Oscillator with enhanced stability using a phonon comb

Abstract

A method and apparatus for enhancing the stability of an oscillator circuit by generating a frequency comb in a nonlinear resonator member in response to a drive frequency, the oscillator circuit comprising a voltage controlled oscillator locked to a particular tooth of a frequency comb generated by the nonlinear resonator member at the drive frequency, the absolute value of a first derivative of the drive frequency with respect to the comb frequency being greater than 1 for the drive frequency, and wherein a second voltage controlled oscillator is coupled to a phase locked loop circuit that controls the locking of the second voltage controlled oscillator to the particular tooth of the frequency comb.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of U.S. Provisional Patent Application Serial No. 62 / 904,052, filed on September 23, 2019, entitled “Enhanced Stability Oscillators using a Phononic Comb,” and U.S. Non-Provisional Patent Application Serial No. 16 / 932,455, filed on July 17, 2020, entitled “Enhanced Stability Oscillators using a Phononic Comb,” the disclosures of which are incorporated herein by reference.

[0003] This application relates to the technology disclosed in the following patent applications: U.S. provisional patent application serial number 62 / 881,069, filed on July 31, 2019, entitled “Phononic Comb Enhanced Gradiometers,” and its corresponding non-provisional U.S. patent application, which was filed on August 17, 2020, entitled “Phononic Comb Enhanced Gradiometers,” serial number 16 / 932,431, the disclosures of which are incorporated herein by reference.

[0004] This application also relates to technology disclosed in the following patent applications: U.S. Provisional Patent Application Serial No. 62 / 890,799, filed on August 23, 2019, entitled “Phononic Comb Enhanced Gravity Gradiometer,” and its corresponding non-provisional U.S. patent application, filed on August 17, 2020, entitled:

[0005] The disclosures of U.S. Provisional Patent Application Serial No. 16 / 932,447, “Phononic Comb Enhanced Gravity Gradiometer,” and its corresponding non-provisional U.S. Patent Application, are incorporated herein by reference.

[0006] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0007] No. Technical Field

[0008] An apparatus and method for increasing the stability of a quartz oscillator. Background Art

[0009] Quartz oscillators have many applications in today's electronics. Low phase noise is required for many applications of quartz oscillators, including radar, navigation, and communications. There is a continuing need to improve phase noise and reduce the size, weight, and power (SWaP) of reference oscillators. Nonlinear effects in MEMS resonators, such as the Duffing effect, have been investigated in the past to improve phase noise.

[0010] Temperature Compensated Crystal Oscillators (TCXOs) are used in many clock applications and have small size and low power (typically, approximately 15 mm in size, respectively). 3 and power is less than 10mW). However, they can drift about 0.2ppm with temperature and have a typical phase noise of -90dBc / Hz at 10Hz. Low-cost TCXOs have 1×10 -9 / g g-sensitivity, and g-hardened TCXO can have about 2×

[0011] 10 -11 / g to 5×10 -11 / g g sensitivity. To achieve higher stability, an oven controlled crystal oscillator (OCXO) can be used. Miniaturized OCXOs typically have a g sensitivity of about 1000 mm 3 The OCXOs are relatively large and use more than 150 mW of power. They offer temperature stability of less than 50 ppb and phase noise of about -120 dBc / Hz at 10 Hz. However, OCXOs can have higher g-sensitivity than g-hardened TCXOs. To further improve temperature stability and phase noise at lower offset frequencies, chip-scale atomic clocks (CSACs) have been developed. However, their size and power are about an order of magnitude larger than even OCXOs, and their g-sensitivity can be several orders of magnitude worse than that of TCXOs. Therefore, there is a need for a true chip-scale clock that has power requirements similar to TCXOs, but higher stability than TCXOs, and g-sensitivity at 10 -11 g sensitivity in the / g range.

[0012] As mentioned above, the nonlinear Duffing effect has been used in the past to try to improve the phase noise of low-cost MEMS oscillators (including MEMS oscillators made of quartz, aluminum nitride, and silicon). For example, see DTChang, HP Moyer, RG Nagle, RL Kubena, RJ Joyce, DJ Kirby, PD Brewer, HD Nguyen, and F.P. Stratton, “Nonlinear UHF Quartz MEMS Oscillator with Phase Noise Reduction,” 26(2): 199-200. th IEEE International Conference on MicroElectroMechanicalSystems, January 20-24, 2013.

