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This work focuses on the analysis and application of such passive devices. From 
Maxwell’s equations, an accurate and efficient technique is developed to model the device 
over a wide frequency range. In particular, we demonstrate techniques for calculating 
the loss when such devices are fabricated in the vicinity of conductive substrates such as 
silicon. Energy couples to a conductive substrate through several mechanisms, such as 
through electrically induced displacement and conductive currents, and by magneticall |   
 
 
 
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