Spectral Analysis of Noise in Switching LC-Oscillators

Spectral Analysis of Noise in Switching LC-Oscillators 71

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

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

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

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

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

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

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

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

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

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

Switching-Oscillator Phase Noise Noise factor: F F( R ) F( I ) F( I ) F( r ) F( I ) TK C B B TCS 1 1 1 1 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

Phase Noise Model of Bipolar Switching LC-Oscillators F 1 1 1 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

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 8 1 1 1 L ~ ~ k 5 10 10 k high loop-gain, high quality LC-tank: e.g., k>>1(=10), c<<1(~0.01) 1 1 k( kc) kc 3 1 1 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

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

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

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

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 1000 10 8.4 e.g., k=10, R TK =100 100 rb 0.84 10 105

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

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

So Far VCO design parameters Design requirement Oscillating frequency.1ghz Tuning range 400MHz Voltage swing 0.7V Phase noise -110dBc@1MHz Supply voltage 3V Power consumption 10mW Technology parameters Values Technology BiCMOS Number of metals 4 Transit frequency 50GHz MIM capacitors available Varactors available 109

Suppression of Noise in Oscillator s Tail-Current Source 110

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

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

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

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

So Far VCO design parameters Design requirement Oscillating frequency.1ghz Tuning range 400MHz Voltage swing 0.7V Phase noise -110dBc@1MHz Supply voltage 3V Power consumption 10mW Technology parameters Values Technology BiCMOS Number of metals 4 Transit frequency 50GHz MIM capacitors available Varactors available 115