[0013] However, none of these previous attempts were entirely successful, in part due to the need to operate at or near the bifurcation point, where the frequency dependence on the drive level is large. Thus, amplitude modulated (AM) noise in the holding circuit can be converted into phase modulated (PM) noise in the output. The present disclosure describes a technique and structure that provides frequency insensitivity to noise on the drive amplitude and reduction of PM noise of the driven oscillator when driven under strong nonlinear Duffing conditions (excursions caused by drive levels before the bifurcation site and / or less than about a few hundred ppm). These capabilities have only recently been demonstrated by the discovery of high-Q phononic combs in quartz AT-cut resonators and by other measurements performed on aluminum nitride resonators at the University of Cambridge (see A. Ganesan et al., "Phononic Frequency Comb via Intrinsic Three-Way

[0014] Mixing”, Phy. Rev. Lett., PRL 118, 033903 (2017), pp. 1-5)

[0015] The inventors have made the first measurements of quartz phonon combs over a range of driving frequencies and have found that for certain modal interactions, powers and frequencies, specific comb teeth

[0016] Based on these characteristics, a new clock topology has been conceived that reduces the phase noise of the clock.

[0017] Phonon combs form when one or more high-Q resonators are driven slightly off their resonant frequency into a nonlinear regime. The inventors have demonstrated that phonon combs can be generated in high-Q quartz resonators. The teeth in these combs exhibit complex behavior relative to the drive frequency and can be used to enhance or suppress frequency shifts in a system. Summary of the Invention

[0018] This disclosure describes a method for enhancing the stability of oscillators using phonon frequency combs.

[0019] When a phonon comb is generated by modal mixing of localized modes within a resonator that is driven slightly off one of its resonant frequencies, the comb teeth can exhibit regions of low drive frequency sensitivity. This effect can be exploited to provide a high-stability reference for locking a second voltage-controlled crystal oscillator (VCXO). Consequently, the output of the second VCXO can be stable compared to its own intrinsic stability. This can be achieved with only a modest increase in size and power compared to a single VCXO, as MEMS-based VCXOs can be integrated in arrays on a single silicon wafer, with each resonator needing only less than 1 mm. 2 In addition, the drive and reference elements can be thermostated to increase stability over temperature, or a temperature-compensated mode can be used. In the case of resonant mode sensors (such as temperature, pressure, and acceleration sensors), more sensitive teeth in the comb can be used to enhance the frequency shift caused by the input stimulus. In the case of oscillators used for timing, stable comb teeth can be used to reduce noise.

[0020] In one aspect, the presently disclosed technology provides an oscillator comprising: a first voltage controlled oscillator, a nonlinear resonator element, a second voltage controlled oscillator, and a phase locked loop (PLL) circuit; wherein the first voltage controlled oscillator comprises at least a first resonator and its sustaining circuit, wherein the first oscillator drives the nonlinear resonator element to produce a frequency comb, wherein the second voltage controlled oscillator is locked to a selected tooth of the comb in use at a frequency in which the absolute value of the first derivative of the driving frequency with respect to the frequency of the selected tooth in the comb is greater than 1, and wherein the PLL circuit controls the locking of the second voltage controlled oscillator to the frequency of the selected tooth.

[0021] In another aspect, the presently disclosed technology provides an oscillator comprising: a plurality of piezoelectric resonators; a first sustain circuit and a second sustain circuit coupled to a first piezoelectric resonator and a second piezoelectric resonator of the plurality of piezoelectric resonators, wherein the first sustain circuit generates a drive signal of a given frequency that is applied to another piezoelectric resonator of the plurality of piezoelectric resonators that generates a frequency comb signal; wherein the second sustain circuit is coupled to a phase-locked loop system, the second resonator being locked to a selected tooth of the frequency comb signal at a particular frequency for which the absolute value of a first-order derivative of the drive frequency signal with respect to the frequency of the selected tooth is greater than 1; and wherein the PLL system controls locking of the second oscillator to the selected tooth of the comb, wherein the absolute value of the first-order derivative is greater than 1.

