own and depends on the

sources elsewhere in the circuit

Types:

1. Passive Practical Voltage Source

2. Passive Practical Current Source

1. Passive Practical Voltage Source

It’s the passive practical source, which delivers energy to the load with constant terminal

voltage, irrespective of the current drawn by the load

2. Passive Practical Current Source

It’s the passive practical source, which delivers energy to the load with constant terminal

voltage, irrespective of the current drawn by the load

Sources in different combination

Types:

1. Ideal sources in different combination

2. Practical sources in different combination

Ideal sources in different combination

Types:

1. Ideal Sources in Series combination

2. Ideal Sources in Parallel combination

Sources

Voltage Sources Current Sources

Ideal Voltage Sources Practical Voltage Sources Ideal Current Sources Practical Current Sources

ParallelConfigruation

Series Configuration

Sources

Dependent Voltage Sources Dependent Current Sources

Ideal Dependent Voltage Sources

Practica Dependentl Voltage SourcesIdeal Dependent Current Sources Practical Dependent Current Sources

ParallelConfigruation

Series Configuration

+

1. Ideal Sources in Series combination

Types:

1. Ideal Voltage sources in Series

2. Ideal Current sources in Series

1. Ideal Voltage sources in Series

Resultant voltage source is of the voltage = VEQ= V1+V2

2. Ideal Current sources in Series

Resultant voltage source is of the voltage = IEQ= I1 = I2

2. Ideal Sources in Parallel combination

Types:

1. Ideal Voltage sources in Parallel

2. Ideal Current sources in Parallel

1. Ideal Voltage sources in Parallel

Resultant voltage source is of the voltage = VEQ= V1 = V2

2. Ideal Current sources in Parallel

Resultant current source is of the voltage = IEQ= I1+I2

Practical sources in different combination

Types:

1. Practical Sources in Series combination 2. Practical Sources in Parallel combination

1. Practical Sources in Series combination

Types:

1. Practical Voltage sources in Series

2. Practical Current sources in Series

1. Practical Voltage sources in Series

Resultant voltage source is of the voltage = VEQ= V1+V2

Resultant voltage source is of the resistance = rEQ= r1+r2

2. Practical Current sources in Series

Resultant Current source is of the voltage = IEQ= VEQ/r, VEQ=V1+V2, V1=I1/r, V2=I2/r

Resultant Current source is of the resistance = rEQ= r1+r2

2. Practical Sources in Parallel combination

Types:

1. Practical Voltage sources in Parallel

2. Practical Current sources in Parallel

1. Practical Voltage sources in Parallel

Resultant voltage source is of the voltage = VEQ= IEQr, IEQ=I1=I2, I1=V1/r, I2=V2/r

Resultant voltage source is of the resistance = rEQ= r1r2/r1+r2

2. Practical Current sources in Parallel

Resultant current source is of the voltage = IEQ= I1+I2

Resultant voltage source is of the resistance = rEQ= r1r2/r1+r2

Linear Network

Linear Element: It's a passive element, which has the linear voltage-current relationship

Linear Dependent Sources: It's dependent current or voltage source whose output

current or voltage is proportional only to the first power of some current or voltage

parameter in the circuit or the sum of such quantities

Linear Network: It's circuit, which consists of only the independent sources, linear

dependent sources, and linear elements.

Properties of Linear Network

1. Superposition property: It states that, in any linear bilateral network containing

several sources, the current through or voltage across any element is equal to the

algebraic sum of all the individual currents flowing or voltages across the element, by the

separate independent sources acting alone, with all independent voltage sources replaced

by the short circuits and all independent current sources replaced by the open circuits

2. Homogeneity property: It states that, if all the sources in the linear network are

multiplied by some constant, then the response across or through any other element of the

linear network also gets multiplied by the same constant

Source Transformations

Identical Sources: Sources are said to be the identical sources, if their terminal voltages

and load currents are same

Equivalent Sources: Sources are said to be the equivalent sources, if their the open

circuit voltage and the short circuit current are same

Types of Source Transformations

1. Voltage source to the Current source transformation

2. Current source to the Voltage source transformation

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VLRL

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EVL

RL I

Practical VoltageSource

PracticalCurrent Source

Source Transformations Let the two sources, voltage and current above are identical sources. So, load current

IL flowing in them are identical

Expression for Load Current, IL:

Practical Voltage Source: IL=E/r+RL ------------- 1

Practical Current Source: IL=I(r/r+RL) ------------- 2

From, Eq. 1 and Eq. 2, E=Ir = Voltage of the Equivalent Voltage Source

I=E/r = Current in the Equivalent Current Source

Transformation of Sources:

