Patent Publication Number: US-10312185-B2

Title: Inductively coupled microelectromechanical system resonator

Description:
FIELD OF THE DISCLOSURE 
     This disclosure relates an oscillator circuit that is inductively coupled to a micromechanical system resonator. 
     BACKGROUND OF THE DISCLOSURE 
     Microelectromechanical system (MEMS) resonators are used for multiple applications, among them low-power, low-phase noise, high stability oscillators. Connecting the MEMS resonators to the circuit as well as packaging are usually challenging aspects of such designs. Multiple approaches have been used, such as: wire-bonding, flip-chip MEMS, CMOS-MEMS, etc. Each approach includes a set of challenges that may limit its application to niche areas. 
     A thin-film bulk acoustic wave (BAW) resonator is a MEMS device that includes a piezoelectric material sandwiched between two electrodes and acoustically isolated from the surrounding medium. MEMS resonator devices using piezoelectric films with thicknesses ranging from several micrometers down to tenth of micrometers resonate in the frequency range of roughly 100 MHz to 10 GHz. Aluminum nitride and zinc oxide are two common piezoelectric materials used in MEMS resonators. 
     Several types of MEMS resonator based oscillators are known, see for example: Padimarri, Arun, Nathan Ickes, and Anantha P. Chandrakasan, “A 0.68V 0.68 mVV 2.4 GHz PLL for Ultra-Low Power RF Systems.” 2015 IEEE Radio Frequency Integrated Circuits Symposium (RFIC) (May 2015); A. Nelson, J. Hu, J. Kaitila, R. Ruby and B. Otis, “A 22 μW, 2.0 GHz FBAR oscillator,” 2011  IEEE Radio Frequency Integrated Circuits Symposium , Baltimore, Md., 2011, pp. 1-4. A high-Q MEMS-based oscillators may have moderate power consumption, low phase noise, and high accuracy/stability. 
     Other solutions to generate low power clocks in the GHz range include ring oscillators and LC (inductor-capacitor) oscillators. Ring oscillators usually produce relatively high power consumption in the milli-watt range (mW&#39;s), produce very high phase noise, and may have poor stability. LC oscillators also produce high power consumption (mW&#39;s), while providing moderate phase noise and poor stability. In some designs, power consumption may be reduced by reducing supply voltage or adjusting biasing of transistors in the oscillator circuit. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Particular embodiments in accordance with the disclosure will now be described, by way of example only, and with reference to the accompanying drawings: 
         FIG. 1  is a cross section of an example solid MEMS resonator; 
         FIG. 2  is a schematic illustrating an equivalent circuit of the MEMS resonator of  FIG. 1 ; 
         FIGS. 3A and 3B  are plots illustrating impedance vs. frequency of the MEMS resonator of  FIG. 1 ; 
         FIG. 4  is a schematic of a prior art oscillator using a MEMS resonator; 
         FIGS. 5-6  are schematics illustrating use of a transformer to step up the impedance of a MEMS resonator; 
         FIGS. 7A and 7B  are plots illustrating impedance vs. frequency of the MEMS resonator and autotransformer of  FIG. 6 ; 
         FIG. 8  is a plot illustrating phase noise; 
         FIGS. 9-10  are block diagrams illustrating alternate embodiments of an auto-transformer; 
         FIG. 11  is an illustration of a MEMS resonator mounted on a CMOS die; 
         FIGS. 12A-12D  illustrate an example of an inductively coupled MEMS resonator; 
         FIG. 13  illustrates an alternative embodiment of a coupling coil; 
         FIGS. 14-18  are cross sectional views illustrating alternative embodiments of an inductively coupled resonator; 
         FIG. 19  is a flow chart illustrating operation of an example MEMS oscillator; and 
         FIG. 20  is a flow chart illustrating operation of an example MEMS oscillator with a removable MEMS resonator. 
     
    
    
