Multilayer Liquid-Metal Stretchable Power Inductors

July 17, 2014 by Jeff Shepard

Highly-stretchable versions of two multilayer inductor topologies, the double planar coil and solenoid, were successfully demonstrated using liquid galinstan in fluidic channels. The research team led by Dr. Nathan Lazarus with the Oak Ridge Associated Universities Fellowship Program, US Army Research Laboratory modeled the electrical behavior upon the application mechanical strain for the inductor topologies and compared with measured results extracted from strain testing of each inductor. Liquid metals are ideally-suited for creating low-resistance traces able to undergo large mechanical strains. In this work, multilayer fluidic channels in soft silicone were used to create two inductor topologies, a solenoid and a double planar coil, based on the liquid metal galinstan, an alloy of gallium, indium and tin. Electromechanical models were developed for the inductance upon stretching for each inductor, finding that the double planar coil has lower strain sensitivity in each direction than the solenoid.

A three-turn double planar coil and six-turn solenoid, with unstretched inductances of approximately 250 nH and 55 nH respectively, were fabricated and tested using custom tensile and compressive strain testing setups and compared with the analytical model. The double planar coil was found to increase in inductance when stretched in either in-plane axes, with a measured rise of approximately 40% for 100% strain. The solenoid decreased in inductance by 24% for 100% strain along the core direction, and increased by 50% for the same strain along the core width.

The inductors were fabricated using a method for creating multilayer fluidic channels using 3D printed molds and tested using custom tensile and compressive strain testing setups. Galinstan and another liquid gallium alloy, eutectic gallium indium (EGaIn), are both far less toxic than mercury (which has been used for similar applications in the past) and have electrical conductivities approximately three times higher. Galinstan remains liquid to a lower temperature than EGaIn (melting points of −19 degrees C and 15.5 degrees C respectively), and would be better-suited to creating a stretchable inductor that might be exposed to an uncontrolled environment.

For applications such as wireless power, the resistance of the device is a very important specification, and will directly impact the power losses in the inductor. As the inductor geometry changes during stretching, the total resistance of the traces will also change. Resistive sensors based on liquid metal deformation in elastomer channels have been previously demonstrated for measuring pressure and strain. The low frequency resistance was also measured using the impedance analyzer for each inductor (figure 10), with unstrained resistances between 100 and 250 mΩ.

The unstrained quality factors at 1 MHz were 8.93 and 9.36 for the X and Y double planar coil and 2.31 and 3.58 for the X and Y solenoid respectively. At a stretch of 2, the quality factors at 1 MHz were 4.76 and 3.53 for the X and Y double planar coil and 3.49 and 2.29 for the X and Y solenoid respectively. This resistance was higher than expected from the resistivity of galinstan (3 × 10−7 Ω m). As calculated from the geometry and bulk resistivity of galinstan, the double planar coil and solenoid inductors, including the connecting traces, were expected to have resistances of 80 and 48 mΩ respectively. Galinstan is known to alloy easily with most other metals, including copper, which could result in a high contact resistance. The bonding process, with partially cured silicone pressed onto the top of the channel, may also have reduced the cross-sectional area.

Both tensile stretching in the X and Y plane and compression in Z were found to result in increases in resistance for the solenoid and double planar coil. The resistance was also calculated using the expected trace dimensions during deformation and bulk resistivity of galinstan; a fixed resistance was also fitted in each case for the unstrained resistance to account for the contact resistance. The resistivity model was found to be accurate for small strains (up to approximately 20–30%), above which the measured resistance was found to increase significantly faster than was predicted. This deviation is believed to be primarily due to the redistribution of the liquid metal during stretching.

For the two compression tests, the pressure applied on the device pushed a portion of the galinstan out into the electrode region, resulting in visible bulging for a stretch below approximately 0.8. This liquid redistribution and resulting increase in resistance may result from the possible collapse of the channels mentioned in . Although the effects were less visible for the tensile tests, the very high stretch applied may have also caused partial pinching off of the liquid metal channels in certain areas.

Since the inductance of a given inductor is heavily geometry dependent, both types of inductors experienced a large change in inductance upon stretching, undesirable for many applications that require consistent performance such as filtering, communication or wireless power. Future efforts will be focused on developing methods for creating usable circuitry with a highly variable stretchable inductor, either through a counteracting stretchable capacitor or through adaptive circuit techniques. One possible technique is to use capacitor switching to tune the circuit resonant frequency, a method that has been previously demonstrated for compensating for varying coupling and circuit parameters in an implanted wireless power coil.