Inductive coupling

The mutual induction or inductive coupling, the mutual magnetic influence between two or more spatially adjacent electrical circuits by the magnetic flux Φ of the electromagnetic induction according to. The mutual induction is the basis of many technical devices, the most important thing is the transformer. In other cases it may be an unwanted effect, such as in the field of electromagnetic compatibility.

Related types of coupling in this context is the capacitive coupling, DC coupling and the radiation coupling dar.

Principle

A current- sat (first) conductor loop effects, depending on their geometry, the generation of a magnetic flux density B in their spatial environment. This is directly proportional to the instantaneous value of the current due to the Biot- Savart law:

, The magnetic flux Φ2 which floods the loop 2 to the surface, is calculated as

Which corresponds to the sum of all scalar products of all infinitesimal area vectors with the magnetic flux density vectors that enforce these patches.

However, the actual realization of the Faraday induction law was that not the river but the time change for the induction is responsible. Thus, the mutual inductance can be derived for analogous to self-induction equation:

Under this definition, the mutual inductance can be considered as a generalization of the self-inductance. You will like these, given in the SI unit Henry [H].

Symmetry

An essential feature is the symmetry of the flux linkages: The mutual inductance of the system 1 to system 2 is the same as for the opposite case:

This relationship facilitated in many cases, the practical calculation of flux linkages. For example, an expression can be easily calculated for the flux linkage of a long coil with a smaller concentrically mounted receiver coil. The reverse case, namely the concatenation of the flow of the small with the large coil would probably encounter major analytical difficulties without knowledge of the above relation. Symmetry described which is also referred to as a magnetic reciprocity theorem can be proved by mathematical means of vector analysis with the aid of Maxwell's equations.

Evidence of magnetic reciprocity

The magnetic field B can be expressed as the rotation of a vector potential:

The magnetic flux through the second conductor loop is then (hereinafter an infinitesimal surface element )

Now, however, the vector potential can be attributed to the line integral of the current in the first conductor loop ( this is a different spelling for the Biot- Savart law ):

This is inserted into the second last equation gives:

Is therefore

Application

In the scope of the electromagnetic compatibility ( EMC) is the mutual inductance referred to as magnetic coupling or inductive coupling, and describes the undesirable generally, magnetic coupling of adjacent electrical circuits. Caused by the current in a circuit magnetic flux as in the adjacent circuit diagram, for example, the circuit composed of the AC voltage source U1, caused by magnetic coupling to the second circuit, represented by the AC voltage source U2, an additional induced source voltage, which in this circuit as unwanted interference can occur.

The modeling can as appropriate as field model ( A) with the variable magnetic field, or equivalent to take place in the field of network theory with the help of the mutual inductance Ms, as is shown in the right figure, in case ( B). Against induced voltage in the second conductor loop, which is caused by the current of the first conductor loop is:

Due to the symmetry of a mutual inductance Ms is a reciprocal four-terminal network.

Due to the higher energy density of the magnetic field as compared to the electric field, a relatively high power transmission may be accomplished at intermediate frequency by means of inductive coupling. This circumstance is utilized for transformers or electric drives, such as the gap motor.

In the field of communications, the inductive coupling is utilized in the inductive transmission, for example in the non-contact signal transmission of the sensor signal between the sensor and the display device or contactless chip cards, so-called RFID.

Literature

  • Pascal luminous man: Introduction to electromagnetic field theory. Pearson Education, Inc., 2005, ISBN 3-8273-7144-9.
  • Horst Stöcker: Paperback physics. 6th edition. Verlag Harri German, Frankfurt am Main 2010, ISBN 978-3-8171-1860-1.
  • Günter Springer: electrical engineering expertise. 18th edition. Europe teaching aids, Wuppertal, 1989, ISBN 3-8085-3018-9.
  • Magnetism
  • Transformer
  • Electromagnetic Störkopplung
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