Electronics Handbook/Circuits/Y Delta Conversion

Configuration

Δ to Y Conversion

$R_a=\frac{R_{\mathrm{a}\mathrm{c}}{R}_{\mathrm{a}\mathrm{b}}}{R_{\mathrm{a}\mathrm{c}}+R_{\mathrm{a}\mathrm{b}}+R_{\mathrm{b}\mathrm{c}}}$

$R_b=\frac{R_{\mathrm{a}\mathrm{b}}{R}_{\mathrm{b}\mathrm{c}}}{R_{\mathrm{a}\mathrm{c}}+R_{\mathrm{a}\mathrm{b}}+R_{\mathrm{b}\mathrm{c}}}$

$R_c=\frac{R_{\mathrm{b}\mathrm{c}}{R}_{\mathrm{a}\mathrm{c}}}{R_{\mathrm{a}\mathrm{c}}+R_{\mathrm{a}\mathrm{b}}+R_{\mathrm{b}\mathrm{c}}}$

Y to Δ Conversion

$R_{\mathrm{a}\mathrm{c}}=\frac{R_a{R}_b+R_b{R}_c+R_c{R}_a}{R_b}$

$R_{\mathrm{a}\mathrm{b}}=\frac{R_a{R}_b+R_b{R}_c+R_c{R}_a}{R_c}$

$R_{\mathrm{b}\mathrm{c}}=\frac{R_a{R}_b+R_b{R}_c+R_c{R}_a}{R_a}$