# Admittance

In electrical engineering, **admittance** is a measure of how easily a circuit or device will allow a current to flow. It is defined as the inverse of impedance. The SI unit of admittance is the siemens (symbol S). Oliver Heaviside coined the term *admittance* in December 1887.^{[1]}

Admittance is defined as

where

The synonymous unit mho, and the symbol ℧ (an upside-down uppercase omega Ω), are also in common use.

Resistance is a measure of the opposition of a circuit to the flow of a steady current, while impedance takes into account not only the resistance but also dynamic effects (known as reactance). Likewise, admittance is not only a measure of the ease with which a steady current can flow, but also the dynamic effects of the material's susceptance to polarization:

where

- is the admittance, measured in siemens.
- is the conductance, measured in siemens.
- is the susceptance, measured in siemens.

## Conversion from impedance to admittance

*Parts of this article or section rely on the reader's knowledge of the complex impedance representation of capacitors and inductors and on knowledge of the frequency domain representation of signals*.

The impedance, Z, is composed of real and imaginary parts,

where

*R*is the resistance, measured in ohms*X*is the reactance, measured in ohms

Admittance, just like impedance, is a complex number, made up of a real part (the conductance, *G*), and an imaginary part (the susceptance, *B*), thus:

where *G* (conductance) and *B* (susceptance) are given by:

The magnitude and phase of the admittance are given by:

where

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.

## See also

Look up in Wiktionary, the free dictionary.admittance |

## References

- ↑ Ushida, Jun; Tokushima, Masatoshi; Shirane, Masayuki; Gomyo, Akiko; Yamada, Hirohito (2003). "Immittance matching for multidimensional open-system photonic crystals".
*Physical Review B*.**68**(15). arXiv:cond-mat/0306260. Bibcode:2003PhRvB..68o5115U. doi:10.1103/PhysRevB.68.155115.