# Novel Gyroscopic Mounting for Crystal Oscillators to Increase Short and Medium Term Stability under Highly Dynamic Conditions

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- •
- Use of mechanical vibration isolation [17].
- •
- •

- •

## 2. Dynamic Loads and Its Affection to Instability of Crystal Oscillator Output

- •
- Steady State Acceleration: Time variant thrust of the host vehicle in both the longitudinal and lateral directions.
- •
- Sinusoidal Vibrations: A series of low frequency sinusoidal vibrations.
- •
- Random Vibration: A combination of band-limited sinusoidal vibrations with random amplitude, frequency and phase.

- •
- Attitude and altitude changes of the host vehicle during the mission.

_{0}is oscillator frequency in Hz, T is the host vehicle mission duration. According to Equations (1)–(4) and Figure 2, frequency and phase disturbances are functions of α and β cosine. Therefore, when $\overrightarrow{A}$ moves away from $\overrightarrow{\mathrm{\Gamma}}$, the oscillator output will be improved.

**Figure 2.**Angular orientation of load $\overrightarrow{A}$ and g-sensitivity vector $\overrightarrow{\mathrm{\Gamma}}$ of crystal blank. (

**a**) Typical state; (

**b**) Critical state (β = 0); (

**c**) Neutral acceleration.

^{‒1}(sinφ/cosα)), when α is increased, the dynamic load-induced disturbances can be reduced and consequently oscillator output stability can be improved.

## 3. Gyroscopic Mounting

**Figure 3.**Modeling of gyroscopic mounting instrument. (

**a**) Gyroscopic-mounting; (

**b**) Dynamic load applied; (

**c**) Mounting on PCB.

_{gyro}: frequency disturbance; Δφ

_{gyro}: phase disturbance; £

_{gyro}(ƒ): phase noise. The maximum effect of gyroscopic mounting appears in the critical state shown in Figure 2b. In this case, gyroscopic mounting protects the system from the maximum probable instabilities.

## 4. G-Sensitivity Vector

_{min}= 2.6° and φ

_{max}= 62° as shown in Figure 5.

## 5. Impacts of Dynamic Loads on Stability of Crystal Oscillator and Proof of Gyro Efficiency

Type | Resonant Frequency | ƒ_{0} | |
---|---|---|---|

OCXO (Oven Control Crystal Oscillator) | 3rd overtone | 10.23 (MHz) | |

Vibration Mode | Crystal Cut | ${\text{\sigma}}_{y}$ (Allan Deviation) | Γ |

Thickness shear | SC-cut | 10^{−11} | 10^{−9}/g |

#### 5.1. Attitude and Altitude Changes of Host Vehicle

**Figure 6.**Crystal oscillator subjected to attitude and altitude changes of host vehicle. (

**a**) Host vehicle trajectory ground track; (

**b**) Attitude and altitude of host vehicle; Adapted from [7]. (

**c**) Orientation of g, Γ and time variant angle δ on crystal.

_{h}< g). Thus the angle between $\overrightarrow{\mathrm{\Gamma}}$ and $\overrightarrow{g}$, and the magnitude of g are time variant parameters. Therefore in either case, the gravity acceleration g plays the role of dynamic load and causes disturbances in oscillator output in the form of clock bias or drift.

_{avr}on the trajectory:

_{h}= acceleration gravity at altitude h.

#### 5.2. Steady State Acceleration (g)

_{long}changes between 0 and 4.2 g on its trajectory, as shown in Figure 8, and the lateral acceleration A

_{lat}changes between 0 and 0.2 g. The impact of this load on the stability of crystal oscillator output directly depends on how it is installed on the host vehicle as shown in Figure 9. To calculate the maximum gyro efficiency, analyses have been performed by assuming vertical installation.

**Figure 8.**Longitudinal steady state acceleration for the Ariane 5 launch vehicle. Adapted from [7].

**Figure 9.**Steady state load applied on the crystal installed on the host vehicle. (

**a**) Horizontally; (

**b**) Vertically.

#### 5.2.1. Impact on Crystal Oscillator Short-Term Stability

#### 5.2.2. Results and Analysis

**Figure 10.**Short-term instability caused by steady state load in critical state β = 0. (

**a**) Frequency deviation of fixed oscillator; (

**b**) Frequency deviation of using gyroscopic mounting; (

**c**) Phase noise of fixed oscillator; (

**d**) Phase noise of gyroscopic mounting.

**Figure 11.**Average instability caused by steady state load. (

**a**) Frequency deviation; (

**b**) Phase noise.

β = 0 2° < |φ| < 62° | Fixed Oscillator | Using Gyro | Gyro Effect |
---|---|---|---|

