FWIW this example in AllanTools generates white pm and compares to the IEEE1139 ADEV formula: https://github.com/aewallin/allantools/blob/master/examples/ieee1139_white_pm.py
two comments: 1. Theoretical white noise has infinite power, so limiting the RMS to some value already implies you have limited the measurement bandwidth (f_h in the formulas) 2. Interestingly my understanding of the phase-meters (Timepod/3120A and/or DIY USRP SDR) is that they don't measure raw phase of the signal much better than a 20ps counter. The trick is to measure the phase between REF/DUT at a high sample-rate, and then dramatically reduce the bandwidth by low-pass filtering numerically. So an ADEV(1s)<1e-13 (100-fold better than a typical counter) is not done via some "magic" 100fs phase-measurement, but instead by doing plain old ~20 ps phase measurements at a high rate and averaging lots of them together. I've been playing with an USRP phase-meter and hope to release some software/results soonish. Anders (ITSF2016/Prague next week) Hi Stu, > If you have white phase noise with standard deviation of 1 then the ADEV > will be sqrt(3). This is because each term in the ADEV formula is based on > the addition/subtraction of 3 phase samples. And the variance of normally > distributed random variables is the sum of the variances. So if your > standard deviation is 0.5 ns, then the AVAR should be 1.5 ns and the ADEV > should be 0.87 ns, which is sqrt(3)/2 ns. You can check this with a quick > simulation [1]. > > Note this assumes that 1 ns quantization error has a normal distribution > with standard deviation of +/- 0.5 ns. Someone who's actually measured the > hp 5334B quantization noise can correct this assumption. > > /tvb > > [1] Simulation: > > C:\tvb> rand 100000 0.5e-9 0 | adev4 /at 1 > rand 100000(count) 5e-010(sdev) 0(mean) > ** tau from 1 to 1 step 1 > 1 a 8.676237e-010 99998 t 5.009227e-010 99998 > > In this 100k sample simulation we see ADEV is close to sqrt(3)/2 ns. The > TDEV is 0.5 ns. This is because TDEV is based on tau * MDEV / sqrt(3). In > other words, the sqrt(3) is eliminated in definition of TDEV. > _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
