Admittance

In electrical engineering, the admittance (Y) is the inverse of the impedance (Z). Electrical engineering, sometimes referred to as electrical and electronic engineering, is a field of Engineering that deals with the study and application of In Mathematics, a multiplicative inverse for a number x, denoted by 1&frasl x or x &minus1 is a number which Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal Alternating current (AC The SI unit of admittance is the siemens. The siemens (symbol S is the SI derived unit of Electric conductance. Oliver Heaviside coined the term in December 1887. Year 1887 ( MDCCCLXXXVII) was a Common year starting on Saturday (link will display the full calendar of the Gregorian calendar (or a Common ^[1]

$Y = Z^{-1} = 1/Z \,$

where

Y is the admittance, measured in siemens

Z is the impedance, measured in ohms

Note that the synonymous unit mho, and the symbol ℧ (an upside-down Omega Ω), are also in common use. The siemens (symbol S is the SI derived unit of Electric conductance. The ohm (symbol Ω) is the SI unit of Electrical impedance or in the Direct current case Electrical resistance, The siemens (symbol S is the SI derived unit of Electric conductance.

Admittance is a measure of how easily a circuit or device will allow a current to flow. Resistance is a measure of the opposition of a circuit to the flow of a steady current, while impedance takes in to account not only the resistance but dynamic effects (known as reactance) as well. Likewise, admittance is not only a measure of the ease with which a steady current can flow (conductance, the inverse of resistance), but also takes in to account the dynamic effects of susceptance (the inverse of reactance). Electrical conductance is a measure of how easily Electricity flows along a certain path through an Electrical element. Electrical resistance is a ratio of the degree to which an object opposes an Electric current through it measured in Ohms Its reciprocal quantity is In Electrical engineering, the susceptance ( B) is the imaginary part of the Admittance.

1 Conversion from impedance to admittance
2 Admittance in mechanics
3 Admittance in geophysics
4 See also
5 References
6 External links

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. Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal Alternating current (AC A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors An inductor is a passive electrical component designed to provide Inductance in a circuit Frequency domain is a term used to describe the analysis of Mathematical functions or signals with respect to frequency

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

$Z = R + jX \,$

where

R is the resistance, measured in ohms

X is the reactance, measured in ohms

$Y = Z^{-1}= \frac{1}{R+jX} = \left( \frac{1}{R+jX} \right) \cdot \left( \frac{R-jX}{R-jX} \right) = \left( \frac{R}{R^2+X^2} \right) + j\left(\frac{-X}{R^2+X^2}\right)$

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

$Y = G + j B \,$

$Y = G + jB = \left( \frac{R}{R^2+X^2} \right) + j \left( \frac{-X}{R^2+X^2} \right)$

Then G (conductance) and B (susceptance) are given by:

$G = \Re(Y) = \left( \frac{R}{R^2+X^2} \right)$

$B = \Im(Y) = \left( \frac{-X}{R^2+X^2}\right)$

The magnitude and phase of the admittance are given by:

$\left | Y \right | = \sqrt {G^2 + B^2} = \frac {1} {\sqrt {R^2 + X^2} } \,$

$\angle Y = \arctan \left( {\frac{B}{G}} \right)= \arctan \left( {\frac{-X}{R}} \right)$

where

G is the conductance, measured in siemens

B is the susceptance, measured in siemens

Admittance in mechanics

In mechanical systems (particularly in the field of haptics), an admittance is a dynamic mapping from force to motion. In Mathematics, the real numbers may be described informally in several different ways Geometric interpretation Geometrically imaginary numbers are found on the vertical axis of the complex number plane An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent Haptic communication is the means by which people and other animals communicate via touching In other words, an equation (or virtual environment) describing an admittance would have inputs of force and would have outputs such as position or velocity. So, an admittance device would sense the input force and "admit" a certain amount of motion.

Similar to the electrical meanings of admittance and impedance, an impedance in the mechanical sense can be thought of as the "inverse" of admittance. That is, it is a dynamic mapping from motion to force. An impedance device would sense the input motion and "impede" the motion with some force.

An example of these concepts is a virtual spring. The equation describing a spring is Hooke's Law,

$F = -kx \,$

If the input to the virtual spring is the spring displacement, x, and the output is the force that the virtual spring applies, F, then the virtual spring would be classified as an impedance. In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the If the input to the virtual spring is the force applied to the spring, F, and the output is the spring displacement, x, then the virtual spring would be classified as an admittance.

Admittance in geophysics

The geophysical conception of admittance is similar to that described above for mechanical systems. The concept is primarily used for describing the small effects of atmospheric pressure on earth gravity. Studies have also been carried out regarding the gravity of Venus. ^[2] Admittance in geophysics takes atmospheric pressure as the input and measures small changes in the gravitational field as the output. Geophysics admittance is commonly measured in μgal/mbar. These units convert according to 1m/s² = 100 gal and 1 bar 100kPa (kN/m²) so in SI units the measurement would be in units of;

$\frac{m/s^2}{N/m^2}$ or $\frac{m^3}{N\mbox{-}s^2}$ or, in primary units $\frac{m^2}{kg}$

However, the relationship is not a straightforward one of proportionality. Rather, an admittance function is described which is time and frequency dependent in a complex way. ^[3]

References

^ Ushida et al. See also SI units Speed of light Meter Ampere Second , "Immittance matching for multidimensional open-system photonic crystals", Phys Rev B, vol 68, no. 15, Oct 2003.
^ Hoogenboom, Smrekar, Anderson, Houseman, "Admittance survey of type 1 coronae on Venus", Journal of Geophysical Research, Vol 109, E03002, 2004
^ Abd El-Gelil, Pagiatakis, El-Rabbany, "Atmospheric Air Density Admittance Function for High Precision Gravity Reduction", Elements: The newsletter of the Canadian Geophysical Union, vol 24, no. 2, July 2006

External links

Conductance, Susceptance, and Admittance

Dictionary

-noun

The act of admitting.
Permission to enter; the power or right of entrance.
Actual entrance; reception.
(UK) (law) The act of giving possession of a copyhold estate.
(physics) The reciprocal of impedance

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Contents

Conversion from impedance to admittance

Admittance in mechanics

Admittance in geophysics

See also

References

External links

Dictionary

admittance

-noun