High Speed Communication Circuits and Systems Lecture 12 Noise in Voltage Controlled Oscillators

Transcription

1 High Speed Communicaion Circuis and Sysems Lecure Noise in Volage Conrolled Oscillaors Michael H. Perro March, 004 Copyrigh 004 by Michael H. Perro All righs reserved. M.H. Perro

2 VCO Noise in Wireless Sysems From Anenna and Bandpass Filer Z in PC board Mixer race RF in IF ou Z Package o LNA To Filer Inerace Reerence Frequency Frequency Synhesizer VCO LO signal Phase Noise o VCO noise has a negaive impac on sysem perormance - Receiver lower sensiiviy, poorer blocking perormance - Transmier increased specral emissions (oupu specrum mus mee a mask requiremen) Noise is characerized in requency domain M.H. Perro

3 VCO Noise in High Speed Daa Links From Broadband Transmier PC board race Z o Package Inerace Z in Amp In Clock and Daa Recovery Daa Clk Daa Ou Daa In Phase Deecor Loop Filer Clk Ou VCO Jier VCO noise also has a negaive impac on daa links - Receiver increases bi error rae (BER) - Transmier increases jier on daa sream (ransmier mus have jier below a speciied level) Noise is characerized in he ime domain M.H. Perro 3

4 Noise Sources Impacing VCO Time-domain view ou() Jier Frequency-domain view PLL dynamics se VCO carrier requency (assume noiseless or now) Exrinsic noise v n () Inrinsic noise S ou () o Phase Noise v c () v in () ou() Exrinsic noise - Noise rom oher circuis (including PLL) Inrinsic noise - Noise due o he VCO circuiry M.H. Perro 4

5 VCO Model or Noise Analysis Time-domain view ou() Jier PLL dynamics se VCO carrier requency (assume noiseless or now) v c () Noe: K v unis are Hz/V Exrinsic noise v n () v in () Inrinsic noise πk v s Φ vn () Φ ou Frequency-domain view S ou () o cos(π o +Φ ou ()) ou() Phase Noise We will ocus on phase noise (and is associaed jier) - Model as phase signal in oupu sine waveorm M.H. Perro 5

6 Simpliied Relaionship Beween ou and Oupu PLL dynamics se VCO carrier requency (assume noiseless or now) Exrinsic noise v n () Inrinsic noise Φ vn () v c () v in () πk v s Φ ou cos(π o +Φ ou ()) ou() Using a amiliar rigonomeric ideniy Given ha he phase noise is small M.H. Perro 6

7 Calculaion o Oupu Specral Densiy Calculae auocorrelaion Take Fourier ransorm o ge specrum - Noe ha * symbol corresponds o convoluion In general, phase specral densiy can be placed ino one o wo caegories - Phase noise ou () is non-periodic - Spurious noise - ou () is periodic M.H. Perro 7

8 Oupu Specrum wih Phase Noise Suppose inpu noise o VCO (v n ()) is bandlimied, non-periodic noise wih specrum S vn () - In pracice, derive phase specrum as Resuling oupu specrum M.H. Perro S sin () S Φou () * - o o S ou () dbc/hz - o o S Φou () 8

9 Measuremen o Phase Noise in dbc/hz S ou () dbc/hz - o o S Φou () Deiniion o L() - Unis are dbc/hz For his case - Valid when ou () is small in deviaion (i.e., when carrier is no modulaed, as currenly assumed) M.H. Perro 9

10 Single-Sided Version S ou () dbc/hz S Φou () Deiniion o L() remains he same o - Unis are dbc/hz For his case - So, we can work wih eiher one-sided or wo-sided specral densiies since L() is se by raio o noise densiy o carrier power M.H. Perro 0

11 Oupu Specrum wih Spurious Noise Suppose inpu noise o VCO is Resuling oupu specrum S sin () * S Φou () - o o - spur spur d spur spur S ou () dbc - o o d spur spur M.H. Perro spur

12 Measuremen o Spurious Noise in dbc S ou () dbc d spur spur - o o Deiniion o dbc spur - We are assuming double sided specra, so inegrae over posiive and negaive requencies o ge power Eiher single or double-sided specra can be used in pracice For his case M.H. Perro

13 Calculaion o Inrinsic Phase Noise in Oscillaors Z acive Z res Acive Negaive Resisance Generaor V ou Resonaor Acive Negaive Resisance Z acive Z res Resonaor i nrn -G m = -R p V ou R p i nrp C p L p M.H. Perro Noise sources in oscillaors are pu in wo caegories - Noise due o ank loss - Noise due o acive negaive resisance We wan o deermine how hese noise sources inluence he phase noise o he oscillaor 3