Δƒ_{Max} | 3.59 × 10^{−}^{2} (Hz) | 1.57 × 10^{−}^{2} (Hz) | −2.02 × 10^{−}^{2} (Hz) (56.27%) |

Δƒ_{Min} | 1.70 × 10^{−}^{3} (Hz) | 7.48 × 10^{−4} (Hz) | −9.61 × 10^{−4} (Hz) (56.53%) |

£(ƒ)_{Max} | −17.42 (dBc/Hz) | −23.11 (dBc/Hz) | −5.69 (dB) |

£(ƒ)_{Min} | −43.86 (dBc/Hz) | −49.56 (dBc/Hz) | −5.69 (dB) |

**Figure 12.**Comparison between steady state load-induced frequency deviation and Allan safety margin. (

**a**) Fixed oscillator; (

**b**) Gyroscopic mounting.

**Figure 13.**Comparison between steady state load-induced phase noise and Allan safety margin. (

**a**) Fixed oscillator; (

**b**) Gyroscopic mounting.

0° < β < 90° | Fixed Oscillator | Using Gyro | GYRO EFFECT |
---|---|---|---|

Δƒ_{Max} | 4.29 × 10^{−}^{2} (Hz) | 1.90 × 10^{−}^{3} (Hz) | −4.10 × 10^{−}^{2} (Hz) (95.57%) |

Δƒ_{Min} | 3.57 × 10^{−5} (Hz) | 9.28 × 10^{−5} (Hz) | +5.7 × 10^{−5} |

£(ƒ)_{Max} | −17.40 (dBc/Hz) | −44.26 (dBc/Hz) | −26.86 (dB) |

£(ƒ)_{Min} | −79.01 (dBc/Hz) | −70.70 (dBc/Hz) | +8.31 (dB) |

0° < β < 90° | Fixed Oscillator | Using Gyro | Gyro Effect |
---|---|---|---|

Δƒ_{Max} | 3.39 × 10^{−}^{2} (Hz) | 2.65 × 10^{−}^{2} (Hz) | −7.40 × 10^{−}^{3} (Hz) (21.83%) |

Δƒ_{Min} | 2.81 × 10^{−5} (Hz) | 1.30 × 10^{−}^{3} (Hz) | 1.27 × 10^{−}^{3} (Hz) |

£(ƒ)_{Max} | −19.46 (dBc/Hz) | −21.61 (dBc/Hz) | −2.15 (dB) |

£(ƒ)_{Min} | −81.07 (dBc/Hz) | −48.05 (dBc/Hz) | 33.02 (dB) |

^{−4}Hz). Only when the β angle is very close to 90°, this mounting causes negligible drawbacks in oscillator output, such that frequency deviation is still less than the Allan deviation (10

^{−4}Hz). Gyroscopic mounting shows its great effects on phase noise for β < 70°. Its drawbacks appear only for β values too close to 90°. However, this drawback is negligible because phase noise is still less than the Allan deviation (−70.05 dBc/Hz).

^{−4}Hz). Its drawback on frequency deviation appears only for β angles too close to 90°. The best effects on phase noise appear for β < 45°. Drawbacks with small values start from β = 60°. Big drawbacks only occur for β close to 90°.

#### 5.3. Sinusoidal Vibrations (f_{v,si} = 2–100 Hz)

**Figure 14.**Sinusoidal vibrations of the Ariane 5 launch vehicle. Adapted from [7].

**Figure 15.**Magnitude and angular orientation of sinusoidal vibrations. (

**a**) α = 38.7°; (

**b**) α = 31°; (

**c**) α = 36.87°.

#### 5.3.1. Impact on Crystal Oscillator Short-Term Stability

_{v,si}< 100; angle α and A

_{ztp}as indicated in Figure 15. Critical state and maximum effect of gyroscopic mounting appears when β = 0.

