In textbooks, design of PI filter is usually derived starting from the noise bandwidth and damping factor. (1) Can the filter coefficients (say K1 and K2) be computed starting from a 'real-world' parameter such as convergence time? (2) Any reference/s for derivations of relationships to find convergence time, mean square error, pull-in range, etc.? Thanks. _____________________________ Posted through www.DSPRelated.com
PLL Filter Design
Started by ●April 1, 2014
Reply by ●April 1, 20142014-04-01
On 1/04/2014 9:16 AM, commsignal wrote:> In textbooks, design of PI filter is usually derived starting from the > noise bandwidth and damping factor. > > (1) Can the filter coefficients (say K1 and K2) be computed starting from a > 'real-world' parameter such as convergence time? > (2) Any reference/s for derivations of relationships to find convergence > time, mean square error, pull-in range, etc.? > > Thanks. > > _____________________________ > Posted through www.DSPRelated.com >Convergence time of a second-order PLL is derived in the book "Phase Locked Loops" by Roland E. Best, and is of the order of T=2/w, where w is the noise bandwidth. (Although I'm most likely wrong about the coefficient, as it depends on the type of phase detector you use.) So, noise bandwidth and convergence time should be pretty much interchangeable parameters, as long as a second-order PLL is concerned. Best also derives the pull-in range for a second-order PLL in that book.
Reply by ●April 1, 20142014-04-01
On Tue, 01 Apr 2014 18:56:20 +0400, Evgeny Filatov wrote:> On 1/04/2014 9:16 AM, commsignal wrote: >> In textbooks, design of PI filter is usually derived starting from the >> noise bandwidth and damping factor. >> >> (1) Can the filter coefficients (say K1 and K2) be computed starting >> from a 'real-world' parameter such as convergence time? >> (2) Any reference/s for derivations of relationships to find >> convergence time, mean square error, pull-in range, etc.? >> >> Thanks. >> >> _____________________________ >> Posted through www.DSPRelated.com >> >> > Convergence time of a second-order PLL is derived in the book "Phase > Locked Loops" by Roland E. Best, and is of the order of T=2/w, where w > is the noise bandwidth. (Although I'm most likely wrong about the > coefficient, as it depends on the type of phase detector you use.) > > So, noise bandwidth and convergence time should be pretty much > interchangeable parameters, as long as a second-order PLL is concerned. > > Best also derives the pull-in range for a second-order PLL in that book.Ditto Wolavar "Phase Locked Loop Circuit Design", or just about any decent PLL book. There are lots of subtleties and a huge bag of tricks, particularly when you deal with nonlinear phenomenon like pull in. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
Reply by ●April 1, 20142014-04-01
On Tue, 01 Apr 2014 10:33:09 -0500, Tim Wescott <tim@seemywebsite.please> wrote:>On Tue, 01 Apr 2014 18:56:20 +0400, Evgeny Filatov wrote: > >> On 1/04/2014 9:16 AM, commsignal wrote: >>> In textbooks, design of PI filter is usually derived starting from the >>> noise bandwidth and damping factor. >>> >>> (1) Can the filter coefficients (say K1 and K2) be computed starting >>> from a 'real-world' parameter such as convergence time? >>> (2) Any reference/s for derivations of relationships to find >>> convergence time, mean square error, pull-in range, etc.? >>> >>> Thanks. >>> >>> _____________________________ >>> Posted through www.DSPRelated.com >>> >>> >> Convergence time of a second-order PLL is derived in the book "Phase >> Locked Loops" by Roland E. Best, and is of the order of T=2/w, where w >> is the noise bandwidth. (Although I'm most likely wrong about the >> coefficient, as it depends on the type of phase detector you use.) >> >> So, noise bandwidth and convergence time should be pretty much >> interchangeable parameters, as long as a second-order PLL is concerned. >> >> Best also derives the pull-in range for a second-order PLL in that book. > >Ditto Wolavar "Phase Locked Loop Circuit Design", or just about any >decent PLL book. > >There are lots of subtleties and a huge bag of tricks, particularly when >you deal with nonlinear phenomenon like pull in. > >-- >Tim Wescott >Control system and signal processing consulting >www.wescottdesign.comIn addition to Best and Wolovar, Gardner's book and, for communication systems, Lindsay and Simon, have a lot of reference material for such things. That being said, the various texts don't always agree, partly because the various terms, like convergence time or acquisition time, aren't universally defined. There are also lots of dependencies on things like SNR, detector responses, etc., which may lead one to eventually take the position that many such things having to do with PLLs are essentially somewhat arbitrary rules of thumb rather than specific, derivable quantities. Basically, YMMV. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●April 1, 20142014-04-01
On Tue, 01 Apr 2014 18:56:14 +0000, Eric Jacobsen wrote:> On Tue, 01 Apr 2014 10:33:09 -0500, Tim Wescott > <tim@seemywebsite.please> wrote: > >>On Tue, 01 Apr 2014 18:56:20 +0400, Evgeny Filatov wrote: >> >>> On 1/04/2014 9:16 AM, commsignal wrote: >>>> In textbooks, design of PI filter is usually derived starting from >>>> the noise bandwidth and damping factor. >>>> >>>> (1) Can the filter coefficients (say K1 and K2) be computed starting >>>> from a 'real-world' parameter such as convergence time? >>>> (2) Any reference/s for derivations of relationships to find >>>> convergence time, mean square error, pull-in range, etc.? >>>> >>>> Thanks. >>>> >>>> _____________________________ >>>> Posted through www.DSPRelated.com >>>> >>>> >>> Convergence time of a second-order PLL is derived in the book "Phase >>> Locked Loops" by Roland E. Best, and is of the order of T=2/w, where w >>> is the noise bandwidth. (Although I'm most likely wrong about the >>> coefficient, as it depends on the type of phase detector you use.) >>> >>> So, noise bandwidth