Abstract:
Disclosed is an oscillator that relies on redundancy of similar resonators integrated on chip in order to fulfill the requirement of one single quartz resonator. The immediate benefit of that approach compared to quartz technology is the monolithic integration of the reference signal function, implying smaller devices as well as cost and power savings.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 11/361,814 filed on Feb. 23, 2006, now U.S. Pat. No. 7,211,926, incorporated herein by reference in its entirety, which claims priority to U.S. Provisional Patent Application Ser. No. 60/660,211 filed on Mar. 9, 2005, incorporated herein by reference in its entirety. This application incorporates herein by reference U.S. Patent Application Publication No. US 2006/0261703 A1. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with Government support under Grant No. N66001-01-1-8967 awarded by DARPA. The Government has certain rights in this invention. 
    
    
     INCORPORATION-BY-REFERENCE OF MATERIAL SUBMITTED ON A COMPACT DISC 
     Not Applicable 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates generally to frequency oscillators, and more particularly the invention relates to the use of temperature dependent resonators to establish oscillation frequency. 
     2. Description of Related Art 
     It has been shown that RF surface micro-machined MEMS resonators were potential replacement part for quartz resonators in reference oscillator applications. The main advantage relies in the form factor and path to on-chip integration, but this is at the expense of accuracy of the resonance frequency and higher temperature drift. 
     Indeed for wireless handset application, state of the art quartz resonators exhibits frequency tolerance of +/−2 ppm after hand trimming involving deposition of infinitesimal quantity of metal at the quartz surface. For the same application, it has become clear that laterally vibrating bulk resonators were the structures of choice to fulfill application requirements in term of frequency, quality factor and power handling. But, in the case of surface micro-machined MEMS resonators, one can evaluate to the first order the fabrication tolerance on the absolute resonance frequency using tolerance on the lateral dimensions. State of the art lithography tools can achieve +/−15 nm in tolerance. For GSM/CDMA, typical resonator dimensions are in the range of 30-60 μm. This translates into an absolute tolerance of higher than 200 ppm. This already high value compared to quartz is assumed without taking into account effect of the stress in the package and other non-idealities in the micromachining process (anchors, alignment between layers, anisotropy . . . ) and makes a difficult trimming of the frequency necessary. 
     In terms of thermal characteristic, research has shown that surface micro-machined resonators (polysilicon, silicon-germanium, or piezoelectric) exhibit a temperature drift of more than 2500 ppm over a −30° C.-85° C. range. This makes the use of compensation techniques developed for quartz crystal oscillators very difficult, where a typical AT-cut first mode resonator experiences a maximum excursion of +/−20 ppm over the full temperature range. 
     BRIEF SUMMARY OF THE INVENTION 
     To address these limitations experienced with MEMS resonators, this invention relies on redundancy of similar resonators integrated on chip in order to fulfill the requirement of one single quartz resonator. The immediate benefit of that approach compared to quartz technology is the monolithic integration of the reference signal function, implying smaller devices as well as cost and power savings. 
     The invention includes a method for integrated temperature sensing using micro-electro-mechanical resonators based oscillators. The method relies on the ability to integrate the MEMS resonators directly on top of the oscillator CMOS circuitry. The system is based on two independent oscillators. Because MEMS resonators are small, redundancy is possible, and two resonators can be used instead of one. Unlike other approaches, it allows to design the resonant frequency and the temperature characteristic of each oscillator independently. The measured quantity is the frequency difference between the two oscillators, which is a precisely known linear function of temperature. 
     The invention and object and features thereof will be more readily apparent from the following detailed description and appended claims when taken with the drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S) 
         FIG. 1  illustrates architecture of an array based temperature compensated reference oscillator in accordance with an embodiment of the invention. 
         FIG. 2  is a graph illustrating temperature characteristic over the full array. 
         FIG. 3  is a graph illustrating temperature characteristic of one resonator over its functional temperature range. 
         FIG. 4  illustrates a MEMS resonator based temperature sensor in accordance with an embodiment of the invention. 
         FIGS. 5(   a ),  5 ( b ) and  5 ( c ) are schematics of double ended tuning fork (DEFT) resonators with different temperature sensitivity. 
         FIG. 6  is a graph of resonance frequency versus temperature which illustrates temperature characteristics of a 24 MH Z  DEFT. 
         FIG. 7  is a graph illustrating temperature characteristics in a dual resonator based frequency reference system. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The invention provides temperature compensation for an oscillator by including an array of resonators with the oscillator, each resonator having a temperature dependent oscillator frequency. A switch selectively switches each resonator with the oscillator circuit depending on temperature. 
     Using the ability to stack resonators (Silicon Germanium for example) directly on top of CMOS chips, it is possible to link an array of similar resonators to a unique oscillator, and switch from one resonator to the other when the frequency of the resonator in use is out of range because of temperature drift. A high level architecture of a temperature compensated oscillator based on this concept is depicted on the diagram in  FIG. 1 . Here an oscillator with automatic gain control  10  has a frequency determined by resonator array  12 . Temperature sensor  14  establishes resonator selection and a digital engine  16  and memory  18  set electrode bias at  20  and varactor capacitance  22 . Oscillator output is applied through buffer amplifier  24 . 
     A thermal sensor provides an absolute measure of the temperature to a digital engine that decides on which resonator to switch on to the oscillator core. Indeed, each resonator is designed so that its frequency excursion stays within a given range over a limited temperature range. For a given resonator active over a given temperature range, the resonator next to it is designed with a frequency offset so that it will fall into the specified frequency range in the next temperature range (higher or lower). This is illustrated in  FIG. 2  showing the juxtaposed temperature characteristic of each resonator of the array. 
     In this example, each resonator has a +/−4000 ppm excursion over the full temperature range. The offset between them is set to 1000 ppm so that the cross over between temperature ranges occurs within +/−500 ppm of the target frequency. As shown in  FIG. 3 , one resonator is active only over a limited temperature range, here from 20 to 30° C. Red double arrows illustrate the absolute tolerance on the resonator frequency. Thanks to a one-time calibration, the switching temperatures are set into a non-volatile memory so that the resonator hits the target frequency at the center of the working temperature range. This makes the system insensitive to absolute fabrication tolerance of each resonator, thus avoiding the need for trimming. 
     Eventually, as shown in  FIG. 1 , a simple technique based on frequency pulling (DC electrostatic force on the resonator structure, or tunable capacitive load) is used to tune the frequency of the active resonator further down within the specification of the application, illustrated by the highlighted window in  FIG. 3 . 
     Through redundancy and on-chip calibration, the system relies on relative tolerance between each resonator, rather than absolute value. This feature provides better overall accuracy. 
     Consider now specific embodiments of a temperature sensor for use in the temperature compensated oscillator as shown schematically in  FIG. 4 . Here oscillator  400  and oscillator  402  provide frequencies f 1  and f 2  which are mixed at  404  and the mixer output is applied through filter  406  to counter  408 , the output of oscillator  400  provided a clock to counter  408 . 
     Compared to other methods enabling monolithic integration of the temperature sensor, the monitored quantity is a signal frequency, which is measured by far higher accuracy than any other. A resembling method used with quartz resonators relies on the use of higher harmonic with the same resonator to measure the difference in frequency drift as a function of temperature. Called “Dual mode oscillators”, the frequency difference is set by the geometry of the quartz, and the mode order picked for measurement. Intrinsically, this makes the frequency ratio between the two modes at least 3. 
     By the use of MEMS resonators, the two measured modes can be set independently both in terms of resonance frequency and temperature drift. Unlike dual-mode quartz based oscillators, both modes can be set at the exact same frequency which saves the use of a multiplier in the first oscillator path to the mixer. 
     Equation 1 shows the temperature characteristic of one MEMS resonator based oscillator, referenced at (f 0 , T 0 ) so that ΔT=T−T 0 . 
     
