ECEN620: Network Theory Broadband Circuit Design Fall 2014

Transcription

1 ECE60: work Thory Broadbad Circui Dig Fall 04 Lcur 6: PLL Trai Bhavior Sam Palrmo Aalog & Mixd-Sigal Cr Txa A&M Uivriy

2 Aoucm, Agda, & Rfrc HW i du oday by 5PM PLL Trackig Rpo Pha Dcor Modl PLL Hold Rag PLL Acquiiio Chapr 5 of Phalock Tchiqu, F. Gardr, Joh Wily & So, 005. Chapr 4 of Pha-Lockd Loop for Wirl Commuicaio, D. Sph, luwr, 00.

3 Liar PLL Modl If h pha ipu ampliud i mall, h h liar modl ca b ud o prdic h rai rpo E ( ) Φ Φ rf ( ) ( ) G( ) F( ) Idally, w wa hi o b zro Pha rror grally icra wih frqucy du o hi high-pa rpo 3

4 Fir-Ordr PLL Trackig Rpo F,, 3dB 3dB ( ) E( ) Pha Sp Rpo Uig h Fial Valu Thorm : Φ lim 0 ( E( ) ) lim 0 Φ ( ) 0 Pha rror hould b zro wih a pha p Trai Rpo : L Φ Φ Trai Rpo i a xpoialy dcayig p 4

5 Fir-Ordr PLL Trackig Rpo F,, 3dB 3dB ( ) E( ) Frqucy Off (Sp) Rpo Uig h Fial Valu Thorm : lim 0 ( E( ) ) lim 0 ( ) Th pha rror i ivrly proporiioal o h loop gai wih a frqucy off Trai Rpo : L ( ) Trai Rpo i a xpoialy riig p 5

6 Fir-Ordr PLL Trackig Rpo F,, 3dB 3dB ( ) E( ) Frqucy Ramp Rpo Aum ha h ipu frqucy i chagig liarly wih im a a ra of Λ ( rad/c ) φ rf ( ) Λ Uig h Fial Valu Thorm : Λ lim 0 3 ( E( ) ) lim 0 3 Λ ( ) Th pha rror will grow o ifiiy if i fii Trai Rpo : L Λ 3 Λ ( ) 6

7 ( ) ( ) ( ) E F,, ζ Pha Sp Rpo ( ) ( ) yourlf Try o compu hi Trai Rpo : pha p Pha rror hould b zro wih a 0 lim lim Valu Thorm : Uig h Fial 0 0 Φ Φ Φ E L Scod-Ordr Typ- PLL Trackig Rpo 7

8 ( ) ( ) ( ) E F,, ζ Frqucy Off (Sp) Rpo ( ) ( ) yourlf Try o compu hi Trai Rpo : frqucy off o h loop gai wih a Th pha rror i ivrly proporiioal lim lim Valu Thorm : Uig h Fial 0 0 E L Scod-Ordr Typ- PLL Trackig Rpo 8

9 ( ) ( ) ( ) E F,, ζ Frqucy Ramp Rpo ( ) ( ) yourlf Try o compu hi Trai Rpo : i fii grow o ifiiy if Th pha rror will lim lim Valu Thorm : Uig h Fial Λ Λ Λ E L Scod-Ordr Typ- PLL Trackig Rpo 9

10 Scod-Ordr Typ- PLL Trackig Rpo F R RC ( ), E( ) Pha Sp Rpo ζ RC, R Uig h Fial Valu Thorm : Φ lim 0 ( E( ) ) lim 0 Pha rror hould b zro wih a pha p Φ 3 RC 0 Trai Rpo : L Φ RC 0

11 Scod-Ordr Typ- PLL Pha Sp Rpo Trai Rpo : L Φ RC ζ RC RC

12 Frqucy Off (Sp) Rpo ( ) ( ) RC RC E Trai Rpo : Typ - PLL o zro wih a Th pha rror go 0 lim lim Valu Thorm : Uig h Fial L Scod-Ordr Typ- PLL Trackig Rpo ( ) ( ) R RC E RC R F,, ζ

13 Scod-Ordr Typ- PLL Frqucy Sp Rpo Trai Rpo : L RC ζ RC RC 3

14 Scod-Ordr Typ- PLL Trackig Rpo F R RC ( ), E( ) Frqucy Ramp Rpo ζ RC, R Uig h Fial Valu Thorm : Λ lim 0 3 ( E( ) ) lim 0 3 Λ 3 RC Λ A cod - ordr yp- PLL ca rack a frqucy ramp wih a dyamic pha lag Trai Rpo : L Λ 3 RC 4

15 Scod-Ordr Typ- PLL Frqucy Ramp Rpo Trai Rpo : L Λ 3 RC ζ RC RC 5

16 Idal Pha Dcor A idal pha dcor ha h am gai (lop) ovr a ±π rag Thi allow h liar PLL modl o b ud for all pha rlaiohip 6

17 Ral Pha Dcor May pha dcor ar oliar ad do o diplay h am gai for a giv pha rlaiohip Thi impli ha h PLL cao b dcribd by h liar modl for larg ipu pha dviaio 7

18 PLL Frqucy Sp Rpo: Liar v Bhavioral Modl Du o o-liarii i loop compo (primarily h ), a ral PLL rpo ca vary igificaly from h liar modl 8

