Modeling, fabrication and testing of MEMS tunable inductors varied with piezoelectric actuators

Modeling, fabrication and measurements of tunable inductors are presented where inductance tuning is achieved through mechanical displacement, by piezoelectric actuation, of mutually-coupled coils. The modified Greenhouse method is utilized as a modeling tool to predict the inductance variations as a function of both translation and angular displacement, where coils and traces which are arbitrarily oriented with respect to one another are considered. The use of this modeling approach is verified through experimental results where electrical measurements of inductances are compared with the modeled inductances. The inductance model compares well with the measurements and within 10% of the measured inductance with a 3% mean error. In addition, the impact of the interconnect widths on tunable inductor performances is assessed for both negatively and positively coupled tunable inductor cases, where devices with interconnect widths ranging between 10 and 40 mu m are considered. Tuning ratios as high as similar to 3.9:1 were measured for the negatively-coupled coil designs with 18 V actuation; this corresponds to minimum and maximum quality factors of 5.72 (at 4.05 GHz with a 2.80 nH inductance) and 14.91 (at 2.25 GHz with 10.86 nH inductance), respectively. For the positively coupled inductors, tuning ratios of similar to 1.2:1 resulted with inductance and peak quality factors of 7.70 nH and similar to 18 (3.69 GHz), respectively. With 18 V actuation, these values tune to 6.57 nH with a Q similar to 18 (4.46 GHz). Residual poling stress was found to limit the practical tuning ratio to similar to 1.8:1 for the negatively coupled coils.