     Other features of the present embodiments will be apparent from the accompanying drawings and from the detailed description that follows. 
     DETAILED DESCRIPTION OF EMBODIMENTS OF THE DISCLOSURE 
     Specific embodiments of the disclosure will now be described in detail with reference to the accompanying figures. Like elements in the various figures are denoted by like reference numerals for consistency. In the following detailed description of embodiments of the disclosure, numerous specific details are set forth in order to provide a more thorough understanding of the disclosure. However, it will be apparent to one of ordinary skill in the art that the disclosure may be practiced without these specific details. In other instances, well-known features have not been described in detail to avoid unnecessarily complicating the description. 
     For many applications, an ultra-low power, low-phase noise, high-stability clock is useful. An oscillator circuit that is coupled to a micromechanical system resonator via a transformer to increase the effective impedance of the resonator will be disclosed herein. Embodiments of the oscillator circuit may be used to produce multi-GHz clock signals with power consumption in the 100μW range. A transformer may be used to boost the impedance of a high-Q, high-stability MEMS resonator. The transformer may be an auto-transformer, such as a multi-tap inductor, which may be fabricated on the MEMS die itself, on the CMOS oscillator die, or may be a standalone external component, for example. Increasing the effective impedance of the MEMS resonator reduces current consumption from the oscillator circuit to generate the same voltage swing. The resonance frequency of the oscillator circuit is still defined by the MEMS resonator, which maintains the same frequency stability and accuracy as a traditional MEMS resonator based oscillator, as long as the transformer is designed such that the primary and secondary resonance is sufficiently separate from the resonance point of the MEMS resonator, as will be explained in more detail below. 
       FIG. 1  is a cross section of an example solid MEMS resonator  100  that may be coupled to an oscillator circuit to produce multi-GHz clock signals. MEMS resonator  100  is a solidly mounted bulk acoustic wave resonator that does not have any air gaps. MEMS resonator  100  may be formed on a silicon substrate using known or later developed semiconductor processing techniques. 
     A multilayer bottom Bragg mirror  102  and top Bragg mirror  103  may be formed on substrate  101 . A distributed Bragg reflector (DBR) is a structure formed from multiple layers of alternating materials with varying refractive index. Each layer boundary causes a partial reflection of a wave. For waves whose bulk wavelength is close to four times the thickness of the layers, the many reflections combine with constructive interference, and the layers act as a high-quality reflector. 
     A bottom electrode  105  and a top electrode  106  may be formed in contact with the adjacent Bragg mirrors  102 ,  103 . In this example, electrodes  105 ,  106  are patterned from a layer of metal, such as Al, Mo, Cu, Au, etc. A piezoelectric layer  107  may be positioned between the top electrode  106  and the bottom electrode  105 . Piezoelectric layer may be fabricated using various piezo materials, such as AIN, quartz, GaN, lithium nobate, etc. A temperature compensating layer  104  of oxide may be formed on top of piezoelectric layer  107 . A protective overcoat layer  108  such as oxide, SiN, glass, etc. may be placed over top Brag mirror  103 . Terminals  109 ,  110  may be in contact with upper electrode  106  and lower electrode  105  and thereby provide terminals for coupling MEMS resonator  100  to an oscillator circuit. 
     Mechanical energy may be confined and isolated within active area  111  as illustrated by plot lines  112  that represent a vibration magnitude within active area  111 . 
     While MEMS resonator  100  is described herein is some detail, other embodiments of the techniques disclosed herein may be used with other types and configurations of MEMS resonators that are currently know or later developed. 
       FIG. 2  is a MBVD (Modified Butterworth Van Dyke) equivalent circuit schematic illustrating an equivalent circuit of MEMS resonator  100  of  FIG. 1 . This example includes a static capacitor C0 and its loss R0, mechanically dynamic capacitor Cm, dynamic inductor Lm, and dynamic loss Rm. MEMS resonator  100  has two resonant frequencies at, the serial resonant frequency fs and the parallel resonant frequency fp. The Lm and Cm account for fs, whereas Lm, Cm, and C0 account for fp. An equivalent impedance (Z) is presented across terminals  109 ,  110 . 
       FIGS. 3A and 3B  are plots illustrating impedance vs. frequency of the MEMS resonator  100  of  FIG. 1 , as measured across terminals  109 ,  110 . Plot line  320  illustrates effective impedance magnitude in volts/amps (V/A) vs. frequency in gigahertz (GHz), while plot line  322  illustrates phase shift in degrees (deg) vs. frequency in GHz. MEMS resonator  100  behaves like an inductor with high Q factor in a narrow frequency band between fs and fp, as indicated at  321  and  323 . In this example, MEMS resonator  100  has an effective impedance of approximately 860 V/A and a 0 degree phase shift at 2.52 GHz with a Q factor greater than 1000. Thus, at resonance, MEMS resonator  100  reduces to a real resistance, that may be referred to as the parallel resistance, R p . as indicated by expression (1). Away from the resonant point  321 , MEMS resonator acts like a 2.5 pf capacitance.
 
 R   p   =Qω   0   L   (1)
 
