Series and Parallel Inductors

Feb 272019

Series and Parallel Inductors

On many occasions, it is necessary to obtain the equivalent value of a set of inductors that are connected in series or parallel. These are the simplest methods to calculate the values (inductance) of series and parallel inductors.

Inductors in series – Series equivalent inductance

The calculation of the equivalent inductor of a set of inductors in series is similar to the calculation of the equivalent resistor of a set of resistors that are in series, then you just need to add their values.

The diagram below shows 3 inductors in series, and the formula used here is: LT = L1 + L2 + L3.

This formula works fine for the 3 inductors in series of the diagram, but if we have any number of inductors is better to use the following formula: LT = L1 + L2 + L3 +……+ LN, where N is the number of inductors in series.

Example 1:

If we have 3 inductors with the following values:

L1 = 10 mH
L2 = 20 mH
L3 = 30 mH

The equivalent inductor is: LT = L1 + L2 + L3 = 10 mH + 20 mH + 30 mH = 60 mH

Example 2:

If we have 4 inductors with the following values:

L1 = 5 mH
L2 = 40 mH
L3 = 20 mH
L4 = 30 mH

The equivalent inductor is: LT = L1 + L2 + L3 + L4 = 5 mH + 40 mH + 20 mH + + 20 mH = 95 mH

Inductors in parallel – Parallel equivalent inductance

The calculation of the equivalent inductor of a set of inductors in parallel is similar to the calculation of the equivalent resistor of a set of resistors that are in parallel.

The diagram above shows 3 inductors in parallel, and the formula used is: 1/LT = 1/L1 + 1/L2 + 1/L3.

This formula works fine for the 3 inductors in parallel of the last diagram, but if we have any number of inductors, we can use the formula: 1/LT = 1/L1 + 1/L2 + 1/L3 + …. 1/LN, where N is the number of inductors connected in parallel.

Example 3: