Holdover in synchronization applications

Last updated January 26, 2024

Two independent clocks, once synchronized, will walk away from one another without limit.^[1] To have them display the same time it would be necessary to re-synchronize them at regular intervals. The period between synchronizations is referred to as holdover and performance under holdover relies on the quality of the reference oscillator, the PLL design, and the correction mechanisms employed.^[2]

Importance

Synchronization is as important as power at the cell site.^[3]

The quote above suggests that one can think of holdover in synchronization applications as analogous to running on backup power.

Modern wireless communication systems require at least knowledge of frequency and often knowledge of phase as well in order to work correctly. Base stations need to know what time it is, and they usually get this knowledge from the outside world somehow (from a GPS Time and Frequency receiver, or from a synchronization source somewhere in the network they are connected to).

But if the connection to the reference is lost then the base station will be on its own to establish what time it is. The base station needs a way to establish accurate frequency and phase (to know what time it is) using internal (or local) resources, and that’s where the function of holdover becomes important.

The importance of GPS-derived timing

A key application for GPS in telecommunications is to provide synchronization in wireless basestations. Base stations depend on timing to operate correctly, particularly for the handoff that occurs when a user moves from one cell to another.^[4] In these applications holdover is used in base stations to ensure continued operation while GPS is unavailable and to reduce the costs associated with emergency repairs, since holdover allows the site to continue to function correctly until maintenance can be performed at a convenient time.^[5]

Some of the most stringent requirements come from the newer generation of wireless base stations, where phase accuracy targets as low as 1μs need to be maintained for correct operation.^[6] However the need for accurate timing has been an integral part of the history of wireless communication systems as well as wireline,^[7] and it has been suggested that the search for reliable and cost effective timing solutions was spurred on by the need for CDMA to compete with lower cost solutions.^[8]

Within the base station, besides standard functions, accurate timing and the means to maintain it through holdover is vitally important for services such as E911 ^[5]

GPS as a source of timing is a key component in not just Synchronization in telecommunications but to critical infrastructure in general.^[9] Of the 18 Critical Resource and Key infrastructure (CIKR^[10])sectors, 15 use GPS derived timing to function correctly.^[11] One notable application where highly accurate timing accuracy (and the means to maintain it through holdover) is of importance is in the use of Synchrophasors in the power industry to detect line faults.^[12].

How GPS-derived timing can fail

GPS is sensitive to jamming and interference because the signal levels are so low^[13] and can easily be swamped by other sources, that can be accidental or deliberate.^[14] Also since GPS depends on line of sight signals it can be disrupted by Urban canyon effects, making GPS only available to some locations at certain times of the day, for example.

A GPS outage however is not initially an issue because clocks can go into holdover,^[15] allowing the interference to be alleviated as much as the stability of the oscillator providing holdover will allow.^[4] The more stable the oscillator, the longer the system can operate without GPS.

Defining holdover

In Synchronization in telecommunications applications holdover is defined by ETSI as:

An operating condition of a clock which has lost its controlling input and is using stored data, acquired while in locked operation, to control its output. The stored data are used to control phase and frequency variations, allowing the locked condition to be reproduced within specifications. Holdover begins when the clock output no longer reflects the influence of a connected external reference, or transition from it. Holdover terminates when the output of the clock reverts to locked mode condition.^[16]

One can regard holdover then as a measure of accuracy or error acquired by a clock when there is no controlling external reference to correct for any errors.

MIL-PRF-55310^[17] defines Clock Accuracy as:

$T(t)=T_{0}+\int _{0}^{t}R(t)\,dt\ +\epsilon (t)=T_{0}+(R_{0}t+{\frac {1}{2}}At^{2}+...)+\int _{0}^{t}E_{t}(t)\,dt+\epsilon (t)$

Where $T_{0}$ is the synchronization error at $t=0$ ; $R(t)$ is the fractional frequency difference between two clocks under comparison; $\epsilon (t)$ is the error due to random noise; $R_{0}$ is $R(t)$ at $t=0$ ; $A$ is the linear aging rate and $E_{1}(t)$ is the frequency difference due to environmental effects.