       FIG. 4  is a schematic of a prior art oscillator circuit  401  that may use a MEMS resonator  400  that may be similar to MEMS resonator  100  as shown in  FIG. 1 . Oscillator circuit  401  may be implemented on a semiconductor substrate using complimentary metal-oxide semiconductor (CMOS) transistors, for example. In this example current sources I1, I2 provide a constant current to cross coupled differential pair PMOS transistors M1, M2 and cross coupled differential pair NMOS transistors M3, M4. MEMS resonator  400  acts as a tank circuit. NMOS transistors M5, M6, and capacitor C 1  are needed to reduce gain at low frequencies. As mentioned above, MEMS resonator  400  may look like a capacitor at low frequency, but will look like an open circuit at DC (direct current) and the circuit might actually latch without the aid of transistors M5, M6. 
     MEMS resonator  400  may be implemented on a semiconductor substrate that is separate from the semiconductor substrate on which oscillator circuit  401  is fabricated. Typically, MEMS resonator  400  may be mounted on the CMOS oscillator chip. Bond wires may be used to connect MEMS resonator terminals  409 ,  410  to bond pads on the CMOS oscillator chip. 
       FIGS. 5-6  are schematics illustrating use of a transformer to step up the impedance of a MEMS resonator, such as MEMS resonator  100  as shown in  FIG. 1 . For both LC and MEMS-based oscillators, the active oscillator core circuit needs to supply enough energy in every oscillation cycle to replenish the losses in the resonator/tank circuit. This is the Barkhausen criterion for oscillation (oscillator loop gain magnitude=1, phase shift around the oscillator loop is 2nπ:n∈ ). In actual oscillator circuits, this usually defines a minimum gain, or transconductance (g m ) of the oscillator transistors, for the oscillation to be sustained. Transistors have a finite transconductance efficiency which may be expressed as g m /I D . A minimum supply current and hence power consumption is required for a given tank circuit or MEMS resonator to sustain oscillation. To satisfy Barkhausen criterion, −g m  needs to overcome the tank losses, as indicated by expression (2). This minimum power consumption is inversely proportional to the tank/MEMS-resonator resistance R p  at resonance. 
     
       
         
           
             
               
                 
                   
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                     1 
                     
                       R 
                       p 
                     
                   
                 
               
               
                 
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     Referring back to  FIG. 3B , the impedance of example MEMS resonator  100  across terminals  108 - 110  at resonance is approximately 850 ohms. Since the phase shift is 0 at resonance, this impedance may also be referred to as a pure parallel resistance, R p . 
     For power efficient oscillator operation in which a minimum possible phase noise is generated for the given amount of power consumption, it is desirable to commutate or switch as much of the oscillator supply current in the tank circuit or MEMS resonator, generating the largest possible voltage swing and having the transistors in the circuit acting like ideal switches. For fully-differential architectures, this implies commutating the full bias current between the positive and negative terminal of the tank circuit with a differential pair of transistors. Ideally, this provides very sharp current transitions. A minimum voltage is required for a differential-pair to fully switch its current between branches, as indicated by expression (3).
 
 V   min =√{square root over ( 2 )}( V   qs   −V   th )  (3)
 