14 Equivalen Model or Noise Calculaions Acive Negaive Resisance Z acive Z res Resonaor i nrn -G m = -R p V ou R p i nrp C p L p Noise Due o Acive Negaive Resisance Compensaed Resonaor wih Noise rom Tank i nrn V ou -G m = -R p R p i nrp C p L p Noise Due o Acive Negaive Resisance Noise rom Tank Z ank Ideal Tank i nrn i nrp V ou C p L p M.H. Perro 4

15 Calculae Impedance Across Ideal LC Tank Circui Z ank C p L p Calculae inpu impedance abou resonance = 0 negligible M.H. Perro 5

16 A Convenien Parameerizaion o LC Tank Impedance Z ank C p L p Acual ank has loss ha is modeled wih R p - Deine Q according o acual ank Parameerize ideal ank impedance in erms o Q o acual ank M.H. Perro 6

17 Overall Noise Oupu Specral Densiy Noise Due o Acive Negaive Resisance Noise rom Tank Z ank Ideal Tank i nrn i nrp V ou C p L p Assume noise rom acive negaive resisance elemen and ank are uncorrelaed - Noe ha he above expression represens oal noise ha impacs boh ampliude and phase o oscillaor oupu M.H. Perro 7

18 Parameerize Noise Oupu Specral Densiy Noise Due o Acive Negaive Resisance Noise rom Tank Z ank Ideal Tank i nrn i nrp V ou C p L p From previous slide F( ) is deined as F( ) M.H. Perro 8

19 Fill in Expressions Noise Due o Acive Negaive Resisance Noise rom Tank Z ank Ideal Tank i nrn i nrp V ou C p L p Noise rom ank is due o resisor R p Z ank ( ) ound previously Oupu noise specral densiy expression (single-sided) M.H. Perro 9

20 Separaion ino Ampliude and Phase Noise Noise Due o Acive Negaive Resisance Noise rom Tank Z ank Ideal Tank i nrn i nrp V ou C p L p Ampliude Noise V sig A v ou V ou A Phase Noise Equipariion heorem (see Tom Lee, p 534) saes ha noise impac splis evenly beween ampliude and phase or V sig being a sine wave - Ampliude variaions suppressed by eedback in oscillaor M.H. Perro 0

21 Oupu Phase Noise Specrum (Leeson s Formula) Oupu Specrum Noise Due o Acive Negaive Resisance Noise rom Tank Z ank Ideal Tank S Vsig () Carrier impulse area normalized o a value o one i nrn i nrp V ou C p L p L(Δ) o Δ All power calculaions are reerenced o he ank loss resisance, R p M.H. Perro

22 Example: Acive Noise Same as Tank Noise Acive Negaive Resisance Resonaor i nrn -G m = -R p V ou R p i nrp C p L p Noise acor or oscillaor in his case is L(Δ) Resuling phase noise -0 db/decade log(δ) M.H. Perro

23 The Acual Siuaion is Much More Complicaed i nrp R p C p L p L p C p R p i nrp Tank generaed noise A V ou V ou A Tank generaed noise i nm M M i nm V s Transisor generaed noise V bias I bias M 3 i nm3 Transisor generaed noise Impac o ank generaed noise easy o assess Impac o ransisor generaed noise is complicaed - Noise rom M and M is modulaed on and o - Noise rom M 3 is modulaed beore inluencing V ou - Transisors have / noise Also, ransisors can degrade Q o ank M.H. Perro 3

24 ( Phase Noise o A Pracical Oscillaor L(Δ) -30 db/decade -0 db/decade Δ / 3 o Q 0log( M.H. Perro Phase noise drops a -0 db/decade over a wide requency range, bu deviaes rom his a: - Low requencies slope increases (oen -30 db/decade) - High requencies slope laens ou (oscillaor ank does no iler all noise sources) Frequency breakpoins and magniude scaling are no FkT P sig log(δ) readily prediced by he analysis approach aken so ar 4

25 ( Phase Noise o A Pracical Oscillaor L(Δ) -30 db/decade -0 db/decade Δ / 3 o Q 0log( FkT P sig log(δ) Leeson proposed an ad hoc modiicaion o he phase noise expression o capure he above noise proile - Noe: he assumed ha F( ) was consan over requency M.H. Perro 5

