Is there a limit to achievable resolution of a phase-locked loop given no noise and arbitrary acquisition time? If so, what is that limit? For example, is 0.1 degree phase resolution of a 10 kHz sinusoid reasonably achievable in practice if we assume >60 dB S/N, no frequency error and tens of seconds to acquire? Thanks.
PLL resolution
Started by ●January 22, 2008
Reply by ●January 22, 20082008-01-22
On Jan 22, 1:20�pm, "Grant" <nos...@nospam.com> wrote:> Is there a limit to achievable resolution of a phase-locked loop given no > noise and arbitrary acquisition time? �If so, what is that limit? > > For example, is 0.1 degree phase resolution of a 10 kHz sinusoid reasonably > achievable in practice if we assume >60 dB S/N, no frequency error and tens > of seconds to acquire? > > Thanks.There was an interesting article in IEEE Trans Comm a while back by Floyd Gardner, called "Frequency Granularity in Phase Locked Loops". You might have a look. John
Reply by ●January 23, 20082008-01-23
On Jan 23, 7:20 am, "Grant" <nos...@nospam.com> wrote:> Is there a limit to achievable resolution of a phase-locked loop given no > noise and arbitrary acquisition time? If so, what is that limit? > > For example, is 0.1 degree phase resolution of a 10 kHz sinusoid reasonably > achievable in practice if we assume >60 dB S/N, no frequency error and tens > of seconds to acquire? > > Thanks.All depends on t he dynamics of your loop. You need to maintain stability whilst having a massive gain at low frequencies. The ultimate would be to have a pure integrator + phase-lead as a filter. The transfer function will then be K/s^2(1+sT1)/(1+sT2)...T1=10T2 (say). You will also need a maximum bandwidth possible which is a function of the 2fcarrier feedthrough term (how much can you stand). It's all servo stuff really. Hardy
Reply by ●January 23, 20082008-01-23
On Jan 22, 1:20�pm, "Grant" <nos...@nospam.com> wrote:> Is there a limit to achievable resolution of a phase-locked loop given no > noise and arbitrary acquisition time? �If so, what is that limit? > > For example, is 0.1 degree phase resolution of a 10 kHz sinusoid reasonably > achievable in practice if we assume >60 dB S/N, no frequency error and tens > of seconds to acquire? > > Thanks.I don't understand your question. An analog VCO has infinite resolution, and in a PLL it can lock exactly to any frequency and any phase (in it's range). The phase error when locked depends on implementation details but can be made to approach zero. Are you using an analog VCO or a DDS based VCO? Mark
Reply by ●January 23, 20082008-01-23
Yes, I understand. But what I'm asking is how small can "made to approach zero" be in practice? It's an analog VCO implemented in DSP. Is 0.1 degree reasonable in practice given very high S/N and long acquisition time? To me that seems amazingly good resolution but I have no experience to base that feeling on. Grant "Mark" <makolber@yahoo.com> wrote in message news:0dacf57c-7ab0-49fb-ad59-23103b704782@d21g2000prf.googlegroups.com... On Jan 22, 1:20 pm, "Grant" <nos...@nospam.com> wrote:> Is there a limit to achievable resolution of a phase-locked loop given no > noise and arbitrary acquisition time? If so, what is that limit? > > For example, is 0.1 degree phase resolution of a 10 kHz sinusoid > reasonably > achievable in practice if we assume >60 dB S/N, no frequency error and > tens > of seconds to acquire? > > Thanks.I don't understand your question. An analog VCO has infinite resolution, and in a PLL it can lock exactly to any frequency and any phase (in it's range). The phase error when locked depends on implementation details but can be made to approach zero. Are you using an analog VCO or a DDS based VCO? Mark
Reply by ●January 23, 20082008-01-23
> > It's an analog VCO implemented in DSP. �Is 0.1 degree reasonable in practice > given very high S/N and long acquisition time? �To me that seems amazingly > good resolution but I have no experience to base that feeling on. > > Grant >I don't know what an analog VCO implemented in DSP means. If it is a real analog PLL the phase error can approach zero as the DC loop gain is increased (i.e. the loop contains an integrator) and subject to any DC offset or other errors. I suspect I still don't understand your question. What does resolution mean to you in this context? Mark
Reply by ●January 23, 20082008-01-23
The application requires the phase of an input audio sinusoid be measured accurately. Specifically I need to measure when the tone's zero crossing occurs within about 0.1 degree. Grant "Mark" <makolber@yahoo.com> wrote in message news:51784ea2-0bac-49c6-893b-a9a64b35f70d@e10g2000prf.googlegroups.com...> > It's an analog VCO implemented in DSP. Is 0.1 degree reasonable in > practice > given very high S/N and long acquisition time? To me that seems amazingly > good resolution but I have no experience to base that feeling on. > > Grant >I don't know what an analog VCO implemented in DSP means. If it is a real analog PLL the phase error can approach zero as the DC loop gain is increased (i.e. the loop contains an integrator) and subject to any DC offset or other errors. I suspect I still don't understand your question. What does resolution mean to you in this context? Mark
Reply by ●January 24, 20082008-01-24
Grant wrote:> Yes, I understand. But what I'm asking is how small can "made to approach > zero" be in practice? > > It's an analog VCO implemented in DSP. Is 0.1 degree reasonable in practice > given very high S/N and long acquisition time? To me that seems amazingly > good resolution but I have no experience to base that feeling on.Part of the answer depends on the digital resolution. However you measure frequency, you can't get closer than one bit. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●January 24, 20082008-01-24
Grant wrote:> The application requires the phase of an input audio sinusoid be measured > accurately. Specifically I need to measure when the tone's zero crossing > occurs within about 0.1 degree.within .1 degree of what reference? or do you mean "to within .1 degree"? How do you measure degrees? If 180 degrees is represented by 12 useful bits, then the best you can hope for is .044 degrees. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●January 24, 20082008-01-24
On Jan 23, 10:41�pm, "Grant" <nos...@nospam.com> wrote:> The application requires the phase of an input audio sinusoid be measured > accurately. �Specifically I need to measure when the tone's zero crossing > occurs within about 0.1 degree. > > Grant > >I suspect what you mean is "accuracy" not resolution.. see http://www.clarke-hess.com/6000.html Mark
