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Frequency Calibration. Above all, what does your client wants?. The client could be yourself. Listen to him!. Talk with the client first, before doing anything. He may want to use it in such a way that only the short term stability is important to him.
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Above all, what does your client wants? The client could be yourself. Listen to him! • Talk with the client first, before doing anything. • He may want to use it in such a way that only the short term stability is important to him. • He may need it for timekeeping, then the stability at long term is important. • He may be able to live with orders of magnitude more uncertainty than the best you can do. • The client’s device may be of low intrinsic accuracy. You do not need to estimate uncertainties orders of magnitude lower than the device under calibration itself, Do not overdo it!
Technique of measurement decides what kind of calibration can be done Frequency counter technique Frequency can be quickly calibrated Uncertainty applicable to time equal to the gating time of the counter Limited by the counter resolution Easy to get high number of degree of freedom Phase/time measurement The longer the measurement period, the better are the results Uncertainty calculation is more complex but covers a wider range of needs The phase plot gives a lot of useful information
Frequency counter technique If the frequency counter does not provide proper statistics, record the data on a computer. You may also want to get rid of outliers. What the counter gives you What the counter sees: Average value Std dev sy traceability Oscillator Reference 5 000 000.000 Hz Frequency counter
y t Alternative method to avoid tying down one counter on one measurement for too long. Take one sequence of measurement (ten 100 s measurements) every day and treat it as a classical measurement This method might reveal a frequency drift! To simplify, t=0 at the barycenter of ti
Uncertainty calculation For the case of a single sequence of of M measurement: Uncertainty of measurement : This is your reference, you should know this value and its degree of freedom n Uncertainty of reference : Uncertainty of trigger : Both from counter specifications Uncertainty of quantization :
Uncertainty calculation II For the case of a single sequence of measurement : This is the degrees of freedom that will be used for each sequence of measurements done in the multiple sequence method.
Uncertainty calculation III This type of calculation is strictly valid only for white frequency noise! If the noise of the measurement system is of the order of the noise of the measurement, it is quite possible that the measurement is limited by the system. Avoid double counting. Use your judgment. It may mean that the method is unsuitable to that particular calibration If the drift value is lower than the uncertainty, this invalidates the concept of drift measurement. It may be only random walk noise that is showing up. Check the manufacturer’s specification. Use another method.
Frequency counter technique II Here is the real phase data of the preceding example Obviously, there is more to it than only a frequency average and a standard deviation. Other techniques need to be called upon. Warning: if your client needs only a frequency value and an uncertainty in the range of the first frequency counter technique, please use this simple method.
Phase measurement techniques • There are two basic methods: • Time interval counter • Phase comparator • Time interval counter technique is usually more limited in accuracy than the phase comparator technique. • Typically a top of the line time interval counter will be good to about 100 ps. • A good phase comparator will be better than one ps resolution. • Except for the ultimate resolution, the technique is essentially the same.
Phase measurement method Using frequency measurements: traceability Oscillator Reference 5 000 000.000 Hz Frequency counter From the frequency recording, rebuild the phase. If the frequency counter has no dead time between measurements this method is perfectly valid. If there is a dead time, the results might be totally wrong, depending on the type of noise present in the measurement. Avoid using it if in doubt.
Phase measurement method Using time interval measurements: traceability Oscillator Reference 123 456.8 ns A Time interval counter B ÷N 1 PPS ÷5×106 Divide by N to reduce the aliasing Advantage: you do not need to measure every second. You can take ten consecutive measurements, average and store every 5 minutes. You lose the information on shorter term than 300 seconds but the noise of the measuring system is probably dominant on shorter time scale.
Record data as soon as possible after powering the device under study. The warm-up period cannot be used to establish the value of the frequency but such a recording will indicate if the manufacturer’s specification about warm-up is still valid. Any departure from the specification may indicate some potential problem. First difference = frequency Case of Rubidium clock with a few days warm-up! Phase measured every 5 minutes
The full data set, minus the warm-up period: three weeks! Slope=-3.0×10-11 0.034×10-11 Frequency reset
ADev is minimum at about a day or two. The number of degrees of freedom is about 8.5 at two days. This was calcuated from Monte-Carlo simulation for flicker frequency noise with T=11×t. This is a reduction from the expected nominal value of 10 for such an interval. Flicker noise has a memory effect reducing the number of degrees of freedom.
Simulation for a set of measurements of length T=11×t, meaning 10 D2 The simulation was carried with flicker frequency noise which is predominant in the ADev plot at the point of interest (mimimum). Monte-Carlo method can simulate any model of noise and gives a more accurate dof. c2(8.5) Monte Carlo simulation
Phase measurement method Using a real phase comparator is the best way to measure the frequency accurately traceability Oscillator Reference 123 456 789.0 ps Phase comparator Record phase measurements for as long as necessary. Proceeds as with previous method from time interval counter. This is needed for short term evaluation of noise.
Here is the phase plot of a Cs high performance against a H-maser, for one day. Total ADev and ADev have been calculated on the following page.
It can be seen that Total ADev reduces the uncertainty on the uncertainy as expressed by ADev. It gives a little more confidence in the evaluation of the frequency. ADev error limits Total ADev error limits
One major question: how to measure the frequency? In presence of pure white phase noise, a linear fit through the data is the optimum frequency evaluator. In presence of frequency noises, the end-to-end measurement is optimal. In any case, the uncertainty should be larger than the difference between the two methods. Difference= 7×10-15
Uncertainty calculation For the case of phase measurement : This is the degrees of freedom to associate with the ADev value used to estimate the frequency of the device under calibration.
conclusion • Always ask the client what are his needs, how he is using the clock to be calibrated. • Do not overdo the calibration but • Do not let any uncertainty unresolved. • This would undermine the value of the calibration.
More about the Monte-Carlo method for calculating the dof Degrees of freedom, the length of measurement and the sample time t. Valid for random walk, for the other type of noise there is a reduction factor which can be as small as ½ for white phase noise.
Even for random walk, the validity of the expression for dof is limited by real life Solution: use the data available as suggested in the ISO Guide on uncertainties. The calculation of ADev needs to be augmented by the calculation of the standard deviation of AVar. This is a valid method that can be illustrated by the moving ADev
6 days of data ADev of above data
