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 2009 1 Outline Spectral Analysis of Noise in LC Oscillators LC tank gm 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 2009 2 Phase Noise Model of Bipolar and CMOS LC Oscillators A Tasic 2009 3 Outline Oscillation Condition LC Tank Noise Folding gm 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 2009 4 LC Oscillator Noise Sources iGTK L 2 L 2 2C 2C vB1 Q1 iN2 GTK RTK 2 RTK 2 iC1 LC tank noise vB2 iB1 transconductor noise Q2 iC2 ITAIL iBCS iN2 I C qI C v N2 rB iB2 QCS 2 KTGTK 2 KTgm 2 2 KTrB bias current source noise iN2 I BCS KTgm CS 1 2rB CS gm CS A Tasic 2009 5 Oscillator and Phase Noise Model iN O f 0 gm cell vN iPM iNO iN O f 0 vNO LC tank iAM iS phase modulating noise component double sided iPM f 0 iPM f 0 1 iN O f 0 iN O f 0 2 1 iN O f 0 iN O f 0 2 phase related noise power single sided 2 vPM TOT 1 iPM f 0 2 iPM f 0 2 A Tasic 2009 Z f0 2 2 iPM TOT 4 CTOT 2 6 gm Cell Transfer Function small signal gain in the presence of a large signal i OUT gIN di OUT dvS t vS g gm 2 d 2f 0 1 2f0 1 f0 g2i 2 T0 T0 4 j 2 i 0t dt T0 4 sin i d gd i d g 2i g t e 2 d 1 2k Fourier domain magnitude complex harmonic components g 4 4f0 g 2 3f0 2f0 g0 f0 A Tasic 2009 g4 g2 f0 2f0 3f0 4f0 7 Oscillation Condition harmonics gm cell and oscillation signal g0 g 2 2f0 vS 2 vS 2 f0 f0 convolution g0vS 2 g 2 vS 2 2f0 g0 vS 2 g2 vS 2 f0 2f0 g2 f0 2f0 vS f 0 g 2 2 oscillation signal vS vS f 0 g0 2 vS f 0 g0 2 vS f 0 g2 2 oscillation condition small signal loop gain k RTKgm 2 g0 g2 GTK RTK g0 g 2 vS RTK duty cycle d 1 2k A Tasic 2009 8 LC Tank Noise Folding convolution g0 and g g 2 2 harmonics and LC tank noise g0 vN vN f0 f0 vN f 0 g0 v N f0 g0v N vN f 0 f0 f0 g0 v N f 0 2f0 g0 v N f 0 f0 f0 2f0 g 2 2f0 g0 vN vN f0 g2 vN f 0 f0 f0 vN f 0 f0 f0 g 2 v N f 0 2f0 f0 2f0 2f0 g2 g 2 v N f 0 2f0 g2 v N f 0 g2v N f 0 A Tasic 2009 f0 2f0 9 LC Tank Noise Folding LC tank noise contribution g0 v N g0v N f0 g0 v N f 0 f0 f0 f0 2f0 g 2 v N f 0 2f0 g 2 v N f 0 g2 v N f0 f0 g0 v N f 0 g 2v N f 0 g0 vN f 0 g 2vN f 0 f0 2f0 g0 vN f 0 g0 vN f 0 g2vN f0 i N O f 0 i N O f 0 2f0 g2v N f0 i N O f 0 i N O f 0 g0 v N f 0 g2vN f0 A Tasic 2009 10 LC Tank Noise Contribution phase modulating noise component 1 iPM iN O f 0 iN O f 0 iN O f 0 2 iPM g0 g2 vN f 0 g 0 g 2 v N f 0 iN O f 0 phase related noise power k 1 g g0 g 2 2 i PM RTK g0 g2 2 v 2N RTK LC tank noise transfer function g 2 RTK g0 g2 2 2 GTK LC tank noise factor 2 2i PM RTK 2 g0 g2 2 v 2N RTK F RTK 4 KTGTK 4 KTGTK 2 2 2GTK v N RTK 4 KTGTK 4 KTGTK 4 KTGTK A Tasic 2009 11 1 gm Cell Noise Folding g 4 convolution g0 and g g 2 vN 3 f0 vN 3 f0 4f0 3f0 vN f0 vN harmonics and f0 gm cell noise g0 g2 vN f0 f0 g0 v N g0v N f0 f0 g0 v N f 0 g 2 v N f 0 f0 g0 v N f 0 g 2 v N f 0 g2 v N f0 3f0 4f0 2f0 g2v N f0 g4 v N 3 f 0 v N 3 f 0 2f0 f0 f0 2f0 vN f0 f0 f0 2f0 2f0 2 f0 2f0 gm cell noise around odd multiples of the oscillation frequency is folded to the LC tank noise around the oscillation frequency A Tasic 2009 12 gm Cell Noise Contribution phase modulating noise component iPM g0 g 2 v N f 0 g2 g2i g4 vN 3 f 0 2 g0 g 2 v N f 0 g2 g2i vN 2i 1 f 0 g 4 v N 3 f 0 g2i 2 g2i v N 2i 1 f 0 phase related noise power k 1 g g0 g 2 2 i PM gm IN g0 g2 2 g2 g4 2 g2i 2 number of g2i harmonic components 2 f0 1 1 d 2 f0 d number of g2i 2 g2i folding pairs 1 2d 2k 2 g2i 2 v 2N gm IN t d 2f0 g gm 2 k 2f0 d A Tasic 2007 13 f gm Cell Noise Contributions phase related noise power 2 i PM gm 1 g 2i 2d IN 2 2 g 2i v N g m 2 2 g22i 2 v N gm d IN 2 2 2 dg v N gm IN gm cell noise transfer function 2 g gm IN 2dg gm 2 2d 2 2 1 2 kGTK 2 2k 2 kGTK gm cell noise factors F 2rB F 2 I C 2 2i PM 2rB 4 KTGTK 2 2i PM 2 I C 4 KTGTK 2 2kGTK 4 KTrB 4 KTGTK 2krB GTK 2 2kGTK 2 KT g m 4 KTGTK kc kGTK g m 1 2 A Tasic 2009 14 IN rB Noise Contribution Be Precise phase related noise power k 1 2 i PM rB 2 g02 4 g22 4 g42 4 g22i 2 v 2N rB Paseval s Theorem 2 2 g rB 2 g 0 2 g 2i i 1 2 2 T2 T2 2 2 g t dt T2 2 4 …