Magnetorquer Designer

A comprehensive tool for designing and optimizing PCB-based magnetorquer coils for spacecraft attitude control. This includes physical optimization, thermal analysis, and automated PCB trace generation.

Usage

1. Configure design constraints in /constraints/[BOARD_NAME]-constraints.json:

   {
     "design_constraints": {
       "num_layers": 6,
       "voltage": 8.2,
       "max_power": 4
       // ... other constraints
     }
   }

2. Run the optimizer:

   python design.py

3. Generate visualization:

   python 2d-sketch.py

4. Create KiCad PCB:

   • Open KiCad PCB Editor
   • Open Python console (Tools > Scripting Console)
   • Copy and paste functions from kicad.py
   • Run main()

Output Files

• design.json: Complete design specifications
• output/magnetorquer_layer_*.png: Layer-by-layer visualizations
• KiCad PCB files with generated traces

Optimization Physics

The optimization process balances multiple physical constraints and objectives to maximize the magnetic moment while ensuring reliable operation. Here's a detailed breakdown of the physics involved:

1. Magnetic Moment Optimization

The primary objective is to maximize the magnetic moment (μ), which determines the torque capability of the magnetorquer:

μ = n * I * A * L
where:
n = number of turns per layer
I = operating current
A = area per turn
L = number of layers

The optimizer balances these factors:

• Increasing turns (n) increases total area but reduces current capacity
• Wider traces allow more current but reduce available turns
• Multiple layers multiply the effect but add thermal challenges

2. Current and Resistance Calculations

Current is limited by both power and thermal constraints:

a) Resistance calculation with temperature compensation:

R = ρ₀(1 + α∆T) * total_length / (w * t)
where:
ρ₀ = base copper resistivity (1.68e-8 Ω⋅m)
α = temperature coefficient (0.00393 /°C)
∆T = temperature rise
w = trace width
t = copper thickness

b) Current limitations:

I = min(V/R, I_thermal, I_max)
where:
V = supply voltage
I_thermal = maximum current based on thermal constraints
I_max = absolute maximum current rating

3. Thermal Analysis

The optimizer solves a complex thermal equilibrium equation for both ground and space scenarios:

Ground testing:

P_in = P_radiation
I²R = εσA(T⁴ - T_ambient⁴)
where:
ε = emissivity
σ = Stefan-Boltzmann constant
A = surface area
T = temperature of the magnetorquer's surface
T_ambient = room temperature

Space operation:

P_in = P_radiation
I²R = εσA(T⁴ - T_space⁴)
T_space = base temperature of satellite components

4. Manufacturing Constraints

The physical design must respect manufacturing limitations:

w_trace ≥ w_min (minimum manufacturable trace width)
s_trace ≥ s_min (minimum trace spacing)
j ≤ j_max (current density limit)
where:
j = I/(w_trace * t_copper)

5. Optimization Strategy

The optimizer uses Sequential Least Squares Programming (SLSQP) to:

1. Start with initial trace width guess
2. For each iteration:
   • Calculate maximum possible turns
   • Determine total resistance
   • Solve thermal equilibrium
   • Calculate resulting magnetic moment
   • Adjust parameters to maximize moment while satisfying constraints

The process uses gradient-based optimization to find the global maximum magnetic moment while satisfying all constraints. Key constraints include:

# Power constraint
I²R ≤ P_max

# Thermal constraint
T_final ≤ T_max

# Current density constraint
I/(w * t) ≤ j_max

# Geometric constraints
n_turns * (w + s) ≤ (outer_dim - inner_dim)/2

Trace Generation Algorithm

The trace generation uses a sophisticated algorithm to create optimal coil patterns:

1. Layer Organization

   • N-1 layers for coil windings (where N is total layers)
   • Final layer reserved for H-bridge connections
   • Each layer alternates winding direction for optimal inductance

2. Turn Calculation

   max_turns = min(
       (outer_length - effective_inner_length) / (2 * turn_pitch),
       (outer_width - effective_inner_width) / (2 * turn_pitch)
   )
   where:
   turn_pitch = trace_width + trace_spacing

3. Clearance Management

   • Maintains minimum clearance from inner cutout
   • Ensures proper spacing for layer interconnects
   • Accounts for manufacturing constraints

4. Layer Interconnections

   • Optimized via placement for layer transitions
   • Minimized crossing points to reduce parasitic effects
   • Maintained consistent impedance through transitions

Dependencies

• Python 3.7+
• NumPy
• SciPy
• Matplotlib
• KiCad 6.0+

License

MIT License

Contributing

Contributions welcome! Please read the contributing guidelines before submitting pull requests.