Bobbin Winding & Resistance

Enter the inside and outside diameter of the winding, the traverse length between bobbin cheeks and a wire gauge. The plate reports how many turns fit, how much wire it takes and what the finished coil will measure on an ohmmeter.

Parameters

Inner winding diameter

D_i

Outer winding diameter

D_o

Winding length (traverse)

L_w

Wire gaugeBare 0.255 mm · enamelled ≈ 0.285 mmAWG

Winding style

Coil temperature

T

°C

Test voltage

V

Fig. 1Half-section of the bobbin through the axis, drawn to scale. 8,540 turns in ≈ 61 layers of 140.

Winding data

Turns

N

8,540

Resistance

R_T

386 Ω

Turns / layer140

Layers61

Mean turn

\ell_{MLT}

134 mm

Wire length1.14 km

Copper mass520 g

Current @ V

I

259 mA

Ampere-turns

NI

2.21 kA·t

Power @ V

P

25.9 W

☞ Copper fill factor 62.1 % of window area.

Resistance of this bobbin vs. wire gauge

How it works

Theory · assumptions · formulas

Counting turns

The winding occupies an annular window of radial depth $h = (D_o - D_i)/2$ and axial length $L_w$ . With insulated wire diameter $d_i$ , a perfect layer winding stacks wires in a square grid:

N = \left\lfloor \frac{L_w}{d_i} \right\rfloor \cdot \left\lfloor \frac{h}{d_i} \right\rfloor

An orthocyclic winding nests each layer into the grooves of the one beneath, so successive layers are only $\tfrac{\sqrt3}{2}\,d_i$ apart, about 15 % more turns in the same window. A scramble (random, machine-wound) coil packs worse; we assume 82 % of the square-grid count, a typical production figure.

Wire length and resistance

Every turn has, on average, the circumference of the mid-depth diameter, the mean length of turn:

\ell_{MLT} = \pi\,\frac{D_i + D_o}{2}, \qquad \ell = N\,\ell_{MLT}

R_T = \rho_{20}\,\bigl[1 + \alpha\,(T - 20\,^{\circ}\mathrm{C})\bigr]\,\frac{\ell}{\pi d^2/4}

with $\rho_{20} = 1.724\times10^{-8}\ \Omega\,\mathrm{m}$ for annealed copper and $\alpha = 0.00393\ \mathrm{K^{-1}}$ . Note $d$ is the bare diameter: insulation takes space but carries no current.

Wire diameters

AWG diameters follow $d = 0.127\,\mathrm{mm}\times 92^{(36-n)/39}$ . The enamelled diameter is approximated as $d_i \approx 1.04\,d + 0.02\ \mathrm{mm}$ , which tracks heavy-build (grade 2) magnet wire within a few percent from AWG 18 to 42.

Practical noteReal coils rarely achieve the theoretical count. Allow 5–10 % for lead-outs, interlayer paper and an imperfect traverse, and expect the measured resistance to come in a little low accordingly.

Because $N \propto 1/d_i^2$ and $R \propto N/d^2$ , resistance climbs roughly as the fourth power of the gauge ratio: each 3 AWG steps multiplies it by about four, as the graph shows on its logarithmic axis.