26 A More Sophisicaed Analysis Mehod Ideal Tank Ampliude Noise i in V ou C p L p V ou A Phase Noise Our concern is wha happens when noise curren produces a volage across he ank - Such volage deviaions give rise o boh ampliude and phase noise - Ampliude noise is suppressed hrough eedback (or by ampliude limiing in ollowing buer sages) M.H. Perro Our main concern is phase noise We argued ha impac o noise divides equally beween ampliude and phase or sine wave oupus - Wha happens when we have a non-sine wave oupu? 6

27 Modeling o Phase and Ampliude Perurbaions Ideal Tank Ampliude Noise i in V ou C p L p V ou A i in () τ o i in () Phase h Φ (,τ) Φ ou () Φ ou () Phase Noise τ o i in () τ o i in () Ampliude h A (,τ) A() A() τ o Characerize impac o curren noise on ampliude and phase hrough heir associaed impulse responses - Phase deviaions are accumulaed - Ampliude deviaions are suppressed M.H. Perro 7

28 Impac o Noise Curren is Time-Varying Ideal Tank Ampliude Noise i in V ou C p L p V ou A i in () τ o τ i in () Phase h Φ (,τ) Φ ou () Φ ou () Phase Noise τ o τ i in () τ o τ i in () Ampliude h A (,τ) A() A() τ o τ I we vary he ime a which he curren impulse is injeced, is impac on phase and ampliude changes - Need a ime-varying model M.H. Perro 8

29 Illusraion o Time-Varying Impac o Noise on Phase T i in () q max 0 V ou () ΔΦ i in () i in () q max q max V ou () V ou () ΔΦ ΔΦ=0 i in () q max 3 V ou () ΔΦ i in () q max 4 V ou () ΔΦ High impac on phase when impulse occurs close o he zero crossing o he VCO oupu Low impac on phase when impulse occurs a peak o oupu M.H. Perro 9

30 Deine Impulse Sensiiviy Funcion (ISF) ( o ) T i in () q max 0 V ou () ΔΦ i in () i in () q max q max V ou () V ou () ΔΦ ΔΦ=0 Γ(π o ) T i in () q max 3 V ou () ΔΦ i in () q max 4 V ou () ΔΦ ISF consruced by calculaing phase deviaions as impulse posiion is varied M.H. Perro - Observe ha i is periodic wih same period as VCO oupu 30

31 Parameerize Phase Impulse Response in Terms o ISF T i in () q max 0 V ou () ΔΦ i in () i in () q max q max V ou () V ou () ΔΦ ΔΦ=0 Γ(π o ) T i in () q max 3 V ou () ΔΦ i in () q max 4 V ou () ΔΦ i in () Φ ou () h Φ (,τ) τ o M.H. Perro τ o 3

32 Examples o ISF or Dieren VCO Oupu Waveorms V ou () Example Example V ou () Γ(π o ) Γ(π o ) ISF (i.e., ) is approximaely proporional o derivaive o VCO oupu waveorm - Is magniude indicaes where VCO waveorm is mos sensiive o noise curren ino ank wih respec o creaing phase noise ISF is periodic In pracice, derive i rom simulaion o he VCO M.H. Perro 3

33 Phase Noise Analysis Using LTV Framework i n () h Φ (,τ) Φ ou () Compuaion o phase deviaion or an arbirary noise curren inpu Analysis simpliied i we describe ISF in erms o is Fourier series (noe: c o here is dieren han book) M.H. Perro 33

34 Block Diagram o LTV Phase Noise Expression Inpu Curren Normalizaion i n () q max cos(π o + θ ) ISF Fourier Series Coeiciens c o Inegraor Φ ou () jπ Phase o Oupu Volage cos(π o +Φ ou ()) ou() c cos((π o ) + θ ) c cos(nπ o + θ n ) c n Noise rom curren source is mixed down rom dieren requency bands and scaled according o ISF coeiciens M.H. Perro 34

35 Phase Noise Calculaion or Whie Noise Inpu (Par ) i n () q max M.H. Perro Noe ha is he single-sided noise specral densiy o i n () i n Δ cos(π o + θ ) cos((π o ) + θ ) cos(3(π) o + θ n ) i n Δ -3 o S X () X A B C D ( q max -3 o - o ( 0 - o o - o - o 0 o o 3 o o 3 o ( qmax ( qmax ( - o i n Δ ( i n Δ - o ( qmax ( qmax ( i n Δ - o ( i n Δ - o S A () 0 o S B () 0 o S C () 0 o S D () 0 o 35