     This voltage swing requires a minimum amount of current switched into the tank resistance R p  at resonance, which again sets a lower limit on the power consumption for the oscillator to be efficient. This lower limit may be higher than Brakhausen criterion limit. This lower limit is also inversely proportional toR p . 
     For a given MEMS resonator available from a vendor, there is a lower limit on oscillator power consumption, below which the oscillator cannot start. Above this lower limit, the oscillator can have very low phase noise. In fact, some applications may tolerate higher phase noise in exchange for lower power consumption, but the lower power limit inherit to most oscillator structures prohibits such trade-off below a certain power level. 
     In various prior-art approaches, attempts have been made to co-design and co-optimize the MEMS resonator with the oscillator circuit to lower the power consumption. Typically, attempts are made to maximize R p  of the MEMS resonator while having enough capacitance to avoid being significantly affected by the circuit parasitics. However, optimization of a MEMS resonator may require a lot of resources in terms of finite-element modeling as well as fabrication and testing. 
     A transformer or an auto-transformer may be used to boost R p  of any MEMS resonator, hence enabling lower power consumption oscillators to be realized, even while using an “off-the-shelf” MEMS resonator. The transformer or auto-transformer may be fabricated on the MEMS die itself as part of the MEMS fabrication process, or may be an external component, for example. 
     Referring to  FIG. 5 , transformer  520  may be coupled between oscillator circuit  501  and MEMS resonator  100 , as shown in more detail in  FIG. 1 . Transformer  520  may be implemented as a transformer with a turns ratio of N:1, where N may typically be less than approximately two, for example. In some embodiments, N may be higher than this example With a turns ratio of N=2, the impedance step-up may be approximately 4×. However, the Q factor of the transformer may limit the impedance step-up ratio. In this example, one of the coils  521  of the transformer may be connected to the oscillator and the other coil  522  may be connected to the MEMS resonator. Coil  521  may be referred to herein as the “primary coil” while coil  522  is referred to as the secondary coil. 
     Oscillator circuit  501  may be implemented on a semiconductor substrate using CMOS transistors, for example. In this example current sources l 1 , l 2  provide a constant current to cross coupled differential pair PMOS transistors M1, M2 and cross coupled differential pair NMOS transistors M3, M4. MEMS resonator  100  acts as a tank circuit. 
     Referring to  FIG. 6 , autotransformer  620  may be coupled between oscillator circuit  501  and MEMS resonator  100 , as shown in more detail in  FIG. 1 . Autotransformer  620  may be implemented as a transformer with a turns ratio of N:1, where N may typically be less than approximately two, for example. In some embodiments, N may be higher than this example. In this example, the entire coil  621  of autotransformer is the primary coil, while a portion  622  of the primary coil functions also as the secondary coil  622   
     Oscillator circuit  501  may be implemented on a semiconductor substrate using CMOS transistors, for example. In this example current sources  11 ,  12  provide a constant current to cross coupled differential pair PMOS transistors M1, M2 and cross coupled differential pair NMOS transistors M3, M4. MEMS resonator  100  acts as a tank circuit. 
       FIGS. 7A and 713  are plots illustrating impedance magnitude and phase vs. frequency of the MEMS resonator  100  and autotransformer  620  of  FIG. 6 . Similar plots may be produced for the MEMS resonator  100  and transformer  520  of  FIG. 5 . This disclosure provides a way to use an existing MEMS resonator to synthesize an oscillator with lower power consumption than traditionally possible. Although the resulting oscillator phase noise might be degraded due to the losses in the auto-transformer itself and the loading of the auto-transformer on the MEMS resonator, embodiments of the current disclosure may extend the power-phase noise performance trade-off to a region that is otherwise non-feasible with traditional designs. 
     In this example, the combined tank circuit (auto-transformer  620 +MEMS resonator  100 ) shows three different resonance peaks. The main resonance peak is at the MEMS resonator resonance frequency f o  as indicated at  721  is usually the peak with the highest Q and the highest R p  and therefore the highest oscillator loop gain. Next, there may be a peak at f 1  as indicated at  722  resulting from the resonance of the auto-transformer secondary with the capacitance of the MEMS resonator (usually f 1 &lt;f o ). There may be another peak at f 2  as indicated at  723  resulting from the resonance of the auto-transformer primary with the parasitic capacitance of the oscillator circuit (usually f 2  &gt;f o ). The peaks at f 1  and f 2  are usually much lower C, (about 100×) than the main peak at f o  and usually no special design or additional component is required to prevent spurious oscillation at these frequencies. However, this might change depending on the specific MEMS resonator and auto-transformer used. 
     In this example, the turns ratio N of autotransformer  620  is approximately 1.3. In this example, f 0  is approximately 2.5 GHz and the effective impedance is approximately 1.7 kohms, which is approximately twice as high as the R p  of MEMS resonator  100  by itself (approximately 850 ohms, as shown in  FIG. 3B ). In this example, f 1  is approximately 1.3 GHz at an impedance of approximately 796 ohms and f 2  is approximately 6.1 GHz at an impedance of approximately 972 ohms. 
     Variations in the inductance and characteristics of auto-transformer  620  due to process variation or temperature mostly affects the resonance peaks at hand h. The main resonance peak at f o  is less sensitive and is only marginally affected by such variations. Q may be the most sensitive parameter to such variations. 
