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Inductors in Series and Parallel 🔗

Just like resistors, inductors can be combined to get the value you want.
Knowing how inductors behave in series and parallel is essential for:

  • Filter design
  • Power supplies
  • EMI control
  • High-current applications

👉 Good layout + correct math = predictable behavior

Inductors in Series​

When inductors are connected end-to-end, their inductances simply add up.

Ltotal=L1+L2+L3+…L_{\text{total}} = L_1 + L_2 + L_3 + \dots

Example​

  • L₁ = 10 mH
  • L₂ = 20 mH
  • L₃ = 30 mH
Ltotal=10+20+30=60 mHL_{\text{total}} = 10 + 20 + 30 = 60 \text{ mH}
note

Series inductors behave exactly like resistors in series.

Key Insights (Series)​

  • Inductances add directly
  • Easy way to achieve higher inductance
  • Total current rating is limited by the weakest inductor
  • Higher inductance → more energy storage

Inductors in Parallel​

When inductors are connected across the same nodes, the total inductance decreases.

1Ltotal=1L1+1L2+1L3+…\frac{1}{L_{\text{total}}} = \frac{1}{L_1} + \frac{1}{L_2} + \frac{1}{L_3} + \dots

For two inductors, a simpler form is often used:

Ltotal=L1×L2L1+L2L_{\text{total}} = \frac{L_1 \times L_2}{L_1 + L_2}

Example​

  • L₁ = 100 mH
  • L₂ = 100 mH

Ltotal=100×100100+100=50 mHL_{\text{total}} = \frac{100 \times 100}{100 + 100} = 50 \text{ mH}

important

Two equal inductors in parallel → half the inductance, double the current capability.

Key Insights (Parallel)​

  • Parallel inductors reduce total inductance
  • Excellent for high-current designs
  • Current is shared between inductors
  • Helps reduce copper losses and heating

Practical Applications 🛠️​

Inductor combinations show up everywhere:

  • Series inductors → EMI and line filtering
  • Parallel inductors → Power supply current sharing
  • LC filters → Mix of series and parallel elements
  • Converters & chokes → Tailored inductance + current rating
tip

In power electronics, parallel inductors are often cheaper and cooler than one oversized inductor.

⚠️ Danger Zone: Mutual Inductance​

Real-world inductors don’t always behave ideally.

  • Nearby inductors can magnetically couple
  • Coupling changes the effective inductance
  • Inductors wound on the same core are strongly coupled
warning

If inductors are:

  • Too close together
  • On the same core
  • Poorly oriented

👉 Your simple math may no longer apply.

Design Rule of Thumb​

  • Uncoupled inductors → use standard series/parallel formulas
  • Coupled inductors → treat as a magnetic system, not separate parts
  • When in doubt → simulate or measure

Key Takeaway​

  • Series → higher inductance
  • Parallel → higher current handling
  • Layout and coupling matter as much as equations

Inductors are obedient on paper — and rebellious on the PCB. 😄