Similarly ITU G.810^[18] defines Time Error as:

$x(t)=x_{0}+y_{0}t+{\frac {D}{2}}t^{2}+{\frac {\phi (t)}{2\pi \nu _{nom}}}$

Where $x(t)$ is the time error; $x_{0}$ is the time error at $t=0$ ; $y_{0}$ is the fractional frequency error at $t=0$ ; $D$ is the linear fractional frequency drift rate; $\phi (t)$ is the random phase deviation component and $\nu _{nom}$ is the nominal frequency.

Implementing holdover

In applications that require synchronization (such as wireless base stations) GPS Clocks are often used and in this context are often known as a GPSDO (GPS Disciplined Oscillator) or GPS TFS (GPS Time and Frequency Source).^[19]

NIST defines a Disciplined Oscillator as:

An oscillator whose output frequency is continuously steered (often through the use of a phase locked loop) to agree with an external reference. For example, a GPS disciplined oscillator (GPSDO) usually consists of a quartz or rubidium oscillator whose output frequency is continuously steered to agree with signals broadcast by the GPS satellites.^[20]

In a GPSDO a GPS or GNSS signal is used as the external reference that steers an internal oscillator.^[13] In a modern GPSDO the GPS processing and steering function are both implemented in a Microprocessor allowing a direct comparison between the GPS reference signal and the oscillator output.^[8]

A Modern GPSDO GPSDO.png — A Modern GPSDO

Amongst the building blocks of a GPS Time and Frequency solution the oscillator is a key component^[11] and typically they are built around an Oven Controlled Crystal Oscillator (OCXO) or a Rubidium based clock. The dominant factors influencing the quality of the reference oscillator are taken to be aging and temperature stability. However, depending upon the construction of the oscillator, barometric pressure and relative humidity can have at least as strong an influence on the stability of the quartz oscillator.^{[ citation needed ]} What is often referred to as "random walk" instability is actually a deterministic effect of environmental parameters. These can be measured and modeled to vastly improve the performance of quartz oscillators. An addition of a Microprocessor to the reference oscillator can improve temperature stability and aging performance^[21] During Holdover any remaining clock error caused by aging and temperature instability can be corrected by control mechanisms.^[22] A combination of quartz based reference oscillator (such as an OCXO) and modern correction algorithms can get good results in Holdover applications.^[23]

The holdover capability then is provided either by a free running local oscillator, or a local oscillator that is steered with software that retains knowledge of its past performance.^[23] The earliest documentation of such an effort comes from the then National Bureau of Standards in 1968 [Allan, Fey, Machlan and Barnes, "An Ultra Precise Time Synchronization System Designed By Computer Simulation", Frequency], where an analog computer consisting of ball-disk integrators implemented a third order control loop to correct for the frequency ageing of an oscillator. The first microprocessor implementation of this concept occurred in 1983 [Bourke, Penrod, "An Analysis of a Microprocessor Controlled Disciplined Frequency Standard", Frequency Control Symposium] where Loran-C broadcasts were used to discipline very high quality quartz oscillators as a caesium replacement in telecommunications wireline network synchronization. The basic aim of a steering mechanism is to improve the stability of a clock or oscillator while minimizing the number of times it needs calibration.^[1] In Holdover the learned behaviour of the OCXO is used to anticipate and correct for future behavior.^[2] Effective aging and temperature compensation can be provided by such a mechanism^[24] and the system designer is faced with a range of choices for algorithms and techniques to do this correction including extrapolation, interpolation and predictive filters (including Kalman filters).^[25]^[26]

Once the barriers of aging and environmental effects are removed the only theoretical limitation to holdover performance in such a GPSDO is irregularity or noise in the drift rate, which is quantified using a metric like Allan deviation or Time deviation.^[27]^{[ unreliable source? ]}

The complexity in trying to predict the effects on Holdover due to systematic effects like aging and temperature stability and stochastic influences like Random Walk noise has resulted in tailor-made Holdover Oscillator solutions being introduced in the market.^[28]

Related Research Articles

Synchronization is the coordination of events to operate a system in unison. For example, the conductor of an orchestra keeps the orchestra synchronized or in time. Systems that operate with all parts in synchrony are said to be synchronous or in sync—and those that are not are asynchronous.

