A Novel Triangularity of Q-Curve Methodology for Si Inductors Design Automation

Abstract

In this article, a simplified equivalent circuit in a proposed closed-form expression is combined with a triangularity quality factor (Q) curve design (TQ) methodology for spiral inductors to obtain an automated optimal design. At first, a closed-form expression is combined with a dual-port equivalent circuit model that has a substrate electromagnetic coupling effect that describes the characteristics of the Taiwan Semiconductor Manufacturing Company (TSMC) 0.35 µm process to produce a spiral inductor. The Q-curve triangularity characteristic relationship is to verify the accuracy of the model. After comparing the simulated and measured values, the total errors of S parameter and errors of inductance are lower than 0.71 and 7%, respectively. In summary, the enumeration method is used to design all structures that satisfy 1.5 and 3.0 nH and obtain the relationship between the Q-curve peak and the triangularity characteristic, which is also used as the condition for an optimal spiral inductor. The TQ design methodology obtains almost the same optimal structural characteristic as the enumeration method, but only uses half the time. Furthermore, under the restriction of multiple conditions, the design of spiral inductors can approach process limits and optimal performance.