#### 5.3.2. Results and Analysis

**Figure 16.**Sinusoidal vibrations-induced short term instability for critical state β = 0. (

**a**) Frequency jitter of fixed oscillator; (

**b**) Frequency jitter of gyroscopic mounting; (

**c**) Phase noise of fixed oscillator; (

**d**) Phase noise of gyroscopic mounting.

**Figure 17.**Average instability caused by sinusoidal vibration. (

**a**) Frequency jitter; (

**b**) Phase noise.

β = 0, 2° < |φ| < 62° | Fixed Oscillator | Using Gyro | Gyro Effect |
---|---|---|---|

Δƒ_{Max} | 1.06 × 10^{−}^{2} (Hz) | 4.80 × 10^{−}^{3} (Hz) | −5.80 × 10^{−}^{3} (Hz) (54.72%) |

Δƒ_{Min} | 8.10 × 10^{−}^{3} (Hz) | 3.70 × 10^{−}^{3} (Hz) | −4.40 × 10^{−}^{3} (Hz) (54.32%) |

£(ƒ)_{Max} | −41.93 (dBc/Hz) | −49.45 (dBc/Hz) | −7.38 (dB) |

£(ƒ)_{Min} | −81.28 (dBc/Hz) | −88.66 (dBc/Hz) | −7.52 (dB) |

**Figure 18.**Comparison between sinusoidal vibrations-induced frequency jitter and Allan deviation safety margin. (

**a**) Fixed oscillator; (

**b**) Gyroscopic mounting.

**Figure 19.**Comparison between sinusoidal vibrations-induced phase noise and Allan deviation safety margin. (

**a**) Fixed oscillator; (

**b**) Gyroscopic mounting.

0° < β <90° | Fixed Oscillator | Using Gyro | Allan Deviation | Gyro Effect |
---|---|---|---|---|

Δƒ_{max} | 8.60 × 10^{−}^{3} (Hz) | 5.94 × 10^{−4} (Hz) | 1 × 10^{−4} (Hz) | −8.00 × 10^{−}^{3} (Hz) |

Δƒ_{min} | 1.14 × 10^{−4} (Hz) | 4.64 × 10^{−4} (Hz) | 1 × 10^{−4} (Hz) | 3.5 × 10^{−4} (Hz) |

£(ƒ)_{min} | −53.31 (dBc/Hz) | −76.56 (dBc/Hz) | −92.04 (dBc/Hz) | −23.25 (dB) |

£(ƒ)_{min} | −124.92 (dBc/Hz) | −112.70 (dBc/Hz) | −126.02 (dBc/Hz) | 12.22 (dB) |

0° < β < 90° | Fixed Oscillator | Using Gyro | Allan Deviation | Gyro Effect |
---|---|---|---|---|

Δƒ_{max} | 1.27 × 10^{−}^{2} (Hz) | 8.10 × 10^{−}^{3} (Hz) | 1 × 10^{−4} (Hz) | −0.0047 (Hz) |

Δƒ_{min} | 1.72 × 10^{−4} (Hz) | 6.30 × 10^{−}^{3} (Hz) | 1 × 10^{−4} (Hz) | 0.0061 (Hz) |

£(ƒ)_{min} | −49.94 (dBc/Hz) | −53.91 (dBc/Hz) | −92.04 (dBc/Hz) | −3.98 (dB) |

£(ƒ)_{max} | −121.29 (dBc/Hz) | −90.04 (dBc/Hz) | −126.02 (dBc/Hz) | 31.26 (dB) |

^{−4}Hz). For 2 < ƒ

_{v,si}< 100, this mounting reduces phase noise −23.25 dBc at most. Its drawbacks appear only when the β value is too close to 90°.

#### 5.4. Random Vibration (20 < ƒ_{RV} < 2000 Hz)

**Figure 20.**Random vibration applied on crystal oscillator 0 < |ξ| < π, 0 < |β| < π. (

**a**) Fixed oscillator; (

**b**) Oscillator on gyroscopic mounting.

^{2}/Hz). Since random vibration is a combination of all the frequencies at the same time, it is necessary to configure this load in the time domain. According to the Parseval’s law, g

_{rms}is equal to 1σ of random vibration. Thus the random vibration in time domain can be shown according to Figure 21b by calculation of g

_{rms}from ASD.

_{rms}. Therefore, beside analysis in time domain, it is necessary to analyze the random vibration in the frequency domain.