and convergence time should be pretty much >>> interchangeable parameters, as long as a second-order PLL is >>> concerned. >>> >>> Best also derives the pull-in range for a second-order PLL in that >>> book. >> >>Ditto Wolavar "Phase Locked Loop Circuit Design", or just about any >>decent PLL book. >> >>There are lots of subtleties and a huge bag of tricks, particularly when >>you deal with nonlinear phenomenon like pull in. >> >>-- >>Tim Wescott Control system and signal processing consulting >>www.wescottdesign.com > > > In addition to Best and Wolovar, Gardner's book and, for communication > systems, Lindsay and Simon, have a lot of reference material for such > things. That being said, the various texts don't always agree, partly > because the various terms, like convergence time or acquisition time, > aren't universally defined. > > There are also lots of dependencies on things like SNR, detector > responses, etc., which may lead one to eventually take the position that > many such things having to do with PLLs are essentially somewhat > arbitrary rules of thumb rather than specific, derivable quantities.I wouldn't say "don't always agree" so much as "present the information differently". But yes, different authors will assign different definitions to the same terms, which can lead to confusion until you realize that there is no International Standards Committee on Scientific Terminology working behind the scenes to tell us what thought is orthodox*. The great drawback of Wolavar, and, I suspect, others, is that it is presented entirely from an analog circuits point of view. There are things you can do when realizing PLLs in software that simply are not practical with analog hardware. Moreover, there are times when you are implementing your signal processing digitally when a PLL simply isn't the best approach to timing acquisition. Alas, I do not have a good book recommendation for the modern age -- I have Wolavar's book because I took the class from Wolavar, and I've always been good at translating the concepts from chips & capacitors into lines of C. So I've never needed an update. * Gosh that sounds like a rant. It really isn't meant to be. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
Reply by ●April 1, 20142014-04-01
..... There are things you can do when realizing PLLs in software that simply are not>practical with analog hardware.Moreover, there are times when you are implementing your signal processing digitally when a PLL simply isn't the best approach to timing acquisition. .....>-- >Tim Wescott >Control system and signal processing consulting >www.wescottdesign.com >Can you please explain the above two a bit more. What additional possibilities/disadvantages are there with software PLLs? And when should the PLL be avoided? Thanks. _____________________________ Posted through www.DSPRelated.com
Reply by ●April 1, 20142014-04-01
On 4/1/14 1:16 AM, commsignal wrote:> In textbooks, design of PI filter is usually derived starting from the > noise bandwidth and damping factor. > > (1) Can the filter coefficients (say K1 and K2) be computed starting from a > 'real-world' parameter such as convergence time? > (2) Any reference/s for derivations of relationships to find convergence > time, mean square error, pull-in range, etc.? >first, i haven't done a real PLL thingie since grad school. something i *have* done in the industry (but still two decades ago) was an ASRC (asynchronous sample rate converter) that has something like a PLL inside (a servo "mechanism" with an inherent integrator in the loop). that said, one thing you have to keep in mind is the inherent integrator, due to the VCO (or NCO) that is essentially in series with your PI controller. essentially a VCO has output frequency (which is the derivative of phase) proportional to the input voltage or an NCO has output frequency equal to the step size (or "stride" or "phase increment" or whatever they call it), which is the input to the NCO. if it's a *phase* discriminator (it *could* be a frequency discriminator instead or some weighted sum of the two) then you need to model that and in doing so, there is an integrator between the NCO input and the output of the discriminator. so instead of PI it's really I and I^2. unless you put a differentiator (so it's "PID") in the controller, there really is no P. just I and I^2. so, for the most part, the I coefficient (is that K2?) is really an I^2 coefficient, and i haven't found much use for it (set it to 0 so my raw controller is just a P controller). but, for whatever reason, you might want to toss in a little "D" in your controller. if you have a differentiator in there, then you will have a net "PI" controller. but otherwise, you really have an I and I^2. in terms of modeling the step response of the PLL (that is a step change in phase) so as to determine stability or overshoot, that should be pretty standard in control theory texts, if you model the loop correctly. with an inherent integrator in the loop, it should be the case that the step response of the phase difference will eventually converge to zero. that's what integrators do in a control loop. so i think the simple thing is just have a regular gain coefficient which, in modeling, will be the "I" coefficient. model that and see what you get. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●April 1, 20142014-04-01
On Tuesday, April 1, 2014 6:16:05 PM UTC+13, commsignal wrote:> In textbooks, design of PI filter is usually derived starting from the > > noise bandwidth and damping factor. > > > > (1) Can the filter coefficients (say K1 and K2) be computed starting from a > > 'real-world' parameter such as convergence time? > > (2) Any reference/s for derivations of relationships to find convergence > > time, mean square error, pull-in range, etc.? > > > > Thanks. > > > > _____________________________ > > Posted through www.DSPRelated.comPLLs are designed for a particular phase margin. You need to draw a Bode plot. Quite easy to do. A PLL is just a servo which works on phase.
