# Calculating Inductance for Ferrite Transformers and Inductors.

24 March 2023

Calculating Inductance for Ferrite Transformers and Inductors.

Inductance is a crucial factor to consider when designing ferrite transformers and inductors because it determines the amount of energy that can be stored in the magnetic field. Ferrite cores are commonly used in these applications due to their high magnetic permeability and low losses.

To calculate the inductance of a ferrite transformer or inductor, several factors must be taken into account, such as the core geometry, the number of turns in the winding, the effective magnetic path length of the core, and the permeability of the core material.

The formulas used to calculate inductance depend on the shape and size of the ferrite core. The most common shapes are toroidal cores, E-cores, and U-cores, and each one has its own set of equations.

Here are the formulas for calculating inductance:

For toroidal cores: L = (μ₀ * μr * N² * A) / (2π * Le)

For E-cores: L = (μ₀ * μr * N² * Ae) / (Le + 0.4 * g)

For U-cores: L = (μ₀ * μr * N² * Ae) / (Le + 2 * (g1 + g2))

In these formulas:

L is the inductance in henries (H)

μ₀ is the permeability of free space in henries per meter (H/m)

μr is the relative permeability of the core material

N is the number of turns in the winding

A is the cross-sectional area of the core in square meters (m^2) for toroidal cores, or Ae is the effective cross-sectional area of the core in square meters (m^2) for E-cores and U-cores

Le is the effective magnetic path length in meters (m)

g is the gap length in meters (m) for E-cores, and g1 and g2 are the gap lengths at each end of the core in meters (m) for U-cores

In addition to these formulas, the AL value is another parameter commonly used to specify the inductance of a ferrite transformer or inductor. The AL value represents the inductance in henries (H) obtained when a specific number of turns (N) are wound on a core of a particular size and shape. The AL value is usually provided by the ferrite core manufacturer and is given in units of nano henries per turn squared (nH/N^2).

To calculate the inductance (L) of a ferrite transformer or inductor using the AL value, you can use this formula:

L = (AL * N²) / 10^9

In this formula:

L is the inductance in henries (H)

AL is the AL value in nano henries per turn squared (nH/N^2)

N is the number of turns in the winding

Using the AL value is a convenient way to quickly estimate the inductance of a ferrite transformer or inductor without calculating it directly from the core geometry. However, it should be noted that the AL value is typically only accurate for a specific range of frequencies and currents and may vary depending on the type and quality of the core material.