Unified Inductance Calculations for On-Chip Planar Spirals

Four unified calculations with only coefficients dependent are proposed for the DC inductance of common on-chip spirals of square, hexagon, octagon and circle. The first two algorithms are based on the derivation of Neumann integral, which evaluate the inductance according to turns rather than discrete segments. The latter two expressions are obtained from a simple modification of published expressions by considering the metal thickness. An automatic script is employed to generate hundreds of thousands of inductor layouts for electromagnetic (EM) simulation. By comparison with the simulated predictions, the proposed calculations show typical errors within around 1-3%, which are competitive for the modeling, design and optimization of integrated inductors.