On the Phase Noise and Noise Factor in Circuits and Systems - New Thoughts on an Old Subject Aleksandar Tasic QCT - Analog/RF Group Qualcomm Incorporated, San Diego A. Tasic 9 1
Outline Spectral Analysis of Noise in LC-Oscillators LC-tank, g m -cell, bias current source noise (Phase-) Noise factor Bipolar vs. CMOS LC-Oscillators LC-Oscillators Noise Reduction Methods Mixer Noise Factor from VCO Noise Factor Oscillator Phase Noise in Receiver s SNR LNA and Mixer Noise Factors in a Receiver BBFilter Noise Transfer vs. LO/Mix Duty A. Tasic 9
Phase Noise Model of Bipolar and CMOS LC-Oscillators A. Tasic 9 3
Outline Oscillation Condition LC-Tank Noise Folding g m -Cell Noise Folding Bias-Current Source Noise Folding Phase-Noise Model of Bipolar LC-Oscillators Phase-Noise Model of CMOS LC-Oscillators Bipolar vs. CMOS LC-Oscillators A. Tasic 9 4
LC-Oscillator Noise Sources i GTK L/ L/ C C R TK / R TK / LC-tank noise i N ( GTK ) KTGTK i C1 v B1 v B ~ ~ Q 1 Q i B1 i B i C transconductor noise i N ( IC ) qic KTgm / v N ( rb ) KTrB I TAIL Q CS i BCS bias current source noise i ( I ) KTg (1 r g ) N BCS m, CS B, CS m, CS A. Tasic 9 5
Oscillator and Phase-Noise Model v N + g m -cell i NO, i i PM * NO(, f ) i NO(, f ) i AM v NO, LC- tank i S phase-modulating noise component (double-sided) 1 * ipm ( f ) in, O( f ) in, O( f ) 1 * ipm ( f ) in, O( f ) in, O( f ) phase-related noise power (single-sided) 1 v i f i f Z f PM, TOT PM, TOT PM ( ) PM ( ) ( ) A. Tasic 9 4 CTOT i 6
g m -Cell Transfer Function small-signal gain in the presence of a large signal i OUT g IN = d i OUT d v S v S t d / f - g = g m / 1 / f Fourier domain (magnitude) complex harmonic components g -4 g - g g g 4 g i ji t g g() t e dt i 1 / f gd T T T /4 /4 sin( i d) i d d 1 k -4f -3f -f -f A. Tasic 9 f f 3f 4f 7
Oscillation Condition harmonics: g m -cell and oscillation signal g g - v S / v S / g -f -f f f convolution: g v S / g v S / g - v S / g v S / -f oscillation signal: -f v ( f ) v ( f ) v ( f ) v ( f ) v g g g g R ( g g ) v R S S S S S TK S TK oscillation condition: g g G TK A. Tasic 9 f f small-signal loop gain: k=r TK g m / duty cycle: d=1/(k) 8
g - LC-Tank Noise Folding convolution: g and g harmonics and LC-tank noise v N ( f ) v N ( f ) g v N ( f ) v N ( f ) g -f -f f f g g v vn ( f ) v N ( f ) g vn ( f ) g N ( f ) -f -f f f g - g g v N ( f ) v N ( f ) v N ( f ) v N ( f ) -f -f f f g - vn ( f ) g - v g vn ( f ) g vn ( f ) N ( f ) -f -f A. Tasic 9 f f 9
LC-Tank Noise Folding LC-tank noise contribution: g g v ( f ) v ( f ) vn ( f ) g v N g N N ( f ) -f -f f f g - v ( f ) v ( f ) v ( f ) vn ( f ) N g - g N g N -f -f f f i ( f ) g v ( f ) g v ( f ) NO, N N i ( f ) g v ( f ) g v ( f ) NO, N N i ( f ) g v ( f ) g v ( f ) NO, N N i ( f ) g v ( f ) g v ( f ) NO, N N A. Tasic 9 1
