Coil Design Extended

Turns, wire length, resistance, current density, thermal estimate

Calculation
Quick Introduction

This calculator supports practical coil predesign by combining magnetic, electrical, and thermal checks. In addition to turns and inductance, it estimates winding resistance, current density, and temperature rise.

Schema:
1) define magnetic target (L or N)
2) verify conductor/current-density constraints
3) estimate copper losses and ΔT
Formulas (MathJax)
\[L=A_L\cdot N^2\]
\[R=\rho\cdot\frac{l_{wire}}{A_{wire}}\]
\[J=\frac{I}{A_{wire}},\quad A_{wire}=\frac{\pi d^2}{4}\]
\[P_{Cu}=I^2R,\quad \Delta T\approx P_{Cu}\cdot R_{th}\]
Legend
  • \(N\): turns
  • \(l_{wire}\): wire length [m]
  • \(R\): winding resistance [Ω]
  • \(J\): current density [A/mm²]
  • \(R_{th}\): thermal resistance [K/W]


Examples
With N=180, circumference=7.5cm and d=0.8mm, wire length is about 13.5m with low-ohmic winding resistance.
For L=3.3mH and AL=120nH/N², around 166 turns are required.
Detailed Documentation & Summary

Coil design requires balancing magnetic, electrical, and thermal constraints. The magnetic part defines turns for target inductance. The electrical part evaluates winding resistance and copper losses. The thermal part checks whether estimated temperature rise is acceptable for the application.

The ΔT model here is a first-order approximation with constant thermal resistance. Accurate predictions should include core losses, mounting conditions, convection, frequency effects (skin/proximity), and temperature-dependent material properties.

Summary
  • Derives N from L and AL
  • Computes wire length, R, J, and copper losses
  • Provides quick ΔT estimate for predesign

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