Patent Publication Number: US-8981875-B2

Title: Tunable MEMS resonators

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 12/488,404, filed Jun. 19, 2009 and scheduled to issue on Jan. 29, 2013 as U.S. Pat. No. 8,362,853. The disclosure of U.S. application Ser. No. 12/488,404 is hereby incorporated by reference in its entirety. 
    
    
     FIELD 
     The present disclosure relates generally to electronics, and more specifically to micro-electro-mechanical system (MEMS) resonators. 
     DESCRIPTION OF THE RELATED TECHNOLOGY 
     MEMS is a technology used to form miniature electro-mechanical devices with mechanical moving parts. These devices may be used to implement various radio frequency (RF) circuit components such as resonators, switches, variable capacitors (varactors), inductors, etc. MEMS devices may have certain advantages over RF circuit components fabricated in other manners, such as higher quality factor (Q), lower insertion loss, better linearity, etc. 
     A MEMS resonator is a MEMS device that can resonate at a particular frequency, which may be referred to as the resonance frequency. A MEMS resonator may be implemented using various structures known in the art. A particular structure and suitable dimensions may be selected to obtain the desired resonance frequency for the MEMS resonator. 
     A MEMS resonator may be used for a low-power application with a small RF signal. In this case, the resonance frequency of the MEMS resonator may not be affected too much by the RF signal. However, the RF signal may be large for a high-power application, such as a transmitter of a wireless communication device. If a large RF signal is applied to the MEMS resonator, then the resonance frequency of the MEMS resonator may be varied by the RF signal, which is typically undesirable. A MEMS resonator that can handle a large RF signal would be desirable. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1 and 2  show cross-sectional views of a tunable MEMS resonator. 
         FIGS. 3 and 4  show different cavity shapes for the tunable MEMS resonator. 
         FIGS. 5 and 6  show two exemplary designs of a movable plate for the tunable MEMS resonator. 
         FIGS. 7 and 8  show use of spacers to prevent shorting of the movable plate. 
         FIG. 9  shows a tunable MEMS resonator with multiple movable plates. 
         FIG. 10  shows an array of four tunable MEMS resonators. 
         FIG. 11  shows a block diagram of a wireless communication device. 
         FIG. 12  shows a tunable filter implemented with tunable MEMS resonators. 
         FIG. 13  shows frequency response of the tunable filter. 
         FIG. 14  shows an oscillator implemented with tunable MEMS resonators. 
         FIG. 15  shows a process for operating a MEMS resonator. 
     
    
    