A crystal oscillator is an electronic oscillator circuit that uses a piezoelectric crystal as a frequency-selective element. The oscillator frequency is often used to keep track of time, as in quartz wristwatches, to provide a stable clock signal for digital integrated circuits, and to stabilize frequencies for radio transmitters and receivers. The most common type of piezoelectric resonator used is a quartz crystal, so oscillator circuits incorporating them became known as crystal oscillators. However, other piezoelectricity materials including polycrystalline ceramics are used in similar circuits.

A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a variable frequency oscillator and a phase detector in a feedback loop. The oscillator's frequency and phase are controlled proportionally by an applied voltage, hence the term voltage-controlled oscillator (VCO). The oscillator generates a periodic signal of a specific frequency, and the phase detector compares the phase of that signal with the phase of the input periodic signal, to adjust the oscillator to keep the phases matched.

In signal processing, phase noise is the frequency-domain representation of random fluctuations in the phase of a waveform, corresponding to time-domain deviations from perfect periodicity (jitter). Generally speaking, radio-frequency engineers speak of the phase noise of an oscillator, whereas digital-system engineers work with the jitter of a clock.

A radio clock or radio-controlled clock (RCC), and often colloquially referred to as an "atomic clock", is a type of quartz clock or watch that is automatically synchronized to a time code transmitted by a radio transmitter connected to a time standard such as an atomic clock. Such a clock may be synchronized to the time sent by a single transmitter, such as many national or regional time transmitters, or may use the multiple transmitters used by satellite navigation systems such as Global Positioning System. Such systems may be used to automatically set clocks or for any purpose where accurate time is needed. Radio clocks may include any feature available for a clock, such as alarm function, display of ambient temperature and humidity, broadcast radio reception, etc.

In electronics and especially synchronous digital circuits, a clock signal is an electronic logic signal which oscillates between a high and a low state at a constant frequency and is used like a metronome to synchronize actions of digital circuits. In a synchronous logic circuit, the most common type of digital circuit, the clock signal is applied to all storage devices, flip-flops and latches, and causes them all to change state simultaneously, preventing race conditions.

<span class="mw-page-title-main">Voltage-controlled oscillator</span> Oscillator with frequency controlled by a voltage input

A voltage-controlled oscillator (VCO) is an electronic oscillator whose oscillation frequency is controlled by a voltage input. The applied input voltage determines the instantaneous oscillation frequency. Consequently, a VCO can be used for frequency modulation (FM) or phase modulation (PM) by applying a modulating signal to the control input. A VCO is also an integral part of a phase-locked loop. VCOs are used in synthesizers to generate a waveform whose pitch can be adjusted by a voltage determined by a musical keyboard or other input.

In electronic instrumentation and signal processing, a time-to-digital converter (TDC) is a device for recognizing events and providing a digital representation of the time they occurred. For example, a TDC might output the time of arrival for each incoming pulse. Some applications wish to measure the time interval between two events rather than some notion of an absolute time.

Clock synchronization is a topic in computer science and engineering that aims to coordinate otherwise independent clocks. Even when initially set accurately, real clocks will differ after some amount of time due to clock drift, caused by clocks counting time at slightly different rates. There are several problems that occur as a result of clock rate differences and several solutions, some being more acceptable than others in certain contexts.

The Precision Time Protocol (PTP) is a protocol used to synchronize clocks throughout a computer network. On a local area network, it achieves clock accuracy in the sub-microsecond range, making it suitable for measurement and control systems. PTP is employed to synchronize financial transactions, mobile phone tower transmissions, sub-sea acoustic arrays, and networks that require precise timing but lack access to satellite navigation signals.

A crystal oven is a temperature-controlled chamber used to maintain the quartz crystal in electronic crystal oscillators at a constant temperature, in order to prevent changes in the frequency due to variations in ambient temperature. An oscillator of this type is known as an oven-controlled crystal oscillator This type of oscillator achieves the highest frequency stability possible with a crystal. They are typically used to control the frequency of radio transmitters, cellular base stations, military communications equipment, and for precision frequency measurement.

Many services running on modern digital telecommunications networks require accurate synchronization for correct operation. For example, if telephone exchanges are not synchronized, then bit slips will occur and degrade performance. Telecommunication networks rely on the use of highly accurate primary reference clocks which are distributed network-wide using synchronization links and synchronization supply units.

