Determining the frequency stability of oscillators

Does anyone knows a formula and the related input parameters in order to determine the necessary frequency stability of an oscillator ?

I guess it shall involve the operating frequency, multiplication factor (20 Log (N)), modulation skin, interference, allowed BER, etc, so that the required frequency stability of an oscillator can be calculated based on input parameters.

I would really appreciate if anyone could indicate a link or provide me an answer about how to calculate it.

Thank you in advance.

An oscillator has some quality factors mentioned below if I understood your question.
-Drift : Temperature effect on oscillator frequency including self heating.
-Pulling : Figure of stability : Function of Load Variations on Oscillator Frequency
-Pushing : Figure of stability : Function of Bias Variations on Oscillator Frequency
These variables can not be calculated easily but simulated or measured because Oscillators are autonomous circuits and they don't have any deterministic input but noise.
Required frequency stability can be calculated from a system study.It's very tough to calculate this accuracy by hand for complex systems. ( Digital Modulated Schemes etc.)
The best way to calculate is to simulate the system against frequency variations and to observe BER or EVM or S/N etc. at the output of the system.
You can define the sensitivity of your system against the oscillator frequency variations.

Sorry, you misunderstood the question.
I do not intend to know the intrinsic quality factors of an oscillator or even calculate them, is the other way aroud, what I need is to know which are the input parameters of a system (system requirements) responsbile for determine the frequency stability of an oscillator.

I give you a practical simple example. Suppose someone wants to reduce the costs of a product which uses an oscillator. You have some categories of oscillators such as OCXO, TCXO, XO, etc....each of possessing its own frequency stability and with different prices. If one has a system based on a low data-rate, robust modulation scheme, etc.....the costs can be further reduced by selecting an oscillator with relaxed specs. I wish to know which are the necessary initial input paramter of a system that impacts over the oscillator choice and if there is a theoretical calculation formula for it. Next step is to simulate it, but first they have to be known.

There will be International Standards for frequency stability for most transmission systems, as well as channel bandwidths. Starting with these, then the tolerance of the oscillator(s) can be calculated for your system. i.e. if you have an upconverter so there are two frequency tolerances involved, its up to you to decide how to apportion the numbers.
Frank

chuckey said:

There will be International Standards for frequency stability for most transmission systems, as well as channel bandwidths. Starting with these, then the tolerance of the oscillator(s) can be calculated for your system. i.e. if you have an upconverter so there are two frequency tolerances involved, its up to you to decide how to apportion the numbers.
Frank

Click to expand...

Again we can see someone who wants a "magic" number to classify an oscillator.
My dear, the secret is not in the oscillator but in the system you need to use an oscillator in!
For a simple AM system you can use a poor-quality oscillator with a poor frequency stability as there is almost nothing to hold a fixed frequency.
In a FM system the oscillator in the transmitter is frequency-modulated, so again, its frequency stability is only defined by law, to fit into a licensed window.
In phase-modulation systems the short-term frequency stability is needed but the long-term stability again only depends on regulations.

Oscillator phase noise is often specified in high-quality systems using PSK, but this problem is pronounced in mm-wave systems where the carrier is generated by frequency multiplication.

To specify and select an oscillator you have to respect the SYSTEM parameters, range of operating temperatures, vibration, noise, and more. So do not attempt to simplify the problem. Look on various oscillator makers and note their frequency stability specifications, phase noise, etc. THey also do not label their products by one number like you would want.

jiripolivka said:

Again we can see someone who wants a "magic" number to classify an oscillator.
My dear, the secret is not in the oscillator but in the system you need to use an oscillator in!
For a simple AM system you can use a poor-quality oscillator with a poor frequency stability as there is almost nothing to hold a fixed frequency.
In a FM system the oscillator in the transmitter is frequency-modulated, so again, its frequency stability is only defined by law, to fit into a licensed window.
In phase-modulation systems the short-term frequency stability is needed but the long-term stability again only depends on regulations.

Oscillator phase noise is often specified in high-quality systems using PSK, but this problem is pronounced in mm-wave systems where the carrier is generated by frequency multiplication.

To specify and select an oscillator you have to respect the SYSTEM parameters, range of operating temperatures, vibration, noise, and more. So do not attempt to simplify the problem. Look on various oscillator makers and note their frequency stability specifications, phase noise, etc. THey also do not label their products by one number like you would want.

Click to expand...

That is exactly as you said ! (It is the system I need that is going to define it) You got the idea, it now needs a little brush......anyone qualified to mention which are the system parameters I have to consider ?

This is an study driven by the main and relevant parameters one should look for define the required stability of a system based on the fact external factors like temperature range, vibration, etc are respected or not accounted. So how the international standards are derived (mask and specs for an oscillator) otherwise ?

I disagree in parts with you regarding your observations on the short term stability : In phase-modulation systems, not always the short term stability is needed and it should not be made as a rule ! In phase-modulation communication systems where the receiver block is implemented with carrier recovery system and depnding on loop bandwidth, the short term stability (random walk frequency, flicker frequency, and often part of random walk phase slope regions) does not count as additive and rapid phase noise since it is strongly attenuated by circuit and the low pass filter (filter order and loop bandwidth) of the PLL in the receiver system. It is the cut-off frequency of the low pass filter that will determine where the jitter shall start to be integrated, so good part of the short term stability is absorbed/attenuated by the carrier recovery circuit in the receiver system part. Summarizing, the jitter (time domain) shall be integrated from aprox. the cut-off frequency of the PLL low pass filter until it reaches Rs (s. rate in the base-band), so then converted to phase noise, if one really wants to analyze the contribution of phase noise that will impact in the long and/or short term stability. The phase noise contribution is dependent upon the implementation of your system. - - - Updated - - -