Electrical Source Transformation
Electrical source transformation is a method of replacing voltage source in a circuit by its equivalent current source and current source by its equivalent voltage source.
The source transformation
technique is required to simplify an electric circuit for analysis.
Let us take a simple voltage source
along with a resistance connected in series
with it. This series resistance normally represents the internal resistance of a practical voltage source
Now, let us short circuit the output terminals of the voltage source
circuit as shown below,
Now, applying Kirchhoff Voltage Law
in the circuit above we get,
Where, I is the current delivers by the voltage source when it is short circuited.
Now, let us take a current source of same current I which produces same open circuit voltage at its open terminals as shown below,
Now, applying Kirchhoff Current Law at node 1, of the above circuit, we get,
From equation (i) and (ii) we get,
The open circuit voltage of both the sources is V and short circuit current of both sources is I. The same resistance connected in series in voltage source is connected in parallel in its equivalent current source.
So, these voltage source and current source are equivalent to each other.
A current source is dual form of a voltage source and a voltage source is dual form of a current source. A voltage source can be converted into equivalent current source and a current source can also be converted into equivalent voltage source.
Voltage Source to Current Source Conversion
Assume a voltage source
with terminal voltage V and the internal resistance r. This resistance is in series. The current supplied by the source is
when the source of the terminals are shorted.
This current is supplied by the equivalent current source
and same resistance r will be connected across the source. Voltage source
to current source
conversion is shown in the following figure.
Current Source to Voltage Source Conversion
Similarly assume a current source
with value I and internal resistance r. Now according to the Ohm’s law
the voltage across the source can be calculated as
Hence, voltage appearing, across the source, when terminals are open, is V.