Pseudo-range multilateration, often simply multilateration (MLAT) when in context, is a technique for determining the position of an unknown point, such as a vehicle, based on measurement of the times of arrival (TOAs) of energy waves traveling between the unknown point and multiple stations at known locations. When the waves are transmitted by the vehicle, MLAT is used for surveillance; when the waves are transmitted by the stations, MLAT is used for navigation. In either case, the stations' clocks are assumed synchronized but the vehicle's clock is not.

A carrier recovery system is a circuit used to estimate and compensate for frequency and phase differences between a received signal's carrier wave and the receiver's local oscillator for the purpose of coherent demodulation.

A frequency synthesizer is an electronic circuit that generates a range of frequencies from a single reference frequency. Frequency synthesizers are used in many modern devices such as radio receivers, televisions, mobile telephones, radiotelephones, walkie-talkies, CB radios, cable television converter boxes, satellite receivers, and GPS systems. A frequency synthesizer may use the techniques of frequency multiplication, frequency division, direct digital synthesis, frequency mixing, and phase-locked loops to generate its frequencies. The stability and accuracy of the frequency synthesizer's output are related to the stability and accuracy of its reference frequency input. Consequently, synthesizers use stable and accurate reference frequencies, such as those provided by a crystal oscillator.

Quartz clocks and quartz watches are timepieces that use an electronic oscillator regulated by a quartz crystal to keep time. This crystal oscillator creates a signal with very precise frequency, so that quartz clocks and watches are at least an order of magnitude more accurate than mechanical clocks. Generally, some form of digital logic counts the cycles of this signal and provides a numerical time display, usually in units of hours, minutes, and seconds.

An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions between such states they interact with a very specific frequency of electromagnetic radiation. This phenomenon serves as the basis for the International System of Units' (SI) definition of a second:

The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency, $, the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s -1 .$

Microelectromechanical system oscillators are devices that generate highly stable reference frequencies used to sequence electronic systems, manage data transfer, define radio frequencies, and measure elapsed time. The core technologies used in MEMS oscillators have been in development since the mid-1960s, but have only been sufficiently advanced for commercial applications since 2006. MEMS oscillators incorporate MEMS resonators, which are microelectromechanical structures that define stable frequencies. MEMS clock generators are MEMS timing devices with multiple outputs for systems that need more than a single reference frequency. MEMS oscillators are a valid alternative to older, more established quartz crystal oscillators, offering better resilience against vibration and mechanical shock, and reliability with respect to temperature variation.

A GPS clock, or GPS disciplined oscillator (GPSDO), is a combination of a GPS receiver and a high-quality, stable oscillator such as a quartz or rubidium oscillator whose output is controlled to agree with the signals broadcast by GPS or other GNSS satellites. GPSDOs work well as a source of timing because the satellite time signals must be accurate in order to provide positional accuracy for GPS in navigation. These signals are accurate to nanoseconds and provide a good reference for timing applications.

The Dick effect is an important limitation to frequency stability for modern atomic clocks such as atomic fountains and optical lattice clocks. It is an aliasing effect: High frequency noise in a required local oscillator (LO) is aliased (heterodyned) to near zero frequency by a periodic interrogation process that locks the frequency of the LO to that of the atoms. The noise mimics and adds to the clock's inherent statistical instability, which is determined by the number of atoms or photons available. In so doing, the effect degrades the stability of the atomic clock and places new and stringent demands on LO performance.

