The A L parameter, or the inductance factor of the core, can be found as follows ( h e in mm):Īs can be seen from the comparison of the inductance calculation, which we derived from the fundamental laws of electromagnetism with the formula based on the effective parameters, the real ring core coincides with the ideal one in the case of a rectangular cross-section without a chamfer. In the absence of a chamfer ( C = 0), the effective and actual heights of the core coincide h e = h,įrom the effective parameters of the core (do not forget about the dimensions in mm), the inductance can be found as follows: In this expression, the actual core height h is substituted by its effective value h e, which takes into account the presence of a chamfer C that reduces the total cross-sectional area of the core. The chamfer is taking into account by the following expression: In these formulas, the dimensions r o, r i, h e are in millimeters, C 1 - mm -1, C 2 - mm -3. The effective factors of a toroidal core with a rectangular cross section are determined as follows: Effective cross-sectional area of the magnetic circuit A e.These are indicated by the suffix "e" added to the symbol. Note that many other manufacturers quote A L as nH/t2 for both types of material. The A L figure for Iron Powder cores is given as uH/100 turns, but for Ferrite cores it is quoted as mH/1000 turns. The dimensional parameters of that substitute toroid are called effective parameters. Manufacturer’s data for Iron Powder and Ferrite cores are in the data tables and show all the required information. In this method, the original core is substituted by an ideal toroidal core such that a coil wound on that toroid would give exactly the same electrical performance and with same number of turns as the original coil. The method for calculating magnetic core coils, which is standard, is recommended for use by the International Magnetic Association in IEC Publication 205, “Calculation of Effective Parameters of Magnetic Piece Parts”. μ r - relative magnetic permeability of the core.In a simplified form, with the dimensions of the core in millimeters and the inductance in micro-Henry, the equation looks like this: I - the value of current through the coil.μ r - actual relative magnetic permeability of the core.The signs in the formulas correspond to the following diagram of a toroidal ferrite core: We divide this area into infinitely thin segments of height h at a distance r from the axis and sum these segments by integrating over the radius:įurther, in accordance with the definition of inductance, we arrive at the following expression: The magnetic flux through the cross-sectional area of the core can be calculated as follows. In accordance with the Ampere's Law, we can calculate the magnetic flux density in the core at an arbitrary distance r from its central axis. We can find the formula for the inductance of a rectangular cross-section toroidal coil step by step based on fundamental laws of electromagnetism. Inductance calculation of a ferrite toroid coil Multilayer air core inductor on a rectangular form.Self-capacitance of single-layer inductor.Features of calculation of power supply chokes.
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