[time-nuts] OCXO PLL gains?

[Magnus Danielson]

Hej Anders,

On 2019-02-01 19:11, Anders Wallin wrote:
> Hi all, is there are rule-of-thumb or simple paper/presentation of how to
> choose PLL-gains?
>
> I have a phase-detector that gives out a slope of roughly 1 V/rad, followed
> by an op-amp circuit with proportional, integral, and double-integral gains
> summed into one voltage [0, 3.3V] on the tune-pine of the OCXO ( +/- 0.6
> ppm pull-range, from datasheet).
>
> So far it locks with only P-gain, but the phase-noise (and ADEV) shows a
> 'bump' somewhere between 10 and 100 Hz offset from the carrier.
> I tried the integrator with a time-constant of 1/16Hz using R 100k  C 100n,
> but it wouldn't lock.
> The thinking was to put the integrator time-constant about where the
> free-running ADEV turns upwards from a 1/tau slope.
>
> So far I didn't enable the double-integrator - not sure if it's worth the
> trouble or not..

OK, I can give you a more in-depth overview, but I just crash this quickly.

Now, let's assume you have a pure phase-detector (such as a mixer), a 
PI-regulator and an oscillator.

This represents a second-degree PLL, which has two key properties: 
natural frequency and damping factor.

The natural frequency depends on the loop bandwidth as it goes though 
the integrator path and the I factor.

The I factor is proportional to the natural frequency in square.

The damping factor depents on the balance between the I and P factors, 
in fact the P factor is proportional to the natural frequency and 
damping factor multiplied.

I've derived the formulas multiple times here on time-nuts, but if you 
need further details, please let me know. Happy to discuss off-list.

The loop-gain, as it goes through the integrator path, will decide the 
bandwidh of the PLL and thus the time-constants of the PLL.

The loop-gain, as it goes through the proportional path, decides the 
damping factor and hence the bump of the PLL.

In general, you want to make sure your damping constant is high enough 
and thus avoid the bump, and then dimension the filter bandwidth to 
bring the best balance between the reference oscillators phase-noise and 
the locked oscillators phase-noise. Essentially you overlay the 
phase-plots of reference and locked oscillator, and where they cross you 
put your cross-over bandwidth, as the PLL will low-pass filtet the 
reference oscillator phase-noise and high-pass filter the 
locked-oscillator phase-noise. The resonance due to lack of damping will 
exagerate the response at the cross-over frequency.

Uhm, this may sound a bit uncoherently, but it all fits together if you 
play around.

For the double-integration path, you need to be careful as the 
root-locus does not guarantee a stable system, as the complex pole-pair 
can move over to the right-hand side and hence severely unstable.

I can make a few recommended readings. The TI application note 
referenced isn't bad, but there is a few books to look at. The TI 
app-note does however cover some of the field the following references 
miss out on.

The Best book may be a good crash-coarse, but ends up not being good at 
teach the basics. It may be good for crashing into the field of PLLs, 
and for some things it's a very handy reference, but for others... not 
so much.

The Gardner book is the one book I recommend. Few books has core 
knowledge so well compressed. If one only gets one book, this would be 
the one I would recommend.

The Wolaver book is really a great complementary book. Great on it's own 
merrits.

I end up using all three to cover enough aspects of the field. I should 
probably be using the TI app-note a little more.

Let's talk about your specific problem and I will help you more.

Cheers,
Magnus