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precision_timing:minimizing_noise_bandwidth [2013/01/08 19:00] (current) |
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| + | ====== Minimizing Noise Bandwidth in Closed Loop Systems ====== | ||
| + | |||
| + | Subject: GPSDO time constant | ||
| + | |||
| + | >> | ||
| + | >>> Magnus Danielson <magnus@rubidium.dyndns.org> wrote: | ||
| + | >>> | ||
| + | >>> For ThunderBolt owners it is pretty straightforward to separately adjust | ||
| + | >>> the Time Constant and damping, which is very nice. Use this opportunity! | ||
| + | >>> | ||
| + | >> | ||
| + | >> Richard Moore wrote: | ||
| + | >> | ||
| + | >> So, Magnus (and Tom), what damping factor do you suggest for a TBolt? | ||
| + | >> I'm running a verrry long TC now. If 1.2 is not actually critically | ||
| + | >> damped, what value would be? Any guesses? BTW, I really like that | ||
| + | >> plot of Tom's that tracks the oven and then gets better from the GPS... | ||
| + | >> | ||
| + | > | ||
| + | > Magnus Danielson wrote: | ||
| + | > | ||
| + | > Dick, | ||
| + | > | ||
| + | > Assuming that damping factors match classical analysis of damping, then | ||
| + | > the square root of 2 is the answer... 1.414 or there about. | ||
| + | > | ||
| + | > I would be more conservative than that. I would consider damping factors | ||
| + | > such as 3-4 or so. I have no support from measurements on GPSDOs but it | ||
| + | > is reasonable that the rise of gain at and near the PLL frequency we see | ||
| + | > for other systems will occur and result in similar effects even here. | ||
| + | > This gain raises the noise floor and amount of gain is directly coupled | ||
| + | > to the damping factor. It's just standard PLL stuff all over again. The | ||
| + | > only difference is that we view the result in ADEV or MDEV views. | ||
| + | > | ||
| + | > Cheers, | ||
| + | > Magnus | ||
| + | > | ||
| + | |||
| + | Hej Magnus | ||
| + | |||
| + | For a second order loop, the noise bandwidth is minimised for a fixed | ||
| + | time constant by choosing a damping factor of 0.5. | ||
| + | Using a damping factor of 1.414 increases the noise bandwidth by about 60%. | ||
| + | Using a damping factor of 0.7071 only increases the loop noise bandwidth | ||
| + | by about 6%. | ||
| + | A damping factor of 0.3 increases the noise bandwidth by about 13%. | ||
| + | |||
| + | Bruce | ||
| + | |||