Module 4
Δ-Y Conversion:
$$ Z_A = \frac{Z_1Z_2+Z_1Z_3+Z_2Z_3}{Z_1} $$
$$ Z_B = \frac{Z_1Z_2+Z_1Z_3+Z_2Z_3}{Z_2} $$
$$ Z_C = \frac{Z_1Z_2+Z_1Z_3+Z_2Z_3}{Z_3} $$
$$ Z_1 = \frac{Z_BZ_C}{Z_A+Z_B+Z_C} $$
$$ Z_2 = \frac{Z_AZ_C}{Z_A+Z_B+Z_C} $$
$$ Z_3 = \frac{Z_AZ_B}{Z_A+Z_B+Z_C} $$
For balanced loads:
$$ Z_\Delta = 3Z_Y $$
Source Conversion:
$$ E = IZ_p $$
$$ Z_s = Z_p $$
$$ I = \frac{E}{Z_s} $$
$$ Z_p = Z_s $$
Determinants:
$$ D = \begin{vmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{vmatrix} = a_{11}a_{22} - a_{12}a_{21} $$