LC-Tank Noise Contribution phase-modulating noise component: 1 ipm in, O( f ) in, O( f ) in, O( f ) in, O( f ) i ( g g ) v ( f ) ( g g ) v ( f ) PM N N phase-related noise power (k>>1, g=g =g ): TK i ( R ) ( g g ) v ( R ) PM LC-tank noise transfer function: ( TK ) ( ) TK g R g g G LC-tank noise factor: N TK PM TK g g v R N TK GTK v R N TK i ( R ) ( ) ( ) ( ) 4KTGTK FR ( TK ) 1 4KTG 4KTG 4KTG 4KTG TK TK TK TK A. Tasic 9 11
g -4 g m -Cell Noise Folding convolution: g and g harmonics and f g m -cell noise g - g g g 4 vn ( 3 f ) vn ( 3 f ) vn ( f ) vn ( f ) vn ( f ) vn ( f ) vn (3 f ) vn (3 f ) -4f -3f -f -f f f 3f 4f gv ( v ( g vn ( f ) v N f ) N f ) g g N ( f ) -f -f f f g - g g - vn ( f ) vn ( f ) g v ( vn ( f ) N f ) -f -f g m -cell noise around odd multiples of the oscillation frequency is folded to the LC-tank noise around the oscillation frequency A. Tasic 9 f f 1
g m -Cell Noise Contribution phase-modulating noise component: i ( g g ) v ( f ) ( g g ) v ( f ) PM N N +( g g ) v (3 f ) ( g g ) v (3 f )... 4 N 4 N +( g g ) v ((i 1) f ) ( g g ) v ((i 1) f ) i i N i i N phase-related noise power (k>>1, g=g =g = ): m IN 4 i i m IN i ( g ) ( g g ) ( g g )... ( g g ) v ( g ) PM N number of g i harmonic components: f 1 1 d f d number of (g i- +g i ) folding pairs: 1 k k d t -g=g m / d/f f /d A. Tasic 7 13 f
g m -Cell Noise Contributions phase-related noise power: 1 gi i ( g ) ( ) ( ) ( ) ( ) PM m IN g i g i v g N m IN v g N m IN dg v g N m IN d d g m -cell noise transfer function: gm 1 g ( g ) dg d( ) ( kg k ) kg g m -cell noise factors: m IN TK TK i ( r ) 4 PM B kgtk KTrB B B TK 4KTGTK 4KTGTK F( r ) kr G kc i I PM C kgtk KT gm C TK m 4KTGTK 4KTGTK ( ) / 1 F( I ) kg / g A. Tasic 9 14
r B Noise Contribution Be Precise phase-related noise power (k>>1): B 4 i B i ( r ) g 4g 4 g... 4 g v ( r ) PM N Paseval s Theorem: T / 4 t 4 ( B) i ( ) (1 ) T 1 T / 3 i T g r g g g t dt g dt g d r B noise factor: i ( r ) PM B F( rb ) kc 4KTG 3 TK A. Tasic 7 15
Bias Current-Source Noise Transfer Function g m -cell large-signal V-to-I transfer function I OUT 1 I OUT VIN -1 1 / f 1/f c i 1 sin((i 1) / ) (i 1) / Fourier domain (magnitude) complex harmonic components c -1 c -3 c 3 c 1-4f -3f -f -f A. Tasic 9 f f 3f 4f 16
phase-related noise power: ipm, DIFF ( IBCS ) 1 ipm ( I BCS ) in ( I BCS ) 4 4 BCS noise transfer function: BCS noise factor: FI ( ) BCS BCS Noise Contribution BCS noise around even multiples of the oscillation frequency is folded to the LC-tank noise around the oscillation frequency 1 g ( I BCS ) 4 i ( I ) KTg (1 r g ) KT kg (1 kc) PM BCS m B m TK 4KTG 4KTG 4KTG TK TK TK 1 1 k(1 kc) k( kc) k F( IC) F( rb) A. Tasic 9 17
