In
electrical engineering, susceptance (''B'') is the imaginary part of
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 reciprocal of impedance, analogous to how conductance & resistance are defined. The SI unit of admittanc ...
, where the real part is
conductance. The
reciprocal
Reciprocal may refer to:
In mathematics
* Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal''
* Reciprocal polynomial, a polynomial obtained from another pol ...
of admittance is
impedance, where the imaginary part is
reactance and the real part is
resistance. In
SI units, susceptance is measured in
siemens.
Origin
The term was coined by
C.P. Steinmetz in a 1894 paper.
In some sources
Oliver Heaviside is given credit for coining the term, or with introducing the concept under the name ''permittance''.
This claim is mistaken according to Steinmetz's biographer.
The term ''susceptance'' does not appear anywhere in Heaviside's collected works, and Heaviside used the term ''permittance'' to mean
capacitance, not ''susceptance''.
Formula
The general equation defining admittance is given by
where
The admittance () is the
reciprocal
Reciprocal may refer to:
In mathematics
* Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal''
* Reciprocal polynomial, a polynomial obtained from another pol ...
of the impedance (), if the impedance is not zero:
and
where
The susceptance
is the imaginary part of the admittance
The magnitude of admittance is given by:
And similar formulas transform admittance into impedance, hence susceptance () into reactance ():
hence
The reactance and susceptance are only reciprocals in the absence of either resistance or conductance (only if either or , either of which implies the other, as long as , or equivalently as long as ).
Relation to capacitance
In electronic and semiconductor devices, transient or frequency-dependent current between terminals contains both conduction and displacement components. Conduction current is related to moving charge carriers (electrons, holes, ions, etc.), while displacement current is caused by time-varying electric field. Carrier transport is affected by electric field and by a number of physical phenomena, such as carrier drift and diffusion, trapping, injection, contact-related effects, and impact ionization. As a result, device
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 reciprocal of impedance, analogous to how conductance & resistance are defined. The SI unit of admittanc ...
is frequency-dependent, and the simple electrostatic formula for capacitance,
is not applicable.
A more general definition of capacitance, encompassing electrostatic formula, is:
where
is the device admittance, and
is the susceptance, both evaluated at the angular frequency in question, and
is that angular frequency. It is common for electrical components to have slightly reduced capacitances at extreme frequencies, due to slight inductance of the internal conductors used to make capacitors (not just the leads), and
permittivity changes in insulating materials with frequency: is ''very nearly'', but ''not quite'' a constant.
Relationship to reactance
Reactance is defined as the imaginary part of
electrical impedance, and is ''analogous'' to but not generally equal to the negative reciprocal of the susceptance – that is their reciprocals are equal and opposite only in the special case where the real parts vanish (either zero resistance or zero conductance). In the special case of entirely zero admittance or exactly zero impedance, the relations are encumbered by infinities.
However, for purely-reactive impedances (which are purely-susceptive admittances), the susceptance is equal to the negative
reciprocal
Reciprocal may refer to:
In mathematics
* Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal''
* Reciprocal polynomial, a polynomial obtained from another pol ...
of the
reactance, except when either is zero.
In mathematical notation:
:
The minus sign is not present in the relationship between
electrical resistance and the analogue of conductance
but otherwise a similar relation holds for the special case of reactance-free impedance (or susceptance-free admittance):
:
If the imaginary unit is included, we get
:
for the resistance-free case since,
:
Applications
High susceptance materials are used in
susceptors built into microwavable food packaging for their ability to convert
microwave radiation into heat.
See also
*
Electrical measurements
*
SI electromagnetism units
References
{{reflist, 25em
Physical quantities
Electrical engineering