Understanding Phase Noise From Digital Components in PLL Frequency Synthesizers. Introduction. The Empirical Model

Transcription

1 Applid Radio abs Undstanding Phas ois om Digital Componnts in P quny Synthsizs Pt Whit Dsign il: D006 0 Dmb 000 ntodution h phas nois of a Phas okd oop (P fquny synthsiz an b a ky paamt in a ommuniations systm dsign. Bing abl to modl th phas nois and to pdit it with som auay is a dsiabl ngining goal. h sous of phas nois within a P synthsiz inlud:. VCO phas nois. osillato phas nois 3. hmal nois and di nois fom omponnts in th loop filt 4. ois fom th digital diids and phas dtto ois sous 3 a wll undstood and an usually b modlld with good auay using masud phas nois data fo th VCO and fn, and onntional nois modls fom iuit thoy fo th loop filt. h on aa that is not wll undstood is th nois ontibutions fom th digital dis; th diids and digital phas dtto. h diids and phas dtto a oftn intgatd in on monolithi intgatd iuit, so it is ommon to spak of th nois fom th digital omponnts as th nois fom th P C. A notabl ontibution to undstanding th nois fom th digital omponnts is a nt publiation by Banj [] whih poposs a simpl mpiial modl whih is shown to gi usful auay. his modl has bn sussful implmntd in a omphnsi P synthsiz analysis pogam []. his pap builds on th xplanations gin in [] and dis th lationship btwn th P C phas nois and th ffti timing jitt psnt at th phas fquny dtto output. h Empiial Modl Consid a standad P fquny synthsiz as shown in igu VCO /s out / ( oop ilt Phas Dtto d /M f Osillato igu - Phas okd oop Synthsiz t is known that within th P loop bandwidth th phas nois is typially dominatd by nois addd by th fquny diids and phas dtto. o fqunis wll blow th loop bandwidth th phas nois plot typially flattns out sulting in th in-band phas nois. A typial phas nois sptum at th output of a P synthsiz is shown in igu. Phas ois (db/hz k 0k 00k M quny (Hz igu - ypial P Output Phas ois h in-band phas nois indiatd in igu is appoximatly 8dB/Hz. Banj [] disod that th nois ontibution fom th digital omponnts in th P C an b summaisd into a singl paamt, th Hz omalizd Phas ois loo, whih an b dtmind fom a patiula masumnt of n band phas nois Hz by: log ( 0log ( ( wh is th diision atio in th loop and is th phas ompaison fquny. n any oth appliation, th in-band phas nois fom th P C an b thn dtmind by: + log ( + 0log ( ( Hz 0 0 0

2 Phas ois in P quny Synthsizs his modl was applid to a wid ang of ational P C s in aious appliations giing usfully auat pditions []. By substituting o into ( gis + log ( 0log ( (3 Hz 0 0 o 0 whih dmonstats that fo a gin P C and dsid output fquny, th phas nois may b dasd by 3dB by doubling th phas ompaison fquny. A slightly diffnt aangmnt shows dpndn of phas nois on fo fixd o. Hz 0 0 o log ( 0log ( (4 Explaining th Empiial Modl Sking insight into th poblm, and indd undstanding of th alidity of th mpiial modl (, w look fo physial posss that xplain th lationship. As th quation is fa fom intuiti, w inlud two huisti xplanations bfo dloping a mo igoous physial modl basd on th timing jitt at th phas dtto. h fist xplanation is basd on []. dgad by 3dB, and so th phas nois to inas by 3dB. (Again w a assuming that th nois ontibutions at ah tansition a qual and unolatd. So fo fixd output fquny, w xpt th phas nois to ay aoding to 0log0(. his ditly xplains th lationship as psntd in (4. ow gin that th phas nois ais aoding to 0log0( whn is fixd, as xplaind piously, so doubling auss th 0log0( tm to add 6dB, so th haling that ous in must anl 3dB of this, so th must b a 0log0( tm as wll, lading to (. A Physial Modl Consid a modl of a P C as shown in igu 3. Vaiabl quny (fom VCO /+ Psal quny t t Phas - q Dtto tpd Phas Dtto ois igu 3 - P C Phas ois Modl sou Phas Dtt Output sink Explanation Engins undstand that any nois on th fn fquny is multiplid by a fato to th VCO output. hus th output phas nois must ha th 0log0( tm shown in (. Claly if w doubld in th P, kping all oth paamts onstant, thn th in-band phas nois would inas by 6dB. W nd to xplain how, if w doubl th ompaison fquny whilst kping onstant, th output phas nois inass by 3dB. n this as, imagin that th is a fixd nois ontibution on ah phas dtto unt puls. So doubling th ompaison fquny will sult in twi as many nois pulss to th loop filt, whih lads to 3dB mo nois. (t has to b assumd that th nois pulss a unolatd to mak this onlusion. his lads to th 0log0( tm in (. Explanation f th VCO is osillating at a fquny o thn th P C is iing o tansitions p sond. h fft of using a digital diid to diid by is to stimat th VCO phas (fo phas loking pupos by onsiding only on tansition out of ah. As a signal stimation poblm, if w doubl w thow away half of th infomation w w using and w would xpt th S/ atio of ou phas stimat to t is appant that at th output of th main diid th is timing jitt (dnotd t sonds m fom sal possibl sous: jitt podud at th input stag wh th VCO wafom is quantisd both du to additi nois on th wantd signal and also to nois affting bias and hn th sliing ll jitt addd by th diids At th output of th fn diid th is timing jitt (dnotd t sonds m fom simila sous in th fn signal path. Dpnding on th stat of th phas-fquny dtto, ith th dg fom th main diid stats th unt puls output and th dg fom th fn diid nds it, o i sa. hus th two timing jitts fom th diids aus a umulati jitt in th width of th puls fom th hag pump, th ms aiation of th jitt is gin by Applid Radio abs Pag of 5 diids t t + t (assuming t and t a unolatd. t is likly that with th us of synhonous diids, that t and t a latily unafftd by diision atios, poidd that intations btwn th two diids a minimisd and th diid ahittu mains onstant.

