About the crystal oscillator ppm

Question

I know ppm stands for parts per million,but I don't know when did the error occur.I have the following conjectures.

1. Determined at the factory,It means that ppm represents the frequency deviation between two crystals.
2. Every time the power is on,This means that the frequency will be different every time the power is turned on, but it is within the error range.
3. when working, this also means that the frequency will change arbitrarily within the error.

Answer 1

Your statement "ppm represents the frequency deviation between two crystals" is misleading. One of those crystals (the reference) is not just any crystal. It's more correct to say that this reference is probably not a crystal at all, and is rather a reference frequency derived from a far more accurate and precise source such as an oven controlled rubidium clock. This reference frequency is used to fine-tune the individual crystals that the manufacturer produces.

A better statement would be: PPM is the deviation from some known reference frequency, of the frequency at which a crystal resonates, that the manufacturer guarantees will never be exceeded during the expected working lifetime of the crystal, and if the crystal is never exposed to conditions which may compromise that guarantee.

"Power cycling" is certainly an issue, but it's actually just causing stresses which I detail below.

Here are the main causes of frequency deviation from nominal:

1. Manufacturer diligence. The crystals are initially cut to standard sizes. Following this they undergo lapping to hone frequency prior to mounting, and electrode manipulation to further fine-tune them while in-circuit. The manufacturer decides when to stop tuning, and will bin their products as, say 20 PPM or 50 PPM, partly based on the time and effort they invested to achieve some target accuracy.

2. Age. Atomic structure of crystals changes over time. Impurities move around in the lattice, and fractures and other imperfections propagate through the structure.

3. Operating stress. As the crystal oscillates, it can undergo gradual structural changes (similar to aging) due to physical deformation.

4. Support stress. The very mounting of the crystal onto a fixed base will deform it to some extent, and over time that stress may relax or worsen as the mounting structure undergoes creep or other mechanical deformations.

5. Temperature. Thermal expansion and contraction will cause stresses in both the support structure and the crystal itself. Excessive temperature induced stress may cause permanent structural changes.

6. Environmental stress. Any forces acting to deform the crystal and/or its supports will of course cause it to deviate in frequency. These can include forces due to orientation (gravity), installation (PCB, soldering etc) and vibration.

7. Environmental purity. Over time, particles which come loose or are deposited onto the crystal or its electrodes from its enviroment will have an effect on frequency.

8. Random. There are any number of sources of noise, electrical and otherwise, some understood, some still a mystery (quantum), that contribute to unpredictability in the crystal's behaviour.

Two helpful documents I referred to here are:

• Quartz Crystal Manufacturing Process

• Understanding Frequency Accuracy in Crystal Controlled Instruments

Answer 2

Any or all of those. If you're working with a really good part then the datasheet might give you some more detailed specs, like ppm/year aging, ppm/hour drift, ppm retrace after power off and then on, ppm/°C thermal sensitivity, etc. In the absence of any such spec, you either have to assume the worst case (random short-term drift across the entire specified range) or make some effort to characterize things yourself.

Answer 3

I think you are confusing time drift and stability. The ppm is used to determine time drift \$t_{drift}\$. Typically crystal oscillators frequency changes from a nominal frequency \$f_{nominal}\$ to an off nominal frequency \$f\$ when subject to different temperatures. If this occurs over time duration \$t\$ then your measured time will be different than your actual time. Some crystals that I have seen typically describe the nominal frequency at 25 deg C , but will shift frequency if subject to other temperatures.

\begin{equation} ppm=\frac{f-f_{nominal}}{f_{nominal}}*10^6 \end{equation}

\begin{equation} t_{drift}=\frac{ppm*t}{10^6} \end{equation}

Example: your crystals nominal frequency is 32,768 Hz. But due to temperature the crystal runs at 32,770 Hz. What is the drift after 1 year (8760 hours). How much faster will the clock run.

\begin{equation} ppm=\frac{32,770-32,768}{32,768}*10^6 = 61 ppm \end{equation}

\begin{equation} t_{drift}=\frac{61*8760}{10^6} = 0.53 hr \end{equation}

Stability describes how the clocks frequency varies due to random processes. This is generally characterized using an method known as the Allan Variance. You can read more about this here: https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication1065.pdf