Permeability numbers are often stated in specifications and product sheets can result from handbooks and web-searches with little understanding of the measurement process, temperature effects, the definition and application and the lack of standardization and calibrations that are all required for accurate and repeatable permeability data. Listed below are the more common, yet very different definitions for Permeability.
Magnetic permeability can be envisioned as ‘conductivity for magnetic flux‘; and materials with high permeability’s allow magnetic flux through more easily than materials with lower permeability’s. Materials with high permeability’s include iron and the other ferromagnetic materials. In comparison, most plastics, wood, non ferrous metals, air and other fluids have very low permeability’s.
Unlike electrical conductivity, magnetic permeability is often a highly non-linear quantity although many designers use it as a constant and accept the inaccuracy of treating a non-linear quantity as linear.
reported in units of Henry’s per meter (H m-1)
The magnetic permeability, μ, of a particular material is defined as the ratio of flux density (magnetic moment-B) to applied magnetic field strength-H:
μ = B / H
This magnetic data is typically obtained from the magnetization curve.
The magnetic permeability is often a highly non-linear quantity although many specifications use it as a constant and do not accept inaccuracy of treating a non-linear quantity as linear.
This form of permeability, where μ is written without a subscript, is reported in SI units as the Absolute permeability.
Relative permeability (μr)
The most commonly used engineering term for permeability is that of Relative permeability described as
μ = μ0 × μr
This form of permeability is usually written with subscripts.
Relative permeability is a variation of absolute permeability, μ, but often perceived more useful because it demonstrates how a particular material affects the relationship between flux density (magnetic moment) and applied field strength. The term ‘relative’ relates to the permeability of a vacuum, μ0
μr = μ/μ0
For example, a material with μr = 3 suggests that the flux density will be three times as great as it would be if we just applied the same field strength to a vacuum.
Many authors and data tables report “permeability” and leave the reader to infer that they mean relative permeability. In the CGS system of units these are one and the same. If a figure greater than 1.0 is quoted then you can be almost certain it is μr.
Differential permeability (μ′)
‘Absolute permeability’ defined above is not the same as the slope of a tangent line to the B-H curve except at the peak (around 80 A m-1 in this case). The latter is called Differential permeability, where
μ′ = dB/dH
The Differential Permeability is calculated and reported by ARkival for material Permeability measurement as X init, X max and X90%.
Also of note is temperature dependence on permeability reporting. For example, if the sample temperature is increased e.g., 20 to 80 centigrade, a typical ferrite can suffer a 25% drop in relative permeability which is also a significant consideration for applications.
Initial permeability (μi)
Magnetic Permeability measurements are obtained from a fully erased sample. Unlike Hysteresis loop measurements, ARkival performs this measurement from a fully erased sample state and applies the magnetizing field (H) until material saturation is demonstrated- whereby sample magnetization is only recorded and presented in a single quadrant.
Initial permeability describes the relative permeability of a material at low values of applied Field B (below 0.1T) whereas the maximum value for μ in a material is frequently a factor of between 2 and 5+ above its initial value.
The Initial (Differential) Permeability reported by ARkival for material Permeability measurement as X init (see discussion above).
Effective permeability (μe)*
Effective permeability is reported in some data sheets for cores which have air gaps. Coil calculations ignore the air gap by assuming use of a material whose permeability is lower than the material used.
For additional information please contact ARkival.