Spectral Analysis of Noise in Switching LC-Oscillators

Transcription

1 Spectral Analysis of Noise in Switching LC-Oscillators 71

2 Sub-Outline Duty Cycle of g m -cell Small-Signal Gain Oscillation Condition LC-Tank Noise g m -cell Noise Tail-Current Source Noise (Phase) Noise Factor Bipolar VCO (Phase) Noise Factor CMOS VCO Bipolar vs. CMOS VCO 7

3 Is it Indeed so Simple? i GTK C V L C V LC-tank noise i C1 v B1 v B Q 1 Q i B1 i B i C transconductor noise Q CS i TCS tail-current source noise noise from the transistors Q 1 and Q is switched ON and OFF noise from current source Q CS is modulated by oscillator switching 73

4 g m -cell Transfer Function small-signal gain in the presence of a large signal I OUT di OUT dv IN VIN -g d/f 0 1/f 0 g i 1/f 0 T 0 T 0 T 0 /4 / 4 ( ) ji0t g t e dt sin( i d ) 1 gi gd d id k Fourier domain (magnitude) complex harmonic components g -4 g - g 0 g g 4-4f 0-3f 0 -f 0 -f 0 f 0 f 0 3f 0 4f 0 74

5 LC-Tank Noise Contribution phase-modulating noise component: 1 ipm in, O ( f0 ) in, O ( f0 ) in, O ( f0 ) in, O ( f0) i ( g g ) v ( f ) ( g g ) v ( f ) PM 0 N 0 0 N 0 phase-related noise power (k>>1, g=g 0 =g ± ): TK 0 i ( R ) ( g g ) v ( R ) PM LC-tank noise transfer function: ( TK ) ( g0 g ) GTK g R LC-tank noise factor: N TK PM TK g0 g v R N TK GTKv R N TK i ( R ) ( ) ( ) ( ) 4KTGTK F( RTK ) 1 4KTG 4KTG 4KTG 4KTG TK TK TK TK 79

6 Collector-Current Current Noise Transfer Function in Limiting Region i C1 V CC CV L CV R TK / R TK / i C1 Q 1 i C1 Q 1 I TAIL i C1 80

7 Collector-Current Current Noise Transfer Function in Limiting Region i C1 i C1 i C1 i C1 R TK / R TK / R TK / R TK / Q 1 Q 1 i C1 I TAIL i ( I ) 0 PM C 81

8 Base-Resistance Noise Transfer Function in Limiting Region V CC R TK / R TK / R TK / R TK / CV L CV Q 1 v B1 g m v B1 Q 1 v B1 g m v B1 Q 1 gm I TAIL I TAIL I TAIL i ( r ) 0 PM B g m -cell input-noise linear and limiting transfer function: g( vn, g m IN ) : 0 -g 1 / f 0 N ( min ) ( N ( B ) N ( C ) / m) 4 B / m v g v r i I g KTr KT g 8

9 g m -Cell Noise Contributions phase-related noise power: 1 gi m IN i i m IN m IN m IN i ( g ) ( g g ) v ( g ) v ( g ) dg v ( g ) PM N N N d d g m -cell noise transfer function: gm 1 g ( g ) dg d( ) ( kg ) kg k g m -cell noise factors: m IN TK TK PM B kgtk KTrB i ( r ) 4 F( rb ) krg B TK kc 4KTG 4KTG TK TK PM C kgtk KT gm i ( I ) / 1 F( IC ) kgtk / gm 4KTG 4KTG TK input g m -cell noise around odd multiples of the oscillation frequency is folded to the LC-tank noise around the oscillation frequency TK 87

10 Tail-Current Noise Transfer Function g m -cell large-signal V-to-I transfer function I OUT 1 I OUT VIN -1 1 /f 0 1/f 0 c i1 sin((i1) / ) (i1) / Fourier domain (magnitude) complex harmonic components c -1 c -3 c 3 c 1-4f 0-3f 0 -f 0 -f 0 f 0 f 0 3f 0 4f 0 9

11 phase-related noise power: ipm, DIFF ( ITCS ) 1 ipm ( ITCS ) in ( ITCS ) 4 4 TCS-noise transfer function: 1 g ( ITCS ) 4 TCS-noise factor: TCS-Noise Contribution i ( I ) (1 ) (1 ) PM TCS KTgm rbgm KT kgtk kc F( ITCS ) 4KTG 4KTG 4KTG TK TK TK 1 1 k(1 kc) k( kc) kf(ic IB ) F( rb ) TCS noise around even multiples of the oscillation frequency is folded to the LC-tank noise around the oscillation frequency 98

12 Switching-Oscillator Phase Noise Noise factor: F F( R ) F( I ) F( I ) F( r ) F( I ) TK C B B TCS F 1 kck( kc) 1 (1 k)( kc) Phase noise: L L L L L L ( R ) ( I ) ( I ) ( r ) ( I ) 4KTG F TK C B B TCS TK (4 CTOT) v (4 CTOT) S L 1 4KTG 1 (1 )( ) TK k kc (4 C ) TOT ( ) 8VT k 99

13 Phase Noise Model of Bipolar Switching LC-Oscillators F kck( kc) Constant phase-noise contributions LC-tank noise contribution ~ 1 g m -cell current shot noise contribution ~ ½ Loop-gain related contributions g m -cell base-resistance noise contribution ~ ck phase-noise contribution of the bias current source is k-times larger then the noise contribution of the g m -cell ~ k(½+ck)! 100

