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Chapter 8 – Methods of Analysis
Lecture 8
by Moeen Ghiyas
19/04/23 1
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
19/04/23 26
19/04/23 27