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The Resonant Body Transistor (RBT) and Oscillator (RBO)

The Resonant Body Transistor (RBT) consists of a sense transistor embedded directly into a resonator body. This is basically a Si based di-electrically transduced Nano Electro Mechanical (NEM) resonator. RBT combines the benefits of high Q factor of the bar resonator and the excellent sensing capability of field effect transistor into a single device. Crystal Oscillators, which are used for stable clock generation, suffer from inherent capacitive feed through at GHz frequencies.RBT can operate in the 1GHz - 15 GHz frequency range with immunity from capacitive feed-through. RBT has the potential to be integrated into standard CMOS for on chip clock generation and RF design. With proper feedback RBT can operate as a Resonant Body Oscillator (RBO). In this work we developed a circuit model of the RBT and designed an RBO.

Fig : Physical Structure of the RBT [1].

Circuit Model of RBT

The  RBT  can be modeled as a 4 terminal circuit component. Three of the terminals  (Gate 1, Drain, Source) are those of a conventional MOSFET and the fourth terminal represents the Drive gate. The electromechanical trans-conductance , ga , transforms the applied AC voltage at gate 2 into an output current at drain through the resonant branch. The parasitic feed-through is modeled with trans-conductance gmb.

Model Response

                                                           Fig: (a) Amplitude response  (b) Phase response of output voltage at drain.

The output current at drain is given by,

Fig: Transient drain current.

The Resonant Body Oscillator (RBO)

The RBT has both frequency selectivity and FET amplification embedded into itself. By closing the drain and drive gate with proper feedback, the RBT can mimic the structure of an Oscillator . The RBO does not require a crystal and it is almost immune to feed-through issues at 10-15GHz range.

The intrinsic gain of RBT is not enough to satisfy the Barkhausen criteria of unity  loop gain. To enhance the gain to unity, further amplification is required. A possible solution is to add amplifier stages in the feedback path. The cascode tuned amplifier is a suitable option.

Fig: Cascode tuned amplifier.

Fig: Schematic of RBO with Biasing

Fig: Frequency response of RBT with amplifiers.

Fig: Developed Oscillation.


Technology: 45nm  (Vdd =1.1 V)

Frequency of Oscillation: 11.13 GHz

Power Dissipation: 5.02 mW

Team Members

Mehdi Sadi

Kaushik Majumder

Prof. Mircea Stan


Hybrid MEMS Lab, MIT




[1] Marathe, R.; Wang, W.; Weinstein, D.; , "Si-based unreleased hybrid MEMS-CMOS resonators in 32nm technology," Micro Electro Mechanical Systems (MEMS), 2012 IEEE 25th International Conference on , vol., no., pp.729-732, Jan. 29 2012-Feb. 2 2012.