Electronics Handbook/Circuits/Y Delta Conversion

Configuration

Δ to Y Conversion

$R_{a}={\frac {R_{\mathrm {ac} }R_{\mathrm {ab} }}{R_{\mathrm {ac} }+R_{\mathrm {ab} }+R_{\mathrm {bc} }}}$

$R_{b}={\frac {R_{\mathrm {ab} }R_{\mathrm {bc} }}{R_{\mathrm {ac} }+R_{\mathrm {ab} }+R_{\mathrm {bc} }}}$

$R_{c}={\frac {R_{\mathrm {bc} }R_{\mathrm {ac} }}{R_{\mathrm {ac} }+R_{\mathrm {ab} }+R_{\mathrm {bc} }}}$

Y to Δ Conversion

$R_{\mathrm {ac} }={\frac {R_{a}R_{b}+R_{b}R_{c}+R_{c}R_{a}}{R_{b}}}$

$R_{\mathrm {ab} }={\frac {R_{a}R_{b}+R_{b}R_{c}+R_{c}R_{a}}{R_{c}}}$

$R_{\mathrm {bc} }={\frac {R_{a}R_{b}+R_{b}R_{c}+R_{c}R_{a}}{R_{a}}}$