🔧 Inductor Values
📐 Circuit Diagram
⚙️ Formula
📋 Impedance Distribution
| Inductor | Inductance | Impedance (XL) |
|---|
📊 Results
Frequency
1000 Hz
Total Leq
—
Total XL
—
Equivalent Inductance
Total Inductive Reactance (XL = 2πfL)
Stored Energy (E = ½LI²) at 1A
Inductors in Series Calculator — Complete Guide to Series Inductance
This inductors in series calculator instantly finds the total equivalent inductance when multiple inductors are wired end-to-end in a single current path using the simple addition formula Leq = L1 + L2 + … + Ln. It also computes the inductive reactance XL = 2πfLeq at any operating frequency, voltage distribution across each inductor, and total stored energy — with a live circuit diagram. Use it for LC filter design, RF matching networks, multi-stage EMI chokes, transformer winding analysis, and any circuit where you need to combine or fine-tune inductance values.
Quick Reference: Series Inductor Formulas
| Quantity | Formula | Notes |
|---|---|---|
| Total Inductance | Leq = L1 + L2 + … + Ln | Always > largest L (M = 0) |
| n Equal Inductors | Leq = n × L | e.g., 3× 10 mH → 30 mH |
| Inductive Reactance | XL = 2π × f × Leq | Ohms; rises with frequency |
| Voltage across Li | Vi = (Li / Leq) × Vtotal | Proportional to inductance |
| Stored Energy | E = ½ × Leq × I² | Same current through all |
| Aiding Mutual | Leq = L1 + L2 + 2M | Fields in same direction |
| Opposing Mutual | Leq = L1 + L2 − 2M | Fields in opposite direction |
The Series Inductor Formula Explained
When inductors are connected in series, the same current flows through every inductor. Each coil opposes changes in that current independently, so their total opposition — their total inductance — simply adds up:
The result is always greater than the largest individual inductor. This is identical to resistors in series and the opposite of capacitors in series. The formula assumes no mutual coupling between inductors (M = 0) — i.e., they are physically separated or magnetically shielded.
Inductive Reactance (XL)
Unlike a resistor, an inductor's opposition to current depends on frequency. The higher the frequency, the harder the inductor pushes back against current changes:
For series inductors: XL(total) = 2π × f × Leq
Example: Leq = 32 mH at f = 1 kHz → XL = 2π × 1000 × 0.032 = 201 Ω
Mutual Inductance in Series Circuits
When inductors are physically close, their magnetic fields interact through mutual inductance M. The total series inductance depends on whether the fields aid or oppose each other:
Leq = L1 + L2 + 2M
Opposing (fields in opposite direction):
Leq = L1 + L2 − 2M
Coupling coefficient: k = M / √(L1 × L2) (0 = no coupling, 1 = perfect coupling)
This mutual coupling is intentional in transformers and coupled inductors, and unintentional (parasitic) when two chokes are mounted too close together on a PCB.
Voltage Distribution in Series Inductors
Because all series inductors carry the same current I, the voltage across each is proportional to its inductance. Larger inductors receive more of the total voltage:
In the time domain: Vi = Li × (dI/dt)
Worked Examples
Example 1: Two Inductors in Series — Reactance
Problem: 10 mH and 22 mH in series at 1 kHz. Find Leq, XL, and voltage split across 12 V.
Leq = 10 + 22 = 32 mH
XL = 2π × 1000 × 0.032 = 201.1 Ω
V1 = (10/32) × 12 = 3.75 V V2 = (22/32) × 12 = 8.25 V ✓ 3.75 + 8.25 = 12 V
Example 2: Three Inductors for Filter Design
Problem: 4.7 µH + 10 µH + 22 µH in series at 10 MHz.
Leq = 4.7 + 10 + 22 = 36.7 µH
XL = 2π × 10⁷ × 36.7×10⁻⁶ = 2306 Ω ≈ 2.31 kΩ
Example 3: Mutual Inductance — Aiding vs Opposing
Problem: Two 10 mH inductors in series, mutual inductance M = 3 mH. Find Leq for both cases.
Aiding: Leq = 10 + 10 + 2(3) = 26 mH
Opposing: Leq = 10 + 10 − 2(3) = 14 mH
Without coupling: Leq = 20 mH — coupling makes a 30% difference!
