Comparative characteristics of on-chip single- and double-level square inductors

Detailed experimental investigations reported in this paper have determined the inductances, Q factors, and resonance frequencies of on-chip square, single-level (SL) and double-level (DL) inductors on silicon substrates, using the equivalent circuit model and the measured S parameters. Parametric studies show the effects of both strip length and inner empty area on the coupling capacitance and resonance frequency. Some scalable formulas are derived for extrapolating inductance and resonance frequency of other inductors. In the DL chips, very strong self-resonance can take place with lower resonance frequency, and the Q factor will be degraded rapidly.