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# Impedance

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### Formulas

﻿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)

In summary:

• use the rectangular form for addition and subtraction,
• use the polar form for multiplication and division.
 NOTATION 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. B C E f G h I j L P Q susceptance capacitance voltage source frequency conductance h-operator current j-operator inductance active power reactive power [siemens, S] [farads, F] [volts, V] [hertz, Hz] [siemens, S] [1Ð120°] [amps, A] [1Ð90°] [henrys, H] [watts, W] [VAreactive, VArs] Q R S t V W X Y Z f w quality factor resistance apparent power time voltage drop energy reactance admittance impedance phase angle angular frequency [number] [ohms, W] [volt-amps, VA] [seconds, s] [volts, V] [joules, J] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [rad/sec]

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1. mg_wanas
Jun 03, 2013

Thanks

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