14 Low/High-Performance VCO Designs high loop-gain, high quality LC-tank, BCS noise eliminated: e.g., k>>1(=10), c<<1(~0.01) 1 1 kc L ~ ~ k k high loop-gain, high quality LC-tank: e.g., k>>1(=10), c<<1(~0.01) 1 1 k( kc) kc L ~ ~ k k 5 10 k low loop-gain, low quality LC-tank: e.g., k~1(=), c~1(~0.5) 3 1 (1 k) 11 L ~ ~ 1 k 8 101

15 Single/Double-Switch Switch CMOS LC-VCOs i ( G ) KTG N TK i GTK TK i D3 V DD i ( I ) KT g N D, P P mp, Q 3 Q 4 i D4 L/ L/ C C i GTK R TK / R TK / L/ L/ C C R TK / R TK / i D1 Q 1 Q i D i ( I ) KTg N D Q CS m i BCS i D1 Q 1 Q i ( I ) KT g N D, N N m, N i D d 1 k i ( I ) N BCS KTg mcs, Q CS i BCS d 1 4k 10

16 Phase Noise Model of CMOS LC-Oscillators Noise factor ( N = P, g m,n =g m,p, g m,n,cs =g m,n ): F F( R ) F( I ) F( I ) SS TK D BCS F 1 k 1 (1 k) SS F F( R ) F(4 I ) F( I ) DS TK D BCS F 1 k 1 (1 k) DS Phase noise: L L L L ( R ) ( I ) ( I ) 4KTG F TK D BCS TK (4 CTOT) v (4 CTOT) S L SS 4KTGTK 1 (1 k) (4 C ) TOT ( ITAILRTK ) L DS 4KTGTK 1 (1 k) (4 C ) 4 TOT ( ITAILRTK ) 103

17 Phase Noise Model of CMOS LC-Oscillators F 1 k Constant phase-noise contributions LC-tank noise contribution ~ 1 g m -cell drain-current thermal noise contribution ~ Loop-gain related contributions bias current source noise contribution ~ k 104

18 CMOS vs. Bipolar LC-Oscillators noise factors (for removed BCS noise): FBIP 1 1 kc FCMOS 1 bipolar VCO better for the same power consumption (v s,bip =v s,cmos ) 3 5 kc 3 kr B R 1 TK e.g., k=10, R TK =1000 rb e.g., k=10, R TK = rb

19 CMOS vs. Bipolar LC-Oscillators power consumption figure of merit: FOM 10log L( ) VCCICC 0 V CC =1.8V,v s,bip =0.4V,v s,ss-cmos =1.V, (3I CC,BIP =I CC,SS-CMOS ) FOM FOM BIP SSCMOS 4.8dB V CC =1.8V,v s,bip =0.4V,v s,ds-cmos =1.V, (1.5I CC,BIP =I CC,DS-CMOS ) FOM FOM BIP DSCMOS 7.8dB 106

20 Phase-Noise Model Conclusions Parametric Phase-Noise Model electrical circuit parameters (loop gain) worst-case phase noise (bandwidth unlimited) Bipolar vs. CMOS LC-Oscillators bipolar loop-gain related contributions v S, BIP ~k (<<V CC ), v S,CMOS ~V CC bipolar capacitive tapping for larger v S, BIP, but also larger k-related noise contributions and power consumption 107

21 So Far VCO design parameters Design requirement Oscillating frequency.1ghz Tuning range 400MHz Voltage swing 0.7V Phase noise Supply voltage 3V Power consumption 10mW Technology parameters Values Technology BiCMOS Number of metals 4 Transit frequency 50GHz MIM capacitors available Varactors available 109

22 Suppression of Noise in Oscillator s Tail-Current Source 110

23 VCO Phase-Noise gm noise power(lc- tank,- PN = signal power cell,current (~k ) source) TCS noise >> LC-tank noise + g m -cell noise VCO noise power ~ 1 or c k phase noise ~ 1/k or const TCS noise suppressed VCO noise power ~ 1 or c k phase noise ~ 1/k or 1/k 111

24 comone miter(c E) resona ntinducti vedegene ration(ri D) resistiv edegener ation(rd ) Bias Noise Reduction Techniques resistive degeneration inductive degeneration filtering? I TAIL ITAIL I TAIL V IN V IN + R - D LD V IN C D high supply required large area if integrated noise injection if discrete transconductor noise always ON reduced output impedance 11

25 Capacitive Filtering AC short 1 0 d / f 0 1 d ' (1 d ) n F '( IC ) ~ k 1/f 0 AC open 1 0 d/ f0 1/f 0 1 d k n F( IC ) ~ for k=10, d=0.5%, d =50.5%, and F >F 113

26 Resonant-Inductive Degeneration (RID) high TCS noise suppression V IN I TAIL no voltage headroom integration C L RID integrated degenerative inductor (L RID ) matched with base-emitter capacitance (C ) at f 0 114

27 So Far VCO design parameters Design requirement Oscillating frequency.1ghz Tuning range 400MHz Voltage swing 0.7V Phase noise Supply voltage 3V Power consumption 10mW Technology parameters Values Technology BiCMOS Number of metals 4 Transit frequency 50GHz MIM capacitors available Varactors available 115