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The free energy back EMF in the inductor core
k11 k12 k13 k14 The initial current in the coil:
k21 k22 k23 k24 The final current in the coil:
Kη2 = 2.964 Mmax/M0 = 3.469 M0/Mmin = 2.714 Mmax/Mmin = 9.417
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The calculator allows to find the optimal parametric dependence of change of inductance of current and mode excitation of the generator to produce maximum efficiency in a closed RL-circuit, where the source of power is back EMF.
Theoretical justification of the additional energy from the back EMF in the inductor core is provided here. Under OEDS means a process that occurs in the coil after an abrupt cessation of flow of current from an external source of energy and the formation of a closed RL-circuit. At this moment there is a current I0, which in this calculator is the start, and which eventually is reduced to zero, gradually standing out in the form of active energy to the load R. If in this process, the inductance varies parametrically, the allocated load energy, in some cases, may exceed the initial energy in the coil. Parametric dependence of inductor current is expressed by the relation:
L = LS‧M(I) where: M(I) = (1 + k11‧I + k12‧I2 + k13‧I3 + k14‧I4 )/(1 + k21‧I + k22‧I2 + k23‧I3 + k24‧I4)
where: LS is the initial inductance of the coil (no current). The coefficients k11k..24 can be arbitrary, even negative. In the latter case, you need to be careful in terms of the range of values M(I) is not included in the negative region.
The left graph shows the resulting podstanovki coefficients k11..k24 dependence M(I), which corresponds to a real dependence of magnetic permeability of ferromagnetic core on the magnetic field. The right graph shows the decay of the current in the inductance depending on time. It will fit real oscillogram taken on the current transformer, which can be included in the circuit of the coil. Above is the calculated value of the coefficient of energy gain Kη2, which represents an increase of efficiency of the second kind.
All values in this calculator — relative. To calculate real values, you need to know the winding details of the coil and core parameters.
The following is a compilation of some values of Kη2 and the corresponding dependencies M(I).
  • 1. Classical inductance, a parametric dependency is missing, no gain. Kη2=1 ".
  • 2. Close to ideal dependence of the M(I). Kη2=8.5 ".
  • 3. Work only on a rising M(I). Kη2=0.82 ". This means that in a real device, the usual efficiency is above 82%, and to increase need to reduce or increase the maximum current in the coil.
  • 4. Sine graph M(I). Kη2=0.96 ".
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