     DETAILED DESCRIPTION 
     The word “exemplary” is used herein to mean “serving as an example, instance, or illustration.” Any design described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other designs. 
     Several exemplary designs of tunable MEMS resonators having adjustable resonance frequency and capable of handling large RF signals are described herein. A tunable MEMS resonator is a MEMS resonator having a resonance frequency that can be varied by adjusting a mechanical moving part with a direct current (DC) voltage. A tunable MEMS resonator may include two or more terminals (or electrodes). An RF signal may be applied to a first terminal, and a DC voltage may be applied to a second terminal. The DC voltage may mechanically move a plate within the MEMS resonator, which may then adjust the resonance frequency of the MEMS resonator. The tunable MEMS resonators described herein may be used for various circuits such as tunable filters, oscillators, etc. The tunable MEMS resonators may also be used for high-power applications such as a transmitter of a wireless communication device. The tunable MEMS resonators may be able to handle a large RF signal and may have a small change in resonance frequency due to the large RF signal. 
       FIG. 1  shows a cross-sectional view of an exemplary design of a tunable MEMS resonator  100  capable of handling a large RF signal. Tunable MEMS resonator  100  includes a bottom part  110  and a top part  160 .  FIG. 1  shows top part  160  being disengaged from bottom part  110 . 
       FIG. 2  shows a cross-sectional view of tunable MEMS resonator  100 , with top part  160  being mated to bottom part  110 . This is the configuration during normal operation. 
       FIG. 3  shows a top view of an exemplary design of tunable MEMS resonator  100  in  FIGS. 1 and 2  with a square cavity  180   a . The cross-sectional views in  FIGS. 1 and 2  are taken along line X-X′ in  FIG. 3 . Greater layout efficiency may be achieved with a square cavity, and more MEMS resonators may be fabricated in a given area with the square cavity. The quality factor (Q) of MEMS resonator  100  may be improved by having rounded corners for square cavity  180   a  and rounded corners for a post  170   a.    
       FIG. 4  shows a top view of another exemplary design of tunable MEMS resonator  100  in  FIGS. 1 and 2  with a circular cavity  180   b . The cross-sectional views in  FIGS. 1 and 2  are taken along line X-X′ in  FIG. 4 . Higher Q may be obtained for MEMS resonator  100  with a circular cavity. 
     Referring back to  FIG. 1 , bottom part  110  includes a substrate  120  upon which various structures, layers, and conductors may be formed. Substrate  120  may be glass, silicon, or some other material. Glass may have better performance as well as lower cost. A conductor line  122  may be formed on top of substrate  120  and may be used to carry an RF signal. A conductor line  124  may also be formed on top of substrate  120  and may be used to carry a DC voltage. Conductor line  124  may couple to an electrode  134 , which may be formed on the top surface of substrate  120  over a center portion of bottom part  110 . Electrode  134  may also be referred to as a biasing electrode, a pad, etc. Lines  122  and  124  and electrode  134  may be formed with metal or some other conductive material. A dielectric layer  128  may cover all or part of the top surface of substrate  120 . A metal layer  130  may be formed on top of dielectric layer  128  over most of the top surface of substrate  120 , except for the center portion of bottom part  110 . 
     A moveable plate  140  may be formed over electrode  134  and may be separated from electrode  134  by a gap  136 . Plate  140  may be implemented with a MEMS switch, as described below, and may be formed with metal or some other conductive material. Plate  140  may also be referred to as a mechanical membrane, etc. 
     Top part  160  includes a cavity  180 , which may be formed around a post  170  ( 170   a ,  170   b ) and may be surrounded by sidewalls  172  ( 172   a ,  172   b ). Post  170  may be aligned with moveable plate  140  in bottom part  110 . The dimension of cavity  180  may be selected based on the desired resonance frequency for tunable MEMS resonator  100 . The bottom surface of top part  160  may be covered by a metal layer  190 . 
     An opening  142  may be formed in metal layer  130  over one end of conductor line  122  in a portion of cavity  180 . RF energy from cavity  180  may be coupled via opening  142  to line  122 . The RF signal on line  122  may be provided to other circuit components to which tunable MEMS resonator  100  is connected. 
     Tunable MEMS resonator  100  operates as follows. Top part  160  may be mated to bottom part  110 , as shown in  FIG. 2 , during normal operation. Cavity  180  is coated with metal, and energy is trapped inside the cavity. Since cavity  180  has low loss, the energy decays slowly. The resonant frequency within cavity  180  may be determined by the dimension of the cavity. 
     A variable capacitor (varactor)  192  may be formed between the bottom of post  170  and moveable plate  140 . The resonance frequency of tunable MEMS resonator  100  may be adjusted or tuned by varying the capacitance of varactor  192 . A DC voltage may be applied to electrode  134  on substrate  120  to cause moveable plate  140  to move down from its normal resting position shown in  FIGS. 1 and 2 . A larger DC voltage may cause plate  140  to move down more toward electrode  134 , which may then result in less capacitance for varactor  192  and hence a higher resonance frequency for MEMS resonator  100 . Conversely, a smaller DC voltage (e.g., zero Volts) may cause plate  140  to be near its resting position, which may then result in more capacitance for varactor  192  and hence a lower resonance frequency for MEMS resonator  100 . 
     The resonance frequency of tunable MEMS resonator  100  may be controlled in various manners. The width a, length b, and height h of cavity  180  may be selected to obtain the desired resonance frequency. Table 1 shows two exemplary designs of tunable MEMS resonator  100 , with dimension being given in millimeters (mm) and resonance frequency being given in megahertz (MHz). Other resonance frequencies and Q may be obtained with other dimensions for cavity  180 . 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                 Resonance 
                   
               
               
                 Width a 
                 Length b 
                 Height h 
                 frequency f o   
                 Q 
               
               
                   
               
             
            
               
                 3.0 mm 
                 3.0 mm 
                 1.5 mm 
                 1630 MHz 
                 200 
               
               
                 3.0 mm 
                 3.0 mm 
                 1.0 mm 
                 1990 MHz 
                 170 
               
               
                   
               
            
           
         
       
     
