Flyback Power Supply – Stability, Oscillations, and Buzzing Issues

First you need to understand that the stability of the frequency is primarily determined by factors other than the crystal. Temperature changes can have a large effect on frequency, for this reason when high accuracy is desired crystals are generally encased in a temperature controlled oven. There are many variants, as high accuracy frequency standards are important for many applications. High accuracy crystal oscillators have generally been superseded by GPS locked oscillators and rubidium oscillators (both atomic clocks).

Anyway getting back to the crystals, the 50-100 MHz ones are most likely operating in overtone mode. So if the circuit wants a frequency of 75MHz the crystal might be cut for 25MHz and the circuit designed to operate at the 3rd overtone. When any crystal oscillator is running in overtone any drift is multiplied by the overtone. For this reason your 50-100 Mhz crystals will be less stable than the other crystals.

In your PC the accuracy of the others is affected by many system specific factors like is there a cooling fan blowing on the crystal and effecting the frequency? Simply moving a card from one slot to another could have an effect.

Finally remember that there is generally little need for much accuracy in today's PCs. For timekeeping the clocks are simply synced via the internet with master clocks elsewhere.

In the "good old days" before GPS, when crystal oscillators were the best that a ham could afford, the key to getting accuracy was to zero beat them against a known frequency standard. Unless you had a friend with an atomic clock, the best source would be WWV, the radio station of the national bureau of standards. You would build a 10 MHz (or back them 10 MCPS) oscillator and then tune in the 10 MHz signal from WWV. If your oscillator was off by 300 Hz you would hear a 300Hz tone from the receiver. One would adjust the oscillator (using a variable loading capacitor perhaps) until the tone went to zero which would mean that the crystal oscillator was at the same frequency of the radio signal.

Here is a longer description of the process How to calibrate a frequency counter in a poor man's fashion The author states: "An accuracy of better than a 0.1 Hertz frequency difference (10-8) is possible with this technique."

It is important to understand that the actual frequency of the oscillator is rarely the same as what is marked on the crystal, it is also a function of the circuit and can be easily adjusted up or down by a couple of KHz or so.

If you happened to live close by WWV this worked extremely well. If you were a couple of thousand miles away the exact frequency of the received signal was not as good as what left the transmitter. This is why GPS based clocks that use multiple signals (satellites) are so much more accurate. It is not that a satellite has a better frequency reference than WWV, it is a function of the propagation of radio waves (phase distortion etc.)

One would repeat this zero beat calibration at regular intervals (say once a month or once a week depending on the accuracy desired). The long term stability of even the best of crystal based oscillators is not all that good. When we got cheap phased locked loops it became possible to build an oscillator that was "locked" to the signal from WWV. Even better was the advent of digital circuits, kalman filters etc. which combined the better short term stability of the crystal with the long term stability of the radio signal. This has lead to $20 digital clocks that hang on the wall and get their calibration from WWV.

Getting back to the surplus crystals pulled from computers, here is an article showing a circuit that uses one and comparing it's performance to a commercial OXCO purchased used for a couple of bucks. DCF77-synchronized oscillator Not surprisingly, the surplus unit was better.

With the complete-homebrew OXCO running stable enough, a test run was made to compare it with the 'commercial' OXCO. Quite disappointing result (though not really a surprice): The 'commercial' OCXO beat the stability of the 'homemade' oscillator by a decade (or even more).

This is exactly why I think people should study stability first using Nyquist plots, THEN using bode plots and the associated gain and phase margin diagrams.

The gain/phase margins are just a convenient way of determining how close the system gets to having poles on the right side of the complex plane, in terms of how close the nyquist plot gets to -1, because after partial fraction expansion those terms with positive poles end up as exponentials of time with positive coefficient, which means it goes to infinity, which means it is unstable.

However, they only work when the nyquist plot is 'normal looking'. It very well may be that it does something like this:

So it violates the phase margin rule, yet the open loop transfer function G(s)H(s) doesn't encircle -1, so 1+G(s)H(s) doesn't have zeroes on the right side, which means the closed loop doesn't have poles on the right side, so it is still stable.

The word conditional comes from the fact that the gain has an upper/lower bounds to keep it this way, and crossing them makes the system unstable (because it shifts the curve enough to change the number of times that -1 is encircled).