A tunable micro-electromechanical systems integrated inductor with a large-displacement electro-thermal actuator is discussed here. 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. 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 which is high compared to previous designs. They can considerably extend the tuning capabilities of critical reconfigurable circuits such as tunable impedance matching circuits, phase shifters voltage controlled oscillators, and low noise amplifiers

Analysis and design of tunable inductor

The operating principle of the presented tunable inductor can be explained on the basis of an integrated transformer configuration, as shown in Fig. 1. The primary coil is the coil whose inductance needs to be controlled. The secondary coil is short circuited and magnetically coupled to the primary one. The magnetic flux linkage between the coils induces eddy currents in the secondary coil. When the magnetic coupling between the inductors is changed, the equivalent inductance seen at the primary port is also changed. This is the main concept behind this tuning approach. However, existing studies have only considered the case where the two coils are identical. Here we analyze for the first time the generalized equivalent circuit of two different coils and investigate the associated design methodology to attain an optimal performance. In addition, we perform high-frequency full-wave simulations with Ansoft's High Frequency Structure Simulator (HFSS) and mechanical simulations with ANSYS to predict the performance of the proposed tunable inductor structure

Electrothermal Actuator

Electrothermal actuators are used for moving secondary short circuit loop wrt primary because simple fabrication, low actuation volts, lack of pull in instability.

Electrothermal actuator working

• It composed of two bimorph (Ti/SiO2)actuator arms anchored on substrate.

• These arms support the short circuited secondary inductor.

• Applied voltage between two anchors induces a current flow on Ti layer resulting in Joules heating and bimorph bends down. It is because of fact that Ti has greater value for the coefficient of thermal expansion than SiO2.

In this tunable inductor, we control the magnetic coupling between the two coils by controlling their relative distance and overlap area. In this technique, a large displacement (>100um) is critical in achieving a significant variation in the magnetic coupling coefficient that leads to a large inductance tuning range. To accomplish a large vertical displacement by MEMS actuation, we adopt an electrothermal actuator due to its simple fabrication process, low actuation voltage, and lack of pull-in instability