Series Inductors With Magnetic Coupling.

Electronic Principles
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The mutual inductance between two coils, L1 and L2, is expressed

in terms of the inductance of each coil and the coefficient of

coupling K. As a formula:

M = √ K L1 L2

Where: M = Mutual inductance in henrys

K = Coefficient of coupling

L1, L2 = Inductance of coils in Henrys

h. Series Inductors Without Magnetic Coupling. When inductors

are well shielded or are located far enough apart from one

another, the effect of mutual inductance is negligible. If

there is no mutual inductance (magnetic coupling) and the

inductors are connected in series, the total inductance is equal

to the sum of the individual inductances. As a formula:

LT = L1 + L2 + L3 + ... Ln

where LT is the total inductance; L1, L2, L3 are the inductances

of L1, L2, L3; and Ln means that any number (n) of inductors may

be used. The inductances of inductors in series are added

together, like the resistance of resistors in series.

i. Series Inductors With Magnetic Coupling. When two inductors

in series are so arranged that the field of one links the other,

the combined inductance is determined as follows:

LT = L1 + L2 2M

where: LT = The total inductance

L1, L2 = The inductances of L1, L2

M = The mutual inductance between the two inductors

When the magnetic fields of the two inductors are aiding each

other, as shown in figure 24 on the following page, the plus

sign is used with M. When the magnetic field of the two

inductors oppose each other, as shown in figure 25 on the

following page, the minus sign is used with M. The factor 2M

accounts for the influence of L1 on L2, and L2 on L1.