Magnetic complex reluctance

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Magnetic complex reluctance is the complex value, which is equal to the relation of the complex effective or amplitude value of a sinusoidal magnetic tension on the passive magnetic circuit or its element and accordingly the complex effective or amplitude value of a sinusoidal magnetic flux in this circuit or in this element.

Magnetic complex reluctance [1-3] is measuring in the units – [1/H] and determining by the formula:

$Z_\mu = \frac{\dot N}{\dot \Phi} = \frac{\dot {N}_m}{\dot {\Phi}_m} = z_\mu e^{j\phi}$

where $z_\mu = \frac{N}{\Phi} = \frac{N_m}{\Phi_m}$ is the relation of the effective or amplitude value of a magnetic tension and accordingly of the effective or amplitude magnetic flux is naming as the magnetic reluctance (amplitude value).

The magnetic reluctance is equal to the modulus of the magnetic complex reluctance. The argument of a magnetic complex reluctance is equal to the difference of the phases of the magnetic tension and the magnetic flux $φ = β - α$ .

Magnetic complex reluctance represents by itself the magnetic resistance to a magnetic flux and is determining by the properties of the magnetic circuit. Since, when the energy loss are in magnetic medium, a magnetic permeability is the complex value (for harmonic regimes), that accordingly the magnetic reluctance in general case represents by itself also the complex value:

$Z_\mu = \frac{1}{\dot {\mu} \mu_0}\frac{l}{S}$