Series vs Parallel Inductors — Complete Comparison
| Inductors in Series | Inductors in Parallel | |
|---|---|---|
| Formula | Leq = ΣLi | 1/Leq = Σ(1/Li) |
| Result vs individual | Always > largest L | Always < smallest L |
| Current through each | Same (series) | Divides (inversely with L) |
| Voltage across each | Divides (proportional to L) | Same on all |
| Analogous to resistors | Resistors in series | Resistors in parallel |
| Analogous to capacitors | Capacitors in parallel | Capacitors in series |
| Used for | Increasing L, filter design, EMI chokes | Current sharing, fine-tuning L, multi-phase |
Inductance Units Reference
| Unit | Symbol | Value in Henries | Typical Use |
|---|---|---|---|
| Henry | H | 1 H | Large power-line chokes, transformers |
| Millihenry | mH | 10⁻³ H | Audio filters, DC-DC converter chokes |
| Microhenry | µH | 10⁻⁶ H | Switching supplies, RF inductors |
| Nanohenry | nH | 10⁻⁹ H | RF, high-frequency, PCB trace inductance |
Common Inductor Types and Series Behaviour
| Type | Inductance Range | Key Feature | Series Use Case |
|---|---|---|---|
| Air-core coil | nH – µH | No saturation, low loss at RF | RF filters, tuned circuits |
| Ferrite-core | µH – mH | High permeability, compact | EMI chokes, switching converters |
| Iron-powder toroid | µH – mH | High saturation current | Power inductors, DC-DC chokes |
| Ferrite bead | Impedance spec | High-frequency loss | Multi-stage EMI suppression |
| Chip inductor (SMD) | nH – µH | Small, high SRF | RF, power management ICs |
Practical Applications
- Custom inductance values: Combine two standard catalogue inductors in series to hit a non-standard target value for LC filter tuning.
- Multi-stage EMI filters: Series chokes at multiple stages provide broadband noise suppression across a wider frequency range.
- LC low-pass filters: Series inductors with shunt capacitors form classic ladder filter topologies (Butterworth, Chebyshev, Elliptic).
- RF impedance matching: Series inductors raise impedance at specific frequencies in L-match and π-match networks.
- Current-limiting chokes: A series inductor limits di/dt during power-on or fault conditions.
- Transformer windings: Series-connected coils on a common core add flux linkage — the basis of autotransformers.
- Power-factor correction: Series inductors with line-frequency capacitors form resonant PFC stages.
Common Mistakes to Avoid
- Ignoring mutual coupling: Two series inductors mounted close on a PCB without magnetic shielding will not simply add — measure actual Leq or use the ±2M formula.
- Mixing units: Convert all values to the same unit (e.g., µH) before summing. A 47 nH + 10 µH = 0.047 µH + 10 µH = 10.047 µH, not 57 anything.
- Core saturation: Each inductor must stay below its saturation current at all operating conditions. Saturated inductance drops dramatically.
- SRF at high frequency: Every real inductor has a self-resonant frequency (SRF) above which it behaves capacitively. Use inductors well below their SRF.
Frequently Asked Questions
Do inductors in series always add up?
Only when there is no mutual coupling (M = 0) — the inductors are physically separated or magnetically shielded. If fields interact, use Leq = L1 + L2 ± 2M.
What happens to inductive reactance when inductors are added in series?
XL(total) = 2πf × Leq increases directly with Leq. Adding more inductors in series raises total impedance at every frequency.
Can I mix different core types in series?
Yes. Ferrite, air-core, and iron-powder inductors can all be combined in series — their inductances simply add. Ensure each type can handle the common series current without saturating.
What is the coupling coefficient k?
k = M / √(L₁ × L₂), ranging from 0 (no coupling) to 1 (perfect coupling). Tightly wound bifilar coils approach k = 1; well-separated coils have k ≈ 0.
Related Calculators
- Inductors in Parallel Calculator — 1/Leq = 1/L1 + 1/L2 + …
- Capacitors in Series Calculator — reciprocal formula (opposite to series inductors)
- RLC Series Resonance Calculator — uses series inductance
- Series Resistor Calculator — same addition formula
- AC Power Calculator — inductive reactive power Q
- Ohm's Law Calculator