[0022] In yet another aspect, the disclosed technology provides a method for enhancing the stability of an oscillator circuit by generating a frequency comb in a nonlinear resonator member in response to a drive frequency, the oscillator circuit comprising a voltage controlled oscillator locked to a particular tooth or selected teeth of a frequency comb generated by the nonlinear resonator member at the drive frequency, wherein the absolute value of a first derivative of the drive frequency with respect to the frequency of the particular tooth of the comb is greater than 1 for the drive frequency, the voltage controlled oscillator being coupled to a PLL circuit for controlling the locking of the voltage controlled oscillator to the particular tooth or selected teeth of the frequency comb.

[0023] In yet another aspect, the presently disclosed technology provides an oscillator circuit that generates a drive signal, the oscillator circuit including a nonlinear resonator member that, in use, generates a frequency comb in response to the drive signal, the oscillator circuit including a voltage-controlled oscillator and a PLL, the voltage-controlled oscillator being locked by the PLL to a specific tooth or selected teeth of the frequency comb generated by the nonlinear resonator member at the drive signal frequency, the absolute value of a first derivative of the drive frequency with respect to the frequency of the specific tooth of the comb being greater than 1 for the drive signal frequency.

[0024] An apparatus and method for increasing the stability of a quartz oscillator by generating a phonon comb in a nonlinear quartz resonator and selecting teeth in the comb for which the absolute value of the first derivative of the drive frequency with respect to the frequency of the selected tooth in the comb is greater than 1, thereby reducing the frequency instability of the quartz oscillator. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a schematic diagram of a phonon frequency comb enhanced VCXO (2) having a driven VCXO (1) comprising a quartz resonator driven off resonance to produce a comb; and a reference VCXO (2) stabilizing the reference VCXO (2) at a point where the slope (defined as the first derivative of the drive frequency with respect to the tooth output) is greater than 1 using the nth tooth of the comb.

[0026] Figure 2 is a graph depicting the comb amplitude of a phonon frequency comb generated when a 100 MHz AT-cut resonator is driven approximately 5 kHz off resonance from its first anharmonic mode at a drive level of 15 dBm.

[0027] Figure 3 Depicts Figure 2 Comb output frequency versus drive frequency for a 100 MHz resonator as described in In this figure, the slope (first derivative) of the drive frequency versus comb frequency curve is plotted over two drive frequency regions.

[0028] Figure 4 Depicts Figure 2 The comb in Figure 1, but with 400Hz FM modulation of the drive frequency applied. The sidebands around each tooth represent the shift of this modulation across each tooth. The tooth to the left of the drive frequency shows the suppression of the relative amplitude of the modulation to the peak amplitude of that tooth. DETAILED DESCRIPTION

[0029] The following description is provided to enable one of ordinary skill in the art to make and use the present invention and to incorporate it in the context of a particular application. Various modifications and uses in different applications will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to a wide range of embodiments. Therefore, the present invention is not intended to be limited to the embodiments presented, but rather to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0030] In the following detailed description, numerous specific details are set forth to provide a more thorough understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced without being limited to these specific details. In other instances, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring the present invention.

[0031] The reader's attention is directed to (i) all papers and documents filed concurrently with this specification and open to public inspection with this specification (the contents of all of which are incorporated herein by reference); and (ii) all papers and documents otherwise incorporated herein by reference (but not physically filed with this specification).

[0032] Unless expressly stated otherwise, all features disclosed in this specification (including any accompanying claims, abstracts, and drawings) may be replaced by alternative features serving the same, equivalent, or similar purposes. Therefore, unless expressly stated otherwise, each feature disclosed is only one example of a generic series of equivalent or similar features.

[0033] Furthermore, any element in a claim that does not explicitly recite “means for performing the specified function” or “step for performing the specified function” should not be construed as a “means” or “step” clause as specified in 35 U.S.C. § 112, paragraph 6. In particular, the use of “the step of” or “the act of” in the claims herein is not intended to invoke the provisions of 35 U.S.C. § 112, paragraph 6.

[0034] Disclosed herein are apparatus and methods for increasing the stability of a quartz oscillator by reducing frequency instabilities using a phonon comb generated in a nonlinear resonator (preferably embodied as a quartz MEMS electromechanical resonator). The frequency comb has been shown to exhibit regions where the frequencies of particular teeth are insensitive (or substantially insensitive) to variations in the difference between the drive frequency (from a crystal oscillator—the "drive oscillator" also preferably being embodied as another quartz MEMS electromechanical resonator) and the resonator modal frequency of the nonlinear resonator. By using these tooth frequencies as references in a phase-locked loop (PLL), a voltage-controlled crystal oscillator (VCXO) can be stabilized to these reference frequencies of the comb.

