Magnetic circuit
A magnetic circuit is a closed path of a magnetic flux Φ. The viewing of magnetic circuits plays a key role mainly in the construction of electric motors, transformers and solenoids. These are mainly coupling processes between the individual components of the magnetic circuits of relevance.
- 2.1 Transformation of an ohmic resistor
- 2.2 Transformation of an electrical inductance
- 2.3 Transformation of an electrical capacitance
- 4.1 Magnetic circuit with air gap
- 4.2 transformer with two windings
- 4.3 transformer with two parallel load circuits
Elements of a magnetic circuit
In a magnetic circuit one can distinguish between two types of signals:
- The magnetic flux, and
- The magnetic tension,
And three basic types of devices:
- The magnetic conductor
- The magnetic resistance with the special case of the magnetic insulator and
- Magnetic coupling elements
Differ. The presentation in the article follows in the physical content of the contexts, as presented in. In their classification, the representation of the authors steering, Pfeifer and Wertschützky follows.
Magnetic flux
The magnetic flux is usually incorporated with a coil as a coupling element in the magnetic circuit. According to its name, it is the magnetic flux to a so-called " Flusskoordinate ". For branches of the magnetic circuit, the magnetic flux behaves according to the Kirchhoff's node equations and is divided into the individual branches.
The correlation between the electrical voltage and the magnetic flux provides the law of induction in the transformed representation with complex numbers:
Here, j is the imaginary unit, ω = 2? F is the angular frequency and N is the number of turns of the coil.
Magnetic voltage and magnetic flux
The magnetomotive force is defined as a line integral over S, the magnetic field strength H between two points P1 and P2 along the way.
The magnetomotive force is generally caused by electrical currents and placed on the coupling element coil in the magnetic circuit. It should however be borne in mind that the electric currents do not cause a magnetic voltage between two points, but a so-called magnetomotive force or magnetic flux. This is a voltage across a closed magnetic path. The magnetomotive force is called to distinguish it from the magnetic tension with the letter and writes
The special feature of the existence of a circulation voltage is that the magnetic potential between two points of the traversed path dependent (non- conservative field ) so that the Kirchhoff's loop rule for magnetic stresses in general can not be applied. In the model of the magnetic circuit " saves" you Kirchhoff's loop rule, however, by the agreement, that the application of the mesh usually no integration paths are considered by coil windings, thereby avoiding internal contradictions of the theory.
Since the coupling coil is usually wound over a magnetically highly conductive coil body, you can make simplified assumptions for the calculation of the magnetic tension. For if in the bobbin only a vanishing magnetic field strength H prevails, the relevant portion of the coil currents generated by the magnetic voltage drops exclusively from outside of the bobbin.
A coil current which has a magnetically highly conductive coil wrapped body N times, caused under the circumstances outside the coil, a magnetomotive force of the size
With the specified reference direction in the drawing.
Magnetic Head
Magnetically conductive connection elements are the analogue of the metallic interconnector in the electrical circuit.
Magnetic conductors characterized in that the ratio of the magnetomotive force and the magnetic flux in the magnetic conductive material is approximately equal to zero
An example of a magnetic head, the magnetic core for a transformer or a coil. The crucial condition for magnetically conductive materials is a high value of the relative permeability. The relative permeability indicates the magnetic conductivity of the substance compared to the vacuum. Typical values for ferromagnetic core materials in coils and transformers are in the range.
Magnetic resistance
Fasteners made of low magnetic conductivity materials such as paramagnetic or diamagnetic materials called magnetic resistances.
Magnetic resistors are characterized in that the ratio of the magnetomotive force and the magnetic flux has a finite real number
Is.
They are the analogue of the electrical resistance. An example of a magnetic resistor is a brief interruption of the magnetic core material of a transformer through an air gap. Superconductors have a permeability and are therefore ideal magnetic insulators.
Electric coil as a magnetic coupling element
Use of coupling elements can bring the effect of networks from other physical fields in the magnetic circuit. A very commonly used coupling element in the magnetic circuit, the electrical coil. It combines electrical circuits to the magnetic circuit, and transmits power between the two networks.
The coupling matrix between the electrical parameters and the magnetic variables is given by:
Here is the imaginary unit, is the angular frequency and the number of turns of the coil., The term in a time-dependent representation of the time integral of the electric voltage - the so-called voltage-time area.
