Tunable spiral inductors

Abstract
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.
Introduction

MEMS are miniaturized device / array of devices combining mechanical and electrical components fabricated using IC batch production techniques. RF MEMS components are used for RF & MW and millimeter wave circuits. They are small devices of feature size of micron order. Fabricated by nano and micro technology. RF micro-electromechanical systems (MEMS) have been a rapidly growing field within the MEMS industry. In particular, a wide range of RF MEMS switches, varactors, and high- inductors have been developed and demonstrated over the last two decades. However, few solutions have been presented for obtaining tunable (or variable) MEMS inductors.
The approaches reported in the literature today for realizing a tunable MEMS inductor include: 1) control of the magnetic-core-material properties by changing the core permeability or displacing the core material; 2) usage of MEMS switches to digitally control the winding; 3) control of the mutual inductance between the turns of the inductor itself; and 4) control of the mutual inductance between the primary inductor and a separate short-circuited inductor.
Each of the demonstrated techniques has serious shortcomings that have not allowed RF designers to utilized tunable inductors in their designs. Changing the core permeability and consumes has resulted in very low quality factors significant amount of dc power (15-300 mW). In addition, movement of the core material requires large and complex actuators. Switchable inductors are limited by the number of switches utilized. Few switches result in a limited set of available values, while many switches drastically drop the quality of the inductor and result in large and narrowband circuits. Controlling the mutual inductance between the turns of the inductor itself has shown very limited inductance variations ( 18%). The fourth technique relies on coupling the inductor to be tuned (primary inductor) to a short-circuited inductor (secondary inductor) and controlling their coupling coefficient. In [4], both the primary and secondary inductors are implemented as single-turn loops. An electrostatic actuator changes the position of the short-circuited loop. This design exhibits a tuning ratio of 1.54:1 and requires very high electrostatic actuation voltages (150 V) and many complex fabrication steps. Besides this tuning ratio, no other information (e.g., quality factor and bandwidth) is given in [4]. The reported results show high inductance tuning ratios of 2:1 and good quality factors of 15-21 for the entire tuning range. However, these are not integrated solutions because they rely on manual movement for reaching the required displacements. In addition, no information is provided in any of these papers on how the inductance and resistance of the short-circuited inductor affect the critical RF parameters of the tunable inductor. Consequently improved designs and implementation methodologies are needed for achieving simple structures with high and continuous tuning ranges, high quality factors, large bandwidth, and low occupied chip area.
Here, measured and theoretical results for an optimized tunable MEMS spiral inductor with an integrated large-displacement electro-thermal actuator are analyzed. The tunable MEMS inductor utilizes an integrated transformer configuration, which is composed of two magnetically coupled inductors. Tunability is achieved by varying the magnetic coupling coefficient (k) that is dominated by the distance between the two inductors. Results derived by a simple equivalent circuit, full-wave simulations, and measurements indicate that optimal RF performance requires minimized resistive losses on the secondary inductor.