ECEN620: Network Theory Broadband Circuit Design Fall 2012

Transcription

1 ECEN60: Netwrk Thery Bradband Circuit Design Fall 01 Lecture 16: VCO Phase Nise Sam Palerm Analg & Mixed-Signal Center Texas A&M University

2 Agenda Phase Nise Definitin and Impact Ideal Oscillatr Phase Nise Leesn Mdel Hajimiri Mdel

3 Phase Nise Definitin An ideal scillatr has an impulse shape in the frequency dmain A real scillatr has phase nise skirts centered at the carrier frequency Phase nise is quantified as the nrmalized nise pwer in a 1Hz bandwidth at a frequency ffset frm the carrier L ( ) = 10lg P sideband ( +,1Hz) P carrier ( dbc/hz) 3

4 Phase Nise Impact in RF Cmmunicatin RX Reciprcal Mixing Strng Nisy TX Interfering with RX At the RX, a large interferer can degrade the SNR f the wanted signal due t reciprcal mixing caused by the LO phase nise Having large phase nise at the TX can degrade the perfrmance f a nearby RX 4

5 Jitter Impact in HS Links RX sample clck jitter reduces the timing margin f the system fr a given bit-errr-rate TX jitter als reduces timing margin, and can be amplified by lw-pass channels 5

6 Ideal Oscillatr Phase Nise The tank resistance will intrduce thermal nise in f = 4kT R The spectral density f the mean - squared nise vltageis v f n = in f Z tank 6

7 Tank Impedance Near Resnance 7 ( ) ( ) ( ) ( ) ( ) tank tank tank tank 1 Tank 1 1 Cnsider frequencies clse t resnance 1 Resnance Frequency: 1 1 = = = = + = + = = = = Q R Z Q R j Z Q R C C R Q C j LC L j LC LC LC L j Z LC LC L j L j C j Z

8 Ideal Oscillatr Phase Nise v f n in = f Z tank = 4kT R R Q = 4kTR Q The Equipartitin Therem[Lee JSSC 000]states that, in equilibrium, amplitude and phase - nise pwer are equal. Therefre, this nise pwer is split 1 evenly between amplitude and phase. L kt Psig Q { } = 10lg ( dbc/hz) Phase nise due t thermal nise will display a - 0dB/dec slpe away frm the carrier 8

9 Other Phase Nise Surces [Perrtt] Tank thermal nise is nly ne piece f the phase nise puzzle Oscillatr transistrs intrduce their wn thermal nise and als flicker (1/f) nise 9

10 Leesn Phase Nise Mdel L FkT P sig Q 3 1 f { } = 10lg ( dbc/hz) Leesn s mdel mdifies the previusly derived expressin t accunt fr the high frequency nise flr and 1/f nise upcnversin A empirical fitting parameter F is intrduced t accunt fr increased thermal nise Mdel predicts that the (1/ ) 3 regin bundary is equal t the 1/f crner f device nise and the scillatr nise flattens at half the resnatr bandwidth 10

11 A 3.5GHz LC tank VCO Phase Nise Measure Phase nise -30dB/decade -0dB/decade -105dBc 11 ELEN60-IC Design f Bradband Cmmunicatin circuit

12 VCO Output Spectrum Example -0dBm RBW=10K PN=-85dBm-(-0dBm)- 10lg 10 (10e3) =-105dBc dbc---in db with respect t carrier -85dBm 1 ELEN60-IC Design f Bradband Cmmunicatin circuit

13 Leesn Mdel Issues The empirical fitting parameter F is nt knwn in advance and can vary with different prcess technlgies and scillatr tplgies The actual transitin frequencies predicted by the Leesn mdel des nt always match measured data 13

14 Harjimiri s Mdel (T. H. Lee) Injectin at Peak (amplitude nise nly) Injectin at Zer Crssing (maximum phase nise) YCLO AMSC-TAMU 14