     Varactor  192  may be designed to obtain the desired nominal resonance frequency. Cavity  180  may be filled with a dielectric material to manipulate (e.g., lower) the resonance frequency. Multiple posts may also be formed within cavity  180  to obtain the desired resonance frequency. Each post may or may not have an associated movable plate forming a varactor for that post. 
     The resonance frequency of tunable MEMS resonator  100  may be varied by mechanically moving plate  140  with the DC voltage, which may then vary the capacitance of varactor  192 . The tuning range of MEMS resonator  100  is the range of resonance frequencies achievable for the MEMS resonator. The tuning range may be dependent on the design of varactor  192 . 
       FIG. 5  shows an exemplary design of movable plate  140  within tunable MEMS resonator  100  in  FIGS. 1 to 4 . In this exemplary design, movable plate  140  is implemented with an MEMS switch having a cantilever structure. An anchor  144  may be formed with a dielectric material or a conductive material on one side of the center portion of bottom part  110 . Movable plate  140  may then be formed over anchor  144  and may be connected to a metal layer. Movable plate  140  may act as a cantilever that may be mechanically moved toward electrode  134  by applying a DC voltage to electrode  134 . 
     The distance between movable plate  140  and dielectric layer  128  may be denoted as g. The distance between movable plate  140  and metal layer  190  covering post  170  may be denoted as d. A maximum capacitance C max  may be obtained with movable plate  140  at its resting position (as shown in  FIG. 5 ), which is a distance of d from metal layer  190 . A minimum capacitance C min  may be obtained with movable plate  140  moved against dielectric layer  128 , which is a distance of d+g from metal layer  190 . The maximum and minimum capacitance may be expressed as: 
     
       
         
           
             
               
                 
                   
                     
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                     = 
                     
                       
                         
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                       d 
                     
                   
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                   Eq 
                   ⁢ 
                   
                       
                   
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                     ( 
                     1 
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                         n 
                       
                     
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                         g 
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                   Eq 
                   ⁢ 
                   
                       
                   
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                     ( 
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     where ∈ 0  is a dielectric constant for air, ∈ r  is a dielectric constant for a dielectric material between plate  140  and metal layer  190  (not shown in  FIG. 5 ), and A is the area of plate  140 . 
     A capacitance tuning range may be expressed as: 
     
       
         
           
             
               
                 
                   
                     
                       C 
                       
                         ma 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         x 
                       
                     
                     
                       C 
                       
                         m 
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                         n 
                       
                     
                   
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                           g 
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                         d 
                       
                       d 
                     
                     . 
                   
                 
               
               
                 
                   Eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     3 
                     ) 
                   
                 
               
             
           
         
       
