How does a PLL work?

I have more results to share. I can accept the phase modulation artifacts, they change the NCO period by less than 7%, so it is not a big issue. I can even lie through teeth and proclaim it to be an EMI-reducing spread spectrum modulator or another continuum transfunctioner. Nonetheless, for completeness I have created a generic second order biquad structure, filled it with various coefficients and simulated in double precision to avoid the most obvious numeric instabilities. I have checked the Gaussian, Butterworth, Chebyshev and elliptic approximations and the -3dB frequencies in the range of 1..50Hz.

As it can be expected, the ripple level of these filters is superb, especially in the case of the elliptic filter for 5.9Hz, which happens to have a zero at 100Hz, BUT the loop is much harder to stabilize. The lock occurs only for a relatively narrow range of gains, while the reference exponential smoother works correctly within the range as wide as an order of magnitude. Lower gain just means increased constant phase error, while too much gain means increased distortion level. The filters are also more agile, but they always introduce a tiny phase lag, while the smoother with sufficient gain doesn't. For some reason 10Hz passband gives the best results, lower bandwidth filters converge too slowly or not at all, while the wider ones are robust, but their ripple level is comparable to that of the smoother. So since the increased complexity doesn't buy me much, I'll stick to the embarassingly primitive smoother.

Moreover, it is possible to add a frequency-dependent gain compensation based on linear interpolation, which, too, works unexpectedly well. The PLL locks in the range of 45..55Hz with a negligible phase offset.

There is something deeply mysterious about this low alpha exponential smoother, its robustness is on the verge of offensiveness, given its crude nature. I think I am onto something, but don't know what that something might be.

Best regards, Piotr

Reply to
Piotr Wyderski
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Piotr, I'm enjoying your posts, (and have never done a HF PLL.) So take this for what it's worth. I've done a few LF loops. If there's a dead band try a bit offset.

Re: the noise reduction when you close the loop. I understand this as a limit on the bandwidth. But it is fun to see! "Zoooop" (the sound as the noise goes away.)

George H.

Reply to
George Herold

On a sunny day (Thu, 28 Sep 2017 00:28:58 +0200) it happened Piotr Wyderski wrote in :

I cannot escape the impression that you are missing something essentially simple. Or at least I cannot decode what you write. That may well be my shortcoming. A little anecdote: When first hearing about logic and logic symbols, somebody presented a counter with feedback. I looked at it and after a high brain activity moment followed by short-circuit halt instruction concluded it could never work. Because it missed that essential ingredient. In the presentation the gates were timeless, had no delay [1]. Logic feedback circuits can only work BECAUSE they have a delay.

[1] If gates have no delay the input is corrected at the same moment as the output resulting in ??

Your stories remind me of that moment. What 'teachers' present is not necessarily what they understand.

Reply to
Jan Panteltje

Could well be, but the problem -- if I may say so -- is that the PLLs work and I am able to make them lock to the given frequency. Their performance is just inferior despite the higher resource consumption compared to an exponential smoother, which basically is a digital equivalent of a first order RC circuit. And frankly, I can't explain that.

Then give it a shot, I'd gladly learn what and whether I'm missing something. I'm no expert in this field, but just have a "circuit" with unexpectedly good performance.

The level of teachers' understanding is a topic for another sad discussion.

Best regards, Piotr

Reply to
Piotr Wyderski

On a sunny day (Thu, 28 Sep 2017 10:17:41 +0200) it happened Piotr Wyderski wrote in :

It is hard to tell without code or circuit. I am in no way a PLL expert, but those always seem to work. I think some people already mentioned some good references.

In the previous paragraph you said 'performance is just inferior' now you say: 'unexpectedly good performance'

so the problem is with your logic :-)

Reply to
Jan Panteltje

In the first paragraph "their" refers to the classic lowpass biquad filtering structures, the latter refers to the exponential smoother.

"Their performance is just inferior despite the higher resource consumption *compared to* an exponential smoother"

Best regards, Piotr

Reply to
Piotr Wyderski

On a sunny day (Thu, 28 Sep 2017 16:21:04 +0200) it happened Piotr Wyderski wrote in :

Ok, got it. The fact remains it is hard to tell without knowing what you control etc etc. In the long ago past I worked in a TV studio, there were more locked loops in there then you may think, from color carrier to hsync to vsync, some over large distances via radio or cable, and at the top the quadruplex video recording where you had to position 4 video heads rotating at 250 rev/second to within a few micron, and then electronically compensate with even more loops the timing errors of the signal coming from it. all in real time synced to some studio reference, and of course tape speed too. I am real familiar with all those solutions and it was, and still is, top electronics. Jim already mentioned one such phase detector system. But without specifying all those variables (like mass of the rotating head, time delays, error margins, lock speed, etc etc) it is not possible to just plonk down a 'fits all' solution. If something works better than expected maybe there are those other factors in play, same if worse. Over time things sort of condense out, that is what I mean by 'fingersptizengefuhl', So always be specific what you are controlling, its properties, requirements.

Reply to
Jan Panteltje

Add a motor, some friction, some inertia, and the fun begins.

A simple tiny motor _may_ be treated as an integrator... beyond that, all hell breaks loose.

In 1968 (at Philco-Ford, Santa Clara) I was involved in designing cruise controls for automobiles... in essence, a PLL... great fun... we towed a 1967 Ford T-bird around to measure all its parameters ;-) ...Jim Thompson

--
| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
| STV, Queen Creek, AZ 85142    Skype: skypeanalog |             | 
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 

             I'm looking for work... see my website. 

Thinking outside the box...producing elegant & economic solutions.
Reply to
Jim Thompson

It's amusing to pull open a CD deck, and find the test points (this works best on a 20-year-old unit, new 'uns don't have test points). One of the test points is the spindle motor loop control, you can watch it while gently braking the disk rotation with a finger. There's some buffering, of course, but basically that is a PLL control voltage.

Another is the radial seek control voltagel, usually (due to eccentric shaft or pressing of the CD) has 1 Hz ripple. The focus control is more likely to have harmonics of 1 Hz.

Reply to
whit3rd

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