15 A time-varying Phase Nise mdel: Hajimiri-Lee mdel Impulse applied t the tank t measure its sensitivity functin i n f The impulse respnse fr the phase variatin can be represented as Γ is the impulse sensitivity functin ISF qmax, the maximum charge displacement acrss the capacitr, is a nrmalizing factr 15 ELEN60-IC Design f Bradband Cmmunicatin circuit

16 ISF Mdel The phase variatin due t injecting nise can be mdeled as: The functin, Γ(x), is the time-varying prprtinality factr and called the impulse sensitivity functin. The phase shift is assumed linear t injectin charge. ISF has the same scillatin perid T f the scillatr itself. The unity phase impulse respnse can be written as: YCLO AMSC-TAMU 16

17 Hw t btain the Impulse sensitivity functin fr a LC scillatr Γ(τ) can be btained using Cadence Cnsider the effect n phase nise f each nise surce 17 ELEN60-IC Design f Bradband Cmmunicatin circuit

18 Typical ISF Example The ISF can be estimated analytically r calculated frm simulatin. The ISF reaches peak during zer crssing and zer at peak. YCLO AMSC-TAMU 18

19 Phase Nise Cmputatin The impulse sensitivity functin is used t btain the phase nise impulse functin h φ ( t, τ ) = ( τ ) u ( t τ ) Γ q max The phase nise can then be cmputed by the superpsitin (cnvlutin) integral f the any arbitrary nise current with the phase nise impulse functin φ ( t) = h ( t, τ ) i( τ ) dτ = Γ( τ ) i( τ ) dτ φ 1 q max t 19

20 ISF Decmpsitin w/ Furier Series In rder t gain further insight, and because the ISF is peridic, it may be expressed as a Γ c 0 ( τ ) = + c cs( n τ + θ ) n= 1 n n Furier series where the cefficients c n are real andθ is the phase f n the nth ISF harmnic. cefficients are deteremined. φ The phase nise can then be cmputed by 1 q c 0 ( t) = i( τ ) dτ + c i( τ ) cs( n τ ) max t n n= 1 This allws the excess phase frm an arbitrary nise surce t be cmputed nce the ISF Furier Essentially, the current nise is and scaled accrding t the ISF cefficients. t dτ mixed dwn frm different frequency bands 0

21 Phase Nise Frequency Cnversin First cnsider a simple case where we have a sinusidal nise current whse frequency is integer multiple m f the scillatin frequency i ( t) = I cs[ ( m + ) t] When perfrming the phase nise cmputatin integral, there will be a negligible cntributin frm all terms ther than n = m ( t) I ( t) The resulting frequency spectrum will shw tw equal sidebands at v φ P ut SBC m m ( t) = cs[ t + φ( t) ], ( ) cm sin q max I 10lg 4q m max 1 Nte that this pwer is prprtinal t there will be tw equally weighted sidebands symmetricabut the carrier with pwer c m. near an ±. Assuming a sinusidal wavefrm 1

22 Phase Nise Due t White & 1/f Surces Extending the previus analysis t the general case f a white nise surce results in P SBC ( ) i n f 10lg 4q m= 0 max m Here nise cmpnents near integer multiples f the carrier frequency all fld near the carrier 1 itself and are weighted by c. Nise near dc gets upcnverted, weighted by cefficient c, s1 0 f nise becmes1 f 3 nise near the carrier. Nise near the carrier stays there. White nise near higher integer multiples f the carrier gets dwncnverted and weighted by 1 f.

23 Hw t Minimize Phase Nise? In rder t minimize phase nise, the ISF cefficients c n shuld be minimized. Using Parseval's therem m= 0 c m π 1 = Γ π 0 ( x) dx = Γ rms The spectrum in the1 f regin can be expressed as Thus, reducing Γ rms L ( ) i n Γrms 10lg f = qmax will reduce the phase nise at all frequencies. 3

24 1/f Crner Frequency Cnsider current nise which includes1 f cntent i n,1 f 1 f = in where 1 f is the1 f crner frequency Frm the previusslide L ( ) i n c0 10lg f = 8qmax 1 f Thus, the1 f 3 crner frequency is 1 3 f = 1 f c 4Γ 0 rms = 1 f Γ Γ dc rms This is generally lwer than the1 f device/circuit nisecrner. If Γ dc is minimized thrugh rise - and fall - time symmetry,then there is the ptential fr dramatic reductins in 1 f nise. 4