     
     If the space between plate  140  and metal layer  190  is filled with air (i.e., no dielectric material), then ∈ r =1, and the capacitance tuning range may be dependent on distances d and g. A larger capacitance tuning range may be obtained with (i) a larger distance g between movable plate  140  and dielectric layer  128  and/or (ii) a smaller distance d between movable plate  140  and metal layer  190 . A larger capacitance tuning range may also be obtained by filling the space between plate  140  and metal layer  190  with a dielectric material having ∈ r &gt;1. 
       FIG. 6  shows another exemplary design of movable plate  140  within tunable MEMS resonator  100  in  FIGS. 1 to 4 . In this exemplary design, movable plate  140  is implemented with an MEMS switch having a bridge structure. The bridge structure may also be referred to as a fixed-fixed beam structure. Two anchors  146  and  148  may be formed on two sides of the center portion of bottom part  110 . Movable plate  140  may then be formed over anchors  146  and  148  and may act as a bridge that may be mechanically moved toward electrode  134  by applying a DC voltage to electrode  134 . 
     The distance between movable plate  140  and dielectric layer  128  may be denoted as g. The distance between movable plate  140  and metal layer  190  covering post  170  may be denoted as d. The maximum capacitance C max  may be obtained with movable plate  140  at its resting position (as shown in  FIG. 6 ), and the minimum capacitance C min  may be obtained with movable plate  140  moved against dielectric layer  128 . The maximum and minimum capacitance may be expressed as shown in equations (1) and (2), respectively. 
       FIGS. 5 and 6  show two exemplary designs of movable plate  140  to enable tuning of MEMS resonator  100 . Movable plate  140  may also be implemented with other MEMS switches and/or other MEMS structures that can mechanically move to vary the capacitance of varactor  192 . 
     A larger capacitance tuning range may be desirable in order to obtain a larger frequency tuning range for MEMS resonator  100 . As shown in equations (1) to (3), a larger capacitance tuning range may be achieved with a smaller distance d between movable plate  140  in bottom part  110  and metal layer  190  in top part  160 . Bottom part  110  and top part  160  may be fabricated separately and mated together, as shown in  FIGS. 1 and 2 . Several schemes may be used to obtain a small distance d between movable plate  140  and metal layer  190  while preventing movable plate  140  from making contact with metal layer  190 . 
       FIG. 7  shows an exemplary design of using dielectric spacers to prevent movable plate  140  from contacting metal layer  190 . In the exemplary design shown in  FIG. 7 , dielectric spacers  182  and  184  may be formed over metal layer  190  on both sides of movable plate  140 . The height z of dielectric spacers  182  and  184  may be selected to be z≧d+g+t, where t is the thickness of movable plate  140 . 
     Dielectric spacers  182  and  184  may be formed over metal layer  190  in top part  160 , as shown in  FIG. 7 . In another exemplary design, dielectric spacers may be formed over metal layer  130  in bottom part  110 . Dielectric spacers may be formed on both sides of movable plate  140 , as shown in  FIG. 7 . In another exemplary design, a dielectric spacer may be formed on only one side of movable plate  140 . 
       FIG. 8  shows another exemplary design of using dielectric spacer to prevent movable plate  140  from contacting metal layer  190 . In the exemplary design shown in  FIG. 8 , a dielectric layer  186  may be formed over metal layer  190  underneath post  170 . The height of dielectric spacer  186  may be selected to be equal to the desired distance d between movable plate  140  and metal layer  190 . 
       FIGS. 7 and 8  show exemplary designs of using dielectric spacer(s) to achieve a small distance between movable plate  140  and metal layer  190  while preventing shorting. A small distance between plate  140  and metal layer  190  without shorting may also be obtained in other manners. 
       FIGS. 1 to 8  show an exemplary design in which a single movable plate  140  is formed under post  170 . In one exemplary design, movable plate  140  may operate as a varactor having a capacitance that may be adjusted in a continuous manner between C min  and C max  with the DC voltage applied to electrode  134 . The resonance frequency of MEMS resonator  100  may be varied by adjusting the capacitance of the varactor. In another exemplary design, movable plate  140  may operate as a varactor having a capacitance that may be switched between C min  and C max  in a digital manner with the DC voltage. 
     There may be a limit on the size of a realizable movable plate, which may be dependent on the MEMS process technology used to fabricate the movable plate. A larger capacitance tuning range and other benefits may be obtained by using multiple movable plates. 
