Editing Admittance (section)

==Conversion from impedance to admittance==
{{complex Z}}
The impedance, {{mvar|Z}}, is composed of real and imaginary parts,
<math display="block">Z = R + jX \,,</math>
where
* {{mvar|R}} is the [[Electrical resistance|resistance]] (ohms); and
* {{mvar|X}} is the [[Electrical reactance|reactance]] (ohms).

<math display="block">Y = Z^{-1}= \frac{1}{R + jX} = \left( \frac{1}{R^2 + X^2} \right) \left(R - jX\right) </math>

Admittance, just like impedance, is a complex number, made up of a [[real number|real]] part (the conductance, {{mvar|G}}), and an [[imaginary number|imaginary]] part (the susceptance, {{mvar|B}}), thus:

<math display="block">Y = G + jB \,,</math>

where {{mvar|G}} (conductance) and {{mvar|B}} (susceptance) are given by:

<math display="block">\begin{align}
  G &= \mathrm{Re}(Y) =  \frac{R}{R^2 + X^2}\,, \\
  B &= \mathrm{Im}(Y) = -\frac{X}{R^2 + X^2}\,.
\end{align}</math>

The magnitude and phase of the admittance are given by:

<math display="block">\begin{align}
  \left | Y \right | &= \sqrt{G^2 + B^2} = \frac{1}{\sqrt{R^2 + X^2}} \\
            \angle Y &= \arctan \left( \frac{B}{G} \right) = \arctan \left( -\frac{X}{R} \right)\,,
\end{align}</math>

where 
* {{mvar|G}} is the [[Electrical conductance|conductance]], measured in [[Siemens (unit)|siemens]]; and
* {{mvar|B}} is the [[susceptance]], also measured in [[Siemens (unit)|siemens]].

Note that (as shown above) the signs of reactances become reversed in the admittance domain; i.e. capacitive susceptance is positive and inductive susceptance is negative.