Inductance of a spiral coil drawn as a copper trace on a PCB, for NFC and wireless charging antennas, filters and sensors. Also gives the inner diameter, approximate trace length and DC resistance.
Model. Mohan et al.'s modified Wheeler formula for square, hexagonal and octagonal spirals: L = K1·μ0·n²·davg/(1 + K2·ρ), with davg = (dout + din)/2 and the fill ratio ρ = (dout − din)/(dout + din). K1, K2 = 2.34, 2.75 (square), 2.33, 3.82 (hexagonal), 2.25, 3.55 (octagonal). Circular spirals use the current-sheet expression L = μ0·n²·davg/2 · [ln(2.46/ρ) + 0.2·ρ²].
Geometry. din = dout − 2nw − 2(n−1)s. The trace length is estimated from the mean perimeter of each turn, and the resistance from the copper resistivity at 20 °C.
Accuracy. About 2–3 % in the original paper for spacing up to about three times the width. A ground plane underneath or nearby copper lowers the inductance. Self-resonance and AC losses are not included.
Yes. Eddy currents in a plane under the coil reduce the inductance and the Q. Keep the area under a planar inductor free of copper.
Count the number of times the trace goes fully around the centre. Fractional turns are allowed.
Power plane pair capacitance, PDN target impedance, plane resonance and decoupling capacitor resonance.
Width a trace needs for a current, or the current a trace can carry, with IPC-2152 and IPC-2221.
Impedance of an outer-layer trace over a plane, with solder mask or embedded, and width for a target impedance.
Impedance of an inner-layer trace between two planes, symmetric or offset, and width for a target.
Differential, odd, even and common-mode impedance of edge-coupled microstrip and stripline pairs.
Impedance of a coplanar waveguide, with or without a ground plane underneath (grounded CPW).