A Broadband and Scalable Lumped Element Model for Fully Symmetric Inductors Under Single-Ended and Differentially Driven Operations

摘要

A broadband and scalable 2-T model is developed to accurately simulate fully symmetric inductors with various dimensions. The 2-T model is defined to reflect the structure of an equivalent circuit with two identical T-model circuits. Two-step de-embedding is assisted by open and through pads for extraction of intrinsic characteristics. The accuracy is validated by 3-D full-wave electromagnetic simulation. A novel parameter extraction flow is established, and a single set of model parameters is derived to be valid for both single-ended and differentially driven topologies. The broadband accuracy is proven by a good match with $S$ -parameters, $L(omega)$, $Re(Z_{rm in}(omega))$, and $Q(omega)$ over frequencies up to 20 GHz. The scalability is justified by good fitting with either a linear or a parabolic function of spiral coil radii. Furthermore, all model parameters are frequency independent so as to ensure computation efficiency. This 2-T model consistently predicts the enhancement of $Q_{max}$ by 20%–30% for the symmetric inductors under a differential excitation. The $Q$ improvement is even better than 100% over broader frequencies beyond $f_{m}(Q_{max})$.