     The autotransformer is a short circuit at DC, which kills any possible oscillator gain at DC. This is useful, since the MEMS resonator  100  by itself behaves as a capacitor all the way up to DC. Thus, if the MEMS resonator  100  is directly connected to a cross-coupled differential pair oscillator circuit  501 , there is potential for this structure to actually latch at DC. Referring back to  FIG. 4 , transistor M, M6 and capacitor C 1  are required to avoid such latch situation, whereas the auto-transformer/inductor  620  eliminates this concern. 
       FIG. 8  is a plot illustrating phase noise in dBc/Hz vs relative frequency in Hz of the MEMS resonator  100  and autotransformer  620  of  FIG. 6 . Similar plots may be produced for the MEMS resonator  100  and transformer  520  of  FIG. 5 . Plot line  825  represents the phase noise produced by the oscillator circuit  501  of  FIG. 6  using MEMS resonator  100  and auto-transformer  620 . Plot line  826  represents noise produced by a prior art oscillator such as oscillator  401  of  FIG. 4 . As can be seen, the phase noise is somewhat higher for oscillator  501  as compared to oscillator  401 . However, as discussed above, in many applications the tradeoff of lower power consumption versus a slightly higher phase noise is acceptable. 
       FIGS. 9  is block diagram illustrating an embodiment of an auto-transformer  920  that may be fabricated on CMOS die  930  during fabrication of the die. CMOS die  930  includes oscillator circuit  501  as shown in more detail in  FIG. 6 . Auto-transformer  920  may be a simple multi-loop structure that may be formed in the interconnect layers of CMOS die  930  using known or later developed semiconductor fabrication techniques. 
     In this example, auto-transformer  920  is configured such that MEMS resonator  100  is connected to a center portion of auto-transformer  920  coil at contact points  936 ,  937 . In another embodiment, MEMS resonator  100  may be connected to a different portion of auto-transformer coil  920 . 
     In this example, MEMS resonator  100  may be formed on a separate semiconductor substrate as described in more detail with regard to  FIG. 1  to form MEMS die  931 . In some embodiments, MEMS die  931  may then be mounted on CMOS die  930 . In another embodiment, MEMS die  931  and CMOS die  930  may then be mounted on a third substrate, such as a circuit board or other type of substrate. In either case, bond wires  932 ,  933  may be used to connect MEMS resonator terminals  109 ,  110  to bond pads  934 ,  935  on CMOS die  930  and thereby to auto-transformer  920 . 
       FIGS. 10  is block diagram illustrating an embodiment of an auto-transformer  1020  that may be fabricated on MEMS die  1031  during fabrication of the die. MEMS die  1031  includes MEMS resonator  100  as shown in more detail in  FIG. 1 . 
     In this example, MEMS resonator  100  may be formed on a separate semiconductor substrate as described in more detail with regard to  FIG. 1  to form MEMS die  1031 . Auto-transformer  1020  may be a simple multi-loop structure that may be formed in the interconnect layers of MEMS die  1031  using known or later developed semiconductor fabrication techniques. The secondary portion of auto-transformer  1020  may be directly connected to terminals  109 ,  110  of MEMS resonator  100 . 
     In some embodiments, MEMS die  1031  may then be mounted on CMOS die  1030 . In another embodiment, MEMS die  1031  and CMOS die  1030  may then be mounted on a third substrate, such as a circuit board or other type of substrate. In either case, bond wires  1032 ,  1033  may be used to connect between bond pads on the primary portion of auto-transformer  1020  to bond, pads  1034 ,  1035  on CMOS die  1030  and thereby to oscillator circuit  501 . 
       FIG. 11  is an illustration of a MEMS resonator  1131  mounted on a CMOS die  1130 . CMOS die  1130  may include oscillator circuit  501  as shown in more detail in  FIG. 6 . In this example, a MEMS resonator such as MEMS resonator  100  may be formed on a separate semiconductor substrate as described in more detail with regard to  FIG. 1  to form MEMS die  1131 . In this example, low modulus die attach material  1138  is used to mount MEMS die  1131  on CMOS die  1130 . 
     However, bond wires add variable parasitics and represent a reliability challenge from a packaging point of view. Such parasitics can also be highly sensitive to temperature and voltages variations, which affects the stability of the MEMS resonator. Bond wires may break if packaging is not properly optimized. Bond pads add extra parasitic capacitance to the circuit. Also, the die attach material  1138  for the MEMS die has to be hard enough to allow for wire bonding, which may couple underlying die stress into the MEMS resonator and thereby produce frequency drift. It also significantly limits the possible final product form factor. For example, the end product cannot be a flip-chip package or a wafer chip-scale package (WCSP) and flip chip with such wirebonding. 
     Connecting a MEMS resonator to an oscillator circuit as well as packaging are usually challenging aspects of such designs. In another example, a MEMS die may be flip-chip mounted to a CMOS die using solder bumps; however, this may introduce stress on the MEMS die. In another example, a MEMS resonator may be fabricated directly onto a CMOS die; however, this may require a special fabrication process. In this case, the MEMS resonator design becomes prohibitively challenging. Stress and temperature compensation may be difficult. Yield might be compromised because any failure on the CMOS or MEMS side is considered a failed product. 
     As will now be disclosed, inductive coupling may be used between a MEMS resonator and a CMOS die to completely eliminate the wiring/electrical connection between the two, which may significantly simplify the packaging solution and allow for MEMS resonators to be used with package form factors that were not previously feasible. 
