Source Transformation

Source transformation is a fundamental technique employed in circuit analysis, offering a valuable tool for simplifying complex electrical circuits. This technique involves the replacement of either a voltage source in series with a resistor by a current source in parallel with a resistor, or vice versa. The key concept here is that when the original sources are deactivated (turned off), the equivalent resistance at the circuit's end terminals remains the same.

It is essential to note that when performing source transformations, the direction of the current source arrow always points toward the positive terminal of the voltage source. This convention ensures consistency and aids in maintaining proper circuit orientation.

However, it is worth mentioning that source transformation is not applicable to ideal voltage sources, as they possess zero internal resistance. In contrast, nonideal voltage sources feature non-zero internal resistance, making them amenable to source transformation. Similarly, ideal current sources with infinite internal resistance cannot be substituted with finite voltage sources.

To illustrate the practical application of source transformation, consider a circuit connected to a non-ideal voltage source (Figure 1) and a non-ideal current source (Figure 2) individually. When the series resistance equals the parallel resistance, and the voltage across the voltage source adheres to Ohm's law, these non-ideal sources become equivalent to each other.

Figure 1: Circuit with to non-ideal voltage source

Figure 2: Circuit with to non-ideal current source

Replacing the nonideal voltage source with the equivalent nonideal current source does not alter the voltage or current characteristics of any element within the circuit. This demonstrates the power of source transformation in simplifying circuit analysis without affecting overall circuit behavior.