Source transformation is a technique to replace a voltage source with a current source for circuit simplification and vice versa.

The equivalent circuits are those who’s V-I characteristic are identical. It is observed that source transformation may simplify a circuit, just like Y-Δ transformation and series–parallel combination solution, especially when the circuit has mixed sources. Source transformation is the technique that correlates the Thevenin and Norton Theorems.

## Voltage to Current Conversion:

Suppose we have the following voltage source shown (on the left side) in the diagram, and we want to transform it to a current source (on the right side). Where V_{s} is the terminal voltage of the source and R_{s} is the internal resistance of the voltage source. With the ease of Ohm’s Law, the source is converted with the following formula:

$I_{s}=\frac{V_{s}}{R_{s}}$

In source transformation, the Voltage source V_{s} is converted into Current Source I_{s} by the above formula. Source internal resistance R_{s} is placed in parallel of current source $I_{S}$.

## Current to Voltage Conversion:

In contrast to the above conversion, if we have a current source (on the right side), we can transform it to a voltage source (on the left side) using the following formula.

The above process can be reversed, if we have a current source (on the right side), we can transform it to a voltage source (on the left side) by the following formula.

The above two circuits are equivalents such that they have an identical voltage-current relationship at terminal a-b. If the sources are switched off, both sources have same resistance R_{s} at terminal a-b. If the terminal a-b are short-circuited, both the same current will flow the same amount of current in R_{s} resistor.

$V_{s}=I_{s}R_{s}$