The impedance Z of a resistance R in series with a reactance X is:
Z = R + jX
Rectangular and polar forms of impedance Z:
Z = R + jX = (R2 + X2)½Ðtan-1(X / R) = |Z|Ðf = |Z|cosf + j|Z|sinf
Addition of impedances Z1 and Z2:
Z1 + Z2 = (R1 + jX1) + (R2 + jX2) = (R1 + R2) + j(X1 + X2)
Subtraction of impedances Z1 and Z2:
Z1 – Z2 = (R1 + jX1) – (R2 + jX2) = (R1 – R2) + j(X1 – X2)
Multiplication of impedances Z1 and Z2:
Z1 * Z2 = |Z1|Ðf1 * |Z2|Ðf2 = ( |Z1| * |Z2| )Ð(f1 + f2)
Division of impedances Z1 and Z2:
Z1 / Z2 = |Z1|Ðf1 / |Z2|Ðf2 = ( |Z1| / |Z2| )Ð(f1 – f2)
- use the rectangular form for addition and subtraction,
- use the polar form for multiplication and division.
|The symbol font is used for some notation and formulae. If the Greek symbols for alpha beta delta do not appear here [ a b d ] the symbol font needs to be installed for correct display of notation and formulae.|
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