# Encyclopedia Magnetica™

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impedance_permeability

# Impedance permeability

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

Impedance permeability typically denoted by μZ - 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 Bpeak and RMS value of the applied magnetic field strength HRMS as the exciting current IRMS 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 Hpeak.2)

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 Bpeak 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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