Series Inductors Calculator

About the Series Inductors Calculator

When inductors are connected in series, their inductances add directly — L_total = L₁ + L₂ + ... — just like resistors in series. However, if the inductors are magnetically coupled (their magnetic fields interact), mutual inductance must be considered. The coupling can be aiding (fields in the same direction) or opposing (fields in opposite directions), changing the total inductance significantly.

The coupling coefficient k ranges from 0 (no coupling) to 1 (perfect coupling). For series-aiding connection: L_total = L₁ + L₂ + 2M, where M = k√(L₁L₂) is the mutual inductance. For series-opposing: L_total = L₁ + L₂ − 2M. This distinction is critical in transformer design, coupled-inductor filters, and wireless power transfer circuits.

This calculator handles up to 8 inductors in series with a shared coupling coefficient. It computes total inductance for both aiding and opposing connections, the uncoupled total, the parallel equivalent (for comparison), and shows individual inductor contributions with reactance values.

When This Page Helps

Calculating series inductance with mutual coupling requires computing mutual inductance for every pair of inductors and applying it correctly for aiding or opposing configurations. With more than two inductors, this becomes tedious. This calculator automates the pairwise mutual inductance calculation and provides both aiding and opposing totals, a parallel equivalent for comparison, and a reactance reference table.

How to Use the Inputs

1. Set the number of series inductors (2 to 8).
2. Enter the coupling coefficient k (0 for uncoupled, up to 1 for maximum coupling).
3. Enter each individual inductor value in the selected unit.
4. Use preset buttons for common configurations.
5. Compare series aiding, opposing, and parallel equivalent results.
6. Review the inductor breakdown table for individual contributions and reactances.
7. Use the visual bar chart to compare connection configurations.

Example Calculation

Tips & Best Practices

• Series inductors are useful for creating non-standard inductance values from standard parts.
• Coupled inductors on the same core share magnetic flux — check the winding direction to determine aiding vs opposing.
• If you measure two different total inductances by reversing one winding, the average eliminates coupling: L_uncoupled = (L_aid + L_opp) / 2.
• At high frequencies, parasitic capacitance between inductor windings can create self-resonance, limiting the useful frequency range.
• For EMI filter design, coupled inductors on a common-mode choke provide differential-mode filtering through leakage inductance.
• Keep series inductors physically separated if you want to minimize unintended mutual coupling.

Mutual Inductance in Practice

Mutual inductance occurs whenever the magnetic field from one inductor passes through the coils of another. The coupling coefficient depends on physical proximity, orientation, and core material. On a shared ferrite core, k can be 0.9-0.99, while for air-core inductors a few centimeters apart, k might be 0.01-0.1. Measuring mutual inductance is straightforward: measure total inductance in aiding and opposing configurations, then M = (L_aid - L_opp) / 4.

Applications of Coupled Series Inductors

Coupled inductor designs are common in switch-mode power supplies, where energy stored in one winding is transferred to another (like a flyback transformer). In EMI filters, common-mode chokes use two tightly coupled windings to present high impedance to common-mode noise while allowing differential signals to pass with minimal impedance.

Inductor Selection Guidelines

When selecting inductors for series connection, ensure all inductors can handle the circuit current without saturating. The weakest inductor (lowest saturation current) determines the maximum current for the series string. Also consider DC resistance — series connection adds the DCR values, which may become significant for power applications.

Frequently Asked Questions

• Do series inductors always add?

  Without coupling, yes — L_total = L₁ + L₂ + ... For coupled inductors, the total can be larger (aiding) or smaller (opposing) due to mutual inductance. In the extreme case of perfect opposing coupling, the total can approach zero.

• What is the coupling coefficient k?

  The coupling coefficient k (0 to 1) measures what fraction of one inductor's magnetic flux links through another. k = 0 means no coupling (separate inductors); k = 1 means perfect coupling (ideal transformer). Typical values for air-core inductors near each other are 0.01-0.3.

• How do I know if inductors are aiding or opposing?

  Wind direction determines this. If current enters both inductors at the "dotted" terminal, they are aiding (fields add). If current enters one at the dot and exits the other at the dot, they are opposing. Dot notation on schematics indicates this.

• Why would I use series inductors instead of a single larger inductor?

  Using multiple series inductors can help distribute voltage stress, reduce core saturation, provide flexibility with standard values, or spread heat dissipation across multiple components.

• Can coupling coefficient be negative?

  Mathematically, k is always 0 to 1. Negative coupling effect is achieved by reversing the winding direction (opposing connection), which subtracts mutual inductance. The calculator allows negative k as a shorthand for opposing connection.

• How does frequency affect series inductance?

  Ideal inductance is frequency-independent. However, real inductors have frequency-dependent core losses, skin effect in windings, and parasitic capacitance. Above the self-resonant frequency, an inductor's impedance decreases (becomes capacitive).