Practical Voltage Source with Series internal resistance = Practical Current Source with

Parallel internal resistance

1. Voltage source to the Current source transformation

Procedure:

1. Calculate the current of the current source, given by I=V/R or I=V/Z

2. Note down the internal resistance of the current source, which is the same as the

internal resistance of the voltage source

3. Convert voltage source with its internal resistance in series, to the current source with

its internal resistance in parallel

2. Current source to the Voltage source transformation

Procedure

1. Calculate the voltage of the voltage source, given by V=IR or V=IZ

2. Note down the internal resistance of the voltage source, which is the same as the

internal resistance of the current source

3. Convert current source with its internal resistance in parallel, to the voltage source with

its internal resistance in series

Source Shifting

It’s the shifting of the position of the sources in the circuit, in such a way that the

resultant current or voltage of the circuit remains same

Types:

1. Voltage Source Shifting

2. Current source Shifting

1. Voltage Source Shifting

Single voltage source can be considered equivalent to the two identical voltage sources in

parallel, when they are pushed through the node, in such a way that the current through

the various elements of the network remains unchanged

L1R1

R1 L1L1

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VL

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Voltage Source Shifting

2. Current source Shifting

Single current source can be considered equivalent to the two identical current sources,

when they are pushed in such a way that, the current at all nodes remains unchanged

Current Source Shifting

A A

B B

CC

I

I

Network Reduction Using Star – Delta Transformation

Conversion Principle: Equivalent resistance between the corresponding points must be

the same

RAB

RBC

RCA

RA

RBRC

A

B C

A

B C

Delta ( ) Network Star ( ) Network

Delta - Star Network Intercoversion

Types:

1. Star-to-Delta network transformation

2. Delta-to-Star network transformation

Delta resistances = RAB, RBC, RCA

Star resistances = RA, RB, RC

1. Star-to-Delta network transformation:

RA=RAB*RCA/∑RAB

RB=RBC*RAB/∑RAB

RC=RCA*RBC/∑RAB

2. Delta-to-Star network transformation :

RAB=RA+RB+RARB/RC

RBC=RB+RC+RBRC/RA

RCA=RC+RA+RCRA/RB

Delta ( ) Network – Star ( ) Network Conversion

RA+RB=RAB(RBC+RCA)/RAB+RBC+RCA=RAB(RBC+RCA)/∑RAB -------- 1

RB+RC= RBC(RCA+RAB)/∑RAB -------- 2

RC+RA=RCA(RAB+RBC)/∑RAB -------- 3

Eq.1 – Eq. 2 : RA-RC=RABRCA-RBCRCA/∑RAB

Eq.3 + Eq. 4 : 2RA=2RABRCA/∑RAB

Therefore, RA=RABRCA/∑RAB -------- 4

And, RB = RBCRAB/∑RAB -------- 5

RC=RBCRCA/∑RAB -------- 6

Star ( ) Network – Delta ( ) Network Conversion

Eq. 4, Eq 5, and Eq. 6 from,

RARB+RBRC+RCRA=RABRBCRCA(RAB+RBC+RCA)/∑R2AB

=RBC RA∑RAB/∑RAB=RARBC from Eq. 5

RBC=RARB+RBRC+RCRA/RA=RB+RC+RBRC/RA

RAB=RA+RB+RARB/RC

RCA=RC+RA+RARC/RB

Loop and Node analysis with linearly dependent and

independent sources for DC and AC networks

DC Source Network: It’s the network, in which only the DC source is present

AC Source Network: It’s the network, in which only the AC source is present

DC-AC Source Network: It’s the network, in which both DC and AC sources are

present

Linearly Dependent Sources: It's dependent current or voltage source whose output

current or voltage is proportional only to the first power of some current or voltage

parameter in the circuit or the sum of such quantities

Linearly Independent Sources: It's independent current or voltage source whose output

current or voltage is proportional only to the first power of some current or voltage

parameter in the circuit or the sum of such quantities

Types of Network Analysis

1. Mesh-Current Analysis (Loop Analysis)

2. Node-Voltage Analysis (Node Analysis)

Loop analysis with linearly dependent and independent sources for DC

and AC networks

Mesh-Current Analysis (Loop-Current Analysis)

Procedure:

1. Network must be the planar network and non-planar network analysis is not

possible to do from the mesh-current analysis

2. Nodes are to be named by letters, to identify the meshes in the circuit

3. Practical current sources are to be converted into the practical voltage sources

4. Voltage sources in series and parallel combinations are to be replaced by their

equivalents

5. Neglect the resistance and/or impedance, in parallel with the ideal voltage sources

or in series with the ideal current sources

6. Arbitrarily, clock or anti-clockwise direction is to assigned for mesh currents.

Usually, clock-wise directions are used

7. Mesh current equations are written for the meshes in the circuit

8. Cramer’s rule or any other method is used to solve the equations for the meshes

and obtain the mesh currents

9. Branch currents are calculated, with the mesh currents obtained

Super Mesh Concept

Mesh-current analysis cannot be used, when an ideal current source is present in a

branch.

