Estimation methods for quality factors of inductors fabricated in silicon integrated circuit process technologies

By examining uses of quality (Q) factors for inductors in silicon integrated circuit design, new methods for estimating quality factors are proposed. These methods extract and factors by numerically adding a capacitor in parallel to measured y₁₁ data of an inductor, and by computing the frequency stability factor and 3-dB bandwidth at the resonant frequency of the resulting network. These parameters are then converted to effective quality factors using relationships for simple parallel RLC circuits. By sweeping the numerically added capacitance value, effective duality factors at varying frequencies are computed. These new techniques, in addition to being more relevant for circuit design, provide physically reasonable estimates all the way up to the self-resonant frequencies of inductors. At moderate to high frequencies, the commonly used Q definition [-Im(y₁₁)/Re(y ₁₁)] can significantly underestimate and can even give unreasonable results. Data obtained using the new methods suggest that quality factors remain high and integrated inductors remain useful all the way up to their self-resonant frequencies, contrary to the behavior obtained using -Im(y₁₁)/Re(y₁₁). These indicate that the commonly used technique can lead to improper use and optimization of integrated inductors