# Calculate jitter of oscillator from PPM

I found oscillators with from 10ppm up to 50ppm and more, but how I can calulate maximum jitter of this oscillators?

With an online calculator I've found with 40Mhz and 50ppm this value: 2.500e-12s Max - Min Period (sec), so 0.0025ns Can I assume that this is Max. Jitter time?

• A 10ppm xtal might drift 10 parts per million across temperature/time. It doesn't reflect what the jitter might be. Jul 3, 2015 at 12:38
• For some oscillators you might find a "phasenoise" specification. This phasenoise has a strong relation to the jitter of the clock. Since it is a random event, statistics are involved so there is no real "Max jitter time". The jitter will have a (gaussion ?) distribution. Jul 3, 2015 at 12:47
• First you need to understand what type of jitter your application cares about. There are many types of jitter (period jitter, cycle to cycle jitter, phase jitter, etc.). Then you need to understand what error rate your application requires, which will determine the population (sample size) of jitter values required to analyze your application. Then you can contact the mfgr to discuss your requirements and they should be able to help. Aug 21, 2017 at 20:25

## 2 Answers

The ppm spec on an oscillator is the accuracy and is (usually) specified over temperature and initial calibration. It says nothing about jitter. You will need to measure it or check the datasheet.

Here's a jitter spec on a typical oscillator (10MHz CTS type)

So the peak-to-peak period jitter is less than 50 picoseconds for this part. JEDEC definition of peak-to-peak is +/-3$\sigma$. In theory the maximum jitter is unbounded (as Rimpelbekkie says) so you need to define an acceptable error rate or something of that ilk in order to talk about maximums.

Following the comment of IC_designer_Rimpelbekkie is the path you want to take. Jitter will manifest itself in the spectral domain as a "skirt" around your desired frequency. An estimate formula of the Noise-to-Carrier Ratio depends inversely on the quality factor squared of your LC tank which again scales inversely with your ppm, thereby: Noise-to-Carrier Ratio ~ ppm^2.

Next, we can safely assume that the jitter can be modelled by a Gaussian Stochastic Process, as it is essentially a contribution of a number of thermal noise sources associated with resistances, resistive channels of MOSFETs, shot noise e.t.c.

Lastly we know that the autocorrelation function is linked to the power spectral density by means of fourier transform. We may therefore be able to estimate the standard deviation!

Deviation of Jitter ~= sqrt(Integrate(ppm^2 * Peak_Value / w^2)).

Edit 1: The integrand, as presented above, is wrong. What I meant was the peak value at the origin, and then decreasing by w^2 around it. Evaluating this expression yields: ppm * sqrt(2*Peak_Value_of_Noise_to_Carrier_Ratio)

Edit 2: Plugging in actual numbers: 50 ppm, -100dBc Noise to Carrier: 0.707 ns. Can anybody comment on whether this seems reasonable?