Linear Phase-Noise Model 41
Sub-Outline Generic Linear Phase-Noise Model Circuit-Specific Linear Phase-Noise Model 4
Generic Linear Phase-Noise Model - Outline Linear Oscillator Model LC-Tank noise active part noise (Phase) Noise Factor Phase-Noise Properties 43
Linear Oscillator Model transconductor noise -g G TK C L LC-tank noise no tail-current source noise LC-tank impedance (noise shaping) LC-tank quality factor j0l j 0 Z( 0) / C 0 0 1 0 RTK 0 0 Z( ) 0C 4G Q 4Q Q GTK TK Q LG 0 1 TK 44
LC-Tank Noise -g i GTK G TK C L tank resistance noise (R TK =1/G TK ) i GTK 4KTG TK tank contribution to the equivalent voltage noise spectral density G v i Z TK 0 GTK GTK ( ) KT ( 0C) 45
Active Part Noise i -g -g i GTK G TK C L active part contribution to the equivalent voltage noise spectral density GTK 0 vg KT A ( 0C) active part noise factor A excess negative conductance additional noise of the active devices ideally A=1 (i.e., g=g TK, and no excess noise from the active part) 46
Phase Noise total voltage noise spectral density v N,TOT v v v TOT GTK g i N,TOT L ( ) v KT 1 vtot 1 0 KT F vs/ vsgtk Q G F TK 0 TOT ( 0C) oscillator noise factor F=1+A resulting phase noise L ( ) FkT P 0 S Q 47
Phase Noise Properties Leeson s phase noise model L ( ) FkT P 0 S Q inversely proportional to tank quality factor (square) inversely proportional to signal power -0dB/decade slope at mid frequencies (~MHz) directly proportional to oscillation frequency (square) phase-noise power consumption figure of merit FOM L( ) VCIC 0 48
Phase Noise Plot 1/f noise Thermal, shot noise Noise floor due to active elements or instrumentation Leeson s modification to capture 1/f and flat noise part L FkT 1/ f PS Q 0 ( ) 1 1 49
Circuit-Specific Linear Phase- Noise Model - Outline Spectral Noise Analysis Circuit Noise Analysis 50
Spectral Noise Analysis - Outline Phasor phase-noise model Oscillation condition LC-tank, g m -cell, tail-current source noise (Phase-) Noise factor 51
VCO Noise Sources 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 g m -cell transistors Q 1 andq always active current source noise always at the common mode 5
VCO Noise Sources LC-tank noise i ( G ) KTG N TK base-resistance thermal noise v ( r ) KTr N B i ( I ) qi KTg / N C C m i ( I ) qi KTg / N B B m B TK collector-current shot noise base-current shot noise tail-current source output noise g 1 i ( I ) KT 1 r g ( r g ) ( ) mcs, N TCS BCS, mcs, BCS, mcs, F T 53
Collector-Current Current Shot Noise splitting of current noise sources i C1 i C V CC CV L CV R TK / R TK / i C1 Q 1 Q i C i C1 Q 1 Q i C I DC i C1 i C 63
Collector-Current Current Shot Noise i C1 i C i C1 i C R TK / R TK / R TK / R TK / Q 1 Q Q 1 Q i C1 i C i C1 i C phase-related noise power: noise factor: C TK ( ) 1 i I R N v ( I ) PM C 4 i ( I ) PM 1 R PM C m m i ( I ) KTg / g 1 F( IC) 4KTG 4KTG 4 g / TK TK TK m SUP C C TK i ( I ) R i ( I ) N N C 64
Base-Current Shot Noise splitting of current noise sources i B i B1 V CC CV L CV R TK / R / TK Q 1 Q Q 1 Q i B1 i B i B1 i B I DC i B1 i B 65
Base Base-Current Shot Noise Current Shot Noise i B i B1 i B i B1 R TK / R / TK R TK / R TK / Q 1 Q Q 1 Q i B1 i B i B1 i B phase-related noise power: noise factor: B TK ( ) 1 i I R N v ( I ) PM B 4 TK TK msup i ( I ) PM PM B m m B 1 R TK B TK i ( I ) KTg / g / 1 F( IB) 4KTG 4KTG 4 g / i ( I ) R i ( I ) N N B 66
Base-Resistance Thermal Noise voltage-to-current transformation V CC R TK / R TK / CV L CV v B1 v B Q 1 Q v B1 g Q m v B1 1 Q gm gm v B g m v B I TAIL 67
Base-Resistance Thermal Noise g m v B1 g m v B g m v B1 g m v B R TK / R TK / R TK / R TK / g m v B1 Q 1 Q g m v B Q 1 Q g m v B1 g m v B g m v B1 g m v B phase-related noise power: noise factor: B m v ( r ) g N i ( r ) PM B PM B m B m B i ( r ) g KTr g r F( rb) c 4KTG 4KTG G TK TK TK 68
Linear-Oscillator Phase Noise Linear-oscillator noise factor: 1 1 3 F F( RTK) F( IC) F( IB) F( rb) 1 c c Linear-oscillator phase noise: L ( f ) L L L L ( R ) ( I ) ( I ) ( r ) 4KTG F TK C B B TK (4 CTOT) v (4 CTOT) L 4KTG 3 ( c ) (4 C ) ( ) TOT TK VT S 69
Linear-Oscillator Phase Noise LC-tank noise contribution ~ 1 g m -cell current shot noise contribution ~ ½ g m -cell base-resistance noise contribution ~ c linear-oscillator noise factor ~ constant (independent of bias condition) But, linear oscillator (loop gain of 1) doesn t oscillate, or at least doesn t oscillate with a predictable amplitude! Oscillator with a loop gain of /(+)=1. oscillates and has ~3dB better phase noise than linear oscillator! 70