A New On-Chip Substrate-Coupled Inductor Model Implemented With Scalable Expressions

Accurate modeling of the on-chip inductor is essential for the design of high-speed, low-power, and low-noise radio-frequency integrated circuits. The conventional model has a measurable discrepancy as the current flowing in the substrate is not correctly considered. The substrate-coupled inductor model, however, considers the losses generated in both the vertical and horizontal directions. This model gives an intelligent explanation of the reduction in equivalent resistance between terminals with increasing frequency as well as the inductance and quality factor (Q-factor). In order to implement a fully scalable model, the circuit elements in the substrate-coupled inductor model are expressed as monomial equations in terms of physical geometry. These equations consider the physical implications of the parameters as well as employing a mathematical fit for extrapolation. Measurements are made on inductors fabricated using a standard 0.35-mum CMOS process and a 0.15-mum silicon-on-insulator CMOS process to successfully verify this model.