How to use it
- Choose delta → star or star → delta.
- Enter the three resistances in ohms. Delta sides are named by the two terminals they join (ab, bc, ca); star arms by the terminal they reach (a, b, c).
- For AC networks turn on impedances and enter the reactance of each arm (inductive +, capacitive −).
- Read the three equivalent arms.
Formulas
Delta to star (Σ = Zab + Zbc + Zca):
- Za = Zab · Zca / Σ
- Zb = Zab · Zbc / Σ
- Zc = Zbc · Zca / Σ
Star to delta (P = ZaZb + ZbZc + ZcZa):
- Zab = P / Zc
- Zbc = P / Za
- Zca = P / Zb
With impedances the products and quotients are complex; the result is shown as R and X of each arm.
Worked example
Delta with Rab = 10 Ω, Rbc = 20 Ω, Rca = 30 Ω: Σ = 60 Ω. Ra = 10 × 30 ÷ 60 = 5 Ω, Rb = 10 × 20 ÷ 60 = 3.3333 Ω, Rc = 20 × 30 ÷ 60 = 10 Ω.
Star with Ra = 5, Rb = 10, Rc = 20 Ω: P = 50 + 200 + 100 = 350. Rab = 350 ÷ 20 = 17.5 Ω, Rbc = 350 ÷ 5 = 70 Ω, Rca = 350 ÷ 10 = 35 Ω.
Impedances: a star of three 3 + j4 Ω arms becomes a delta of three 9 + j12 Ω sides, three times the star.
Tips
- Bridges that are not balanced (no series or parallel pair to combine) become solvable after one Y-Δ step: turn one delta into a star, then combine in series and parallel.
- Label the terminals first. Mixing up which star arm sits opposite which delta side is the most common mistake.
- Equivalence is only at the three terminals. Currents inside the network differ.