**Figure 21.**Mechanical random vibration for the Ariane 4 launch vehicle. (

**a**) ASD (g

^{2}/Hz); Adapted from [32]. (

**b**) Time domain representation.

#### 5.4.1. Random Vibration in Time Domain

_{rms}

**Figure 22.**Maximum instability (ξ = φ) caused by random vibration for ƒ

_{RV}= 2000 (Hz). (

**a**) Frequency jitter of fixed oscillator; (

**b**) Frequency jitter of gyroscopic mounting; (

**c**) Phase noise of fixed oscillator; (

**d**) Phase noise of gyroscopic mounting.

**Figure 23.**Comparison between system instability in different states. (

**a**) Maximum state ξ = φ, β = 0; (

**b**) Minimum state, ξ − φ = 90°or β = 90°.

Random Vibration Induced Instability | ||||
---|---|---|---|---|

2.6° < φ < 38°, RV = 3σ, ξ = φ, β = 0 | Fixed Oscillator | Using Gyro | Allan | Gyro Effect |

Max gyro effect on Δƒ | 2.24 × 10^{−}^{1} (Hz) | 7.80 × 10^{−}^{3} (Hz) | 1 × 10^{−4} (Hz) | −2.16 × 10^{−}^{1} (Hz) (96.42%) |

Max gyro drawback on Δƒ | 3.90 × 10^{−}^{3} (Hz) | 1.14 × 10^{−}^{1} (Hz) | 1 × 10^{−4} (Hz) | +1.10 × 10^{−}^{1} (Hz) |

Max gyro effect on £(ƒ) | −85.03 (dBc/Hz) | −114.17 (dBc/Hz) | −152.04(dBc/Hz) | −29.14 (dB) |

Max gyro drawback on £(ƒ) | −120.19 (dBc/Hz) | −91.31 (dBc/Hz) | −152.04(dBc/Hz) | +28.88 (dB) |

β = 0, 2° < |φ| < 62° | Fixed Oscillator | Using Gyro | Gyro Effect | |
---|---|---|---|---|

Δƒ | 1σ (68.3%) | 0.0697 (Hz) | 0.0273 (Hz) | 0.0424 (Hz) |

2σ (95.6%) | 0.1394 (Hz) | 0.0546 (Hz) | 0.0847 (Hz) | |

3σ (99.7%) | 0.2091 (Hz) | 0.0819 (Hz) | 0.1271 (Hz) | |

£(ƒ) | 1σ (68.3%) | −88.16 (dBc/Hz) | −96.89 (dBc/Hz) | −8.73 (dB) |

2σ (95.6%) | −82.55 (dBc/Hz) | −91.28 (dBc/Hz) | −8.73 (dB) | |

3σ (99.7%) | −79.27 (dBc/Hz) | −87.99 (dBc/Hz) | −8.73 (dB) |

#### 5.4.2. Random Vibration in Frequency Domain

**-**term stability

_{v}< 2000 (Hz), RV: according to Equations (28)–(31), 0 < |β| < π, 0 < |ξ| < π, 0 < |φ| < π/2, Critical state or maximum gyroscopic mounting effect appears when: β = kπ & ξ − φ = kπ (k = 0, 1).

