Substituting (dH/dI) with (N/l e) and A with A e: For small AC, L can be assumed constant throughout AC excitation and is approximated by the biased inductance (L DC).Īnother way of looking at this is by rewriting the relationship between B and L as: B pk=f(L,I)ī can be rewritten in terms of inductance by considering Faraday’s equation and its effect on inductor current: Method 3, for small ▲H, determine B pk from biased inductance. Reworking Example 3 (0 Amps DC, 8 Amps pk-pk) Reworking Example 2 (20 Amps DC, 8 Amps pk-pk) Reworking Example 1 (20 Amps DC, 2 Amps pk-pk) ▲H is multiplied by 100 because l e is expressed in cm, while B pk units include m. The effective perm with DC bias is more commonly written in terms of % of initial perm and can be obtained from the DC bias curve or curve fit equation: For small AC, this slope can be modeled as a constant throughout AC excitation, with μ approximating the effective perm at DC bias (μ e):
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The instantaneous slope of the BH curve is defined as the absolute permeability, which is the product of permeability of free space (μ 0=4π x10 -7) and the material permeability (μ), which varies along the BH curve. Method 2, For small ▲H, approximate B pk from effective perm with DC bias. This effect can be achieved with DC bias, or by selecting a lower permeability material. Lower permeability results in less B pk, even if the current ripple is the same. Note the significant influence of DC bias on core loss, comparing Example 3 with Example 2.
Plotted below are the operating ranges for each of the three examples.
Inductor current is 20 Amps DC with ripple of 2 Amps peak-peak at 100kHz.ġ.) Calculate H and determine B from BH curve or curve fit equation:Ģ.) Determine Core Loss density from chart or calculate from loss equation:Įxample 2 – AC current is 40% of DC current:Īpproximate the core loss for the same 20-turn inductor, with same inductor current of 20 Amps DC but ripple of 8 Amps peakpeak at 100kHz.ġ.) Calculate H and determine B from BH curve fit equation:Īpproximate the core loss for the same 20-turn inductor, now with 0 Amps DC and 8 Amps peak-peak at 100kHz. 47-50), B AC max, B AC min and therefore B pk can be determined.Įxample 1 – AC current is 10% of DC current:Īpproximate the core loss of an inductor with 20 turns wound on Kool Mμ p/n 77894A7 (60μ, le=6.35cm, Ae=0.654 cm 2, AL=75 nH/T 2). The value of B pk can typically be determined by first calculating H at each AC extreme:įrom H AC max, H AC min, and the BH curve or equation (listed as DC Magnetization in Magnetics Powder Core Catalog pgs.
B pk= f(H)įlux density (B) is a non-linear function of magnetizing field (H), which in turn is a function of winding number of turns (N), current (I), and magnetic path length ( l e ). Method 1 – Determine B pk from DC Magnetization Curve. The task of core loss calculation is to determine B pk from known design parameters. Units typically used are (mW/cm 3 ) for PL, Tesla (T) for B pk, and (kHz) for f. Where a, b, c are constants determined from curve fitting, and B pk is defined as half of the AC flux swing: It can be approximated from core loss charts or the curve fit loss equation: Core loss density (PL) is a function of half of the AC flux swing (½ B=B pk ) and frequency ( f ).
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To compare core performance of all five Magnetics powder core materials, download our Curve Fit Equation tool or view our list of Powder Core Calculations.Ĭore loss is generated by the changing magnetic flux field within a material, since no magnetic materials exhibit perfectly efficient magnetic response. The article below provides a step-by-step method to calculate losses generated by powder cores under certain conditions.
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