[0035] Low phase noise is required for many applications including radar, navigation and communications. There is a continuing need to improve phase noise and reduce the SWaP of reference oscillators. Nonlinear effects such as Duffing in MEMS resonators have been studied in the past to improve phase noise. The present disclosure describes a related but different effect that can occur in a resonator when the resonator is driven nonlinearly. When a phonon comb is generated by modal mixing of localized modes within a resonator that are driven slightly away from one of its resonant frequencies, the comb teeth can exhibit regions of low drive frequency sensitivity. These regions of low drive frequency sensitivity can exist to the right or left of the drive frequency (at frequencies higher or lower than the drive frequency). This effect can be used to provide a high stability reference for locking a second VCXO. As a result, the output of the second VCXO can be stable compared to its own inherent stability. This can be achieved with only a modest increase in size and power compared to a single VCXO because MEMS-based VCXOs can be integrated in array form on a single silicon wafer, with each resonator needing only less than 1 mm 2 .

[0036] Now refer to Figure 1 ,use Figure 2 、 Figure 3 and Figure 4 Supporting data for a quartz AT-cut resonator frequency comb shown in , describing an embodiment of the disclosed technology.

[0037] Figure 1The basic components of an embodiment of the present invention are shown as a first VCXO (VCXO1) including two resonators 30 and 40, a second VCXO (VCXO2) acting as a sensor or oscillator, and electronics including a mixer, a phase detector, and a PLL circuit. The drive signal generated by the first VCXO (VCXO1) is preferably amplified and stabilized using an automatic gain control circuit 38. At a frequency f D The output of S1 is applied to the θ With appropriate mode coupling within the resonator 40 and under the nonlinear Duffing bifurcation condition (for which f θ strongly depends on the amplitude of S1) below the drive level, such as Figure 2 As shown and in Figure 3 The frequency comb S2 is generated graphically within the driving frequency range in f Θ 、f Θ ±Δ, f Θ ±2Δ, f Θ ±3Δ...f Θ Frequency combs are generated at ±nΔ to demonstrate the nonlinear response in the preferred quartz material of the resonator, where Δ = f D -f θ When so driven, resonator 40 may be characterized as a nonlinear resonator element forming a nonlinear resonator oscillator (NLXO).

[0038] like Figure 3 As shown, it has been observed that for a particular tooth of the comb (see Figure 3 The output frequency of the teeth can be independent (or substantially independent) of the drive frequency for a range of drive frequencies, as evidenced by a large slope (or substantially large slope) of a graph of drive frequency versus comb output frequency. A "large" slope, as that term is used herein, is characterized by Figure 3 Although an infinite slope might be ideal so that the output frequency of the tooth is independent (or substantially independent) of the drive frequency, a slope greater than 1 is preferable to using only the drive frequency f D The output frequency of the selected tooth as the clock is less dependent on the drive frequency f D This is an improvement.

[0039] In most oscillators, the far-out phase noise is determined by the electronic noise in the holding circuit. This noise will not be present on the modes of the resonators that are not used within the hold; therefore, by locking the second VCXO (VCXO2) to a selected one of these teeth (the nth tooth) within the PLL and using the error signal of the PLL to correct the relative changes in frequency between VCXO (VCXO2) and S2, the output frequency of the second VCXO (VCXO2) can be stabilized to the level provided by the nth tooth of the comb. Using the feedback tuning signal to the varactor diode in VCXO (1), the frequency of the drive signal S1 can be tuned to the highest slope and lowest noise conditions. For ease of illustration, in Figure 1 Only the higher frequency teeth are shown in detail, while Figure 3 The teeth on either side of the drive frequency are identified in FIG. 1 , and it will be understood that Figure 2 At the frequencies shown, the comb typically appears at the drive frequency f D on both sides.

