Circuit Parameters
Topology
Core cross-section A [cm²]4.0 cm²
Mean path length lc [cm]10.0 cm
Air gap lg [mm]0.5 mm
Turns N100
Current I [A]1.0 A
Relative permeability μr2000
Frequency f [Hz]50 Hz
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Flux Φ [μWb]
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Flux density B [T]
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MMF = NI [A·T]
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Inductance L [mH]
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Reluctance [MA/Wb]
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Core loss [W]
Magnetic Circuit Cross-Section
Flux Φ vs MMF (NI)
Inductance L vs Current I (Nonlinear μr Effect)
Magnetic Circuit Analysis
Reluctance (magnetic resistance):
$$\mathcal{R}_{core} = \frac{l_c}{\mu_0 \mu_r A}, \quad \mathcal{R}_{gap} = \frac{l_g}{\mu_0 A_{eff}}$$Ampere's law: $NI = \Phi (\mathcal{R}_{core} + \mathcal{R}_{gap})$
Inductance: $L = N^2 / (\mathcal{R}_{core} + \mathcal{R}_{gap}) = N\Phi/I$
Fringing correction: $A_{eff} \approx (\sqrt{A} + l_g)^2$
Design note: Increasing air gap lg reduces L ∝ 1/(R_core + R_gap) but improves DC bias linearity. Energy-storage inductors require a gap; transformers should minimize gap to maximize turns ratio efficiency. FEM analysis captures fringing accurately for large gaps.