36 Phase Noise Calculaion or Whie Noise Inpu (Par ) ISF Fourier S A () Series Coeiciens Inegraor i ( n A c qmax Φ ou () o Δ jπ ( qmax ( - o ( i n Δ - o ( qmax ( qmax ( i n Δ - o ( i n Δ - o 0 o S B () 0 o S C () 0 o S D () 0 o B C D c c c 3 Phase o Oupu Volage cos(π o +Φ ou ()) ou() M.H. Perro 36

37 Specral Densiy o Phase Signal From he previous slide Subsiue in or S A (), S B (), ec. Resuling expression M.H. Perro 37

38 Oupu Phase Noise S Φou () S ou () dbc/hz 0 - o 0 o S Φou () We now know Δ Resuling phase noise M.H. Perro 38

39 The Impac o / Noise in Inpu Curren (Par ) i n () q max M.H. Perro Noe ha is he single-sided noise specral densiy o i n () i n Δ cos(π o + θ ) cos((π o ) + θ ) cos(3(π) o + θ n ) i n Δ -3 o S X () X A B C D ( q max -3 o - o ( 0 - o o - o - o 0 o o 3 o o 3 o / noise ( qmax ( qmax ( - o i n Δ ( i n Δ - o ( qmax ( qmax ( i n Δ - o ( i n Δ - o S A () 0 o S B () 0 o S C () 0 o S D () 0 o 39

40 The Impac o / Noise in Inpu Curren (Par ) ( qmax ( qmax ( - o i n Δ - o ( qmax ( qmax ( ( i n Δ - o ( i n Δ i n Δ - o S A () 0 o S B () 0 o S C () 0 o S D () 0 o ISF Fourier Series Coeiciens A B C D c o c c c 3 Inegraor Φ ou () jπ Phase o Oupu Volage cos(π o +Φ ou ()) ou() M.H. Perro 40

41 Calculaion o Oupu Phase Noise in / 3 region From he previous slide Assume ha inpu curren has / noise wih corner requency / Corresponding oupu phase noise M.H. Perro 4

42 ( Calculaion o / 3 Corner Frequency L(Δ) (A) -30 db/decade -0 db/decade Δ / 3 (B) o Q 0log( FkT P sig log(δ) (A) (B) (A) = (B) a: M.H. Perro 4

43 Impac o Oscillaor Waveorm on / 3 Phase Noise ISF or Symmeric Waveorm V ou () ISF or Asymmeric Waveorm V ou () Γ(π o ) Γ(π o ) Key Fourier series coeicien o ISF or / 3 noise is c o - I DC value o ISF is zero, c o is also zero For symmeric oscillaor oupu waveorm - DC value o ISF is zero no upconversion o licker noise! (i.e. oupu phase noise does no have / 3 region) For asymmeric oscillaor oupu waveorm - DC value o ISF is nonzero licker noise has impac M.H. Perro 43

44 Issue We Have Ignored Modulaion o Curren Noise i nrp R p C p L p L p C p R p i nrp Tank generaed noise A V ou V ou A Tank generaed noise i nm M M i nm V s Transisor generaed noise V bias I bias M 3 i nm3 Transisor generaed noise In pracice, ransisor generaed noise is modulaed by he varying bias condiions o is associaed ransisor - As ransisor goes rom sauraion o riode o cuo, is associaed noise changes dramaically Can we include his issue in he LTV ramework? M.H. Perro 44

45 Inclusion o Curren Noise Modulaion i in () i n () h Φ (,τ) Φ ou () α(π o ) T = / o Recall α(π o ) 0 By inspecion o igure We hereore apply previous ramework wih ISF as M.H. Perro 45

46 Placemen o Curren Modulaion or Bes Phase Noise Bes Placemen o Curren Modulaion or Phase Noise Wors Placemen o Curren Modulaion or Phase Noise T = / o T = / o α(π o ) α(π o ) 0 0 Γ(π o ) Γ(π o ) Phase noise expression (ignoring / noise) Minimum phase noise achieved by minimizing sum o square o Fourier series coeiciens (i.e. rms value o e ) M.H. Perro 46

47 Colpis Oscillaor Provides Opimal Placemen o T = / o L I () V ou () V ou () V bias α(π o ) I () M C 0 I bias C Γ(π o ) Curren is injeced ino ank a boom porion o VCO swing - Curren noise accompanying curren has minimal impac on VCO oupu phase M.H. Perro 47