**Figure 25.**Analysis of random vibration in frequency domain for ξ = φ, β = 0. (

**a**) Frequency jitter of fixed oscillator; (

**b**) Frequency jitter of gyroscopic mounting; (

**c**) Phase noise of fixed oscillator; (

**d**) Phase noise of gyroscopic mounting.

**Figure 26.**Analysis of random vibration in frequency domain for 0° < |ξ | < 180°, β = 0, φ = 2σ = 38°.(

**a**) Frequency jitter of fixed oscillator; (

**b**) Frequency jitter of gyroscopic mounting; (

**c**) Phase noise of fixed oscillator; (

**d**) Phase noise of gyroscopic mounting.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Rohde, U.L.; Poddar, A.K.; Boeck, G. The Design of Modern Microwave Oscillators for Wireless Applications: Theory and Optimization; Wiley: New York, NY, USA, 2005. [Google Scholar]
- Rohde, U.L.; Poddar, A.K.; Lakhe, R. Electromagnetic interference and start-up dynamics in high-frequency crystal oscillator circuits. Microw. Rev.
**2010**, 7, 23–33. [Google Scholar] - Maffezzoni, P.; Zhang, Z.; Daniel, L. A Study of Deterministic Jitter in Crystal Oscillators. IEEE Trans. Circuits Syst.
**2014**, 61, 1044–1054. [Google Scholar] [CrossRef] - Mancini, O. Tutorial: Precision Frequency Generation Utilizing OCXO and Rubidium Atomic Standards with Applications for Commercial, Space, Military, and Challenging Environments; IEEE Long Island Chapter; Frequency Electronics, Inc.: New York, NY, USA, 2004. [Google Scholar]
- Lutwak, R. Principles of Atomic Clocks. In Tutorial of EFTF-IFCS; Symmetricom-Technology Realization Center: San Francisco, CA, USA, 2011. [Google Scholar]
- Lombardi, M.A. Fundamentals of Time and Frequency. In The Mechatronics Handbook; CRC Press: Boca Raton, FL, USA, 2002; Chapter 17. [Google Scholar]
- Arian5 User’s Manual. Available online: http://www.Arianespace.com (accessed on 1 June 2015).
- Norton, J.R.; Cloeren, J.M.; Sulzer, P.G. Brief history of the development of ultra-precise oscillators for ground and space applications. In Proceeding of the 50th IEEE Annual Symposium on Frequency Control, Honolulu, HI, USA, 5–7 June 1996; pp. 47–57.
- Walls, F.L.; Vig, J.R. Fundamental Limits on the Frequency Stabilities of Crystal Oscillators. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**1995**, 42, 576–589. [Google Scholar] [CrossRef] - Warrington, B. Next-generation frequency standards. In Tutorial of IEEE International Frequency Control Symposium; Australian National Measurement Institute: Baltimore, MD, USA, 2012. [Google Scholar]
- Hausman, H. Oscillator Oddities: The Art of Oscillator Design, and Its Impact on System Performance. MITEQ, Inc.: Hauppauge, NY, USA, 11 April 2007. [Google Scholar]
- Howe, D.A. Phase Noise and Vibration Tolerance in Microwave Oscillators: Needs vs. State-of-the-Art; Tutorial of National Institute of Standards & Technology (NIST): Boulder, CO, USA, 2006. [Google Scholar]
- Allan, D.W. Time and Frequency (The-Domain) Characterization, Estimation, and Prediction of Precision Clocks and Oscillators. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**1987**, 34, 647–654. [Google Scholar] [CrossRef] [PubMed] - Morley, P.E.; Haskell, R.B. Method for measurement of the sensitivity of crystal resonators to repetitive stimuli. In Proceeding of IEEE International Frequency Control Symposium and PDA Exhibition, New Orleans, LA, USA, 29–31 May 2002; pp. 61–65.
- Driscoll, M. Low Noise Signal Generation and Verification Techniques. In Proceedings of Symposium on Ultrasonic Electronics, Chiba, Japan, 13–15 November 2012.
- Rosati, V.J. Suppression of Vibration-Induced Phase Noise in Crystal Oscillators: An Update. In Proceeding of 41st IEEE Annual Frequency Control Symposium, Philadelphia, PA, USA, 27–29 May 1987.
- Fu, W.; Qian, Z.; Huang, X.; Tan, F. Analysis of Two-stage Passive Vibration Isolation System for Crystal Oscillator at High-frequency Vibration. In Proceedings of IEEE International Frequency Control Symposium Joined with 22 European Frequency and Time Forum, Besancon, France, 20–24 April 2009; pp. 501–504.
- Labruzzo, G.; Polidoro, P.; Driscoll, M.; Kolnowski, G. VHF, Quartz Crystal Oscillator Exhibiting Exceptional Vibration Immunity. In Proceedings of 50th IEEE International Frequency Control Symposium, Honolulu, HI, USA, 5–7 June 1996; pp. 473–480.
- Driscoll, M.M. Reduction of Quartz Crystal Oscillator Flicker-of-Frequency and White Phase Noise (floor) Levels and Acceleration Sensitivity via Use of Multiple Resonators. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**1993**, 40, 427–430. [Google Scholar] [CrossRef] [PubMed] - Tiersten, H.F.; Zhou, Y.S. The increase in the in-plane acceleration sensitivity due to its thickness asymmetry. In Proceeding of 45th IEEE Annual Symposium on Frequency Control, Los Angeles, CA, USA, 29–31 May 1991; pp. 289–297.
