A novel model for spiral inductor based on a unified CPW circuit model

A novel equivalent circuit model for a spiral inductor is proposed based on a unified coplanar waveguide (CPW) transmission line model. The spiral inductor can be treated as a network of several individual conductor paths. The individual conductor loss is similar to the loss in CPWs, which can be explained by the unified model. The coil current of the inductor induces an eddy current in the silicon substrate which is magnetically coupled with the metal line. The substrate eddy current loss and coupling with the spiral line are modeled by an RL ladder structure and mutual inductance. Single turn spiral inductors have been designed and fabricated on various resistivity substrates. A good agreement is obtained between the measurement and the equivalent circuit even above the self-resonance frequency. This work demonstrates that the performance of spiral inductors can be predicted and investigated by the proposed equivalent circuit.