Analytical calculation for DC inductances of rectangular spiral inductors with finite metal thickness in the PEEC formulation

Inductances of rectangular spiral inductors with finite metal thickness are evaluated by the partial element equivalent circuit (PEEC) technique. The six-fold partial self and mutual inductance integrals resulting from the PEEC partitions are found to have analytical expressions, so that the singularities of the integrands can be overcome and the theoretical or "exact" results can be obtained very efficiently. Via and underpath required for input/output connection can also be included in the calculation. Calculated inductance values for 20 square spiral inductors are checked against measured data published in open literature. Dependence of inductance values on metal thickness is investigated for two specific spiral structures.