# Magnetic impedance

Magnetic impedance (SI Unit: -Ω−1) is the ratio of a sinusoidal magnetic tension ${\displaystyle N_{\mathrm {m} }}$ to a sinusoidal magnetic current ${\displaystyle I_{\mathrm {Mm} }}$ in a gyrator-capacitor model. Analogous to electrical impedance, magnetic impedance is likewise a complex variable.

${\displaystyle z_{\mathrm {M} }={\frac {N}{I_{\mathrm {M} }}}={\frac {N_{\mathrm {m} }}{I_{\mathrm {Mm} }}}}$

Magnetic impedance is also called the full magnetic resistance. It is derived from:

${\displaystyle r_{\mathrm {M} }=z_{\mathrm {M} }\cos \phi }$, the effective magnetic resistance (real)
${\displaystyle x_{\mathrm {M} }=z_{\mathrm {M} }\sin \phi }$, the reactive magnetic resistance (imaginary)

The phase angle ${\displaystyle \phi }$ of the magnetic impedance is equal to:

${\displaystyle \phi =\arctan {\frac {x_{\mathrm {M} }}{r_{\mathrm {M} }}}}$