Low-Power MEMS-Based Pierce Oscillator Using a 61-MHz Capacitive-Gap Disk Resonator.

A 61-MHz Pierce oscillator constructed in 0.35- [Formula: see text] CMOS technology and referenced to a polysilicon surface-micromachined capacitive-gap-transduced wine-glass disk resonator has achieved phase noise marks of -119 dBc/Hz at 1-kHz offset and -139 dBc/Hz at far-from-carrier offsets. When divided down to 13 MHz, this corresponds to -132 dBc/Hz at 1-kHz offset from the carrier and -152 dBc/Hz far-from-carrier, sufficient for mobile phone reference oscillator applications, using a single MEMS resonator, i.e., without the need to array multiple resonators. Key to achieving these marks is a Pierce-based circuit design that harnesses a MEMS-enabled input-to-output shunt capacitance more than 100× smaller than exhibited by macroscopic quartz crystals to enable enough negative resistance to instigate and sustain oscillation while consuming only [Formula: see text] of power-a reduction of  âˆ¼ 4.5× over previous work. Increasing the bias voltage of the resonator by 1.25 V further reduces power consumption to [Formula: see text] at the cost of only a few decibels in far-from-carrier phase noise. This oscillator achieves a 1-kHz-offset figure of merit (FOM) of -231 dB, which is now the best among published chip-scale oscillators to date. A complete linear circuit analysis quantifies the influence of resonator input-to-output shunt capacitance on power consumption and predicts further reductions in power consumption via reduction of electrode-to-resonator transducer gaps and bond pad sizes. The demonstrated phase noise and power consumption posted by this tiny MEMS-based oscillator are attractive as potential enablers for low-power "set-and-forget" autonomous sensor networks and embedded radios.

RF Channel-Select Micromechanical Disk Filters-Part II: Demonstration.

This Part II of a two-paper sequence presents fabrication and measurement results for a micromechanical disk-based RF channel-select filter designed using the theory and procedure of Part I. Successful demonstration of an actual filter required several practical additions to an ideal design, including the introduction of a 39-nm-gap capacitive transducer, voltage-controlled frequency tuning electrodes, and a stress relieving coupled array design, all of which combine to enable a 0.1% bandwidth 223.4-MHz channel-select filter with only 2.7 dB of in-band insertion loss and 50-dB rejection of out-of-band interferers. This amount of rejection is more than 23 dB better than a previous capacitive-gap transduced filter design that did not benefit from sub-50-nm gaps. It also comes in tandem with a 20-dB shape factor of 2.7 realized by a hierarchical mechanical circuit design utilizing 206 micromechanical circuit elements, all contained in an area footprint of only [Formula: see text]. The key to such low insertion loss for this tiny percent bandwidth is Q 's >8800 supplied by polysilicon disk resonators employing for the first time capacitive transducer gaps small enough to generate coupling strengths of Cx/Co  âˆ¼  0.1 %, which is a 6.1× improvement over previous efforts. The filter structure utilizes electrical tuning to correct frequency mismatches due to process variations, where a dc tuning voltage of 12.1 V improves the filter insertion loss by 1.8 dB and yields the desired equiripple passband shape. Measured filter performance, both in- and out-of-channel, compares well with predictions of an electrical equivalent circuit that captures not only the ideal filter response, but also parasitic nonidealities that distort somewhat the filter response.

RF Channel-Select Micromechanical Disk Filters-Part I: Design.

This Part I of two papers introduces a design flow for micromechanical RF channel-select filters with tiny fractional bandwidths capable of eliminating strong adjacent channel blockers directly after the antenna, hence reducing the dynamic range requirement of subsequent stages in an RF front-end. Much like VLSI transistor circuit design, the mechanical circuit design flow described herein is hierarchical with a design stack built upon vibrating micromechanical disk building blocks capable of Q 's exceeding 10 000 that enable low-filter passband loss for tiny fractional bandwidths. Array composites of half-wavelength coupled identical vibrating disks constitute a second level of hierarchy that reduces the filter termination impedance. A next level of hierarchy couples array composites with full-wavelength beams to affect fully balanced differential operation. Finally, identical differential blocks coupled with quarter-wavelength beams generate the desired passband. Part II of this study corroborates the efficacy of this design hierarchy via experimental results that introduce a 39-nm-gap capacitive transducer, voltage-controlled frequency tuning, and differential operation toward demonstration of a 0.1% bandwidth, 223.4-MHz channel-select filter with only 2.7 dB of in-band insertion loss and 50 dB of stopband rejection.

