Surrogate modeling and variability analysis of on‐chip spiral inductors

Abstract

This paper presents an approach to the analysis of on‐chip integrated spiral inductors in terms of parametric variabilities. An enhanced single‐π model is proposed to compensate for high frequency deviations. In addition to the single‐π model parameters, the skin effect and the proximity effect are included in the surrogate model to reflect high frequency behavior much more accurately while retaining a simple structure. Y‐parameters of the equivalent circuit are derived to extract the frequency‐dependent inductance and quality factor representations using the shunt and differential configurations. This study introduces a novel algorithm able to yield model parameter values through iterations converging on the predetermined inductance curve within an error margin of 5%. High‐Q and low‐Q characteristics of inductors arising from process variations were also captured with the proposed algorithm, along with the failure points of the inductance, the quality factor, and the self‐resonance frequency. Variability analysis results demonstrate that the differential configuration is more robust to inductance and quality factor failures, but also that it is more vulnerable to self‐resonance frequency failures.

Metamodelling Techniques for the Optimal Design of Low-Noise Amplifiers

“…Surrogate modelling is a kind of an interpolation technique that, in contrast with the conventional approaches that focus on the linear regression term, deals with the error term by considering the correlation between the instances. It has rapidly become a popular method to solve the computation time problems related to constraint and performance evaluations [20][21][22][23][24][25][26][27][28][29][30][31]. Actually, it offers a very interesting advantage since, in many engineering applications, particularly in analogue circuit design, such evaluations/measures can be very time consuming, mainly when using an in-loop technique.…”

“…Nowadays, metamodelling is used in many engineering domains: aeronautics [18], mechanics [19], electronics [20][21][22][23][24], telecommunication [25], and management science [26], to name a few.…”