Reply by ●April 2, 20142014-04-02
On Tue, 01 Apr 2014 16:14:53 -0500, commsignal wrote:> ..... > > There are things you can do when realizing PLLs in software that simply > are not >>practical with analog hardware. > > > Moreover, there are times when you are implementing your signal > processing digitally when a PLL simply isn't the best approach to timing > acquisition. > > ..... >>-- >>Tim Wescott Control system and signal processing consulting >>www.wescottdesign.com >> >> > Can you please explain the above two a bit more. What additional > possibilities/disadvantages are there with software PLLs? And when > should the PLL be avoided?On the first: mostly, you can do a lot more with phase detectors, and its much easier to do gain-scheduled acquisition (i.e., switching the gains in the filter based on acquisition time or lock detection). On the second: I'm not the best person to ask, but often when you have packetized data it's better to do a pass to acquire a timing lock, then do another pass to actually decode the data. This falls apart if the frequency difference between transmit and receive is great with respect to the packet duration, and of course it makes no sense at all if the transmission is continuous. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●April 2, 20142014-04-02
On 1/04/2014 10:56 PM, Eric Jacobsen wrote:> On Tue, 01 Apr 2014 10:33:09 -0500, Tim Wescott > <tim@seemywebsite.please> wrote: > >> On Tue, 01 Apr 2014 18:56:20 +0400, Evgeny Filatov wrote: >> >>> On 1/04/2014 9:16 AM, commsignal wrote: >>>> In textbooks, design of PI filter is usually derived starting from the >>>> noise bandwidth and damping factor. >>>> >>>> (1) Can the filter coefficients (say K1 and K2) be computed starting >>>> from a 'real-world' parameter such as convergence time? >>>> (2) Any reference/s for derivations of relationships to find >>>> convergence time, mean square error, pull-in range, etc.? >>>> >>>> Thanks. >>>> >>>> _____________________________ >>>> Posted through www.DSPRelated.com >>>> >>>> >>> Convergence time of a second-order PLL is derived in the book "Phase >>> Locked Loops" by Roland E. Best, and is of the order of T=2/w, where w >>> is the noise bandwidth. (Although I'm most likely wrong about the >>> coefficient, as it depends on the type of phase detector you use.) >>> >>> So, noise bandwidth and convergence time should be pretty much >>> interchangeable parameters, as long as a second-order PLL is concerned. >>> >>> Best also derives the pull-in range for a second-order PLL in that book. >> >> Ditto Wolavar "Phase Locked Loop Circuit Design", or just about any >> decent PLL book. >> >> There are lots of subtleties and a huge bag of tricks, particularly when >> you deal with nonlinear phenomenon like pull in. >> >> -- >> Tim Wescott >> Control system and signal processing consulting >> www.wescottdesign.com > > > In addition to Best and Wolovar, Gardner's book and, for communication > systems, Lindsay and Simon, have a lot of reference material for such > things. That being said, the various texts don't always agree, > partly because the various terms, like convergence time or acquisition > time, aren't universally defined. > > There are also lots of dependencies on things like SNR, detector > responses, etc., which may lead one to eventually take the position > that many such things having to do with PLLs are essentially somewhat > arbitrary rules of thumb rather than specific, derivable quantities. > > Basically, YMMV. > > > Eric Jacobsen > Anchor Hill Communications > http://www.anchorhill.com >IMHO, Best's book is better as an introductory text, while Gardner's book is a good reference text. Gardner's book is more rigorous and it's advantage is that it covers digital PLLs in great detail. I couldn't read a lot of Lindsay and Simon because that book is heavily packed with math. A book by Michael Rice is easier and also contains a chapter on PLLs.
