Analysis of scaling-rule and size-reduction limit of spiral inductors to maximize quality factor

A scaling-rule of planar RF spiral inductors is estimated by using closed-form expression where spiral inductors are modeled with appropriate parasitic components. It is found that there is a size-reduction limit that maximizes quality factor of the inductor when the device occupation area is reduced while keeping both the inductance and the center frequency of the quality factor constant. For example the quality factor at the center frequency becomes maximized when the outer size reduced to 146 μm in a given structure of the spiral inductors for several GHz region of operating frequency.