As the electrical coil
- An electrical potential size () in a magnetic flux size () and
- An electrical flow size () in a magnetic potential size ()
To understand the effect of electrical components to the magnetic circuit, it is possible to convert the electric quantities by using the transformation equations for the magnetic coil sizes.
Transformation of an ohmic resistor
In the case of an electric resistance R there is a constant ratio of an electric voltage and electric current.
Using the transformation equations results in a coil with N turns it into a magnetic impedance of:
An electrical short R = 0 consequently causes a magnetic idle while an electric idle causes a magnetic short circuit. The physical cause of the magnetic short-circuit is based on the model assumption that the coil surrounds a coil body having a high magnetic conductivity.
It should be noted that an electric resistance of the coil leads to a magnetic impedance of the mold. The ohmic resistance of the coil, therefore, causes no magnetic resistance in the magnetic circuit, but a magnetic inductance. The authors sweetness, burgers and other means the electrical resistance on the coupling element coil in something allgemeingültigerer View as eddy current element and run: While the electrical resistance is an energy consumer, is the magnetic resistance of an energy storage dar. Opposed to this is the inductance L is an energy storage device, and the eddy current element ( magnetic induction ), an energy consumer.
Transformation of an electrical inductance
An electrical inductance L in the magnetic circuit leads to a purely real magnetic resistance with a positive sign:
Transformation of an electrical capacitance
An electrical capacitance C results in the magnetic circuit to a purely real magnetic resistance with a negative sign:
In principle, also other coupling elements to physical areas, such as the mechanism can be defined. So for example, causes the change of the magnetic flux in a magnetic circuit with air gap, a change in force to the opposing pole faces. In his system theoretical considerations alone three different steering coupling principles: the electromagnetic principle, the principle of electrodynamics and the piezo- magnetic principle, can be described for each of their own switching elements.
Analogously to the electrical circuit
The laws of magnetic flux are defined analogously to the laws in the electrical circuit. The magnetic flux Φ is in this case analogous to the electric current I, the reluctance Rm considered analogous to the resistance R and the voltage analogous to the magnetic electric voltage U.
In analogy to the electrical resistance can be in the magnetic circuit of the so-called magnetic resistance
Define.
In many magnetic materials, the magnetic resistance is approximately constant. One speaks in this context of the Ohm's law of magnetic circuit
The reluctance defined by the magnetic permeability and the geometric dimensions analogous to resistivity:
In magnetic circuits which are described by lumped components, the Kirchhoff's laws apply:
About the Kirchhoff's laws of magnetic circuits can be calculated.
Examples
Magnetic circuit with air gap
The figure shows the structure of a simple magnetic circuit. A coil with N turns is traversed by an electrical current I and thereby generating a magnetic flux density B2. by
One obtains the magnetic flux in the core of the winding. The core is used for the targeted space guiding the magnetic flux in the magnetic circuit and is made of materials with high magnetic conductivity, for example as a ferrite core is performed.
In an ideal ferromagnetic material without leakage flux applies:
However, because there are no ferromagnetic materials ideal in practice, losses occur as a result of the leakage flux. The exact calculation of the leakage flux is rarely closed analytically accessible and it is usually done via computer-aided numerical approximation methods. In practice, the scattering losses on standardized magnetic cores are calculated σ using predetermined coefficients:
Where V2, n is the magnetic voltages of each section represent.
Transformer with two windings
In the model of the magnetic circuit is supplied with the voltage of the transformer with the secondary-side electric load is measured as a simple circuit that the magnetic flux
Is fed.
The magnetic voltage is calculated according to the law for the magnetic components impedance corresponding to:
Using the equation can be calculated from the electric current in the secondary winding
Which corresponds to the known transformation equations for the transformer.
Transformer with two parallel load circuits
Advantages of the modeling, which are in analogy to the electrical circuit, resulting in only branched magnetic circuits.
The voltage source generates a magnetic flux
Which according to the node equation for the magnetic circuit to the two partial flows and divides.
The distribution can be calculated using the current divider rule from the AC bill. For the two partial fluxes results in:
Substituting the components relations
A so form all the voltages and the currents in the two windings passive.
For the voltages applies:
And accordingly
Due to the parallel connection is identical magnetic stresses result in two sub-branches:
This results in using for the currents: