Source Transformation: Current and Voltage Source Conversion

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 seriesparallel 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 Vs is the terminal voltage of the source and Rs 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 V­s is converted into Current Source I­­­­s by the above formula. Source internal resistance Rs is placed in parallel of current source $I_{S}$.

Source Conversion

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 Rs at terminal a-b. If the terminal a-b are short-circuited, both the same current will flow the same amount of current in Rs resistor.

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

Source Transformation in AC:

Source transformation is not limited to resistive circuits but is also valid for capacitive and inductive circuits. The technique can be used for AC circuits as well as for dependent sources too. The technique is the product of Thévenin’s Theorem and Norton’s Theorem and is similarly limited by those conditions.
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