       FIG. 9  shows a top view of an exemplary design of a tunable MEMS resonator  900  with multiple movable plates  940  formed under a post  970 . In general, any number of movable plates  940  may be formed under post  970 . The number of realizable movable plates  940  may be dependent on the size/area of post  970  and the size of each movable plate  940 . Each movable plate  940  may be (i) moved in a continuous manner by varying a DC voltage for that movable plate or (ii) moved in a digital manner by switching the DC voltage for the movable plate. More movable plates  940  may provide a larger capacitance tuning range, which may in turn allow for a larger tuning range for MEMS resonator  900 . More movable plates  940  may also provide more capacitance, which may allow for a lower resonance frequency for MEMS resonator  900 . 
       FIGS. 1 to 4  show a single tunable MEMS resonator  100  that may be used to implement various circuit blocks such as tunable filters. A tunable filter may also be implemented with multiple tunable MEMS resonators to obtain better performance, e.g., greater attenuation of out-of-band signals. 
       FIG. 10  shows a top view of an exemplary design of an array of four tunable MEMS resonators  1000   a ,  1000   b ,  1000   c  and  1000   d , which may be used for a tunable filter. In this exemplary design, each tunable MEMS resonator  1000  has a cavity  1080  formed around a post  1070  and surrounded by sidewalls  1072 . Although not shown in  FIG. 10 , each tunable MEMS resonator  1000  may have one or more movable plates formed over post  1070  and used to adjust the resonance frequency. The surfaces of cavity  1080  for each tunable MEMS resonator  1000  may be covered with metal layers, e.g., as shown in  FIGS. 1 to 4 . Openings  1082  may be formed in the metal layers covering the sidewalls of adjacent MEMS resonators to pass RF signals between these MEMS resonators. An opening  1084  may be formed in the metal layer covering the bottom part of MEMS resonator  1000   c  to couple an input RF signal from a first RF conductor line (not shown in  FIG. 10 ). An opening  1086  may be formed in the metal layer covering the bottom part of MEMS resonator  1000   d  to couple an output RF signal to a second RF conductor line (not shown in  FIG. 10 ). 
     In general, a tunable MEMS resonator may be implemented with a top part and a bottom part. The bottom part may include a movable plate (e.g., implemented with a MEMS switch) and biasing circuits. The top part may have a cavity and a post. The cavity may be filled with a dielectric material to manipulate the resonance frequency. By actuating the movable plate, the field inside the cavity changes, and the resonance frequency and impedance of the cavity would also change. 
     The tunable MEMS resonator utilizes the biasing circuits to actuate the movable plate independent of the RF signal path. This may allow the tunable MEMS resonators to handle high power, e.g., more than 2 Watts. The high resonant field inside the cavity is isolated from the bias circuits and also from the outside environment. This makes it possible to realize high-Q resonance. The movable plate is located inside the cavity whereas the biasing circuits are located outside the cavity. This allows the movable plate to be sealed and avoids packaging issues. This also reduces energy loss due to the biasing circuits. The tunable MEMS resonator may be used in place of film bulk acoustic resonator (FBAR) and surface acoustic wave (SAW) filters and duplexers. 
     The tunable MEMS resonators described herein may be used for various electronics devices such as wireless communication devices, cellular phones, personal digital assistants (PDAs), handheld devices, wireless modems, laptop computers, cordless phones, broadcast receivers, Bluetooth devices, consumer electronics devices, etc. For clarity, the use of the tunable MEMS resonators in a wireless communication device, which may be a cellular phone or some other device, is described below. 
       FIG. 11  shows a block diagram of an exemplary design of a wireless communication device  1100 . In this exemplary design, wireless device  1100  includes a data processor  1110  and a transceiver  1120 . Transceiver  1120  includes a transmitter  1130  and a receiver  1150  that support bi-directional wireless communication. In general, wireless device  1100  may include any number of transmitters and any number of receivers for any number of communication systems and any number of frequency bands. 
     In the transmit path, data processor  1110  processes data to be transmitted and provides an analog output signal to transmitter  1130 . Within transmitter  1130 , the analog output signal is amplified by an amplifier (Amp)  1132 , filtered by a lowpass filter  1134  to remove images caused by digital-to-analog conversion, amplified by a variable gain amplifier (VGA)  1136 , and upconverted from baseband to RF by a mixer  1138 . The upconverted signal is filtered by a filter  1140  to remove images caused by the frequency upconversion, further amplified by a power amplifier (PA)  1142 , routed through a duplexer/switch  1144 , and transmitted via an antenna  1146 . Filter  1140  may be located prior to PA  1142  (as shown in  FIG. 11 ) or after PA  1142 . 
