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Admitance

 

An impedance Z comprising a resistance R in series with a reactance X can be converted to an admittance Y comprising a conductance G in parallel with a susceptance B:
Y = Z -1 = 1 / (R + jX) = (R - jX) / (R2 + X2) = R / (R2 + X2) - jX / (R2 + X2) = G - jB
G = R / (R2 + X2) = R / |Z|2
B = X / (R2 + X2) = X / |Z|2
Using the polar form of impedance Z:
Y = 1 / |Z|Ðf = |Z| -1Ð-f = |Y|Ð-f = |Y|cosf - j|Y|sinf

Conversely, an admittance Y comprising a conductance G in parallel with a susceptance B can be converted to an impedance Z comprising a resistance R in series with a reactance X:
Z = Y -1 = 1 / (G - jB) = (G + jB) / (G2 + B2) = G / (G2 + B2) + jB / (G2 + B2) = R + jX
R = G / (G2 + B2) = G / |Y|2
X = B / (G2 + B2) = B / |Y|2
Using the polar form of admittance Y:
Z = 1 / |Y|
Ð-f = |Y| -1Ðf = |Z|Ðf = |Z|cosf + j|Z|sinf

The total impedance ZS of impedances Z1, Z2, Z3,... connected in series is:
ZS = Z1 + Z1 + Z1 +...
The total admittance YP of admittances Y1, Y2, Y3,... connected in parallel is:
YP = Y1 + Y1 + Y1 +...

In summary:
- use impedances when operating on series circuits,
- use admittances when operating on parallel circuits.