References

1 2 "Smart Clock: A New Time" (PDF). IEEE. 6 December 1992. Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)
1 2 "AN-1002 (Rev. 0)" (PDF). Retrieved 28 September 2012.
↑ "Synchronization Deployment Considerations for IP RAN Backhaul Operators" (PDF). Juniper Networks. 2011. Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)
1 2 Faisal A. Khan (December 2007). "Impacts of GPS-Based Synchronization Degradation on Cellular Networks" (PDF). IGNSS. Archived from the original (PDF) on 12 May 2013. Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)
1 2 "Understanding the concepts of synchronization and holdover". Eetimes.com. Retrieved 28 September 2012.
↑ "WCDMA and LTE Synchronization Aspects" (PDF). Archived from the original (PDF) on 12 June 2009. Retrieved 12 September 2011.
↑ "Clocks for the Synchronized Network" . Retrieved 21 October 2012.
1 2 Peter Kuykendall; Dr. Peter V. W. Loomis. "In Sync with GPS: GPS Clocks for the Wireless Infrastructure" (PDF). Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)
↑ Dr. James Carroll; Mr. Kirk Montgomery. "Global Positioning System Timing Criticality Assessment - Preliminary Performance Results" (PDF). Archived from the original on 9 October 2012. Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)
↑ "CIKR Resource Center". Archived from the original on 16 October 2011. Retrieved 12 September 2011.
1 2 R. James Caverly (27 April 2011). "GPS Critical Infrastructure". Archived from the original on 24 March 2012. Retrieved 21 October 2012.
↑ "Signal" (PDF). Retrieved 28 September 2012.
1 2 "The Global Positioning System (GPS) and Satellite Time Transfer". March 2010. Retrieved 21 October 2012.
↑ "GPS.gov: National Space-Based Positioning, Navigation, and Timing Advisory Board" (PDF). Pnt.gov. 21 August 2012. Archived from the original (PDF) on 24 March 2012. Retrieved 28 September 2012.
↑ "Sync University". Sync University. 15 December 2004. Archived from the original on 2 April 2012. Retrieved 28 September 2012.
↑ "ETS 300 462-1 - Edition 01 - Transmission and Multiplexing (TM); Generic requirements for synchronization networks; Part 1: Definitions and terminology for synchronization networks" (PDF). Archived from the original (PDF) on 31 March 2012. Retrieved 28 September 2012.
↑ "Performance specification: Oscillator, Crystal-Controlled, General Specification For" (PDF). 1998. Archived from the original (PDF) on 31 May 2010. Retrieved 12 September 2011.
↑ tsbmail. "G.810 : Definitions and terminology for synchronization networks". Itu.int. Retrieved 28 September 2012.
↑ "GPS Time and Frequency Systems" (PDF). Retrieved 21 October 2012.
↑ "Time and Frequency from A to Z". Tf.nist.gov. Archived from the original on 11 September 2012. Retrieved 28 September 2012.
↑ Wacker, Mike F.; Villella, A. (2008). "Improvements in OCXO performance by the use of an on-board microprocessor". 2008 IEEE International Frequency Control Symposium. Ieeexplore.ieee.org. pp. 159–164. doi:10.1109/FREQ.2008.4622980. ISBN 978-1-4244-1794-0. S2CID 46081633.
↑ Hui Zhou; Charles Nicholls; Thomas Kunz; Howard Schwartz (November 2008). "Frequency Accuracy & Stability Dependencies of Crystal Oscillators" (PDF). Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)
1 2 Michael A. Lombardi (September 2008). "The Use of GPS Disciplined Oscillators as Primary Frequency Standards for Calibration and Metrology Laboratories" (PDF). NCSL International. Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)
↑ Fabrizio Tappero; Andrew G. Dempster; Toshiaki Iwata (2007). "Phase error reduction method for free-run QZSS clock" (PDF). IEEE. Archived from the original (PDF) on 12 May 2013. Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)
↑ Proceedings ^{[ dead link ]}
↑ c.w.t. Nicholls, G.C. Carleton (2004). "Adaptive OCXO drift correction algorithm". Proceedings of the 2004 IEEE International Frequency Control Symposium and Exposition, 2004. Ieeexplore.ieee.org. pp. 509–517. doi:10.1109/FREQ.2004.1418510. ISBN 0-7803-8414-8. S2CID 33745348.
↑ Leap second
↑ "MD-023: Extended Holdover Crystal Oscillator" (PDF). Vectron International. June 2011. Retrieved 21 October 2012.

External links

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[smartclock-1] 1 2 "Smart Clock: A New Time" (PDF). IEEE. 6 December 1992. Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)

[analog1-2] 1 2 "AN-1002 (Rev. 0)" (PDF). Retrieved 28 September 2012.

[3] "Synchronization Deployment Considerations for IP RAN Backhaul Operators" (PDF). Juniper Networks. 2011. Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)

[autogenerated1-4] 1 2 Faisal A. Khan (December 2007). "Impacts of GPS-Based Synchronization Degradation on Cellular Networks" (PDF). IGNSS. Archived from the original (PDF) on 12 May 2013. Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)

[eetimes1-5] 1 2 "Understanding the concepts of synchronization and holdover". Eetimes.com. Retrieved 28 September 2012.