       FIGS. 12A-12D  illustrate an example of a MEMS resonator  100  that is inductively coupled to an oscillator circuit  501 . MEMS resonator  100  is described in more detail with regard to  FIG. 1 , while oscillator circuit  501  is described in more detail with regard to  FIG. 5 .  FIG. 12A  illustrates how a planar inductor  1240  may be fabricated on the MEMS die  1230  using a known or later developed metallization process for the MEMS die. Planar inductor  1240  may be connected to the MEMS resonator terminals  109 ,  110 , referring again to  FIG. 1 . Crossovers  1242 ,  1243  may be easily fabricated using a second metal layer. They may be position as illustrated in  FIG. 12A  to provide a balanced inductor configuration. In another embodiment, a different planar inductor configuration may be used in which is single crossover is used, for example. 
     Similarly, a planar inductor  1241  may be fabricated on the CMOS die  1231  using a known or later developed metallization process for the CMOS die, as illustrated in  FIG. 12B  Planar inductor  1241  may be connected to the oscillator circuit  501 , referring again to  FIG. 5 . Crossovers  1244 ,  1245  may be easily fabricated using a second metal layer. They may be position as illustrated in  FIG. 12B  to provide a balanced inductor configuration. In another embodiment, a different planar inductor configuration may be used in which is single crossover is used, for example. 
       FIG. 12C  is a cross sectional view illustrating MEMS die  1230  flipped over and positioned on top of CMOS die  1231  with planar inductor  1240  in alignment with planar inductor  1241  and in close proximity. A passivation layer  1246  may be applied to the top surface of MEMS die  1230  and CMOS die  1231 . A thin layer of soft die attach material  1248  may be used to secure MEMS die  1230  to CMOS die  1231 . In this example, die attach material  1248  is approximately  20  um in thickness so that planar inductor  1240  may be in close proximity to planar inductor  1241 . Because there are no wire bonds, a much softer die attach material may be used in this example and may provide better stress relief for the MEMS die. 
     In this manner, a transformer is formed that couples MEMS resonator  100  to oscillator circuit  501  in a configuration that is similar to the configuration of  FIG. 5  with N=1, since in this example, planar inductor  1240  and  1241  both have three turns. 
       FIG. 12D  illustrates another embodiment in which a planar inductor  1249  that has four turns may be fabricated on CMOS die  1231  in place of planar inductor  1241 . In this case, a transformer that has a turns ratio of 1.33:1 may be formed, where N=1.33. In this case, the effective impedance of MEMS resonator is increased and allows lower power operation of oscillator circuit  501 , as described in more detail above. 
     In an example design, the planar inductor  1240  on MEMS die  1230  shown in  FIG. 12A  may have three turns with an outer radius of 220 μm, with each loop having a width of 15 μm and a loop to loop separation of 10 μm. The metal layer may include 1.1 μm thick aluminum and 1.6 μm copper. The planar inductor  1249  on CMOS die  1231  shown in  FIG. 12D  may have four turns with an outer radius of 200 μm, with each loop having a width of  8  pm and a loop to loop separation of 4 μm. The metal layer may include 1 μm thick aluminum, for example. In this example, die attach material  1248  is approximately 20 um in thickness so that planar inductor  1240  may be in close proximity to planar inductor  1241 . Other designs may use thicker metals and/or thinner die attach to achieve a higher Q. 
       FIG. 13  illustrates an alternative embodiment of a MEMS die  1330 . In this example, a planar inductor  1340  is positioned around MEMS resonator  100  in order to reduce die area, as compared to the configuration of  FIG. 12A . In a similar manner, a planar inductor may be positioned around oscillator circuit  501  to save die area on the oscillator die. 
       FIG. 14  is a cross sectional view illustrating an embodiment of an inductively coupled resonator in an encapsulated integrated circuit (IC) package  1400 . In this example, a CMOS die  1231  as shown in  FIG. 12B  is mounted on a die attach pad (DAP) of a leadframe using a known or later developed die attach process. Leadframe contacts  1441  may surround the periphery of IC package  1400 . Bond wires  1442  may be used to connect bond pads on CMOS die  1231  to leadframe contacts  1441 , using known or later developed wire bonding techniques. 
     Some integrated circuits have no-lead packages such as quad-flat no-leads (QFN) and dual-flat no-leads (DEN) devices that physically and electrically couple integrated circuits to printed circuit boards. Flat no-lead devices, also known as micro leadframe (MLF) and small outline no-leads (SON) devices, are based on a surface-mount technology that connects integrated circuits to the surfaces of printed circuit boards without through-holes in the printed circuit boards. Perimeter lands  1441  on the package provide electrical coupling to the printed circuit board. In this example, IC package  1400  is a quad-flat no-leads (QFN) package; however, in other embodiments various known or later developed packaging configurations, such as DEN, MLF, SON, dual inline packages (DIP), etc, may be fabricated using the techniques disclosed herein to form an encapsulated package that includes a MEMS resonator inductively coupled to an oscillator circuit. 
     In this example, MEMS die  1230  as shown in  FIG. 12A  is flipped over and positioned on CMOS die  1231  such that planar inductors on each die are in alignment and in close proximity, as illustrated in more detail with regards to  FIG. 12C . A blob of protective material  1443  may be placed over MEMS resonator to isolate it from the encapsulation material and provide stress relief. 
     The completed assembly may then be encapsulated using an encapsulation material  1442 , such as epoxy resin or other known or later developed encapsulation materials. An entire lead frame strip may then be covered with a layer of mold compound to encapsulate the ICs. The leadframe strip may then be singulated into individual packaged ICs by cutting along cut lines, for example. 
