In electrical engineering, the admittance (Y) is a measure of how easily a circuit or device will allow a current to flow. It is defined as the inverse of the impedance (Z). The SI unit of admittance is the siemens (symbol S). Oliver Heaviside coined the term in December 1887.[1]
where
Note that 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
Contents |
The impedance, Z, is composed of real and imaginary parts,
where
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 suceptance is negative.
In mechanical systems (particularly in the field of haptics), an admittance is a dynamic mapping from force to motion. 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,
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. 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.
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 1 Gal = 0.01 m/s2 and 1 bar = 100 kPa, so in SI units the measurement would be in units of;
or or or, in primary units
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]