change language

 

Effects of mutual inductance

Mutual inductance can operate either to increase the inductance of a pair of series connected inductors, or to decrease it. This is because the magnetic fields might reinforce each other, or they might act against each other.

When two inductors are connected in series, and there is reinforcing mutual inductance between them, the total inductance L is given in the formula:

L = L1 + L2 + 2M

where L1 and L2 are the values of the individual inductors, and M is the mutual inductance. All inductances must be expressed in the same size units.

Problem 10-5
 Suppose two coils, having values of 30 μH and 50 μH, are connected in series so that their 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)1/2 =19.4 μH. Then the total inductance is equal to L= L1 + L2 + 2M= 30 + 50 + 38.8 =118.8 μH, rounded to 120 μH because only two significant digits are justified.

When two inductors are connected in series and the mutual inductance is in opposition, the total inductance L is given by the formula

L = L1 + L2 + 2M

where, again, L1 and L2 are the values of the individual inductors.

10-5 Illustration for Problem

Problem 10-6
 There are two coils with values L1 = 835 μH and L2 = 2.44 mH. They are connected in series so that their coefficient of coupling is 0.922, acting so that the coils oppose each other, as shown in Fig. 10-6. What is the net inductance of the pair?

10-6 Illustration for Problem

First, calculate M. Notice that the coil inductances are specified in different units.
Convert them both to microhenrys, so that L2 becomes 2440 μH. Then M = 0.922(835 x 2440)1/2 = 1316μH. The total inductance is therefore L = L1 + L2 - 2M = 835 + 2440 - 2632 = 643 μH.

It is possible for mutual inductance to increase the total series inductance of a pair of coils by as much as a factor of 2, if the coupling is total and if the flux reinforces. Conversely, it is possible for the inductances of two coils to cancel each other. If two equal-valued inductors are connected in series so that their fluxes oppose, the result will be theoretically zero inductance.

Google