A Substrate Model for On-Chip Tapered Spiral Inductors With Forward and Reverse Excitations

In this brief, closed-form analytical expressions are obtained to accurately calculate the oxide and substrate (both lateral/vertical) capacitances of the pi-equivalent circuit model for on-chip tapered spiral inductors. A lateral RC substrate network using the above-mentioned expressions is shown to significantly improve the model accuracy, especially with lower substrate resistivities. Furthermore, improvement in Q(max) with reverse excitation in tapered spirals is also accurately predicted by the proposed model. The accuracy of the proposed model is validated till 15 GHz using several inductor geometries across process parameters suitable for the design of RF circuits. Excellent agreement is observed between the model, electromagnetic simulations, and measurements.