19 PLL Hold Rag (Siuoidal ) A PLL Hold Rag i h ipu frqucy rag ovr which h PLL ca maiai aic lock w/ Liar Modl h Sady -Sa Pha Error i φ Fir - Ordr : Scod - Ordr Typ -: Scod - Ordr Typ - : Wih a iuoidal pha dcor, h pha rror i Sic i cao xcd, h lock frqucy i coraid o Hold Rag : iφ H ( rad/c) Th hold rag i fii for a yp- PLL, ad horically ifii for a yp- PLL. Howvr i pracic i will b limid by aohr PLL block, uch a h uig rag. 9

20 Fir-Ordr PLL Phalock Acquiiio (Siuoidal ) Aumig a impl fir - ordr PLL wih a iuoidal F ( ) Iaaou Frqucy: Siuoidal Pha Dcor Oupu : o v i c ( ) ( φ ) Aum h ipu igal i a a frqucy diffr from, uch ha h o ipu pha i rf ad rf o 0

21 Fir-Ordr PLL Phalock Acquiiio (Siuoidal ) φ ou ( ) v ( ) d φ ( 0) i( φ ( )) d φ ( 0) o o c Th PLL oupu pha i ou o o Th PLL pha rror i ou φ φ rf φ ou ( rf o ) i φ( ) o ( ) d φ ( 0) ou Diffriaig hi w.r.. im yild h followig oliar diffrial quaio dφ d ( ) i ( φ( ) ) whr

22 Fir-Ordr PLL Hold Rag (Siuoidal ) dφ d If h PLL i lockd, ( ) i i ( φ ) ( φ ( )) Sic i cao xcd, h lock frqucy i coraid o 0 Hold Rag : H < ( rad/c)

23 Fir-Ordr PLL Phalock Acquiiio (Siuoidal ) ormalizig h fir - ordr PLL diffrial quaio by φ ormalizd Frqucy Error, φ i ( φ ) φ I h pha - pla plo, hr ar ull whr 0 d gaiv - lop ull ar abl lock poi, d Pha Error, φ whil poiiv - lop ull ar uabl Evry cycl (π irval) coai a abl ull, hu φ cao chag by mor ha o cycl bfor lockig Thr i o cycl lippig i h lockig proc A cycl lip occur wh h pha rror chag by mor ha π wihou lockig 3

24 Fir-Ordr PLL Phalock Acquiiio Tim (Siuoidal ) I ordr o fid h phalock acquiio im, w d o formally olv If φ ( ) i( φ ( )) d φ ( 0) i zro ad φ o ou ( 0) i mall, uch ha i( φ ) φ, h approxima oluio i h liar modl pha p rpo Howvr, if φ φ ( 0) ( ) φ ( 0) i larg, h rpo will dvia from hi liar approximaio ad ca icra igificaly ou φ i ( φ ) Hr 0 4

25 Fir-Ordr PLL Lock Failur (Siuoidal ). φ i ( φ ) Fir-Ordr PLL Corol Volag Hold Rag : H < ( rad/c) If h frqucy off xcd h PLL hold rag, h pha rror will ocilla aymmrically a h PLL udrgo cycl lip 5

26 Scod-Ordr Typ- PLL Phalock Acquiiio (Siuoidal ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 i i 0 Th PLL oupu pha i i i Th filr rpo i h im - domai ca b xprd a Aumig a cod - ordr yp- PLL wih a iuoidal ou o ou o c o ou c d d d d v d d v v v F φ φ φ φ φ φ φ 6

27 Scod-Ordr Typ- PLL Phalock Acquiiio (Siuoidal ) φ φ rf φ ou ( ) rf o i φ( ) φ Th PLL pha rror i 0 co ( ) d i( φ ( )) d d φ ( 0) Diffriaig hi wic w.r.. im yild h followig oliar diffrial quaio ( φ ) φ i( φ ) 0 0 ou 7

28 Scod-Ordr Typ- PLL Phalock Acquiiio (Siuoidal ) For hi Scod - Ordr Typ - PLL, h aural frqucy ad dampig facor ar, ζ 4 Subiuig hi io h oliar diffrial quaio yild h followig φ ζ co ( φ ) φ i( φ ) 0 o clod form oluio xi, ad umrical chiqu ar rquird o olv 8

29 Scod-Ordr Typ- PLL Phalock Acquiiio (Siuoidal ) φ ζ co ( φ ) φ i( φ ) 0 Acquiiio wih a pha rror φ ad φ v im Pha Pla Plo : φ v φ 9

30 Scod-Ordr PLL Pha Pla Plo (Siuoidal ) A uabl igulariy i calld a Saddl Poi A rajcory ha rmia o a addl poi i calld a Spararix φ ζ co ( φ ) φ i( φ ) 0 If a rajcory li bw h pararic, i will lock wihou cycl lippig If a rajcory li ouid h pararic, i will cycl lipplig o or mor im bfor lockig (if a all) 30

31 Scod-Ordr PLL Pull-Ou Rag ad Lock Tim (Siuoidal ) Th Pull-Ou Rag i h maximum frqucy p ha ca occur bfor h loop lock wihou cycl lippig.8 If a frqucy p i l ha h pull - ou rag, acq ( ζ ) for ζ bw 0.5 ad.4 pha PO frq 4 4. B ( f ) for pha rror l ha 0% h PLL acquiio im ca b approximad a 3 L Hr, B L i h PLL oi badwidh B L 0 H ( f ) df (Hz) Aumig F ( ), B L ζ 4ζ (Hz) 3

32 Scod-Ordr PLL Lockig Ouid of h Pull-Ou Rag (Siuoidal ) Mulipl cycl lip ar obrvd bfor h loop lock 3

33 x Tim Pha Dcor Circui 33