title: Tutorial 901: Magnetic Domain Introduction¶

Tutorial 901: Magnetic Domain Introduction¶

Overview¶

Learn to model magnetic circuits using the permeance-capacitance analogy. This tutorial introduces magnetic domain simulation for transformers, inductors, and coupled magnetic components.

Level: Advanced (3/3)

Duration: 45-60 minutes

Series: Magnetics & Mechanical

Status: Placeholder - Circuit files to be added

Learning Objectives¶

By the end of this tutorial, you will: - [ ] Understand the permeance-capacitance analogy - [ ] Model simple magnetic circuits - [ ] Simulate flux and MMF in magnetic components - [ ] Connect magnetic domain to electrical circuits

Prerequisites¶

• Complete 201 - Buck Converter
• Understanding of magnetic circuit fundamentals (reluctance, permeance, MMF)
• Familiarity with transformer operation

Theory¶

Permeance-Capacitance Analogy¶

Magnetic circuits can be modeled using electrical analogies:

Magnetic Circuit Model¶

    MMF Source          Reluctance Path
    (N×I)               (Core + Air Gap)
      │                      │
      ○ ─────────────[R_core]────[R_gap]─────┐
      │                                       │
      └───────────────────────────────────────┘
                         Φ (flux)

Core Material Properties¶

Saturation Modeling¶

Non-linear B-H characteristic:

B = Bsat × tanh(H/Hsat)  (simplified model)

Or using piecewise linear approximation:

     B
     │      ╱─────── Bsat
     │     ╱
     │    ╱
     │   ╱
     │  ╱
─────┼─╱──────────── H
     │╱

Magnetic Components in GeckoCIRCUITS¶

Available Components¶

Coupled Inductor Model¶

        ┌─────●─────┐
        │     ║     │
       L1     ║ M   L2
        │     ║     │
        └─────●─────┘

    M = k × √(L1 × L2)
    k = coupling coefficient (0-1)

Building Magnetic Models¶

Example 1: Simple Inductor with Core¶

1. Define core geometry:
2. Cross-section area: Ac = 100 mm²
3. Magnetic path length: lc = 50 mm

4. Air gap: lg = 1 mm

5. Calculate reluctances:

   Rc = lc / (μ0 × μr × Ac)
   Rg = lg / (μ0 × Ac)
   

6. Calculate inductance:

   L = N² / (Rc + Rg) = N² × P_total
   

Example 2: Flyback Transformer¶

Model as coupled inductor with: - Primary inductance Lp (magnetizing) - Leakage inductance Llk - Turns ratio n - Coupling coefficient k < 1

    Primary           Secondary
    ┌──[Llk]──●═══════●──┐
    │         ║       ║   │
    │        Lm      Ls   │
    │         ║       ║   │
    └─────────●═══════●───┘
              k = 0.95-0.99

Example 3: Saturable Reactor¶

For controlled inductance (magnetic amplifier): - DC bias winding controls saturation level - AC winding provides variable inductance - Used in: dimmers, welding power supplies

Simulation Setup¶

Time Step Considerations¶

Magnetic domain may require smaller time step: - Fast flux changes during switching - Core loss modeling needs accurate dB/dt

Recommended: dt < 1/(100 × fs)

Initial Conditions¶

• Set initial flux or inductor current
• Avoid starting from zero (long settling)
• For transformers, ensure no DC flux buildup

Expected Results¶

Waveforms to Observe¶

1. Flux (Φ): Should stay below saturation
2. Flux Density (B): B = Φ/Ac
3. Magnetizing Current: Non-linear at saturation
4. Core Loss: Increases with frequency and Bmax

Saturation Effects¶

When B → Bsat: - Inductance drops dramatically - Current spikes occur - Losses increase - Waveform distortion

Exercises¶

Exercise 1: Linear Inductor¶

1. Model a 100μH inductor with ferrite core
2. Apply 10V at 100kHz
3. Verify: V = L × di/dt

Exercise 2: Saturation¶

1. Add saturation (Bsat = 0.3T) to the inductor
2. Increase voltage until saturation occurs
3. Observe: Current waveform distortion

Exercise 3: Coupled Inductor (Flyback)¶

1. Model flyback transformer: Lp = 500μH, n = 10:1, k = 0.98
2. Simulate energy transfer
3. Measure: Leakage inductance effect on voltage spike

Exercise 4: Core Loss¶

1. Add core loss model (Steinmetz equation)
2. Compare efficiency at 50kHz vs 200kHz
3. Calculate: Core loss contribution to total loss

Core Loss Modeling¶

Steinmetz Equation¶

Pcore = k × f^α × Bmax^β × Volume

Typical coefficients for ferrite: - k ≈ 1.5 (material constant) - α ≈ 1.5 (frequency exponent) - β ≈ 2.5 (flux density exponent)

iGSE (Improved Generalized Steinmetz)¶

For non-sinusoidal waveforms:

Pcore = (1/T) × ∫ ki |dB/dt|^α × (ΔB)^(β-α) dt

Common Issues¶

Related Tutorials¶

• 902 - Transformer Design - Detailed transformer modeling
• 903 - Inductor Saturation - Saturation effects
• Flyback Converter - Application example

References¶

1. McLyman, W.T. "Transformer and Inductor Design Handbook"
2. Kazimierczuk, M.K. "High-Frequency Magnetic Components"
3. Erickson & Maksimovic, Chapter 13: "Basic Magnetics Theory"

Circuit Files¶

Status: Placeholder - Circuit files to be created - magnetic_basic.ipes - Simple magnetic circuit - inductor_saturation.ipes - Saturable inductor model - coupled_inductor.ipes - Flyback transformer model

Tutorial Version: 1.0 (Placeholder) Last updated: 2026-02 Compatible with GeckoCIRCUITS v1.0+