Phase-Noise Model of Bipolar Switching LC-Oscillators Noise factor: F F( R ) F( I ) F( r ) F( I ) TK C B BCS 1 1 1 F 1 kc k( kc) 1 (1 k) kc( k) 3 3 Phase noise: L L L L L ( R ) ( I ) ( r ) ( I ) 4KTG F TK C B BCS TK (4 CTOT ) v (4 CTOT ) S v S 8 kv T L 1 1 (1 k) kc( k) 4KTGTK 3 (4 C ) TOT ( ) 8V T k A. Tasic 9 18
Phase Noise Model of Bipolar Switching LC-Oscillators 1 1 F 1 kc k( kc) 3 Constant phase-noise contributions LC-tank noise contribution ~ 1 g m -cell current shot noise contribution ~ ½ Small-signal loop-gain related contributions g m -cell base-resistance noise contribution ~.66ck phase-noise contribution of the bias current source is k-times larger then the noise contribution of the g m -cell ~ k(½+ck)! A. Tasic 9 19
Low/High-Performance VCO Designs high ss loop-gain, high quality LC-tank, BCS noise eliminated: e.g., k>>1(=1), c<<1(~.1) 1 1 kc 3 7.8 1 1 1 L ~ ~ k 5 1 1 k high ss loop-gain, high quality LC-tank, BCS noise present: e.g., k>>1(=1), c<<1(~.1) 1 1 k( kc) kc 3 1 1 L ~ ~ k k 5 1 k low ss loop-gain, low quality LC-tank, BCS noise present: e.g., k~1(=), c~1(~.5) 7 3 (1 k) 6 5 L ~ ~1 k 4 A. Tasic 9
ingle/double-switch CMOS LC-VCOs i N ( GTK ) KTGTK i GTK i D3 V DD i ( I ) KT g N D, P P m, P 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 N ( I D ) KT gm Q CS i BCS i D1 Q 1 Q i ( I ) KT g N D, N N m, N i D d N G g TK m i ( I ) KT g N BCS m, CS A. Tasic 9 Q CS i BCS d C 1 G TK g m
Phase Noise Model of CMOS LC-Oscillators Noise factor ( N = P, g m,n =g m,p ): F F( R ) F( I ) F( I ) SS TK D BCS F 1 g /(4 G ) SS m, CS TK F F( R ) F(4 I ) F( I ) DS TK D BCS F 1 g / G DS m, CS TK Phase noise: L L L L ( R ) ( I ) ( I ) 4KTG F TK D BCS TK (4 CTOT ) v (4 CTOT ) S L SS 4KTG TK (4 C ) 1 gm, CS /(4 GTK ) ( I R ) TAIL TK L DS 4KTG TK (4 C ) 1 gm, CS / G 4 ( I R ) TAIL TK TK A. Tasic 9
Phase Noise Model of CMOS LC-Oscillators F 1 g / G m, CS Constant phase-noise contributions LC-tank noise contribution ~ 1 g m -cell drain-current thermal noise contribution ~ Small-signal loop-gain related contributions (?) bias current source noise contribution ~ g m,cs /G TK (k ) TK A. Tasic 9 3
CMOS vs. Bipolar LC-Oscillators noise factors (for removed BCS noise): FBIP 1 1 3 kc F CMOS 1 bipolar VCO better for the same power consumption (v s,bip =v s,cmos ) 3 5 kc 3 3 kr B R TK 8 e.g., k=1, R TK =8 e.g., k=1, R TK =8 r B 8 1 8 A. Tasic 9 r B 8 1 8 4
CMOS vs. Bipolar LC-Oscillators power consumption figure of merit: L FOM 1log ( ) VCC ICC V CC =1.8V, v s,bip =.4V, v s,ss-cmos =1.V, (3I CC,BIP =I CC,SS-CMOS ) FOM FOM 4.8dB BIP SS CMOS V CC =1.8V, v s,bip =.4V, v s,ds-cmos =1.V, (1.5I CC,BIP =I CC,DS-CMOS ) FOM FOM 7.8dB BIP DS CMOS A. Tasic 9 5
