### Table of Contents

# Impedance permeability

Stan Zurek, Impedance permeability, Encyclopedia Magnetica, http://e-magnetica.pl/doku.php/impedance_permeability |

**Impedance permeability** typically denoted by * μ_{Z}* - a type of magnetic permeability which is used to quantify the effectiveness of the given magnetic material in producing useful magnetic flux from a given level of exciting magnetising current, without analysing the specific components of the magnetising currents (e.g. resistive-like for power loss, rather than inductive-like for pure inductive reactance).

^{1)}

The definition of **impedance permeability** is based on measuring the peak magnetic flux density *B _{peak}* and RMS value of the applied magnetic field strength

*H*as the exciting current

_{RMS}*I*and simplistically assuming that the signal is sinusoidal, so that the scaling is made just by multiplying by √2 in order to obtain the apparent peak value

_{RMS}*H*.

_{peak}^{2)}

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This type of definition is very convenient in practice, because RMS current is easily measurable by most ammeters (and also RMS voltage can be used to derive *B _{peak}* from Faraday's law of induction).

In a general case, the values of permeability calculated with this method will differ by some amount from the amplitude magnetic permeability based on true measured peak values of *B* and *H*, especially at higher amplitudes of excitation where the distortions in either *B* or *H* cannot be neglected, even when the excitation is set up to be purely sinusoidal. This is because for distorted (non-sinusoidal) waveforms the relationship between peak, average, and RMS values is no longer linear.

(expressed as absolute permeability) | $$ μ_z = \frac{B_{peak}}{H_{peak,a}} = \frac{B_{peak}}{H_{RMS} · \sqrt{2}} = \frac{B_{peak} · l}{I_{RMS} · N · \sqrt{2}} $$ | (H/m) |

(expressed as relative permeability) | $$ μ_z = \frac{B_{peak}}{H_{peak,a}·μ_0} = \frac{B_{peak}}{H_{RMS} · \sqrt{2}·μ_0} = \frac{B_{peak} · l}{I_{RMS} · N · \sqrt{2}·μ_0} $$ | (unitless) |

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