[0040] for Figure 3 The drive frequency of the resonator 40 is shown to be in response to the comb frequency. The output frequency of the second VCXO (VCXO2) can be stabilized to a drive oscillator (f D ) provides the level of the first tooth to the left of the frequency, because the slope (its first derivative) of the comb frequency of the drive frequency to this tooth is 2.96 in this range. When the oscillator is driven (f D ) Ideally, the slope is even steeper (closer to infinity) at frequencies in the range of 100.1660 MHz to 100.1662 MHz, and the slope of the drive frequency versus the comb frequency (its first derivative) should be as large as possible (and when Figure 3 The slope is infinite when the comb frequency response is shown to be perfectly vertical.) The "undetermined" region is due to the fact that the slope is too large to be calculated with the equipment used for these measurements.

[0041] Drive frequency f D It is not surprising that the slope of is equal to +1. Figure 3 As the tooth slope becomes closer to absolute vertical (along Figure 3 Clockwise from f D As the tooth moves (in a clockwise direction), they approach infinite slope (where the tooth frequency is desirably independent of the drive frequency). As the slope of the tooth moves past vertical (again rotating in a clockwise direction), the slope value becomes negative. As long as the absolute value of the slope of the selected tooth is greater than 1, it has the desired response to the drive frequency f DIf the slope of the selected teeth is further increased, the insensitivity to the drive frequency is further improved.

[0042] The reader will note that Figure 3 The scale of the drive frequency is very narrow compared to the scale of the measured comb frequency, so (f D The slope 1 of is close to but not quite vertical in this figure. Figure 3 The slope of the teeth can have positive or negative values on either side of the vertical (or large) slope in . Since ideally the absolute value of the first derivative of the drive frequency with respect to the frequency of the teeth in the comb should be greater than 1 (and preferably much greater than 1, and even more preferably infinite), the slope of the teeth can be positive or negative on either side of the vertical (or large) slope in . Since ideally the absolute value of the first derivative of the drive frequency with respect to the frequency of the teeth in the comb should be greater than 1 (and preferably much greater than 1, and even more preferably infinite), the slope of the teeth can be positive or negative on either side of the vertical (or large) slope in . D ) of the teeth of the NLXO operation Figure 1 The clock will be used to generate Figure 3 A preferred option for the NLXO of the comb shown. If the absolute value of the first derivative of the drive frequency with respect to the frequency of a selected tooth of the comb is greater than 1, then a specific comb tooth is achieved for the drive frequency f D Reduced sensitivity to changes.

[0043] exist Figure 3 , the slopes for the individual teeth listed in the upper row are measured over the range corresponding to the longer arrows, while the slopes for the individual teeth listed in the lower row are measured over the range corresponding to the shorter arrows.

[0044] Figure 4 This reduction in sensitivity of a particular comb tooth to changes in the drive frequency is also shown in , where 400 Hz FM modulation is added to the drive frequency. The increase in the signal-to-noise ratio (S / N) of the first tooth to the left of the drive frequency indicates that this comb tooth can reduce noise on the drive signal.

[0045] The inventors of the disclosed technology have observed that the high frequency jitter of the first VCXO (VCXO1) can be significantly reduced using this technique. Since most of the phase noise of the oscillator is due to the holding circuit ( Figure 1 The noise is caused by the noise in the VCXO1 in the embodiment of FIG, so this noise will not be present in the resonator 40, so the large slope region of the comb ( Figure 3 to the left of the comb in the middle) will tend to filter out electronic noise.

[0046] The above design can be implemented in a quartz MEMS process, where the VCXO (1), resonator (1), resonator (2) and VCXO (2) are all integrated with the PLL on a common semiconductor (e.g., silicon) substrate using a quartz piezoelectric resonator. This will provide a device with a size of approximately 20 mm or less. 3Chip-scale oscillators (proven to be 2×3mm in size) 2 (See R.L. Kubena et al., “A Fully Integrated Quartz MEMS VHF TCXO,” 2017 IEEE Frequency Control Symposium, Besançon, France, pp. 68-71, July 2017, incorporated herein by reference.) Furthermore, to achieve additional stability over temperature, these components can be thermostated, resulting in a comb-enhanced OCXO. Finally, while quartz resonators have demonstrated high-Q combs with these unique characteristics, other MEMS resonators formed from materials such as silicon or aluminum nitride can be used instead, as long as they exhibit the desired nonlinear and modal coupling effects.