Phase-Noise Model Conclusions Parametric Phase-Noise Model electrical circuit parameters (ss loop gain) worst-case phase noise (bandwidth unlimited) Bipolar vs. CMOS LC-Oscillators bipolar ss 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 A. Tasic 9 6
Verification of the Phase-Noise Model A. Tasic 7 7
VCO Noise Contributions f ~5.74GHz, R TK ~34 i GTK, n~1.65, c~.5, V CC =.V C V L V CC V TUNE C V LC-tank noise ~ 1 i C1 v B1 ~ C B ~ v B Q 1 Q C A C B C A i C transconductor noise ~ n(.5+.66c k) i B1 i B I TAIL Q CS i BCS bias current-source noise ~ n(.5+c k) k A. Tasic 7 8
g m -Cell Noise Contributions k=.5g m R TK <.5g m,actual R TK =.5g m R TK /(1+g m r E )=k actual 1,95,9 F(I C ) simulations calculations F( rb ) nkc 1.65.5 k.7 k 3 3,85,8,75,7 4 6 8 9,6,5 k 1,5 F (r B ) simulations calculations 1 n FI ( C ).87,5 k 4 6 8 9,6 A. Tasic 7 9
Bias Noise Contributions 7 6 5 F (I C,CS ) simulations calculation s F( r ) knkc 1.65.5 k.41 k B, CS 4 3 1 18 16 14 1 F (r B,CS ) simulation calculation s 4 6 8 9,6 k 1 8 6 4 1 F( IC, CS ) nk.8k 4 6 8 9.6 k A. Tasic 7 3
Suppression of Bias Current-Source Noise in LC-Oscillators A. Tasic 9 31
Outline Contribution of Bias Current-Source Noise to Phase Noise of LC-Oscillators Techniques for Reduction of Bias Current- Source Noise Noise Analysis of Degenerated Bias Current Source Bias Noise Suppression - Design Example A. Tasic 9 3
VCO Noise Contributions i GTK C V L V CC C V LC-tank noise ~ 1 V TUNE i C1 v B1 v B ~ Q 1 ~ Q C A C B C B C A i C transconductor noise ~.5+c k i B1 i B I TAIL Q CS i BCS bias current-source noise ~ (.5+c k) k A. Tasic 9 33
VCO Noise Contributions f ~5.74GHz, R TK ~34, n~1.65, c~.5, V CC =.V 1% 9% 8% 7% 6% 5% 4% 3% r B,CS I C,CS r B BCS: ~85% % 1% % I C R TK 4 6 8 9.6 A. Tasic 9 g m : ~15% k 34
Phase-Noise Ratio PNR 1 9 8 7 6 5 4 3 1 n k( nkc) L( RTK ) L( IC ) L( rb ) L( I BCS ) 1 L( R ) ( ) ( ) n TK L IC L rb 1 nkc 3 PNR[dB] PNR=8.dB k 4 6 8 9.6 A. Tasic 7 35
common emitter (CE) resonant inductive degeneration (RID) resistive degeneration (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 A. Tasic 9 transconductor noise always ON reduced output impedance 36
Capacitive Filtering AC short 1 d / f 1 d' (1 d) n F '( IC ) ~ k 1/f AC open 1 d/ f 1/ f 1 d k n F( IC ) ~ for k=1, d=5%, d =5.5%, and F >F A. Tasic 9 37
Bias Current Source with Resonant-Inductive Degeneration V IN C I TAIL L RID matched to C at f r B,CS noise contribution reduced transconductance gain small at resonance series resonance I B,CS noise contribution small L RID I C,CS noise contribution removed common-base like configuration (gain of 1) parallel resonance emitter open at resonance (I C,CS floats) A. Tasic 9 38
