Poles–zeros analysis and broadband equivalent circuit for on‐chip spiral inductors

Abstract

Summary Poles and zeros of the transfer function determine the performance and the key features of the circuit network, such as phase, gain, and bandwidth. In this paper, the contribution of the poles and zeros to the transfer function has been shown. The factors η p and η z are proposed to account for the poles contribution to the peak and the zeros contribution to the valley of transfer function, respectively. A novel broadband equivalent circuit combining the physics‐based circuit model and behavioral macro‐model (black‐box) network is proposed for accurately characterizing on‐chip spiral inductors. The physics‐based elements are extracted using the linear dependence of a set of characteristic functions on variables (such as ω 2 ) or other functions in a certain frequency range. The macro‐model network described by rational functions is determined using vector fitting approaches. The proposed modeling method is validated by the on‐chip spiral inductor fabricated with 0.13‐µm SiGe BiCMOS aluminum process. Excellent agreements are obtained between the measured data and calculation for the proposed model up to 40 GHz. Copyright © 2015 John Wiley & Sons, Ltd.