3 Phas ois in P quny Synthsizs h phas-fquny dtto (PD and hag pump will add nois of its own. h digital logi in th PD will add futh timing jitt as will th hag pump. n addition, many hag pump PD iuits nabl both hag pumps bifly to liminat th phas dtto dad spot. his sults in som fdthough of th hag pump unt nois, (popotional to th atiation tim. o analys this nois w popos to tat it as an additional timing jitt. t is likly that this is an auat modl fo th as wh th phas o is small (y shot pulss fom th phas dtto, that is in th lokd stat. hus th total nois fom th PD is inludd as th timing jitt t pd in igu 3. So it is poposd that th nois fom th P C is modlld as timing jitt on th output puls fom th hag pump phas dtto, total ms timing jitt gin by σ t + t + t pd ational- Chips (5 h modl an b xtndd to fational- hips whih ha in-built fational ompnsation with a omposit hag pump output. n this as, if w inlud t f as th timing jitt psnt at th PD output fom th fational ompnsation, thn th total timing jitt is gin by σ pd t + t + t + t f (6 Of ous, th nois analysis of this is only auat if th timing jitt is unolatd fom sampl to sampl, that is th fational ompnsation iuity is sussfully moing th fational spus and laing only whit nois. Analysis of iming Jitt W will now analys th fft on this timing jitt on P nois pfoman. h modl will b applid to th hag pump phas fquny dtto, but it is qually appliabl to oth implmntations of th PD. h idal phas-fquny dtto with unt pump output podus a puls of unt ah phas ompaison yl, (ssntially ah fn dg th duation of th puls is popotional to th phas o. W assum that th kth ompaison yl ous at tim k. hus fo phas o ( k th idal duation τ k of th unt puls is gin by ( k τ k π wh with th phas ompaison fquny. (7 W now inlud a timing jitt, so that at tim k th unt puls has th idal duation plus th timing jitt τ k ( k (8 + tk π wh th timing jitt is psntd by t k, a andom aiabl with zo man and aian σ t k. hus somtims th pulss a too long, somtims too shot, th ms aiation of th puls width is σ. Consid th P shown in igu 4 Osillato θ ( Rf M - + Phas Dtto D Digital ois oop ilt ( VCO θ ( Synthsiz Output s V igu 4 - P Blok Diagam Applid Radio abs Pag 3 of 5

