A novel closed-form approach for comparing the Q-factor responses between the asymmetric and symmetric on-chip inductors

This paper proposes an equivalent transmission-line circuit for on-chip inductors and derives the quality (Q) factor response in terms of the transmission-line circuit parameters in closed form. The derived formulas are general and suitable for all kinds of on-chip inductors to account for their frequency dependences of Q factors. For demonstration, a series of asymmetric inductors and another series of same valued symmetric inductors have been fabricated on the same silicon substrate. The measured Q-factor responses for both kinds of inductors agree quite well with the formula predictions. The symmetric inductors have a higher equivalent characteristic impedance so as to correspond to a higher peak Q-factor frequency than the asymmetric inductors. The presented formulas can also uniquely distinguish the improvement in Q-factor responses due to the reduction of conductor loss or dielectric loss.