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We propose a tunable microelectromechanical systems integrated inductor with a large-displacement electrothermal actuator. Based on a transformer configuration, the inductance of a spiral inductor is tuned by controlling the relative position of a magnetically coupled short-circuited loop. The magnetic coupling between the inductors can be changed from 0.17 to 0.8 through an electrothermal actuator that can change their relative position by over 140 mum . For the first time, we investigate the impact of this tuning scheme on the inductance and quality factor and propose optimal designs. While a previous preliminary study has focused on keeping the ratio between the two coupled inductors close to one, we find that optimal performance is a weak function of this ratio. Instead, it primarily depends on the resistive loss of the short-circuited coil. Our theoretical studies are backed by a variety of fabricated and measured tunable inductors that show a ~2:1 inductance tuning ratio over a wide frequency range of approximately 25 GHz. In addition, the maximum and minimum quality factors of the tunable inductor are measured to be 26 and 10, respectively, which agree well with the theoretically expected values.