       FIG. 15  is a cross sectional view illustrating another embodiment of an inductively coupled resonator in an encapsulated integrated circuit (IC) package  1500 . In this example, a CMOS die  1531 , which may be similar to CMOS die  1231  as shown in  FIG. 12B , is mounted on a die attach pad (DAP) of a leadframe using a known or later developed die attach process. Leadframe contacts  1441  may surround the periphery of IC package  1400 . Bond wires  1442  may be used to connect bond pads on CMOS die  1530  to leadframe contacts  1441 , using known or later developed wire bonding techniques. 
     In this example, MEMS die  1230  as shown in  FIG. 12A  is placed in a groove within DAP  1540 . In this case, MEMS die  1230  may be left “floating” and not physically attached to CMOS die  1531  in order to reduce stress on MEMS die  1230 . Alternatively, a thin layer of soft die attach material may be used to secure MEMS die  1230  to DAP  1540  and/or to CMOS die  1531 . CMOS die  1531  may be thinned down for better coupling between a planar inductor in MEMS die  1230  and planar inductor  1541  on CMOS die  1531 . 
       FIG. 16  is a cross sectional view illustrating another embodiment of an inductively coupled resonator in a flip-chip or WCSP package configuration  1600 . In this example, a CMOS die  1631 , which may be similar to CMOS die  1231  as shown in  FIG. 12B , is mounted on a printed circuit board (PCB)  1650  with solder bumps  1651  using a known or later developed flip-chip process. An encapsulation material blob  1642  may be placed over CMOS die  1631  in some embodiments. 
     In this example, MEMS die  1230  may be attached to CMOS die  1631  using a thin layer of soft die attach material, such as die attach material  1248  as shown in  FIG. 12C . 
       FIG. 17  is a cross sectional view illustrating another embodiment of an inductively coupled resonator in a flip-chip or WCSP package configuration  1700 . In this example, a CMOS die  1631 , which may be similar to CMOS die  1231  as shown in  FIG. 12B , is mounted on a printed circuit board (PCB)  1650  with solder bumps  1651  using a known or later developed flip-chip process. An encapsulation material blob  1642  may be placed over CMOS die  1631  in some embodiments. 
     In this example, MEMS die  1230  may be attached to PCB  1650  using a thin layer of soft die attach material, such as die attach material  1248  as shown in  FIG. 12C . In this manner, MEMS die  1230  is not in contact with CMOS die  1631  and die to die stress is thereby eliminated. 
       FIG. 18  is a cross sectional view illustrating another embodiment of an inductively coupled resonator in a flip-chip or WCSP package configuration  1800 . In this example, a CMOS die  1631 , which may be similar to CMOS die  1231  as shown in  FIG. 12B , is mounted on a printed circuit board (PCB)  1650  with solder bumps  1651  using a known or later developed flip-chip process. An encapsulation material blob  1642  may be placed over CMOS die  1631  in some embodiments. 
     In this example, MEMS die  1230  may be attached to PCB  1650  using a thin layer of soft die attach material, such as die attach material  1248  as shown in  FIG. 12C . CMOS die  1631  may be resting on MEMS die  1230  and/or attached to MEMS die  1230  using a layer of soft die attach material  1248 . 
       FIG. 19  is a flow chart illustrating operation of an example oscillator that uses a MEMS resonator, such as MEMS resonator device  100  as illustrated in  FIG. 1 . A MEMS resonator may be used as a tank circuit to create a resonant frequency, as indicated at box  1900 , and as described in more detail above. 
     The MEMS resonator may be inductively coupled to an oscillator circuit using a transformer with a turns ratio of N:1, as indicated at box  1902 . 
     In some embodiments, N may be selected to be greater than one, as indicated at box  1902 . As described in more detail above with regard to  FIG. 7A , the effective impedance of the MEMS resonator will be increased when N&gt;1. Increasing the effective impedance of the MEMS resonator reduces the current required to operate the oscillator circuit. 
     In some embodiments, the transformer may be fabricated on a die holding the MEMS resonator as indicated at box  1903  and described in more detail with regards to  FIG. 10 . In some embodiments, the transformer may be an auto-transformer as illustrated in  FIG. 6  and  FIG. 10 . 
     In some embodiments, the transformer may be fabricated on a die holding the oscillator circuit as indicated at box  1904  and described in more detail with regards to  FIG. 9 . In some embodiments, the transformer may be an auto-transformer as illustrated in  FIG. 6  and  FIG. 9 . 
     In some embodiments as indicated at box  1905 , a primary coil of the transformer may be fabricated on a die holding the oscillator circuit as shown in more detail in  FIG. 12B , and a secondary coil of the transformer may be fabricated on a die holding the MEMS resonator as shown in more detail in  FIG. 12A . In this case, the turns ratio may be selected to be 1:1, or may be selected to be N:1, where N&gt;1 to thereby increase the effective resistance of the MEMS resonator and reduce current required by the oscillator circuit. 
     In some embodiments, the transformer may be implemented as a stand-alone component as indicated at box  2906 . 
     In any case, the oscillator circuit, MEMS resonator, and transformer may be encapsulated in a single IC package as indicated at box  1907  and described in more detail with regard to  FIGS. 14-18 . 
     In this manner, a low-phase noise MEMS-based oscillators with significantly lower power consumption than fundamentally possible with the MEMS resonator by itself may be implemented. The transformer coupling techniques disclosed herein extend the range of phase-noise/power consumption trade-off. 
     The transformer coupling techniques disclosed herein reduce the need for extensive MEMS process and MEMS device optimization, which may be a complex and resource intensive process. 
     Using auto-transformers that can be integrated on the MEMS die or the CMOS die does not compromise the integration potential of the MEMS resonator and does not significantly penalize the system in terms of its size. 
     Furthermore, in the case of inductive coupling as disclosed in  FIG. 12C  and elsewhere, an oscillator or a filter on a CMOS circuit may be connected to an on-CMOS die inductor without any pads or ESD structures as shown in  FIG. 128 , which greatly simplifies the circuit design and reduces parasitic capacitance and inductance. Core oscillator circuitry is no longer connected to external pads. 
