Chapter 8 – Methods of Analysis

Lecture 8

by Moeen Ghiyas

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Introduction

Current Sources ... (Voltage Sources already done)

Source Conversions

Current Sources in Parallel & Series

Branch Current Analysis Method

The step-by-step procedure learnt so far cannot be

applied if the sources are not in series or parallel.

In this chapter , we will try to learn analysis methods

required to solve networks with any number of

sources in any arrangement

Source Conversion Method

Branch-current analysis

Mesh analysis

Nodal analysis

All the methods can be applied to linear bilateral

networks

The term linear indicates that the characteristics of the

network elements (such as the resistors and capacitor /

inductor in steady state condition) are independent of the

voltage across or current through them.

The second term, bilateral, refers to the fact that there is no

change in the behaviour or characteristics of an element if

the current through or voltage across the element is

reversed.

The current source is often referred to as the dual of

the voltage source, where duality implies

interchange ability

A voltage source or battery supplies a fixed voltage,

and the source current can vary;

but the current source supplies a fixed current to the

branch in which it is located, while its terminal

voltage may vary as determined by the network to

which it is applied

The interest in the current source is due primarily to

semiconductor devices such as the transistor, being

current-controlled devices.

Or simply we can say,

A current source determines the current in the

branch in which it is located and the magnitude and

polarity of the voltage across a current source are a

function of the network to which it is applied.

Example - Find the voltage Vs and the currents I1 and I2 for

the network of fig

Solution:

. Applying KCL

An ideal voltage or current source should have no

internal resistance, but that’s not the case in reality

For the voltage source, if Rs = 0 or is so small

compared to any series resistor that it can be ignored,

then we have an “ideal” voltage source.

For the current source, if Rs = ∞ or is large enough

compared to other parallel elements that it can be

ignored, then we have an “ideal” current source

Source conversions are equivalent only at their external

terminals

The internal characteristics of each are quite different.

We want the equivalence to ensure that the applied load of

will receive the same current, voltage, and power from

each source and in effect not know, or care, which source

is present.

In fig below, if we solve for the load current IL, we obtain

If we multiply this by a factor of 1, which we can choose to

be Rs /Rs, we obtain

Example - Convert the voltage source to a current source,

and calculate the current through the 4Ω load for each

source.

Example - Determine the current I2 in the network

Solution:

If two or more current sources are in parallel, they

may all be replaced by one current source having

the magnitude and direction of the resultant, which

can be found by summing the currents in one

direction and subtracting the sum of the currents in

the opposite direction

Current sources of different current ratings are not

connected in series,

just as voltage sources of different voltage ratings

are not connected in parallel

Networks with two isolated voltage sources cannot be

solved using the approach learnt so far

However, augmenting Reduce & Return approach

with source conversion techniques may provide

solution at times (as already learnt)

But, there is no linear dc network for which a solution

cannot be found by Branch Current Analysis Method

(Only method not restricted to bilateral networks)

Five steps

Step 1 – Assign a current direction - arbitrary to each branch

Since there are three distinct branches (cda, cba, ca), three

currents of arbitrary directions (I1, I2, I3) are assigned

Step 2 – Indicate the polarities for each resistor

Step 3 KVL – The best way to determine how many times

Kirchhoff’s voltage law will have to be applied is to

determine the number of “windows” in the network.

Step 4 KCL – Apply Kirchhoff’s current law at the minimum

number of nodes that will include all the branch currents. The

minimum number is one less than the number of independent

nodes of the network.

Step 5 – Simultaneous solution of linear equations

Example – Apply the branch-current method to the network.

Step 1, Assign arbitrary current directions;

Step 2, we draw polarities

Step 3 – Apply KVL in all loops

Step 4 – Apply KCL at node a (one less than total nodes)

Step 5 – Simultaneous solution of 3 equations for 3 unknowns

Step 5 – Simultaneous solution of 3 equations for 3 unknowns

Using determinants

Introduction

Current Sources

Source Conversions

Current Sources in Parallel & Series

Branch Current Analysis Method

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