Circuit Diagram for Noise Transfer Functions B C r B,CS i B,CS C,CS E ~ (v B - v E )g m,cs i C,CS i OUT,CS v B,CS ~ L RID i C,CS to i OUT : v B,CS short, i B,CS open i B,CS to i OUT : v B,CS short, i C,CS open v B, CS to i OUT : i C,CS open, i B,CS open A. Tasic 7 39
i N iout ( I ) B, CS Bias Current-Source Noise Contributions i 1 v r f j C OUT T, CS ( f) gm( ) ( 1 N B, CS ) T, CS T LRID j LRID g m, CS ( f ) 1 C rb, CS 1 f g 1 ( ) m, CS j C rg B m LRID j L f RID T 1 f series resonance i N iout ( I ) C, CS g parallel resonance m, CS ( f ) 1 1 C rb, CS 1 f g 1 ( ) m, CS j C rg B m LRID j L f RID T, CS A. Tasic 7 4 1 parallel resonance
BCS w/ RID vs. BCS w/o RID BCS noise with degeneration g f 1 f i 4kT ( ) r g m, CS T, CS CS, RID B, CS m, CS f ft, CS BCS noise without degeneration g f 1 i 4kT 1 ( ) r g m, CS T, CS CS B, CS m, CS f more than a factor (f T,CS /f ) noise reduction after RID f ics, RID ics ft, CS for (f T,CS /f )=5, a factor of 5 reduction A. Tasic 7 41
VCO Noise Contributions after RID applied to BCS f ~5.74GHz, L RID ~1.3nH, R TK ~34, n~1.65, c~.5, V CC =.V 1% BCS: ~6% r B,CS I C,CS 8% r B 6% 4% g m : ~94% I C % R TK % 4 6 8 9.6 k A. Tasic 9 4
5.7GHz band VCO buffer RID LC-tank -g-cell m 5 metals active area.1mm buffer L RID =.6nH, 7-turns,.1mm A. Tasic 7 43
VCO w/ RID vs. VCO w/o RID to ground to ground to TCS transistors to ground A. Tasic 9 44
Phase Noise (w/ RID vs. w/o RID) without RID with RID 6dB phase-noise improvement with RID -11dBc/Hz @1MHz from A. Tasic 5.7GHz 9 @ 4.8mA&.V 45
RID Conclusions BCS noise >> g m -cell and LC-tank noise Resonant inductive degeneration good suppression of high frequency BCS noise low voltage operation small chip area (vs. discrete solutions) BCS DC noise upconversion large area (vs. resistive degeneration) poorer noise suppression at high supplies (vs. resistive degeneration) A. Tasic 9 46
Oscillator Conclusions Spectral Analysis of Noise in LC-Oscillators Phase-Noise Model LC-tank, g m -cell, bias current source contributions Bipolar vs. CMOS LC-Oscillators Oscillator Noise Reduction Methods Resonant-Inductive Degeneration A. Tasic 9 47
Future Worries Low-(Supply and Swing)-Voltage Operation Linear and Quasi-Linear Phase-Noise Model Low-Performance Oscillators Noise-Reduction Methods A. Tasic 9 48
Conclusions A. Tasic 9 49
Conclusions Spectral Analysis of Noise in LC-Oscillators LC-tank, g m -cell, bias current source noise contributions Bipolar and CMOS VCO Noise Factors LC-Oscillators Noise Reduction Methods Mixer Noise Factor from VCO Noise Factor Oscillator Phase Noise in Receiver s SNR Mixer Noise Factor in a Receiver LNA Noise Factor in a Receiver BBFilter Noise Transfer vs. LO/Mix Duty A. Tasic 9 5