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How to calculate inductance?

inductance handbook formulaWe 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 self-resonance frequency.



The medium level is based on the simplified model of the inductor introduced by J.C.Maxwell.
 Advantages: acceptable calculation accuracy for radio-enthusiasts 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 60-70% of the self-resonant frequency (or rather 1-resonance) 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 self-resonance 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:maxwell formula

 

Whereeq102maxwell model

  •     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 single-layer, multi-layer 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.

Screenshots 

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