Analysis and Design of Coupled Inductive Bridges for Magnetic Sensing Applications

This paper presents the analysis and design of a novel magnetic sensor. We study the underlying physics of inductance shift sensors as a special case of the broader family of magnetic energy deviation sensors. The result is a quantitative definition of performance metrics with all assumptions and approximations explicitly stated. This analysis is then used to design a modified ac Wheatstone bridge that uses two inductor-pairs in a cross-coupled configuration, to half its size and double its transducer gain while maintaining a fully differential structure with a matched frequency response. A proof-of-concept sensor was fabricated with peripheral circuitry in a 65-nm bulk CMOS process to operate between 770 and 1450 MHz with an effective sensing area of 200 \mu \text{m}\,\,\times 200 \mu \text{m}. The new bridge sensor is fully characterized at a frequency of 770 MHz and demonstrates a reliable and continuous detection of 4.5- \mu \text{m} iron-oxide magnetic beads over time periods longer than 30 min, appreciably longer than previously reported works.