[0047] Having now described the present invention in accordance with the requirements of the patent law, those skilled in the art will understand how to change and modify the present invention to meet their specific requirements or conditions. Such changes and modifications can be made without departing from the scope and spirit of the present invention disclosed herein.

[0048] As required by law, the foregoing detailed description of exemplary and preferred embodiments is provided for purposes of illustration and disclosure. It is not intended to be exhaustive or to limit the invention to the precise form described, but rather to enable others skilled in the art to understand how the invention may be adapted for a particular use or implementation. The possibility of modification and variation will be readily apparent to those skilled in the art. The description of the exemplary embodiments is not restrictive; exemplary embodiments may include tolerances, feature dimensions, specific operating conditions, engineering specifications, and the like, and may vary between implementations or as the prior art changes, and no limitation should be implied thereby. Applicants have made this disclosure relative to the prior art, but also contemplate advancements, and future adaptability may take those advancements into account, i.e., in light of the then-current state of the art. The scope of the invention is defined by the claims as written and applicable equivalents. Reference to a claim element in the singular is not intended to mean "one and only one," unless expressly stated otherwise. Furthermore, no element, component, method, or process step in this disclosure is intended to be dedicated to the public, regardless of whether the element, component, or step is explicitly recited in a claim. Unless a claim element herein is expressly recited using the phrase “means for…,” no claim element herein is to be construed under the provisions of 35 U.S.C. Section 112 as it exists on the filing date of this application, and no method or process step herein is to be construed under such provisions unless the step(s) comprising… are expressly recited using the phrase “step(s) comprising….”

[0049] Without departing from the scope of the present invention, the systems, devices and methods described herein may be modified, added to or omitted. The components of the systems and devices may be integrated or separated. In addition, the operations of the systems and devices may be performed by more, fewer or other components. The method may include more, fewer or other steps. In addition, the steps may be performed in any suitable order. As used herein, "each" refers to each member of a set or each member of a subset of a set.

[0050] The drawings in this application are presented in black and white, but Figures 2 to 4 Color versions of the figures can be found in Appendix A of this patent application. The color versions of these figures present certain data more clearly than their black and white versions, so persons interested in this technology may wish to request a color copy of Appendix A from the U.S. Patent and Trademark Office.

[0051] In 2019, HRL Laboratories, LLC of Malibu, CA, demonstrated the generation of high-fidelity phonon frequency combs in quartz resonators, the results of which are reported in a paper entitled “Phononic Comb Generation in High-Q Quartz Resonators,” RL Kubena et al., Appl. Phys. Lett. 116, 053501 (2020), which is attached hereto as Appendix B. Appendix B is incorporated herein by this reference.

[0052] Broadly speaking, the present application discloses at least the following: a method and apparatus for enhancing the stability of an oscillator circuit by generating a frequency comb in a nonlinear resonator member in response to a drive frequency, the oscillator circuit comprising a voltage controlled oscillator locked to a particular tooth of a frequency comb generated by the nonlinear resonator member at a drive frequency, the absolute value of a first derivative of the drive frequency with respect to the comb frequency being greater than 1 for the drive frequency, and wherein a second voltage controlled oscillator is coupled to a phase locked loop circuit that controls the locking of the second voltage controlled oscillator to the particular tooth of the frequency comb.

[0053] The concept of the present invention includes the following contents:

[0054] Concept 1. An oscillator comprising:

[0055] a first voltage controlled oscillator, a nonlinear resonator element, a second voltage controlled oscillator, and a phase locked loop (PLL) circuit;

[0056] The first voltage-controlled oscillator at least includes a first resonator and a sustaining circuit thereof.

[0057] wherein the first oscillator drives the nonlinear resonator element to generate a frequency comb in use,

[0058] wherein the second voltage controlled oscillator is locked, in use, to a selected tooth of the comb at a frequency at which the absolute value of the first derivative of the drive frequency with respect to the frequency of the selected tooth of the comb is greater than 1, and

[0059] The phase-locked loop circuit controls the locking of the second voltage-controlled oscillator to the frequency of the selected tooth.

[0060] Concept 2. The oscillator of Concept 1, wherein each of the resonators comprises a piezoelectric quartz resonant member.

