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901 - Magnetic Domain

Permeance-capacitance modeling for magnetic circuits.

Overview

GeckoCIRCUITS uses the permeance-capacitance analogy for magnetic circuit simulation, enabling: - Core saturation modeling - Leakage inductance effects - Coupled inductors and transformers - Non-linear magnetic behavior

Magnetic-Electrical Analogy

Permeance-Capacitance Model

Magnetic Electrical Unit
MMF (F) Voltage (V) A-turns / V
Flux (Φ) Charge (Q) Wb / C
dΦ/dt Current (I) V / A
Permeance (P) Capacitance (C) H / F
Reluctance (R) 1/C 1/H / 1/F

Why This Analogy?

The permeance-capacitance model: - Allows integration with electrical circuit - Handles non-linear permeability naturally - Supports multiple windings on single core - Models leakage paths explicitly

Basic Components

Permeance (Magnetic Capacitor)

\[P = \frac{\mu_0 \mu_r A}{l}\]

Where: - μ₀ = 4π × 10⁻⁷ H/m - μᵣ = relative permeability - A = cross-sectional area - l = magnetic path length

Winding (Gyrator)

Converts electrical current to MMF: $\(F = N \cdot i\)$ $\(v = N \cdot \frac{d\Phi}{dt}\)$

Air Gap

\[P_{gap} = \frac{\mu_0 A_{eff}}{l_g}\]

With fringing factor for accurate modeling.

Building Magnetic Circuits

Simple Inductor

Electrical:          Magnetic:

  ●──[winding]──●    MMF ──[P_core]── GND
       │  │               │
      ~~~        Leakage:[P_leak]
       N turns            │
                         GND

Transformer (Two Windings)

    Primary           Secondary
       │                 │
   [winding]         [winding]
       │                 │
       └──[P_core]──────┘
              │
          [P_leak]
              │
             GND

Saturation Modeling

B-H Curve

Non-linear permeability: $\(B = f(H) = \mu_0 \mu_r(H) \cdot H\)$

Jiles-Atherton Model

Physics-based hysteresis model with parameters: - Ms = saturation magnetization - a = domain wall density - k = pinning coefficient - c = reversibility - α = domain coupling

Piecewise Linear

Simpler approach with: - Initial permeability μᵢ - Saturation flux Bsat - Saturated permeability μsat ≈ μ₀

Core Loss Modeling

Steinmetz Equation

\[P_v = k \cdot f^\alpha \cdot B^\beta\]

Typical values: - Ferrite: α ≈ 1.3, β ≈ 2.5 - Iron powder: α ≈ 1.5, β ≈ 2.0

Improved GSE (iGSE)

For non-sinusoidal waveforms: $\(P_v = \frac{1}{T}\int_0^T k_i \left|\frac{dB}{dt}\right|^\alpha (\Delta B)^{\beta-\alpha} dt\)$

GeckoCIRCUITS Setup

Creating Magnetic Components

  1. Add permeance element from magnetic component library
  2. Set core parameters:
  3. Material (ferrite, iron powder)
  4. Dimensions (A, l)
  5. Saturation characteristics
  6. Add windings and connect to electrical circuit
  7. Add leakage permeance if needed

Material Database

GeckoCIRCUITS includes common materials: - N87, N97, N49 (ferrite) - Kool Mμ, MPP (powder core) - Nanocrystalline

Simulation Exercises

  1. Model inductor with saturation
  2. Compare linear vs non-linear core
  3. Observe flux vs current (B-H loop)
  4. Calculate core losses at different frequencies