Effects of mutual inductance

Chapter Effects of mutual inductance

Teach Yourself Electricity and Electronics Third Edition Book
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Teach Yourself Electricity and Electronics Third Edition Book

  • Mutual inductance can be minimized by using shielded wires and toroidal induc-tors. The most common shielded wire is coaxial cable. Toroidal inductors are dis-cussed a little later in this chapter.Coefficient of couplingThe coefficient of coupling, specified by the letter k, is a number ranging from 0 (nocoupling) to 1 (maximum possible coupling). Two coils that are separated by a sheet ofsolid iron would have essentially k0; two coils wound on the same form, one rightover the other, would have practically k1.Mutual inductanceThe mutual inductance is specified by the letter M and is expressed in the same unitsas inductance: henrys, millihenrys, microhenrys, or nanohenrys. The value of M is afunction of the values of the inductors, and also of the coefficient of coupling.For two inductors, having values of L1 and L2 (both expressed in the same sizeunits), and with a coefficient of coupling k, the mutual inductance M is found by multi-plying the inductance values, taking the square root of the result, and then multiplyingby k. Mathematically,Mk (L1L2)1/2Effects of mutual inductanceMutual inductance can operate either to increase the inductance of a pair of series con-nected inductors, or to decrease it. This is because the magnetic fields might reinforceeach other, or they might act against each other.When two inductors are connected in series, and there is reinforcing mutual in-ductance between them, the total inductance L is given in the formula:LL1 L2 2Mwhere L1 and L2 are the values of the individual inductors, and M is the mutual induc-tance. All inductances must be expressed in the same size units.Problem 10-5Suppose two coils, having values of 30 µH and 50 µH, are connected in series so thattheir fields reinforce, as shown in Fig. 10-5, and that the coefficient of coupling is 0.5.What is the total inductance of the combination?First, calculate M from k. According to the formula for this, given above, M.5(50× 30)1/ 219.4µH. Then the total inductance is equal to LL1 L2 2M30 50 38.8118.8µH, rounded to 120 µH because only two significant digits are justified.When two inductors are connected in series and the mutual inductance is in oppo-sition, the total inductance L is given by the formulaLL1 L2 2Mwhere, again, L1 and L2 are the values of the individual inductors.188 Inductance