A negative-capacitance equivalent circuit model for parallel-plate capacitive-gap-transduced micromechanical resonators.

A small-signal equivalent circuit for parallel-plate capacitive-gap-transduced micromechanical resonators is introduced that employs negative capacitance to model the dependence of resonance frequency on electrical stiffness in a way that facilitates circuit analysis, that better elucidates the mechanisms behind certain potentially puzzling measured phenomena, and that inspires circuit topologies that maximize performance in specific applications. For this work, a micromechanical disk resonator serves as the vehicle with which to derive the equivalent circuits for both radial-contour and wine-glass modes, which are then used in circuit simulations (via simulation) to match measurements on actual fabricated devices. The new circuit model not only correctly predicts the dependence of electrical stiffness on the impedances loading the input and output electrodes of parallel-plate capacitive- gap-transduced micromechanical device, but does so in a visually intuitive way that identifies current drive as most appropriate for applications that must be stable against environmental perturbations, such as acceleration or power supply variations. Measurements on fabricated devices confirm predictions by the new model of up to 4× improvement in frequency stability against dc-bias voltage variations for contour- mode disk resonators as the resistance loading their ports increases. By enhancing circuit visualization, this circuit model makes more obvious the circuit design procedures and topologies most beneficial for certain mechanical circuits, e.g., filters and oscillators.

1.52-GHz micromechanical extensional wine-glass mode ring resonators.

Vibrating polysilicon micromechanical ring resonators, using a unique extensional wine-glass-mode shape to achieve lower impedance than previous UHF resonators, have been demonstrated at frequencies as high as 1.2 GHz with a Q of 3,700, and 1.52 GHz with a Q of 2,800. The 1.2-GHz resonator exhibits a measured motional resistance of 1 MOmega with a dc-bias voltage of 20 V, which is 2.2 times lower than the resistance measured on radial contourmode disk counterparts at the same frequency. The use of larger rings offers a path toward even lower impedance, provided the spurious modes that become more troublesome as ring size increases can be properly suppressed using methods described herein. With spurious modes suppressed, the high-Q and low-impedance advantages, together with the multiple frequency on-chip integration advantages afforded by capacitively transduced micromechanical resonators, make this device an attractive candidate for use in the front-end RF filtering and frequency generation functions needed by wireless communication devices.

MEMS technology for timing and frequency control.

An overview on the use of microelectromechanical systems (MEMS) technologies for timing and frequency control is presented. In particular, micromechanical RF filters and reference oscillators based on recently demonstrated vibrating on-chip micromechanical resonators with Q's > 10,000 at 1.5 GHz are described as an attractive solution to the increasing count of RF components (e.g., filters) expected to be needed by future multiband, multimode wireless devices. With Q's this high in on-chip abundance, such devices might also enable a paradigm shift in the design of timing and frequency control functions, where the advantages of high-Q are emphasized, rather than suppressed (e.g., due to size and cost reasons), resulting in enhanced robustness and power savings. Indeed, as vibrating RF MEMS devices are perceived more as circuit building blocks than as stand-alone devices, and as the frequency processing circuits they enable become larger and more complex, the makings of an integrated micromechanical circuit technology begin to take shape, perhaps with a functional breadth not unlike that of integrated transistor circuits. With even more aggressive three-dimensional MEMS technologies, even higher on-chip Q's are possible, such as already achieved via chip-scale atomic physics packages, which so far have achieved Q's > 10(7) using atomic cells measuring only 10 mm3 in volume and consuming just 5 mW of power, all while still allowing atomic clock Allan deviations down to 10(-11) at one hour.

1.156-GHz self-aligned vibrating micromechanical disk resonator.

A new fabrication methodology that allows self-alignment of a micromechanical structure to its anchor(s) has been used to achieve vibrating radial-contour mode polysilicon micromechanical disk resonators with resonance frequencies up to 1.156 GHz and measured Q's at this frequency >2,650 in both vacuum and air. In addition, a 734.6-MHz version has been demonstrated with Q's of 7,890 and 5,160 in vacuum and air, respectively. For these resonators, self-alignment of the stem to exactly the center of the disk it supports allows balancing of the resonator far superior to that achieved by previous versions (in which separate masks were used to define the disk and stem), allowing the present devices to retain high Q while achieving frequencies in the gigahertz range for the first time. In addition to providing details on the fabrication process, testing techniques, and experimental results, this paper formulates an equivalent electrical circuit model that accurately predicts the performance of these disk resonators.