Unit-4 Magnetic Circuits
Topics to be Discussed Magnetic Coupling. Coefficient of Coupling (k). Sign of Mutual Voltage. Dot Convention. September 9, 0 Magnetic Circuits
Magnetically Coupled Circuits A part of magnetic flux produced by a coil in one circuit interlinks with the coil in other circuit. When current in one coil changes, there occurs a change in the flux linking with the other. As a result, there is an induced emf in the other coil, v or v( t) September 9, 0 Magnetic Circuits 3 M
The constant of proportionality M is called coefficient of mutual inductance, or simply mutual inductance. MUTUAL INDUCTANCE is the ability of one inductor to induce a voltage across a neighbouring inductor, measured in henrys (H). A circuit element called mutual inductor does not exist. It is defined with reference to two pairs of terminals(i.e., 4 terminals). The physical device whose operation is based inherently on mutual inductance is called transformer. September 9, 0 Magnetic Circuits 4
Magnetic Coupling Current i flowing in coil establishes a total magnetic flux Φ. Only a part of this flux, Φ, links with the coil. The remaining flux Φ is confined to coil itself. Thus, Φ Φ + Φ. September 9, 0 Magnetic Circuits 5
The emf induced in coil due to the current i is given as v N dφ Also, v M dφ M N or M N dφ M is mutual inductance of coil with respect to coil. Or M incates voltage response at L due to current source at L. September 9, 0 Magnetic Circuits 6
The emf induced in coil due to the current i is given as v N dφ Also, v M dφ( t) M N or M N dφ M is mutual inductance of coil with respect to coil. September 9, 0 Magnetic Circuits 7
Mutual Inductance from Geometrical Viewpoint : The flux that links with the coil is only a part of Φ. That is, Φ where 0 k. kφ M N N dφ I kn ( l / N Φ I I kn μa) N N l μa kφ I M M M kn NμA l September 9, 0 Magnetic Circuits 8
Coefficient of Coupling (k) It is a measure of how close is the coupling between two coils. It gives an idea of what portion of the flux produced by one coil links with the other coil. The flux that links with the coil is only a part of Φ. That is, Φ kφ where 0 k. If k, the coils are tightly coupled. The entire flux produced in one coil links with the other. If k 0, the coils are magnetically isolated. It can be shown that k L M L September 9, 0 Magnetic Circuits 9
Note that the voltage due to mutual inductance is present independently of and in adtion to any voltage due to self-induction. In other words, the voltage across the terminals of coil is composed of two terms, v L + M Similarly, v L + M September 9, 0 Magnetic Circuits 0
Sign of Mutual Voltage The sign depends not only on the current rections, but also on the way the two coils are wound. The induced voltage may be positive or negative. The choice of polarity is made by examining the way in which both coils are physically wound and applying Lenz s law in conjunction with the right-hand-rule. The procedure is inconvenient in circuit analysis since it is fficult to show the construction details of the coil in circuit schematics. use the dot convention (often predetermined) Dot convention is a convenient way of determining the sign of mutual voltage, without going into the physical construction of the two coils. September 9, 0 Magnetic Circuits
THE DOT CONVENTION COUPLED COILS WITH SAME & DIFFERENT WINDING CONFIGURATION September 9, 0 Magnetic Circuits
DOT CONVENTION A current entering the dotted terminal of one coil produces an open circuit voltage which is positively sensed at the dotted terminal of the second coil. A current leaving the dotted terminal of one coil produces an open circuit voltage which is negatively sensed at the dotted terminal of the second coil. September 9, 0 Magnetic Circuits 3
DOT CONVENTION (a) (b) (c) (d) September 9, 0 Magnetic Circuits 4 Fig. (a) is equivalent to Fig. (d), and Fig. (b) is equivalent to Fig. (c)
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Dots mark reference polarity for voltages induced by each flux September 9, 0 Magnetic Circuits 6
v v L M + M + L v v L M M + L Equivalent to a negative mutual inductance September 9, 0 Magnetic Circuits 7
Write the equations for v( t ), v ( t ) + Convert to basic case v L M v M L v L + M v M L ( t ) September 9, 0 Magnetic Circuits 8