       
         
           
             
               
                 
                   
                     
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     The measured frequency, called “beat frequency”, is given by
 
 f   b   =f   1   −f   2   (2)
 
     Its temperature characteristic can be derived as follows in terms of each resonator temperature characteristic: 
     
       
         
           
             
               
                 
                   
                     
                       
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     And thus, as a function of temperature, the frequency drift is: 
     
       
         
           
             
               
                 
                   
                     
                       
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                   ( 
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     The beat frequency is then measured by a counter. This can be a frequency or period meter that provides a near linear function of temperature. 
     As stated before, because the two structures are independent, resonance frequencies are independent, unlike quartz resonators where the frequencies are related to each other by the order of their mode. By designing each structures so that they have their resonance frequency as close as possible while their linear temperature coefficient is set to be different, one can maximize the beat frequency linear coefficient for high temperature sensitivity. At the same time, higher order coefficients α 2 , i  and α 3 , i  of each resonator are close enough to have the beat frequency non-linear coefficients close to zero. The tolerance on the measurement, i.e. the beat frequency fb is thus given by the relative tolerance between the frequency of the resonators which can be made small through careful layout matching made possible by the fact that both resonators are integrated on-chip and close to each other. This results in better accuracy. 
     Design of MEMS resonators with tailored frequency-temperature characteristics: More specifically, while the frequency is set by the dimension of the structures, one can take advantage of the thermal expansion coefficient mismatch between the structural layer and the silicon substrate to set the overall temperature coefficient of each oscillator. This concept is illustrated and applied in  FIG. 5   a  in the case of a Double Ended Tuning Fork (DETF) resonator. 
       FIG. 6  shows the experimental temperature characteristic of a 24 MHz DETF on the blue curve, while the red curve is the extracted characteristic of the same resonator when the effect of thermal expansion mismatch has been removed, and normalized at 25° C. Those curves exhibit a slope of −85 ppm/° C. and −48 ppm/° C. respectively. 
     Indeed, it can be shown that the resonance frequency of the first mode of DETF follows to the first order the equation hereafter: 
                     f     !     1   ⁢           ⁢   st   ⁢           ⁢   mode         =       1     2   ⁢   π       ·           199.   ⁢           I   M     ⁡     (   T   )       ·     E   ⁡     (   T   )             L   ⁡     (   T   )       3         +     4.89   ·       F   ⁡     (   T   )         L   ⁡     (   T   )               0.389   ·     ρ   SiGe     ·   W   ·   L   ·   h                   (   5   )               
with
 
