The gyrator–capacitor model[1] - sometimes also the capacitor-permeance model[2] - is a lumped-element model for magnetic circuits, that can be used in place of the more common resistance–reluctance model. The model makes permeance elements analogous to electrical capacitance (see magnetic capacitance section) rather than electrical resistance (see magnetic reluctance). Windings are represented as gyrators, interfacing between the electrical circuit and the magnetic model.
The primary advantage of the gyrator–capacitor model compared to the magnetic reluctance model is that the model preserves the correct values of energy flow, storage and dissipation.[3][4] The gyrator–capacitor model is an example of a group of analogies that preserve energy flow across energy domains by making power conjugate pairs of variables in the various domains analogous. It fills the same role as the impedance analogy for the mechanical domain.
https://en.wikipedia.org/wiki/Gyrator–capacitor_model#Magnetic_inductance
Electromagnetic or magnetic induction is the production of an electromotive force across an electrical conductor in a changing magnetic field.
Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction. Lenz's law describes the direction of the induced field. Faraday's law was later generalized to become the Maxwell–Faraday equation, one of the four Maxwell equations in his theory of electromagnetism.
Electromagnetic induction has found many applications, including electrical components such as inductors and transformers, and devices such as electric motors and generators.
https://en.wikipedia.org/wiki/Electromagnetic_induction
The gyrator–capacitor model[1] - sometimes also the capacitor-permeance model[2] - is a lumped-element model for magnetic circuits, that can be used in place of the more common resistance–reluctance model. The model makes permeance elements analogous to electrical capacitance (see magnetic capacitance section) rather than electrical resistance (see magnetic reluctance). Windings are represented as gyrators, interfacing between the electrical circuit and the magnetic model.
The primary advantage of the gyrator–capacitor model compared to the magnetic reluctance model is that the model preserves the correct values of energy flow, storage and dissipation.[3][4] The gyrator–capacitor model is an example of a group of analogies that preserve energy flow across energy domains by making power conjugate pairs of variables in the various domains analogous. It fills the same role as the impedance analogy for the mechanical domain.
Magnetic inductance[edit]
In the context of the gyrator-capacitor model of a magnetic circuit, magnetic inductance (inductive magnetic reactance) is the analogy to inductance in an electrical circuit. In the SI system, it is measured in units of -Ω−1. This model makes magnetomotive force (mmf) the analog of electromotive force in electrical circuits, and time rate of change of magnetic flux the analog of electric current.
For phasor analysis the magnetic inductive reactance is:
Where:
- is the magnetic inductivity (SI unit: s·Î©−1)
- is the angular frequency of the magnetic circuit
In the complex form it is a positive imaginary number:
The magnetic potential energy sustained by magnetic inductivity varies with the frequency of oscillations in electric fields. The average power in a given period is equal to zero. Due to its dependence on frequency, magnetic inductance is mainly observable in magnetic circuits which operate at VHF and/or UHFfrequencies.[citation needed]
The notion of magnetic inductivity is employed in analysis and computation of circuit behavior in the gyrator–capacitor model in a way analogous to inductance in electrical circuits.
A magnetic inductor can represent an electrical capacitor.[4]: 43 A shunt capacitance in the electrical circuit, such as intra-winding capacitance can be represented as a series inductance in the magnetic circuit.
https://en.wikipedia.org/wiki/Gyrator–capacitor_model#Magnetic_inductance
A magnetic circuit is made up of one or more closed loop paths containing a magnetic flux. The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials like iron, although there may be air gaps or other materials in the path. Magnetic circuits are employed to efficiently channel magnetic fields in many devices such as electric motors, generators, transformers, relays, lifting electromagnets, SQUIDs, galvanometers, and magnetic recording heads.
The law relating magnetic flux, magnetomotive force, and magnetic reluctance in an unsaturated magnetic circuit, Hopkinson's law bears a superficial resemblance to Ohm's law in electrical circuits, resulting in a one-to-one correspondence between properties of a magnetic circuit and an analogous electric circuit. Using this concept the magnetic fields of complex devices such as transformers can be quickly solved using the methods and techniques developed for electrical circuits.
Some examples of magnetic circuits are:
- horseshoe magnet with iron keeper (low-reluctance circuit)
- horseshoe magnet with no keeper (high-reluctance circuit)
- electric motor (variable-reluctance circuit)
- some types of pickup cartridge (variable-reluctance circuits)
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