48 Summary o LTV Phase Noise Analysis Mehod Sep : calculae he impulse sensiiviy uncion o each oscillaor noise source using a simulaor Sep : calculae he noise curren modulaion waveorm or each oscillaor noise source using a simulaor Sep 3: combine above resuls o obain e ( o ) or each oscillaor noise source Sep 4: calculae Fourier series coeiciens or each e ( o ) Sep 5: calculae specral densiy o each oscillaor noise source (beore modulaion) Sep 6: calculae overall oupu phase noise using he resuls rom Sep 4 and 5 and he phase noise expressions derived in his lecure (or he book) M.H. Perro 48

49 Alernae Approach or Negaive Resisance Oscillaor R p C p L p L p C p R p A V ou V ou A M M V s I bias V bias M 3 Recall Leeson s ormula M.H. Perro - Key quesion: how do you deermine F( )? 49

50 F( ) Has Been Deermined or This Topology R p C p L p L p C p R p A V ou V ou A M M V s I bias V bias M 3 Rael e. al. have come up wih a closed orm expression or F( ) or he above opology In he region where phase noise alls a -0 db/dec: M.H. Perro 50

51 Reerences o Rael Work Phase noise analysis - J.J. Rael and A.A. Abidi, Physical Processes o Phase Noise in Dierenial LC Oscillaors, Cusom Inegraed Circuis Conerence, 000, pp Implemenaion - Emad Hegazi e. al., A Filering Technique o Lower LC Oscillaor Phase Noise, JSSC, Dec 00, pp M.H. Perro 5

52 Designing or Minimum Phase Noise R p C p L p A V ou V ou (A) (B) (C) M M I bias V s (A) Noise rom ank resisance (B) Noise rom M and M V bias M 3 (C) Noise rom M 3 M.H. Perro To achieve minimum phase noise, we d like o minimize F( ) The above ormulaion provides insigh o how o do his - Key observaion: (C) is oen quie signiican 5

53 Eliminaion o Componen (C) in F( ) A R p C p V ou L p M M I bias V s V ou V bias M 3 i nm3 C Capacior C shuns noise rom M 3 away rom ank - Componen (C) is eliminaed! Issue impedance a node V s is very low - Causes M and M o presen a low impedance o ank during porions o he VCO cycle Q o ank is degraded M.H. Perro 53

54 Use Inducor o Increase Impedance a Node V s A R p C p V ou L p M M T = / o V bias I bias L V s M 3 V ou High impedance a requency o i nm3 C Volage a node V s is a reciied version o oscillaor oupu - Fundamenal componen is a wice he oscillaion requency Place inducor beween V s and curren source - Choose value o resonae wih C and parasiic source capaciance a requency o Impedance o ank no degraded by M and M - Q preserved! M.H. Perro 54

55 Designing or Minimum Phase Noise Nex Par R p C p L p (A) (B) (C) A V ou M M V ou (A) Noise rom ank resisance T = / o L V s High impedance a requency o (B) Noise rom M and M (C) Noise rom M 3 I bias V bias M 3 i nm3 C M.H. Perro Le s now ocus on componen (B) - Depends on bias curren and oscillaion ampliude 55

56 Minimizaion o Componen (B) in F( ) R p C p L p (B) A V ou V ou Recall rom Lecure M M V s I bias So, i would seem ha I bias has no eec! - No rue wan o maximize A (i.e. P sig ) o ge bes phase noise, as seen by: M.H. Perro 56

57 Curren-Limied Versus Volage-Limied Regimes R p C p L p (B) A V ou V ou M M V s I bias Oscillaion ampliude, A, canno be increased above supply imposed limis I I bias is increased above he poin ha A sauraes, hen (B) increases Curren-limied regime: ampliude given by Volage-limied regime: ampliude sauraed Bes phase noise achieved a boundary beween hese regimes! M.H. Perro 57

58 Final Commens Hajimiri mehod useul as a numerical procedure o deermine phase noise - Provides insighs ino / noise upconversion and impac o noise curren modulaion Rael mehod useul or CMOS negaive-resisance opology - Closed orm soluion o phase noise! - Provides a grea deal o design insigh Anoher numerical mehod - Specre RF rom Cadence now does a reasonable job o esimaing phase noise or many oscillaors Useul or veriying design ideas and calculaions M.H. Perro 58