     In the receive path, antenna  1146  receives signals from base stations and provides a received signal, which is routed through duplexer/switch  1144  and provided to receiver  1150 . Within receiver  1150 , the received signal is amplified by a low noise amplifier (LNA)  1152 , filtered by a bandpass filter  1154 , and downconverted from RF to baseband by a mixer  1156 . The downconverted signal is amplified by a VGA  1158 , filtered by a lowpass filter  1160 , and amplified by an amplifier  1162  to obtain an analog input signal, which is provided to data processor  1110 . 
       FIG. 11  shows transmitter  1130  and receiver  1150  implementing a direct-conversion architecture, which frequency converts a signal between RF and baseband in one stage. Transmitter  1130  and/or receiver  1150  may also implement a super-heterodyne architecture, which frequency converts a signal between RF and baseband in multiple stages. 
     A transmit local oscillator (TX LO) generator  1170  receives an oscillator signal from a voltage controlled oscillator (VCO)  1172  and provides a TX LO signal to mixer  1138 . A phase locked loop (PLL)  1174  receives control information from data processor  1110  and provides a control signal to VCO  1172  to obtain the TX LO signal at the proper frequency. A receive LO (RX LO) generator  1180  receives an oscillator signal from a VCO  1182  and provides an RX LO signal to mixer  1156 . A PLL  1184  receives control information from data processor  1110  and provides a control signal to VCO  1182  to obtain the RX LO signal at the proper frequency. 
       FIG. 11  shows an exemplary transceiver design. In general, the conditioning of the signals in transmitter  1130  and receiver  1150  may be performed by one or more stages of amplifier, filter, mixer, etc. These circuit blocks may be arranged differently from the configuration shown in  FIG. 11 . Furthermore, other circuit blocks not shown in  FIG. 11  may also be used to condition the signals in the transmitter and receiver. Some circuit blocks in  FIG. 11  may also be omitted. All or a portion of transceiver  1120  may be implemented on an analog integrated circuit (IC), an RF IC (RFIC), a mixed-signal IC, etc. 
     Data processor  1110  may perform various functions for wireless device  1100 , e.g., processing for transmitted and received data. A memory  1112  may store program codes and data for data processor  1110 . Data processor  1110  may be implemented on one or more application specific integrated circuits (ASICs) and/or other ICs. 
     As shown in  FIG. 11 , a transmitter and a receiver may include various analog circuits. Each analog circuit may be implemented in various manners and may include one or more tunable MEMS resonators described herein. For example, tunable MEMS resonators may be used in filter  1140 , filter  1154 , duplexer  1144 , VCO  1172 , VCO  1182 , etc. 
       FIG. 12  shows a schematic diagram of an exemplary design of a tunable filter  1200  implemented with two tunable MEMS resonators  1220   a  and  1220   b . Tunable filter  1200  may be used for filter  1140 , duplexer  1144 , filter  1154 , and/or other filters in wireless device  1100 . Within tunable filter  1200 , a transformer  1210  models the coupling between an RF conductor and tunable MEMS resonator  1220   a , e.g., models RF opening  142  in  FIG. 1  or RF opening  1084  in  FIG. 10 . Transformer  1210  receives an input signal, Vin, at one end of a primary winding  1212  and has one end of a secondary winding  1214  coupled to node A. The other ends of windings  1212  and  1214  are coupled to circuit ground. Tunable MEMS resonator  1220   a  is coupled between node A and circuit ground. An inductor  1228  models the coupling between tunable MEMS resonators  1220   a  and  1220   b  (e.g., RF opening  1082  in  FIG. 10 ) and is coupled between nodes A and B. Tunable MEMS resonator  1220   b  is coupled between node B and circuit ground. A transformer  1230  models the coupling between tunable MEMS resonator  1220   b  and an RF conductor. Transformer  1230  has one end of a primary winding  1232  coupled to node B and one end of a secondary winding  1234  providing an output signal, Vout. The other ends of windings  1232  and  1234  are coupled to circuit ground. 
     Tunable MEMS resonators  1220   a  and  1220   b  may each be implemented, e.g., as shown in  FIGS. 1 through 4 . As shown in  FIG. 12 , each tunable MEMS resonator  1220  may be modeled with a varactor  1222  coupled in parallel with an inductor  1224 . Tunable filter  1200  may have a bandpass frequency response, as described below. The center frequency of the passband may be varied by adjusting the capacitance of varactor  1222  in each tunable MEMS resonator  1220 . 
       FIG. 13  shows plots of the frequency response of tunable filter  1200  in  FIG. 12 . A plot  1312  shows the frequency response of tunable filter  1200  with C max  selected for varactor  1222  in each MEMS resonator  1220 . A plot  1314  shows the frequency response of tunable filter  1200  with C min  selected for varactor  1222  in each MEMS resonator  1220 . As shown in  FIG. 13 , a wide tuning range from approximately 850 MHz (cellular band) to 1900 MHz (PCS band) may be achieved for tunable filter  1200 . Furthermore, high Q of approximately 150 may be obtained for 850 MHz, and high Q of approximately 250 may be obtained for 1900 MHz. 
     In general, a tunable filter may be implemented with any number of tunable MEMS resonators. More MEMS resonators may be used to provide sharper roll-off, higher Q, greater out-of-band rejection, etc. 