     The techniques disclosed herein eliminate wirebonding and may significantly simplify packaging and provide better reliability by eliminating bond wire breakage. Elimination of bond wires eliminates the parasitic inductance and the variability associated with bond wires. A much softer die attach material may be used when wirebonding is not used, which may help with stress-relief for the MEMS die. 
     The techniques disclosed herein allow new package form factors, such as flip-chip package and WCSP packaging that were not previously feasible with wirebonding. 
     Other Embodiments 
     While the disclosure has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. Various other embodiments of the disclosure will be apparent to persons skilled in the art upon reference to this description. For example, while only an oscillator circuit was described herein, a CMOS die may contain many other circuits in addition to an oscillator circuit, such as one or more processing cores and associated memory circuits, amplifiers, filters, interface circuits for sending or receiving data from an external node, etc. 
     While a solid MEMS resonator  100  as shown in  FIG. 1  was described herein, other embodiments of the techniques disclosed herein may use other types or configurations of MEMS resonators that are currently known or later developed, such as: silicon-germanium devices, aluminum nitride devices, quartz devices, polycrystalline diamond devices, etc. 
     Planar inductors may be formed with thinner or thicker metal layers, different loop size, different loop to loop spacing, etc. than described herein. 
     While oscillator circuits were described herein, the techniques disclosed herein may be used to implement resonant filter circuits using MEMS resonators. 
     An embodiment may use a single MEMS resonator or identical MEMS resonators in series for oscillator/filter applications. 
     Other embodiments may use a combination of parallel and series MEMS resonators with small mismatch in their resonance frequency to create arbitrary filter structures. 
     Inductive coupling may be applicable to other resonator and filter configurations. For example, a MEMS resonator filter may be constructed that is inductively coupled the output of a power amplifier for BLE (Bluetooth Low Energy) applications. 
       FIG. 20  is a flow chart illustrating operation of an example MEMS oscillator with a removable MEMS resonator. In this example, an oscillator circuit may be packaged with a primary coil of a transformer as indicated at  2000 , as described in more detail above, such as illustrated in  FIG. 12B . The packaged oscillator may be used as part of a security system, for example. 
     A MEMS resonator may be packaged with a secondary coil of the transformer as indicated at  2002 , as described in more detail above, such as illustrated in  FIG. 12A . The MEMS resonator may be included in an identification badge, or other security system access device, for example. 
     The security system access device with the MEMS resonator may then be placed proximate the oscillator circuit in the security system as indicated at  2004 . For example, a security badge containing the MEMS resonator may be inserted in a slot or placed on pad in a manner that the secondary coil will be in dose physical proximity to the primary coil. 
     The MEMS resonator may then be inductively coupled to the oscillator using the primary coil on the first device positioned in proximity to the secondary coil on the second device. The MEMS resonator may then be used as a tank circuit of the oscillator to produce a resonant frequency of operation as indicated at  2006 . In this manner, the security badge may be validated, for example. 
     The package with the MEMS resonator may then be removed from proximate the oscillator to cause the resonant frequency oscillation to cease, as indicated at  2008 . 
     When the MEMS resonator is removed, the oscillator still has an inductor in the form of the primary coil and thereby forms a tank circuit (like a VCO). Depending on how the tank circuit is designed, the oscillator may then oscillate at a different oscillation frequency, or might not oscillate at all. However, the circuit may be designed to detect if the MEMS resonator is existing or not. 
     This may be useful for security purposes, such as wireless physical dongles for car keys, house keys, etc., identification badges, package labels, etc. 
     Certain terms are used throughout the description and the claims to refer to particular system components. As one skilled in the art will appreciate, components in digital systems may be referred to by different names and/or may be combined in ways not shown herein without departing from the described functionality. This document does not intend to distinguish between components that differ in name but not function. In the following discussion and in the claims, the terms “including” and “comprising” are used in an open-ended fashion, and thus should be interpreted to mean “including, but not limited to . . . .” Also, the term “couple” and derivatives thereof are intended to mean an indirect, direct, optical, and/or wireless electrical connection. Thus, if a first device couples to a second device, that connection may be through a direct electrical connection, through an indirect electrical connection via other devices and connections, through an optical electrical connection, and/or through a wireless electrical connection. 
     Although method steps may be presented and described herein in a sequential fashion, one or more of the steps shown and described may be omitted, repeated, performed concurrently, and/or performed in a different order than the order shown in the figures and/or described herein. Accordingly, embodiments of the disclosure should not be considered limited to the specific ordering of steps shown in the figures and/or described herein. 
     It is therefore contemplated that the appended claims will cover any such modifications of the embodiments as fall within the true scope and spirit of the disclosure.