Magnetic complex impedance

Magnetic complex impedance 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 current in this circuit or in this element.

Magnetic complex impedance [1, 2] is measuring in units – [$\frac{1}{\Omega}$] and determining by the formula:

$Z_M = \frac{\dot N}{\dot {I}_M} = \frac{\dot {N}_m}{\dot {I}_Mm} = z_M e^{j\phi}$

where $z_M = \frac{N}{I_M} = \frac{N_m}{I_{Mm}}$ is the relation of the effective or amplitude value of a magnetic tension and accordingly of the effective or amplitude magnetic current is naming as the full magnetic resistance (magnetic impedance). The full magnetic resistance (magnetic impedance) is equal to the modulus of the complex magnetic impedance. The argument of a complex magnetic impedance is equal to the difference of the phases of the magnetic tension and magnetic current ϕ = β − α. Complex magnetic impedance can be presented in following form:

Z_M = z_Me^jϕ = z_Mcos ϕ + jz_Msin ϕ = r_M + jx_M

where r_M = z_Mcos ϕ is the real part of the complex magnetic impedance, naming as the effective magnetic resistance; x_M = z_Msin ϕ is the imaginary part of the complex magnetic impedance, naming as the reactive magnetic resistance. The full magnetic resistance (magnetic impedance) is equal

$z_M = \sqrt{r_{M}^2 + x_{M}^2}$ , $\phi = \arctan {\frac{x_M}{r_M}}$

References

• Popov V. P. The Principles of Theory of Circuits. – M.: Higher School, 1985, 496 p. (In Russian).
• Küpfmüller K. Einführung in die theoretische Elektrotechnik, Springer-Verlag, 1959.