Voltage to Current Source Transformation Theorem

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

The equivalent circuits are those whose V-I characteristics 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 with the Thevenin and Norton Theorems.

Voltage to Current Source Transformation:

Suppose we have the following voltage source shown (on the left side) in the diagram, and we want to transform it into 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:

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In source transformation, the Voltage source V_­s is converted into Current Source I­­­­_s by the above formula. Source internal resistance R_s are placed in parallel with the current source I_S.

Current to Voltage Source Transformation:

In contrast to the above conversion, if we have a current source (on the right side), we can transform it into 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 into 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 the same resistance Rs at terminal a-b. If the terminal a-b is short-circuited, both the same current will flow the same amount of current in the R_s resistor.

AC Source Transformation:

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. The technique is the product of Thévenin’s Theorem and Norton’s Theorem and is similarly limited by those conditions.