Solution:

1. Unknown Voltage Assignment Method

2. Super Mesh Creation Method

1. Unknown Voltage Assignment Method

Procedure:

1. Assign an unknown voltage across the ideal current source

2. Apply KVL for each mesh and source current and mesh current relation equations to

obtain

3. Solve the obtained equations

It’s found to be the difficult and lengthy, when compared to the other method

2. Super Mesh Creation Method

Procedure:

1. Consider the two meshes having ideal current source in common, as only one mesh

called the super mesh

2. Ignore the mesh, having an ideal current source at its perimeter, not common with

other meshes (Since, it can be considered as the element in common with other outside

mesh)

3. Apply the KVL, to the meshes to be considered

Node analysis with linearly dependent and independent sources for DC

and AC networks

Node-Voltage Analysis

Node: It’s the point in the network, where tow elements meet

Principal node: It’s the node, where two or more elements meet

Reference Node: It’s the node with the zero potential

Procedure:

1. Network can be Planar or Non-planar network for using the node-voltage

analysis

2. Reference node is to be selected among the principal nodes

3. Node voltages are to be assigned to all, except the reference node

4. Practical voltage sources are to be converted into practical current sources

5. Current sources in series and parallel combinations are to be replaced by their

equivalents

6. Neglect the resistance and/or impedance, in series with the ideal voltage sources

or in parallel with the ideal current sources

7. Currents in the all branches are assumed arbitrarily in any direction

8. Node-voltage equations are to be written at each node

9. Cramer’s rule or other methods are to be used to solve the node-voltage equations

and obtain the node voltages

10. Branch currents are to be calculated, using the node voltages obtained

Super Node Concept

Node-Voltage analysis cannot be used when, an ideal voltage source is present in a

branch in the electrical circuit (Since, the current to the node due to the ideal voltage

source can’t be calculated)

Solution:

1. Unknown Current Assignment Method

2. Super Node Creation Method

1. Unknown Current Assignment Method

Procedure:

1. Assign an unknown current to the branch having the ideal current source

2. Apply KCL at each node obtain the equations and solve the equations

It’s found to be the difficult and lengthy, when compared to the other method

2. Super Node Creation Method

Procedure:

1. Consider the two nodes having ideal voltage source between them, as only one node

called the super node

3. Apply the KCL, at each node to obtain the equations and solve the equations

Concepts of super node and super mesh

Super mesh concept

Super Mesh: Mesh-current analysis cannot be used, when an ideal current source is

present in a branch.

Solution:

1. Unknown Voltage Assignment Method:

2. Super Mesh Creation Method

1. Unknown Voltage Assignment Method:

Procedure:

1. Assign an unknown voltage across the ideal current source

2. Apply KVL for each mesh and source current and mesh current relation equations to

obtain

3. Solve the obtained equations

It’s found to be the difficult and lengthy, when compared to the other method

2. Super mesh creation method

Procedure:

1. Consider the two meshes having ideal current source in common, as only one mesh

called the super mesh

2. Ignore the mesh, having an ideal current source at its perimeter, not common with

other meshes (Since, it can be considered as the element in common with other outside

mesh)

3. Apply the KVL, to the meshes to be considered

Super node concept

Super Node: Node-Voltage analysis cannot be used whenever, an ideal voltage source is

present in a branch in the electrical circuit (Since, the current to the node due to the ideal

voltage source cannot be calculated)

Solution:

1. Unknown Current Assignment Method

2. Super node creation method

1. Unknown Current Assignment Method

Procedure:

1. Assign an unknown current to the branch having the ideal current source

2. Apply KCL at each node obtain the equations and solve the equations

It’s found to be the difficult and lengthy, when compared to the other method

2. Super Node Creation Method

Procedure:

1. Consider the two nodes having ideal voltage source between them, as only one node

called the super node

3. Apply the KCL, at each node to obtain the equations and solve the equations