[0061] Concept 3. The oscillator of Concept 1 or 2, wherein the second voltage controlled oscillator is locked to a specific tooth of the comb at a frequency at which the absolute value of the first derivative of the drive frequency with respect to the frequency of the comb is greater than 2.5.

[0062] Concept 4. An oscillator comprising:

[0063] a plurality of piezoelectric resonators;

[0064] a first sustain circuit and a second sustain circuit, the first sustain circuit and the second sustain circuit being coupled to a first piezoelectric resonator and a second piezoelectric resonator of the plurality of piezoelectric resonators,

[0065] wherein the first sustain circuit generates a driving signal of a given frequency, the driving signal being applied to another piezoelectric resonator among the plurality of piezoelectric resonators, the another piezoelectric resonator generating a frequency comb signal;

[0066] wherein the second holding circuit is coupled to a phase-locked loop system, the second resonator being locked to a selected tooth of the frequency comb signal at a specific frequency, for which the absolute value of a first-order derivative of the drive frequency signal with respect to the frequency of the selected tooth of the comb is greater than 1; and

[0067] wherein the phase-locked loop system controls the locking of the second oscillator to the selected tooth of the comb, wherein the absolute value of the first-order derivative is greater than 1.

[0068] Concept 5. The oscillator of Concept 4, wherein each of the resonators comprises a piezoelectric quartz resonant member.

[0069] Concept 6. The oscillator of Concept 4 or 5, wherein the second resonator is locked to a specific tooth of the comb at a frequency at which the absolute value of the first derivative of the drive frequency with respect to the comb frequency is greater than 2.5.

[0070] Concept 7. A method for enhancing the stability of an oscillator circuit by generating a frequency comb in a nonlinear resonator member in response to a drive frequency, the oscillator circuit comprising a voltage controlled oscillator locked to a particular or selected tooth of the frequency comb generated by the nonlinear resonator member at a drive frequency, the absolute value of a first derivative of the drive frequency with respect to the comb frequency being greater than 1 for the drive frequency, the voltage controlled oscillator being coupled to a phase locked loop circuit for controlling the locking of the voltage controlled oscillator to the particular or selected tooth of the frequency comb.

[0071] Concept 8. The method of Concept 7, wherein the nonlinear resonator member comprises a piezoelectric quartz member.

[0072] Concept 9. The method according to Concept 7 or 8, wherein the voltage controlled oscillator comprises a resonant member composed of quartz.

[0073] Concept 10. The method of any one of Concepts 7-9, wherein the voltage controlled oscillator is locked to the particular tooth or the selected tooth of the comb at a frequency for which the absolute value of the first derivative of the drive frequency with respect to the comb frequency is greater than 2.5.

[0074] Concept 11. The method of any of Concepts 7-10, wherein the voltage controlled oscillator comprises a resonator member, and wherein both the nonlinear resonator member and the resonator member included in the voltage controlled oscillator comprise a piezoelectric quartz member.

[0075] Concept 12. The method of Concept 11, wherein both resonator members are thermostatically controlled to improve the temperature stability of the comb teeth.

[0076] Concept 13. An oscillator circuit generating a drive signal, the oscillator circuit comprising a nonlinear resonator member, the nonlinear resonator member generating, in use, a frequency comb in response to the drive signal, the oscillator circuit comprising a voltage controlled oscillator and a phase locked loop, the voltage controlled oscillator being locked by the phase locked loop to a particular tooth or selected teeth of the frequency comb generated by the nonlinear resonator member at a drive signal frequency, the absolute value of a first derivative of the drive frequency with respect to the comb signal frequency being greater than 1 for the drive signal frequency.

[0077] Concept 14. The oscillator circuit of Concept 13, wherein the nonlinear resonator member comprises a piezoelectric quartz member.

[0078] Concept 15. The oscillator circuit of Concept 13 or 14, wherein said voltage controlled oscillator is locked to a particular tooth of said comb at a frequency for which the absolute value of the first derivative of said drive frequency with respect to said comb frequency is greater than 2.5.

[0079] Concept 16. The oscillator circuit of any of Concepts 13-15, wherein the voltage controlled oscillator comprises a resonator member, and wherein both the nonlinear resonator member and the resonator member included in the voltage controlled oscillator comprise a piezoelectric quartz member.

[0080] Concept 17. The oscillator circuit of Concept 16, wherein both resonator components are thermostatted to improve the stability of the comb teeth over temperature.