[6] "WCDMA and LTE Synchronization Aspects" (PDF). Archived from the original (PDF) on 12 June 2009. Retrieved 12 September 2011.

[7] "Clocks for the Synchronized Network" . Retrieved 21 October 2012.

[timing1-8] 1 2 Peter Kuykendall; Dr. Peter V. W. Loomis. "In Sync with GPS: GPS Clocks for the Wireless Infrastructure" (PDF). Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)

[9] Dr. James Carroll; Mr. Kirk Montgomery. "Global Positioning System Timing Criticality Assessment - Preliminary Performance Results" (PDF). Archived from the original on 9 October 2012. Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)

[10] "CIKR Resource Center". Archived from the original on 16 October 2011. Retrieved 12 September 2011.

[autogenerated2-11] 1 2 R. James Caverly (27 April 2011). "GPS Critical Infrastructure". Archived from the original on 24 March 2012. Retrieved 21 October 2012.

[12] "Signal" (PDF). Retrieved 28 September 2012.

[autogenerated3-13] 1 2 "The Global Positioning System (GPS) and Satellite Time Transfer". March 2010. Retrieved 21 October 2012.

[14] "GPS.gov: National Space-Based Positioning, Navigation, and Timing Advisory Board" (PDF). Pnt.gov. 21 August 2012. Archived from the original (PDF) on 24 March 2012. Retrieved 28 September 2012.

[15] "Sync University". Sync University. 15 December 2004. Archived from the original on 2 April 2012. Retrieved 28 September 2012.

[16] "ETS 300 462-1 - Edition 01 - Transmission and Multiplexing (TM); Generic requirements for synchronization networks; Part 1: Definitions and terminology for synchronization networks" (PDF). Archived from the original (PDF) on 31 March 2012. Retrieved 28 September 2012.

[17] "Performance specification: Oscillator, Crystal-Controlled, General Specification For" (PDF). 1998. Archived from the original (PDF) on 31 May 2010. Retrieved 12 September 2011.

[18] tsbmail. "G.810 : Definitions and terminology for synchronization networks". Itu.int. Retrieved 28 September 2012.

[19] "GPS Time and Frequency Systems" (PDF). Retrieved 21 October 2012.

[20] "Time and Frequency from A to Z". Tf.nist.gov. Archived from the original on 11 September 2012. Retrieved 28 September 2012.

[21] Wacker, Mike F.; Villella, A. (2008). "Improvements in OCXO performance by the use of an on-board microprocessor". 2008 IEEE International Frequency Control Symposium. Ieeexplore.ieee.org. pp. 159–164. doi:10.1109/FREQ.2008.4622980. ISBN 978-1-4244-1794-0. S2CID 46081633.

[22] Hui Zhou; Charles Nicholls; Thomas Kunz; Howard Schwartz (November 2008). "Frequency Accuracy & Stability Dependencies of Crystal Oscillators" (PDF). Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)

[Lombardi-23] 1 2 Michael A. Lombardi (September 2008). "The Use of GPS Disciplined Oscillators as Primary Frequency Standards for Calibration and Metrology Laboratories" (PDF). NCSL International. Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)

[24] Fabrizio Tappero; Andrew G. Dempster; Toshiaki Iwata (2007). "Phase error reduction method for free-run QZSS clock" (PDF). IEEE. Archived from the original (PDF) on 12 May 2013. Retrieved 21 October 2012.{{cite journal}}: Cite journal requires |journal= (help)

[25] Proceedings ^{[ dead link ]}

[26] .w.t. Nicholls, G.C. Carleton (2004). "Adaptive OCXO drift correction algorithm". Proceedings of the 2004 IEEE International Frequency Control Symposium and Exposition, 2004. Ieeexplore.ieee.org. pp. 509–517. doi:10.1109/FREQ.2004.1418510. ISBN 0-7803-8414-8. S2CID 33745348.

[27] Leap second

[28] "MD-023: Extended Holdover Crystal Oscillator" (PDF). Vectron International. June 2011. Retrieved 21 October 2012.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

[28]