Calculated using the Modified Wheeler Formula for planar spiral inductors (Mohan et al., 1999).

$L_{single} = K_1 \cdot \mu_0 \cdot \frac{N^2 \cdot d_{avg}}{1 + K_2 \cdot \rho}$

Multilayer (Series): Mutual inductance between layers is approximated. $L_{tot} = M \cdot L_{single} + 2 \sum M_{ij}$. $M_{ij} \approx k_{ij} \sqrt{L_i L_j}$.

Multilayer (Parallel): Via stitching parallel layers reduces DC Resistance. Inductance drops slightly due to negative coupling (since $L_{tot} \approx \frac{L_{single} + M}{2}$ for 2 layers).

• $d_{avg} = (d_{out} + d_{in}) / 2$
• Fill Ratio $\rho = (d_{out} - d_{in}) / (d_{out} + d_{in})$
• Square: $K_1 = 2.34, K_2 = 2.75$
• Hexagonal: $K_1 = 2.33, K_2 = 3.82$
• Octagonal: $K_1 = 2.25, K_2 = 3.55$