Hi. Phase noise of a PLL is usually specified over a few discrete frequency points. For example, at 10kHz, 30kHz, 100kHz, 1MHz... My question is if the lowest specified frequency is at F1Hz, then what phase noise characteristic do we assume for the frequency range between 0Hz to F1Hz? Shall we assume a 1/F slope from 0Hz to F1Hz? Or is it 1/F^2 slope? Or something else? Thanks! -- Regards, ckiancho
Phase Noise of PLL
Started by ●June 14, 2005
Reply by ●June 14, 20052005-06-14
ckiancho wrote:> Hi. > > Phase noise of a PLL is usually specified over a few discrete frequency > points. For example, at 10kHz, 30kHz, 100kHz, 1MHz... My question is if the > lowest specified frequency is at F1Hz, then what phase noise characteristic > do we assume for the frequency range between 0Hz to F1Hz? Shall we assume a > 1/F slope from 0Hz to F1Hz? Or is it 1/F^2 slope? Or something else?Probably not. Assuming that you mean F1 to be F-subscript-1 (F_1 is more usual unless context provides more information), and the noise is non-zero there, 1/f noise would get out of hand at f=0. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●June 15, 20052005-06-15
Jerry Avins wrote:> ckiancho wrote: > >> Hi. >> >> Phase noise of a PLL is usually specified over a few discrete >> frequency points. For example, at 10kHz, 30kHz, 100kHz, 1MHz... My >> question is if the lowest specified frequency is at F1Hz, then what >> phase noise characteristic do we assume for the frequency range >> between 0Hz to F1Hz? Shall we assume a 1/F slope from 0Hz to F1Hz? Or >> is it 1/F^2 slope? Or something else? > > > Probably not. Assuming that you mean F1 to be F-subscript-1 (F_1 is more > usual unless context provides more information), and the noise is > non-zero there, 1/f noise would get out of hand at f=0. > > JerryIIRC phase noise of an oscillator starts way out from the carrier as constant (f^0), then goes through a region where it's 1/f, then 1/f^2 -- the book I have even shows it going to 1/f^3. At some point it must level out, however, if for no other reason than because the energy density must integrate to a finite energy level, and 1/f^x, x>=1, integrates to infinity. A PLL combines the phase noise of two oscillators: the VCO and the reference oscillator. Even with a perfect reference that 1/f^3 noise starts poking up through the white noise, and even with a perfect loop the reference oscillator will start showing its noise. -- ------------------------------------------- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●June 15, 20052005-06-15
Tim Wescott wrote:> Jerry Avins wrote: > > > ckiancho wrote: > > > >> Hi. > >> > >> Phase noise of a PLL is usually specified over a few discrete > >> frequency points. For example, at 10kHz, 30kHz, 100kHz, 1MHz... My > >> question is if the lowest specified frequency is at F1Hz, then what > >> phase noise characteristic do we assume for the frequency range > >> between 0Hz to F1Hz? Shall we assume a 1/F slope from 0Hz to F1Hz? Or > >> is it 1/F^2 slope? Or something else? > > > > > > Probably not. Assuming that you mean F1 to be F-subscript-1 (F_1 is more > > usual unless context provides more information), and the noise is > > non-zero there, 1/f noise would get out of hand at f=0.I think that's what makes phase noise interesting. As long as the psd goes to zero as 1/f^alpha, with 0 < alpha < 1, you can model this as a stationary random process. The fact that you have a pole at zero can be tolerated as long as it is integrable towards zero (which it is, given the bounds of alpha). If it is integrable, you can take the inverse Fourier transform to compute the ACF of that noise (given that f decays fast enough for high frequencies). Such an ACF decays with 1/t^(1-alpha) and is therefore not integrable (towards infinity). Due to this slow decay rate of the ACF, these noises are sometimes called long-range correlated. They are fitting models for almost all time series connected to climatology (hydrology is the most well known), but also for music, DNA, financial markets (have a look at http://misbehaviorofmarkets.com/), sun spots, you name it.