       FIG. 14  shows a schematic diagram of an exemplary design of an oscillator  1400  implemented with two tunable MEMS resonators  1420   a  and  1420   b . Oscillator  1400  may be used for oscillator  1172 , oscillator  1182 , and/or other oscillators in wireless device  1100  in  FIG. 11 . Oscillator  1400  includes an amplifier  1410  that provides signal amplification for a differential oscillator signal comprising Voscp and Voscn signals. Amplifier  1410  includes N-channel metal oxide semiconductor (NMOS) transistors  1412  and  1414  having their sources coupled to node Z. NMOS transistor  1412  has its drain coupled to node X and its gate coupled to node Y. NMOS transistor  1414  has its drain coupled to node Y and its gate coupled to node X. NMOS transistors  1412  and  1414  are thus cross-coupled. A current source  1408  is coupled between node Z and circuit ground and provides a bias current of Ibias for NMOS transistors  1412  and  1414 . The Voscp and Voscn signals are provided via nodes X and Y, respectively. 
     Tunable MEMS resonator  1420   a  is coupled between node X and a power supply voltage, Vdd. Tunable MEMS resonator  1420   b  is coupled between node Y and the supply voltage. Tunable MEMS resonator  1420   a  and  1420   b  may each be implemented, e.g., as shown in  FIGS. 1 through 4 . As shown in  FIG. 14 , each tunable MEMS resonator  1420  may be modeled with a varactor  1422  coupled in parallel with an inductor  1424 . The oscillation frequency of oscillator  1400  may be varied by adjusting the capacitance of varactor  1422  in each tunable MEMS resonator  1420 . 
     In general, a MEMS resonator may comprise a first part and a second part. The first part (e.g., top part  160  in  FIG. 1 ) may comprise a cavity and a post. The second part (e.g., bottom part  110  in  FIG. 1 ) may be mated to the first part and may comprise a movable plate positioned under the post. The movable plate may be mechanically moved by a DC voltage to vary the resonance frequency of the MEMS resonator. The second part may comprise an electrode formed under the movable plate and applied with the DC voltage. 
     In an exemplary design, the cavity may have a rectangular shape and may be surrounded by four sidewalls formed in the first part, e.g., as shown in  FIG. 3 . The four sidewalls may have rounded corners to improve performance, e.g., as also shown in  FIG. 3 . In another exemplary design, the cavity may have a circular shape and may be surrounded by a circular sidewall formed in the first part, e.g., as shown in  FIG. 4 . In yet another exemplary design, the cavity may have an arbitrary shape contour and may be surrounded by an arbitrary shape contour wall formed in the first part. For all exemplary designs, the cavity may be empty or filled with a dielectric material. 
     The post may be positioned in the middle of the cavity, e.g., as shown in  FIGS. 3 and 4 . In an exemplary design, the post may have a rectangular shape with rounded corners, e.g., as shown in  FIG. 3 . In another exemplary design, the post may have a circular shape, e.g., as shown in  FIG. 4 . In yet another exemplary design, the post may have an arbitrary contour shape. The first part may further comprise one or more additional posts formed within the cavity. 
     In an exemplary design, the movable plate may be attached to the second part via an anchor and operated as a cantilever, e.g., as shown in  FIG. 5 . In another exemplary design, the movable plate may be attached to the second part via first and second anchors and operated as a bridge, e.g., as shown in  FIG. 6 . The movable plate may also be implemented in other manners with a MEMS switch or some other MEMS structure. In an exemplary design, the second part may further comprise at least one additional movable plate located under the post, e.g., as shown in  FIG. 9 . Each additional movable plate may be mechanically moved by a respective DC voltage to vary the resonance frequency of the MEMS resonator. 
     In an exemplary design, the second part may comprise a substrate, a dielectric layer formed over the substrate, and a metal layer formed over the dielectric layer, e.g., as shown in  FIG. 1 . The second part may be covered by the metal layer (e.g., metal layer  130 ) on the surface facing the first part. The first part may also be covered by a metal layer (e.g., metal layer  190 ) on the surface facing the second part. 
     In one exemplary design, a dielectric layer (e.g., dielectric layer  186  in  FIG. 8 ) may be formed over the metal layer on the first part between the post and the movable plate. In another exemplary design, at least one dielectric spacer (e.g., dielectric spacers  182  and  184  in  FIG. 7 ) may be formed on at least one side of the movable plate and may be used to prevent shorting of the movable plate to the metal layer in the first part. In yet another exemplary design, no dielectric layer or spacer is formed between the movable plate and the metal layer on the first part. 
     In another aspect, an apparatus may comprise a filter that receives an input signal and provides an output signal, e.g., as shown in  FIG. 12 . The filter may comprise at least one MEMS resonator. Each MEMS resonator may have a movable plate for adjusting the resonance frequency of the MEMS resonator. The filter may have a tunable frequency response that may be determined based on the resonance frequency of each MEMS resonator, e.g., as shown in  FIG. 13 . 
