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Published: 02 June 2015

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How to calculate inductance?
We can use different methods to calculate the inductance using numerical methods or handbook formulas. They can be conditionally divided into three levels  high, medium and low level.
High level involves the use of programs having a common name  electromagnetic simulators. For example, Comsol Multisystems with RF module, Ansys HFSS, etc. Their work is based on the differential Maxwell's equations for the electromagnetic field providing the boundary conditions.
Advantages: accurate calculation of inductance and other parameters of the coil with any geometry of winding in any frequency range.
Disadvantages: these programs are quite complex and require prior learning, require large computational resources, the calculation takes a long time. Can be used for professional work or if the inductor is used at or above the selfresonance frequency.
The medium level is based on the simplified model of the inductor introduced by J.C.Maxwell.
Advantages: acceptable calculation accuracy for radioenthusiasts practice, opportunity of using in simple programs, low demands on processing power of the computer.
Disadvantages: less accurate calculations than the high level; the calculation isn't possible for any winding geometry and may be only in the frequency range that does not exceed 6070% of the selfresonant frequency (or rather 1resonance) of the coil.
The low level is based on simple handbook formulas. These formulas are based on the simplification of medium level formulas or on the basis of a set of measurements of the real coils.
Advantages: simple calculation, undemanding to resources of the computer
Disadvantages: the formulas work only with restricted geometry of the winding and at frequencies much lower than the selfresonance frequency.
More about medium level calculation that Col32 uses... The great physicist J.C. Maxwell has showed in the late XIX century in his famous work  "A Treatise on Electricity and Magnetism." that the mutual inductance between two infinitely thin circular coaxial conductors can be calculated as follows:
Where
 M  mutual inductance;
 r1, r2  radii of the two circular filaments;
 x  distance between the centers of the circles bounded by these filaments;
 K, E  elliptic integrals of the first and second kind;
A numerical method for the calculation of the Maxwell's formula reduced to numerical methods for solving elliptic integrals.
By using Maxwell's equation can be calculated inductance of a singlelayer, multilayer or flat coil and the mutual inductance of two separate coils. Errors related to the coaxial circular filaments approximation (in fact we deal a round wire helix) can be reduced through additional corrections.