4 Phas ois in P quny Synthsizs W ha mod all nois fom th diids and phas dtto, and inludd th fft of th timing jitt as th Digital ois addd at th output of th phas dtto in igu 4. W dnot th fquny domain psntation of th nois by and th tim domain wafom by (t. ow (t onsists of andom pulss of unt, th lngth of th kth puls is t k. f t k is positi thn th puls has lngth t k and th unt th sam sign as th wantd puls and, if t k is ngati thn th puls has lngth tk and th unt th opposit sign to th wantd puls. hus th wafom of th digital nois (t is as shown in igu 5 (t p 0 - p t k tim igu 5 - Digital ois Wafom Rtuning to igu 4, th output phas of th synthsiz is gin by θ ˆ( θ( M + + D + (9 Within th loop bandwidth, wh jπ f >>, th ontibution to th output phas nois fom th digital nois is gin by θ ˆ( s digital nois D (0 So th in-band phas nois an b dtmind ditly fom th sptum of (t. h sptum of (t is did in Appndix A, giing th sult that th in-band phas nois is 0log0(πσ + 0log0( + 0log0( ( umial Rsults ypial alus fo th Hz nomalizd phas nois publishd in [] and oth aas a in th ang -00dB/Hz to -0dB/Hz. abl shows th osponding alus of timing jitt. Hz db/hz RMS Jitt ps hus, to podu a P C with stat of th at Hz of aound -5dB/Hz quis th ffti ms timing jitt of th phas dtto output pulss to b no mo than.8ps. ational- synthsis hips may b tatd h as simply poiding a non-intgal alu of. h modn hips poid intnal fational spuious ompnsation. With no fational spuious ompnsation, th ms timing jitt at th phas dtto would b both lag (lots of phas modulation and ha olation btwn sampls (giing dist spu. o th modn hips that ontain intnal spuious ompnsation, th nt fft is that in fational mod all that is appant fom outsid th hip is a andom timing jitt at th phas dtto. As long as th a no lag dist spuious omponnts, thn ( should still b appliabl. t is also asy to di fom ths sults th sliing auay quid on th VCO and fn fquny inputs to th P C. Sinusoidal fn wafoms of th typial V p-p bom poblmati at fqunis of th od of 0MHz and blow du to th diffiultis of digital onsion with low piosond jitt. atos influning Hz h modl of th phas nois ontibution by th P hip gin by ( is only of gat us if w a abl to us masumnts of Hz mad in on P to pdit Hz in oth P s. his is th sam as quation ( with Hz 0log0(πσ ( hus, th mpiial quation ( is ntily onsistnt with th bing a fixd amount of timing jitt psnt on th phas dtto output, indpndnt of th diision atio and th phas ompaison fquny. t is known that th phas nois oftn ais with hag pump unt [], typially impoing at high unts. t is diffiult to spulat on th xat dtails of this without knowing th implmntation dtails of spifi hag pumps, how som manufatu s outlin shmatis indiat that th high-unt hag pump is ahid by th paalll opation of multipl hag pumps. n this as it would b xptd that th hag pump nois would dop by 3dB ah tim th numb of hag pumps was doubld (assuming that th nois fom ah was unolatd. his should apply both to th timing jitt nois and also to any unt nois fdthough du to th minimum Applid Radio abs Pag 4 of 5

5 Phas ois in P quny Synthsizs puls width. Any olation btwn th nois fom indiidual pumps would lad to a lss bnfit. As th fundamntal aus of Hz is timing jitt, oth fatos that afft th timing jitt may afft Hz. A signifiant sou of aiability h fo som modn hips may b th opating oltag, as many dis an opat o a onsidabl ang of pow supply oltags. Also, in any appliation, it is ssntial to nsu that th sliing jitt addd at th VCO and fn inputs dos not dominat Hz, dgading th pfoman of th P C. Conlusions t has bn shown that th mpiial lationship publishd lating th phas nois ontibutd by th P diids and phas dtto a onsistnt with a onsistnt andom timing jitt psnt on th pulss at th output of th phas dtto. h lationship btwn th ffti timing jitt and th phas nois has bn did. REERECES:. Banj, Dan P Pfoman, Simulation and Dsign ational Smionduto SimP P dsign and simulation softwa, Appndix A Diation of Equation h nois wafom sulting fom th timing jitt is shown in igu 5. o omput th pow sptal dnsity of this wafom, it is possibl to pod onntionally by omputing th autoolation funtion and thn taking th oui tansfom, how it is asi to pod ditly: h two sidd pow sptal dnsity S(f of a nois poss x(t is dfind as X ( f S( f lim wh j πft X ( f x( t dt so f lim lim / / ( t p k tms j πft t dt jπft..(a wh, th numb of phas dtto pulss in th intgation tim. As w a assuming that th jitt piods a unolatd, thn pσ f lim as t > σ p σ < k h singl-sidd PSD is gin by f, so th ms phas diation in a Hz bandwidth aound f is θ ms d f D jπ f + jπf..(a..(a3 inluding a fato of as f is doubl-sidd. h lationship btwn SSB phas nois sidbands and ms phas diation is θ ms d ( f and so ( f f D jπf + jπf p whih, using D gis an in-band π ( jπ f >> phas nois of o πσ..(a4..(a5 ( + 0 db/hz 0log0(πσ + 0log0( 0log ( whih is quation (. o futh infomation isit Applid Radio abs Pag 5 of 5