[0081] Concept 18. A method for enhancing the stability of a quartz oscillator by generating a phononic comb in a nonlinear quartz resonator and selecting teeth in the comb for which the absolute value of the first derivative of a drive frequency signal with respect to the frequency of the selected tooth of the comb is greater than 1, thereby reducing frequency instability of the quartz oscillator.

Claims

1. An oscillator comprising: a first voltage controlled oscillator, a nonlinear resonator element, a second voltage controlled oscillator, and a phase locked loop circuit; The first voltage-controlled oscillator at least includes a first resonator and a sustaining circuit thereof, wherein the first voltage-controlled oscillator driving the nonlinear resonator element at a drive frequency to generate, in use, a frequency comb signal, wherein the second voltage controlled oscillator is locked, in use, to a selected tooth of the frequency comb signal at a frequency at which the absolute value of the first derivative of the drive frequency with respect to the frequency of the selected tooth in the frequency comb signal is greater than 1, and The phase-locked loop circuit controls the locking of the second voltage-controlled oscillator to the frequency of the selected tooth.

2. The oscillator according to claim 1, wherein The nonlinear resonator element and the first resonator each include a piezoelectric quartz resonant member.

3. The oscillator according to claim 1, wherein The second voltage controlled oscillator is locked to a specific tooth of the frequency comb signal at a frequency at which an absolute value of a first derivative of the drive frequency with respect to the frequency of the frequency comb signal is greater than 2.

5.

4. The oscillator according to claim 1 , wherein the nonlinear resonator element and the first resonator are respectively a third piezoelectric resonator and a first piezoelectric resonator among a plurality of piezoelectric resonators; The sustain circuit of the first voltage-controlled oscillator forms a first sustain circuit coupled to the first piezoelectric resonator among the plurality of piezoelectric resonators, and the second voltage-controlled oscillator includes a second sustain circuit coupled to the second piezoelectric resonator among the plurality of piezoelectric resonators, wherein The first sustain circuit generates a driving signal of a given frequency, the driving signal being applied to the third piezoelectric resonator among the plurality of piezoelectric resonators, the third piezoelectric resonator generating the frequency comb signal; Wherein, the second maintaining circuit is coupled to a phase-locked loop system; and wherein the phase-locked loop system controls locking of the second voltage-controlled oscillator to the selected tooth of the frequency comb signal, wherein the absolute value of the first-order derivative is greater than 1.

5. The oscillator according to claim 4, wherein The resonators each include a piezoelectric quartz resonant member.

6. The oscillator according to claim 4, wherein The selected tooth of the frequency comb signal has a frequency at which an absolute value of a first derivative of the drive frequency with respect to the frequency of the selected tooth of the frequency comb signal is greater than 2.

5.

7. A method for enhancing the stability of an oscillator circuit by generating a frequency comb signal in a nonlinear resonator member in response to a drive frequency generated by a first voltage controlled oscillator having a first sustaining circuit, the oscillator circuit further comprising a second voltage controlled oscillator locked to a particular or selected tooth of the frequency comb signal generated by the nonlinear resonator member at the drive frequency, the absolute value of a first derivative of the drive frequency with respect to the frequency of the particular or selected tooth of the frequency comb signal being greater than 1 for the drive frequency, the second voltage controlled oscillator being coupled to a phase locked loop circuit for controlling the locking of the second voltage controlled oscillator to the particular or selected tooth of the frequency comb signal.

8. The method according to claim 7, wherein: The nonlinear resonator member includes a piezoelectric quartz member.

9. The method according to claim 7, wherein: The second voltage-controlled oscillator includes a resonant member made of quartz.

10. The method according to claim 7, wherein: The second voltage controlled oscillator is locked to the specific tooth or the selected tooth of the frequency comb signal at a frequency for which the absolute value of the first derivative of the drive frequency with respect to the frequency of the specific or selected frequency comb signal is greater than 2.

5.

11. The method according to claim 7, wherein: The second voltage-controlled oscillator includes a resonator member, and wherein both the nonlinear resonator member and the resonator member included in the voltage-controlled oscillator include a piezoelectric quartz member.

12. The method according to claim 11, wherein Both resonator components are thermostatted to improve the stability of the frequency comb signal teeth over temperature.

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