     In an exemplary design, the filter may comprise a single MEMS resonator, e.g., as shown in  FIGS. 1 to 4 . In another exemplary design, the filter may comprise multiple MEMS resonators coupled together via inter-resonator coupling, e.g., as shown in  FIGS. 10 and 12 . In one exemplary design, each MEMS resonator may comprise a first part (e.g., top part  160  in  FIG. 1 ) and a second part (e.g., bottom part  110  in  FIG. 1 ). The first part may comprise a cavity and a post. The second part may be mated to the first part and may comprise the movable plate located under the post. The movable plate may be mechanically moved by a DC voltage to vary the resonance frequency of the MEMS resonator. 
     In one exemplary design, the apparatus may be a wireless communication device, e.g., as shown in  FIG. 11 . The filter may be used in a transmitter or a receiver in the wireless communication device to pass a desired signal and to attenuate undesired signals and noise. The filter may also be used for other electronics devices. 
     In yet another aspect, an apparatus may comprise an oscillator that generates an oscillator signal. The oscillator may comprise (i) an amplifier to provide amplification for the oscillator signal and (ii) at least one MEMS resonator coupled to the amplifier, e.g., as shown in  FIG. 14 . Each MEMS resonator may have a movable plate for adjusting the resonance frequency of the MEMS resonator. The oscillator may have a tunable oscillation frequency that may be determined based on the resonance frequency of each MEMS resonator. 
     In an exemplary design, the amplifier may comprise (i) a first transistor (e.g., NMOS transistor  1412 ) providing amplification for a non-inverting signal of the oscillator signal and (ii) a second transistor (e.g., NMOS transistor  1414 ) providing amplification for an inverting signal of the oscillator signal. The at least one MEMS resonator may comprise (i) a first MEMS resonator (e.g., MEMS resonator  1420   a ) coupled to the first transistor and (ii) a second MEMS resonator (e.g., MEMS resonator  1420   b ) coupled to the second transistor. Each MEMS resonator may be implemented as described above. 
     In one exemplary design, the apparatus may be a wireless communication device, e.g., as shown in  FIG. 11 . The oscillator signal may be used to generate an LO signal for a transmitter or a receiver in the wireless communication device. The oscillator may also be used for other electronics devices. 
       FIG. 15  shows an exemplary design of a process  1500  for operating a MEMS resonator. A DC voltage may be applied to an electrode of a MEMS resonator comprising a movable plate and a cavity (block  1512 ). The DC voltage may be varied to mechanically move the movable plate of the MEMS resonator and vary the resonance frequency of the MEMS resonator (block  1514 ). In one exemplary design, the DC voltage may be set to either (i) a first value to obtain the maximum resonance frequency for the MEMS resonator or (ii) a second value to obtain a minimum resonance frequency for the MEMS resonator. In another exemplary design, the DC voltage may be adjusted to a value between the first and second values. In general, the DC voltage may be varied in two or more discrete steps or in a continuous manner. An RF signal may be received from the cavity of the MEMS resonator (block  1516 ). 
     The tunable MEMS resonators described herein may be fabricated with various MEMS process technologies known in the art. The tunable MEMS resonators may be fabricated on a substrate (e.g., a glass or silicon substrate) and may be encapsulated in a suitable package. A substrate with tunable MEMS resonators may also be packaged together with a semiconductor IC die. The tunable MEMS resonators may also be fabricated on a semiconductor IC (e.g., a CMOS IC) using semiconductor process technology. 
     An apparatus implementing the tunable MEMS resonators described herein may be a stand-alone device or may be part of a larger device. A device may be (i) a stand-alone IC package, (ii) a set of one or more IC packages that may include memory ICs for storing data and/or instructions, (iii) an RFIC such as an RF receiver (RFR) or an RF transmitter/receiver (RTR), (iv) an ASIC such as a mobile station modem (MSM), (v) a module that may be embedded within other devices, (vi) a receiver, cellular phone, wireless device, handset, or mobile unit, (vii) etc. 
     In one or more exemplary designs, the functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media may be any available media that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Also, any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and blu-ray disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media. 
     The previous description of the disclosure is provided to enable any person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other variations without departing from the scope of the disclosure. Thus, the disclosure is not intended to be limited to the examples and designs described herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.