Appendix 2 Practical estimation of holdover time. Terasync

Whether it is based on GPS or PTP, one of the critical parameters for telecom system synchronization source is how much time it will continue to function properly in case of the reference failure (holdover). Whether the cause is a poor GPS reception due to various reasons (rain, snow, heavy foliage, difficult urban conditions, etc.), antenna or receiver failure or PTP master problems, the only available source that remains is the local oscillator. Its quality and the ambient temperature changes, as well as the frequency synthesis resolution are the main factors that will determine how long the traffic will continue to flow as usual (supply voltage variations and another environmental conditions such as vibrations can also add to the equation, but usually are small and can be neglected). For sure, the operators would prefer holdover time to be as long as possible, but the extra cost can be too high.

Let’s discuss the factors that affect the holdover time. The key parameter is the oscillator’s frequency stability in the operating temperature range. This parameter is specified as a worst case (maximum variation possible). Unfortunately, it is hard to know the typical value. Due to the manufacturing technology limitations it can vary even in one production batch. Therefore, in the calculation maximum value is usually used, which makes the result a bit conservative. If some statistical information of the batch is available, more precise results can be achieved.

Another parameter is aging, which is caused by changes of the physical properties of quartz crystal and other materials used in the oscillator construction over time. The contribution of the frequency offset due to aging is usually not significant at lower stability oscillators, e.g. TCXO, but for high-end oscillators, e.g. DOCXO, it can be at order of magnitude of the temperature effects. Aging is also specified by the manufacturers as a worst case, and the typical value is hard to determine as well. Although the measurements itself are quite long, statistics can be gathered and used instead of the extreme values.

The frequencies of the local clocks are steered digitally during the normal operation, in according to the GPS 1 PPS pulse or PTP timing packets. The steering resolution is not infinite, therefore at the moment of the reference loss the frequency is not exactly the nominal. This initial frequency offset, although small, causes additional phase error accumulating over time. The value depends on the digital loop parameters, and can be determined with a fairly high degree of precision.

In order to evaluate realistic holdover time, we also have to make some assumptions about the ambient temperature variation. For the outdoor cabinet equipment, meteorological observation data that includes the temperatures can be used. Additionally, fast temperature changes due to various reasons (such as direct sunlight irradiation that is followed by shadow, wind blows, sudden rain, etc.) can be taken into account. For the indoor equipment, the variation is usually smaller. Even without climate control it rarely goes beyond 0.5 deg. Celsius per hour.

Let’s present some typical holdover times, calculated using the data described above, for uncontrolled indoor environment. We will assume 10 microseconds as a maximum allowed phase deviation, and will determine the holdover time for various types of oscillators. With low cost TCXO this time will be around 30 minutes, while with a high precision TCXO it will achieve hour and a half. Maybe not enough time for the technician to come and fix the problem, but can be good enough, for example, in case of temporary satellites reception problem at some hour of the day. Not bad for the lower cost devices. However, in order to allow even barely enough time for the repair team to arrive, we need a high quality OCXO that will give us a little more than 6 hours of spare time, and will be a few times more expensive than a good TCXO. And if we want 24 hours of holdover, the answer will definitely be DOCXO, which in its turn costs a few times more than the aforementioned OCXO. The wish to go beyond this number will bring us to the realm of atomic clock standards, such as Rubidium or even Cesium, with all the expenses associated with it. Very long holdover time rise the synchronization solution price beyond measure, and usually can be justified only in case when the equipment is located far away from the civilization and the technical support is difficult. In many cases it would be wiser to implement some sort of redundancy scheme instead, thus achieving pretty high degree of reliability for a significantly lower cost. It can be cheaper to install two completely separate synchronization devices with lower cost oscillators instead of one with an expensive atomic reference.

 Summary (time until 10 microsecond of phase error is accumulated, uncontrolled indoor environment)