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

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
_ln
(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
).