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Inductors in Series and Parallel

Inductors can be connected in series or parallel to obtain a target inductance, current rating, or physical package arrangement. The simple formulas are useful, but they are valid only when the inductors are not magnetically coupled and are operated below saturation.

Learning Objectives

By the end of this lesson, you should be able to:

  • calculate equivalent inductance for uncoupled series and parallel networks;
  • explain why current rating, winding resistance, and saturation matter;
  • recognize when mutual inductance invalidates the simple formulas;
  • use the calculator to check practical combinations.

Series Inductors

In series, the same current flows through each inductor. For uncoupled ideal inductors, inductance adds directly:

$$
L_\text{total}=L_1+L_2+L_3+\dots
$$

Worked Example

Three inductors are connected in series:

  • L1 = 10 mH
  • L2 = 22 mH
  • L3 = 47 mH

$$
L_\text{total}=10+22+47=79\ \text{mH}
$$

The equivalent inductance is 79 mH, but the current rating is not the sum of the current ratings. The series string is limited by the first inductor that saturates or overheats.

Parallel Inductors

In parallel, each inductor has the same voltage across it. For uncoupled ideal inductors:

$$
\frac{1}{L_\text{total}}=\frac{1}{L_1}+\frac{1}{L_2}+\frac{1}{L_3}+\dots
$$

For two inductors:

$$
L_\text{total}=\frac{L_1L_2}{L_1+L_2}
$$

Worked Example

Two 100 uH inductors in parallel give:

$$
L_\text{total}=\frac{100\times100}{100+100}=50\ \text{uH}
$$

Parallel inductors can increase current capability, but only if their DC resistance, inductance tolerance, core material, and thermal environment allow current to share reasonably.

Ideal Formula Summary

Connection Equivalent inductance Current behavior
Series adds directly same current in every inductor
Parallel reciprocal sum current splits between branches
flowchart LR A["Need higher inductance"] --> B["Use series inductors"] C["Need lower inductance or more current"] --> D["Use parallel inductors"] B --> E["Check saturation current and winding resistance"] D --> E E --> F["Measure or simulate when coupling is possible"]

Mutual Inductance: The Blocking Detail

The formulas above assume the inductors are uncoupled. If magnetic flux from one inductor links another, mutual inductance changes the effective value.

For two series-coupled inductors:

$$
L_\text{series}=L_1+L_2\pm2M
$$

M is mutual inductance. The sign depends on winding orientation. This is why two coils on the same core are not just "two separate inductors."

Real-World Design Checks

When combining inductors, check:

  • saturation current: above this, inductance falls and current can rise dangerously;
  • RDC: winding resistance creates voltage drop and heat;
  • tolerance: common inductors can vary by 20 percent or more;
  • core losses: important at high ripple frequency;
  • layout coupling: nearby inductors can unintentionally interact;
  • thermal sharing: parallel parts do not share current well if one gets hotter.

Try It: Series/Parallel Inductor Calculator

Select series or parallel mode and enter two to five inductance values in millihenries.

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Practical Examples

EMI Filtering

Series inductors and common-mode chokes slow high-frequency noise current. The inductance value is only one part of the choice; impedance versus frequency and current rating matter more in real filters.

Power Converters

Parallel inductors may reduce copper loss or spread heat. They must be matched carefully because unequal resistance and saturation points cause unequal ripple current.

RF and High-Speed Boards

At high frequency, package and trace inductance can be comparable to the component value. A layout that looks like a simple series network on paper may behave like a coupled magnetic system.

Common Mistakes

  • Adding current ratings blindly for parallel inductors.
  • Using series/parallel formulas for coupled windings.
  • Ignoring saturation current in power circuits.
  • Treating inductance tolerance as exact.
  • Forgetting that the physical layout can change behavior.

Summary

Uncoupled series inductors add directly. Uncoupled parallel inductors combine by reciprocal sum. Real designs must also account for saturation, winding resistance, heating, tolerance, and mutual coupling. The formulas are the starting point, not the whole design review.

Further Reading