Office of Technology Transfer – University of Michigan

Quality Factor Boosting Via Mechanically Coupled Arraying

Technology #3716

Questions about this technology? Ask a Technology Manager

Download Printable PDF

Clark T.C. Nguyen
Managed By
Keith Hughes
Assistant Director, Physical Sciences & Engineering 734-764-9429
Patent Protection
US Patent Pending


To date, oscillators comprised of several mechanically-coupled resonators combined with sustaining transistor circuits have been demonstrated with phase noise performance commensurate with GSM cellular phone specifications for reference oscillators. These oscillators owe their performance largely to the sheer Q of their constituent resonators. However, there are other applications, such as filters, where both high Q and low impedance are desirable. Unfortunately, these two qualities have so far not been readily available simultaneously in any single CAD-definable micromechanical resonator design. So far, only capacitively-transduced resonators have achieved Q’s over 50,000 at UHF frequencies, but with high impedance. On the other hand, piezoelectric resonators with CADdefined frequencies have achieved impedances below 100 Ω, but only with Q’s in the single-digit thousands. A method for combining the most attractive individual characteristics of these devices to simultaneously obtain low impedance from the piezo- device and high-Q from the capacitive ones is highly desirable.


Researchers at University of Michigan developed a mechanical circuit-based technology that boosts the function of a low Q vibrating resonator by embedding it into a mechanically-coupled array of higher Q resonators. This raises the functional Q by a factor approximately equal to the number of resonators in the array. The availability of such a circuit-based Q-enhancement technique has far reaching implications, especially considering the possibility of raising the functional Q of a piezoelectric resonator by merely mechanically coupling it to an array of much higher Q capacitively-transduced ones to simultaneously obtain the most attractive characteristics of both technologies: low impedance from the piezo-device and high-Q from the capacitive ones.

Applications and Advantages


  • MEMS, Micromechanical circuit


  • Q’s boosted almost 9 times
  • Enhances the manufacturing repeatability of micromechanical resonator-based products