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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:


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.


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%.


precision_timing/minimizing_noise_bandwidth.txt · Last modified: 2013/01/08 19:00 (external edit)
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