- Tiersten, H.F.; Zhou, Y.S. An analysis of the in-plane acceleration sensitivity of contoured quartz resonators with rectangular supports. In Proceeding of 44th IEEE Annual Symposium on Frequency Control, Baltimore, MD, USA, 23–25 May 1990; pp. 461–467.
- Zhou, Y.S.; Tiersten, H.F. On the influence of a fabrication imperfection on the normal acceleration sensitivity of contoured quartz resonators with rectangular supports. In Proceedings of 44th IEEE Annual Symposium on Frequency Control, Baltimore, MD, USA, 23–25 May 1990; pp. 452–460.
- Haskell, R.B.; Buchanan, J.E.; Morley, P.E.; Desai, B.B.; Esmiol1, M.A.; Martin, M.E.; Stevens, D.S. State-of-the-Art in the Design and Manufacture of Low Acceleration Sensitivity Resonators. In Proceedings of IEEE International, Montreal, QC, Canada, 23–27 August 2004; pp. 672–677.
- Stewart, J.T.; Morley, P.E.; Stevens, D.S. Theoretical and experimental results for the acceleration sensitivity of rectangular crystal resonators. In Proceeding of 53 IEEE Annual Symposium on Frequency Control, Besancon, France, 13–16 April 1999; pp. 489–493.
- Driscoll, M.M. Quartz crystal resonator G-sensitivity measurement methods and recent results. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**1990**, 37, 386–392. [Google Scholar] [CrossRef] [PubMed] - Przyjemski, J.M. Improvement in system performance using a crystal oscillator compensated for acceleration sensitivity. In Proceeding of 32 IEEE annual Symposium on Frequency Control, Atlantic City, NJ, USA, 31 May–2 June 1978; pp. 426–431.
- Su, W. A novel method to suppress vibration-induced phase noise of crystal oscillators. J. Control Eng. Pract.
**2004**, 12, 1065–1070. [Google Scholar] [CrossRef] - Nelson, C. Reducing Phase Noise Degradation Due to Vibration of Crystal Oscillators. Master’s Thesis, Iowa State University, Ames, IA, USA, 2010. [Google Scholar]
- Vig, J.R.; Ballato, A. Frequency Control Devices; U.S. Army Communications—Electronics Command: Fort Monmouth, NJ, USA, 2000.
- Filler, R.L. The Acceleration Sensitivity of Quartz Crystal Oscillators: A Review Invited Paper. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**1988**, 3, 297–305. [Google Scholar] [CrossRef] [PubMed] - Space Engineering Testing; ECSS-E-10-03A; ESA Publications Division: Noordwijk, The Netherlands, 2002.
- Wijker, J. Random Vibrations in Spacecraft Structures Design Theory and Application; Springer: Dordrecht, The Netherlands, 2009. [Google Scholar]
- Wijker, J.J. Spacecraft Structures; Springer-Verlag: Berlin/Heidelberg, Germany, 2008. [Google Scholar]
- Yang, C.Y. Random Vibration of Structures; John Wiley &Sons, Inc.: New York, NY, USA, 1986. [Google Scholar]
- Lalanne, C. Random Vibration; Hermes Penton Ltd.: London, UK, 2002; Volume 3. [Google Scholar]
- Salzenstein, P.; Kuna, A.; Sojdr, L.; Chauvin, J. Significant step in ultra-high stability quartz crystal oscillators. Electron. Lett.
**2010**, 46, 1433–1434. [Google Scholar] [CrossRef] - Fry, S.J. Acceleration Sensitivity Characteristics of Quartz Crystal Oscillators, Granary Tech Briefs; Granary Industries Inc.: Mechanicsburg, PA, USA, 2006. [Google Scholar]
- Haskell, R.B.; Morley, P.E.; Stevens, D.S. High Q Precision SC cut resonators with low acceleration sensitivity. In Proceeding of the 56th IEEE International Frequency Control Symposium and PDA, New Orleans, LA, USA, 29–31 May 2002; pp. 111–118.
- Ballato, A. Doubly Rotated Thickness Mode Plate Vibrators. In Physical Acoustics; Academic Press Inc.: Fort Monmouth, NJ, USA, 1977; Volume XIII, pp. 115–181. [Google Scholar]
- Lombardi, M.A. The Use of GPS Disciplined Oscillators as Primary Frequency Standards for Calibration and Metrology Laboratories. J. Meas. Sci.
**2008**, 3, 56–65. [Google Scholar]

© 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Abedi, M.; Jin, T.; Sun, K.
Novel Gyroscopic Mounting for Crystal Oscillators to Increase Short and Medium Term Stability under Highly Dynamic Conditions. *Sensors* **2015**, *15*, 14261-14285.
https://doi.org/10.3390/s150614261

**AMA Style**

Abedi M, Jin T, Sun K.
Novel Gyroscopic Mounting for Crystal Oscillators to Increase Short and Medium Term Stability under Highly Dynamic Conditions. *Sensors*. 2015; 15(6):14261-14285.
https://doi.org/10.3390/s150614261

**Chicago/Turabian Style**

Abedi, Maryam, Tian Jin, and Kewen Sun.
2015. "Novel Gyroscopic Mounting for Crystal Oscillators to Increase Short and Medium Term Stability under Highly Dynamic Conditions" *Sensors* 15, no. 6: 14261-14285.
https://doi.org/10.3390/s150614261