Feb 272019
 

Series and Parallel Inductors – Series & Parallel equivalent inductance

On many occasions it is necessary to obtain the equivalent value of a set of inductors that are connected in series or parallel.

This are the simplest methods to calculate the values (inductance) of series and parallel inductors.

Inductors in series

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.

Inductors in series and Equivalent series inductor - Series and Parallel Inductors

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

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.

Inductors in parallel and Equivalent parallel inductor - Series and Parallel Inductors

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:

  • L1 = 20 mH
  • L2 = 100 mH
  • L3 = 50 mH

The equivalent inductor in parallel is:

1/LT = 1/L1 + 1/L2 + 1/L3 = 1/20 mH + 1/100 mH + 1/50 mH = 0.05 + 0.01 + 0.02 = 0.08.

1/LT = 0.08, then LT = 1/0.08 = 12.5 mH

Example 4:

  • L1 = 100 mH
  • L2 = 100 mH
  • L3 = 100 mH
  • L4 = 100 mH

The equivalent inductor in parallel is:

1 / LT = 1/L1 + 1/L2 + 1/L3 + 1/L4 = 1/100 mH + 1/100 mH + 1/100 mH + 1/100 mH = 0.01 + 0.01 + 0.01 + + 0.01 = 0.04.

1/LT = 0.04, then LT = 1/0.04 = 25 mH

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