Delta-Wye Transformation
Description
This MicroSim displays a three-terminal resistor network in both Delta (Δ) and Wye (Y) configurations side by side. Adjust the resistor values in either configuration and the other is computed automatically using the conversion formulas. The equivalent resistance between any pair of terminals is shown for both networks and confirmed to be equal, demonstrating the transformation's validity.
Key Concepts
- The Delta-to-Wye conversion: \(R_a = \frac{R_{ab} R_{ca}}{R_{ab}+R_{bc}+R_{ca}}\), with cyclic permutations for \(R_b\) and \(R_c\).
- The Wye-to-Delta conversion: \(R_{ab} = R_a + R_b + \frac{R_a R_b}{R_c}\), with cyclic permutations.
- Both networks present identical terminal behavior — the same voltages and currents at the three terminals.
- Delta-Wye transforms are used to simplify bridge circuits and unbalanced three-phase networks.
- The special case of equal resistors: a balanced delta \(R_\Delta\) converts to a balanced wye \(R_Y = R_\Delta / 3\).