Transfer function analysis and broadband scalable model for on-chip spiral inductors

Recent models for on-chip spiral inductors have been extensively examined and compared by transfer function analysis. Through the calculation of the transfer functions for the models, including T-, 1-π, and 2-π models, the pros and cons of equivalent circuit topology of each model are evaluated. It is found that the number of poles provided by a certain topology is a constant, while complex poles are responsible for the broadband fitting capacity of the model. The 2-π model has the most poles and the best broadband fitting capacity, while 1-π and T-models are better solutions considering both accuracy and efficiency. A novel broadband model combining the advantages of the physics-based circuit model and behavioral macro-model is proposed for accurately characterizing RF behaviors of spiral inductors. A number of inductors with various geometries have been fabricated to verify the model. Excellent agreements are obtained between the measured data and calculation from the proposed model up to 40 GHz. This modeling method is also applicable to other passive components such as transmission lines and transformers.