25 Cyclstatinary Nise Treatment Transistr drain current, and thus nise, can change dramatically ver an scillatr cycle. The LTV mdel can easily handle this by treating it as the prduct f statinary white nise Here i n0 nise surce, and α ( x) and a peridic functin. i n Γ ( t) = i ( t) α( t) is a statinary white nise surce whse peak valueis equal t that f eff n0 frmulate an effective ISF ( x) = Γ( x) α( x) 0 the cyclstatinary is a peridic unitless functin with a peak valuef unity. Using this, we can 5

26 Key Oscillatr Design Pints As the LTI mdel predicts, scillatr signal pwer and Q shuld be maximized Ideally, the energy returned t the tank shuld be delivered all at nce when the ISF is minimum Oscillatrs with symmetry prperties that have small Γ dc will prvide minimum 1/f nise upcnversin 6

27 Phasr-Based Phase Nise Analysis Mdels nise at sideband frequencies with mdulatin terms The α 1 and α terms sum c-linear with the carrier phasr and prduce amplitude mdulatin (AM) The φ 1 and φ terms sum rthgnal with the carrier phasr and prduce phase mdulatin (PM) 7

28 Phasr-Based LC Oscillatr Analysis This phasr-based apprach can be used t find clsedfrm expressins fr LC scillatr phase nise that prvide design insight In particular, an accurate expressin fr the Leesn mdel F parameter is btained L FkT Psig Q { } = 10lg ( dbc/hz) 8

29 LC Oscillatr F Parameter L FkT Psig Q { } = 10lg ( dbc/hz) 1st Term = Tank Resistance Nise nd Term = Crss-Cupled Pair Nise 3rd Term = Tail Current Surce Nise The abve expressin gives us insight n hw t ptimize the scillatr t reduce phase nise The tail current surce is ften a significant cntributr t ttal nise 9

30 Tail Current Nise The switching differential pair can be mdeled as a mixer fr nise in the current surce Only the nise lcated at even harmnics will prduce phase nise. YCLO AMSC-TAMU 30

31 Lading in Current-Biased Oscillatr The current surce plays rles It sets the scillatr bias current Prvides a high impedance in series with the switching transistrs t prevent resnatr lading YCLO AMSC-TAMU 31

32 Nise Filtering in Oscillatr Only thermal nise in the current surce transistr arund nd harmnic f the scillatin causes phase nise. In balanced circuits, dd harmnics circulate in a differential path, while even harmnics flw in a cmmn-mde path A high impedance at the tail is nly required at the nd harmnic t stp the differential pair FETs in tride frm lading the resnatr. YCLO AMSC-TAMU 3

33 Nise Filtering in Oscillatr Tail-biased VCO with nise filtering. YCLO AMSC-TAMU 33

34 Phase Nise w/ Tail Current Filtering Tail current nise filtering prvides near 7dB imprvement 34

35 Nise Filtering in Oscillatr A tp-biased VCO ften prvides imprved substrate nise rejectin and reduced flicker nise YCLO AMSC-TAMU 35

36 Next Time Divider Circuits 36

37 In general the impulse sensitivity functin is peridic with a fundamental frequency equal t the scillating frequency The input sensitivity functin can be characterized as a Furier Series: An the phase nise is then Therefre: 37 ELEN60-IC Design f Bradband Cmmunicatin circuit

38 If the input nise is represented as Due t the peridicity f the terms, the series cnverge t (n=m term nly): Phase nise Nise Γ (m-1) 0 m 0 m 0 38 ELEN60-IC Design f Bradband Cmmunicatin circuit

39 If the input nise is represented by its pwer distributin functin Fr small nise level V V V ut ut ut = V V V cs cs cs ( t + φ( t) ) ( t) V0 sin( t) sin( φ( t) ) ( t) V ( sin( t) ) φ( t) 0 39 ELEN60-IC Design f Bradband Cmmunicatin circuit