> > > > Jerry > > IIRC phase noise of an oscillator starts way out from the carrier as > constant (f^0), then goes through a region where it's 1/f, then 1/f^2 -- > the book I have even shows it going to 1/f^3. At some point it must > level out, however, if for no other reason than because the energy > density must integrate to a finite energy level, and 1/f^x, x>=1, > integrates to infinity.Which integral did you mean exactly? Regards, Andor
Reply by ●June 16, 20052005-06-16
Then if I have 2 example phase noise specifications: PLL #1: 10kHZ 100kHz 1MHz 10MHz -50dBc -60dBc -70dBc -80dBc PLL#2: 1 kHz 10kHZ 100kHz 1MHz 10MHz -30dBc -50dBc -60dBc -70dBc -80dBc Both PLLs have the same spec for frequencies 10kHz and above. PLL#2 has an additional reading at 1kHz. In this case, can we tell which is the better PLL? "Andor" <an2or@mailcircuit.com> wrote in message news:1118820004.683810.70830@g49g2000cwa.googlegroups.com...> Tim Wescott wrote: >> Jerry Avins wrote: >> >> > ckiancho wrote: >> > >> >> Hi. >> >> >> >> Phase noise of a PLL is usually specified over a few discrete >> >> frequency points. For example, at 10kHz, 30kHz, 100kHz, 1MHz... My >> >> question is if the lowest specified frequency is at F1Hz, then what >> >> phase noise characteristic do we assume for the frequency range >> >> between 0Hz to F1Hz? Shall we assume a 1/F slope from 0Hz to F1Hz? Or >> >> is it 1/F^2 slope? Or something else? >> > >> > >> > Probably not. Assuming that you mean F1 to be F-subscript-1 (F_1 is >> > more >> > usual unless context provides more information), and the noise is >> > non-zero there, 1/f noise would get out of hand at f=0. > > I think that's what makes phase noise interesting. As long as the psd > goes to zero as 1/f^alpha, with 0 < alpha < 1, you can model this as a > stationary random process. The fact that you have a pole at zero can be > tolerated as long as it is integrable towards zero (which it is, given > the bounds of alpha). If it is integrable, you can take the inverse > Fourier transform to compute the ACF of that noise (given that f decays > fast enough for high frequencies). Such an ACF decays with > 1/t^(1-alpha) and is therefore not integrable (towards infinity). Due > to this slow decay rate of the ACF, these noises are sometimes called > long-range correlated. They are fitting models for almost all time > series connected to climatology (hydrology is the most well known), but > also for music, DNA, financial markets (have a look at > http://misbehaviorofmarkets.com/), sun spots, you name it. > >> > >> > Jerry >> >> IIRC phase noise of an oscillator starts way out from the carrier as >> constant (f^0), then goes through a region where it's 1/f, then 1/f^2 -- >> the book I have even shows it going to 1/f^3. At some point it must >> level out, however, if for no other reason than because the energy >> density must integrate to a finite energy level, and 1/f^x, x>=1, >> integrates to infinity. > > Which integral did you mean exactly? > > Regards, > Andor >
Reply by ●June 16, 20052005-06-16
ckiancho wrote:> Then if I have 2 example phase noise specifications: > > PLL #1: > 10kHZ 100kHz 1MHz 10MHz > -50dBc -60dBc -70dBc -80dBc > > PLL#2: > 1 kHz 10kHZ 100kHz 1MHz 10MHz > -30dBc -50dBc -60dBc -70dBc -80dBc > > Both PLLs have the same spec for frequencies 10kHz and above. PLL#2 has an > additional reading at 1kHz. In this case, can we tell which is the better > PLL? >no, we can only tell you that PLL#2 is specified more thoroughly. -- ------------------------------------------- Tim Wescott Wescott Design Services http://www.wescottdesign.com
