Editing Y-Δ transform (section)

===Equations for the transformation from Y to Δ===<!--This section is linked from [[Template:Network analysis navigation]]. Changing this heading will break the template unless updated there also.-->
The general idea is to compute an impedance <math>R_\Delta</math> in the Δ circuit by

:<math>R_\Delta = \frac{R_P}{R_\text{opposite}}</math>

where <math>R_P = R_1 R_2 + R_2 R_3 + R_3 R_1</math> is the sum of the products of all pairs of impedances in the Y circuit and <math>R_\text{opposite}</math> is the impedance of the node in the Y circuit which is opposite the edge with <math>R_\Delta</math>. The formulae for the individual edges are thus

:<math>\begin{align}
  R_\text{a} &= \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_1} = R_2+R_3+\frac{R_2R_3}{R_1} \\[3pt]
  R_\text{b} &= \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_2} = R_1+R_3+\frac{R_1R_3}{R_2} \\[3pt]
  R_\text{c} &= \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_3} = R_1+R_2+\frac{R_1R_2}{R_3}
\end{align}</math>

Or, if using [[admittance]] instead of resistance:
:<math>\begin{align}
  Y_\text{a} &= \frac{Y_3 Y_2}{\sum Y_\text{Y}} \\[3pt]
  Y_\text{b} &= \frac{Y_3 Y_1}{\sum Y_\text{Y}} \\[3pt]
  Y_\text{c} &= \frac{Y_1 Y_2}{\sum Y_\text{Y}}
\end{align}</math>

Note that the general formula in Y to Δ using admittance is similar to Δ to Y using resistance.