Electronics Handbook/Circuits/Y Delta Conversion
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Electronics Handbook
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Circuits
Configuration
Δ to Y Conversion
R
a
=
R
a
c
R
a
b
R
a
c
+
R
a
b
+
R
b
c
{\displaystyle R_{a}={\frac {R_{\mathrm {ac} }R_{\mathrm {ab} }}{R_{\mathrm {ac} }+R_{\mathrm {ab} }+R_{\mathrm {bc} }}}}
R
b
=
R
a
b
R
b
c
R
a
c
+
R
a
b
+
R
b
c
{\displaystyle R_{b}={\frac {R_{\mathrm {ab} }R_{\mathrm {bc} }}{R_{\mathrm {ac} }+R_{\mathrm {ab} }+R_{\mathrm {bc} }}}}
R
c
=
R
b
c
R
a
c
R
a
c
+
R
a
b
+
R
b
c
{\displaystyle R_{c}={\frac {R_{\mathrm {bc} }R_{\mathrm {ac} }}{R_{\mathrm {ac} }+R_{\mathrm {ab} }+R_{\mathrm {bc} }}}}
Y to Δ Conversion
R
a
c
=
R
a
R
b
+
R
b
R
c
+
R
c
R
a
R
b
{\displaystyle R_{\mathrm {ac} }={\frac {R_{a}R_{b}+R_{b}R_{c}+R_{c}R_{a}}{R_{b}}}}
R
a
b
=
R
a
R
b
+
R
b
R
c
+
R
c
R
a
R
c
{\displaystyle R_{\mathrm {ab} }={\frac {R_{a}R_{b}+R_{b}R_{c}+R_{c}R_{a}}{R_{c}}}}
R
b
c
=
R
a
R
b
+
R
b
R
c
+
R
c
R
a
R
a
{\displaystyle R_{\mathrm {bc} }={\frac {R_{a}R_{b}+R_{b}R_{c}+R_{c}R_{a}}{R_{a}}}}