                 I   M     ⁡     (   T   )       =           W   ⁡     (   T   )       3     ·     h   ⁡     (   T   )         12           
the moment of inertia.
 
     The denominator under the square root represents the effective mass of the resonating system. The first term on the numerator is the stress-free effective spring constant on the structure, dependant on temperature T through expansion on the dimensions (length L, Width W, and Thickness h) and temperature coefficient of the Young&#39;s Modulus E. The second term represents the effect of any axial force applied to the tines of the resonator. In the case of  FIG. 5   a , the mismatch between structural material (e.g. SiGe) and the substrate (e.g. Si) creates an axial force on the tines that can be expressed as follows: 
                     F   ⁡     (   T   )       =         σ   ⁡     (   T   )       ·     W   ⁡     (   T   )       ·     h   ⁡     (   T   )         =           α   TSi     -     α   TSiGe         1   +       α   TSiGe     ·   dT         ·     E   ⁡     (   T   )       ·   dT               (   6   )               
where αT is the thermal expansion coefficient for each material, and dT represents the excursion from the nominal temperature.
 
     Unlike the first term in equation (5), this component only depends on the configuration of the anchor. Indeed as depicted in  FIG. 5   b , the anchor can be design so that the tuning fork remains insensitive to thermal expansion mismatch. Here the thermal expansion mismatch is expressed along a direction orthogonal to the resonator tines while the stress-free effective spring constant remains unchanged. In that case, s(T) in equation (6) becomes zero. 
       FIG. 5   c  provides an additional example where the orientation of the anchor allows tailoring the influence of such a mismatch. This concept shown in the specific example of the DETF structure can be applied to any mechanical structure that exhibits resonance frequency sensitivity to temperature as a function of the anchor configuration (Disks, Squares . . . ). It is also worthy to note that, although the concept can be applied to other materials like metals, where there is also an expansion coefficient mismatch with the silicon substrate, SiGe as the structural material for the resonator allows for a much better loss factor, and thus much better stability of the measured frequency. This feature results in better accuracy of the measurement. 
     Temperature compensation for reference oscillators: While having the slope as high as possible is desirable in the case of the temperature sensor, it is also possible to make it as low as possible to compensate for the temperature drift of the resonator. The beat frequency fb becomes the reference signal. Note that in the diagram of  FIG. 1 , the counter is not longer used for that application. 
     For example, if the target reference frequency is a 13 MHz signal, one can design the two resonators so that:
 
At  T=T 0,  f   b   =f   1   −f   2 =13 MHz
 
At the same time, in equation (4), it is possible with proper design to have:
 
∀ i α   1,   i f   10 =α 2,   i ,f   20  
 
at least with the first order coefficient. This results in the characteristic depicted in  FIG. 7 , where the beat frequency is a near constant function of temperature.
 
     In summary, on-chip temperature measurement provides an accurate true value compared to external sensing. The frequency difference between the two fully integrated oscillators is a measure of the temperature at the exact location where the resonator is vibrating. It eliminates any temperature gradient between the resonator and the temperature sensor. Absence of thermal lag (thermal path difference, difference in thermal time constant) avoid hysteretic behavior. In the case of temperature compensation, integration of redundant MEMS structures with similar behavior enables mutual compensation of non-idealities like temperature drift. 
     Advantages of the oscillator and sensor in accordance with the invention include:
         Single chip reference oscillator   No hand-trimming of the frequency is necessary   On-chip temperature compensation   High sensitivity   No thermal lag/No hysteretic behavior thanks to mutual self temperature sensing   Ability to compensate for first order temperature coefficient of both resonator   The tolerance on the measurement is set by the relative tolerance between the frequencies of each resonator which can be low compared to the absolute tolerance of each resonator.   Low power consumption thanks to on-chip integration.       

     While the invention has been described with reference to specific embodiments, the description is illustrative of the invention and is not to be construed as limiting the invention. Various modification and applications may occur to those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.