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Announcements. 1. Course assistant reception day in the next week: Monday instead of Sunday. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5. Fundamentals of low-noise design. v bt 2 = 4 k T r b. i csh 2 = 2 q I C. i bsh 2 = 2 q I B. K f I B f. i bf 2 =.

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  1. Announcements 1. Course assistant reception day in the next week: Monday instead of Sunday.

  2. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design 5.5. Fundamentals of low-noise design

  3. vbt2= 4kTrb icsh2= 2qIC ibsh2= 2qIB Kf IB f ibf 2= 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.2. BJT noise model 5.5.2. BJT noise model C Noiseless vbt rb B icsh ibf ibsh E NB: icf =0 ict =0

  4. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model 5.4.3. JFET noise model D Noiseless G idf idt igsh S igsh2= 2qIG idt2= 4kT/(3/2gm) Kf ID f idf 2= NB: idsh =0

  5. id vgs 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model Equivalent small-signal model gmvgs ig G D rgs ro igsh idf idt

  6. id vgs vgs 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model Equivalent small-signal model gmvgs ig G D rgs ro 1/gm igsh idf idt

  7. vgs 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model Equivalent small-signal model gmvgs ig G D ro ~1/gm igsh idf idt

  8. RS id vs vgs ? vn s 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model A. Total input noise gmvgs ig G D ro ~1/gm igsh idf idt 1) Total input noise vs. time, vn s(t).

  9. igsh Rs RS vs ? vn s vn s(t)=vst(t)+igsh(t)RS+[idf (t)+idt(t)](1/gm) 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model A. Total input noise gmvgs ig G D id vgs ro ~1/gm igsh idf idt 1) Total input noise vs. time, vn s(t).

  10. RS vs ? vn s vn s vn s(t)=vst(t)+igsh(t)RS+[idf (t)+idt(t)](1/gm) 2) Power spectral density of the total input noise, vn s2(f). vn s2=4kTRS +igsh2RS2+(idf 2+idt2)/gm2 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model A. Total input noise gmvgs igsh Rs ig G D id vgs ro ~1/gm idf idt 1) Total input noise vs. time, vn s(t).

  11. en in ? vn s vn s en2= vn s2= (idf 2+idt2)/gm2 RS = RS =0 vn s2 RS2 in2==igsh2 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model B. en- in noise model gmvgs igsh Rs RS ig G D id vs vgs ro ~1/gm idf idt vn s2=4kTRS +igsh2RS2+(idf 2+idt2)/gm2

  12. en in 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model BJT JFET en- in noise model f >> ff Vp = 2 V IDSS= 10 mA IG = 10 pA en=1.8 nV/Hz0.5 in=1.8 fA/Hz0.5 en /in=1 MW RS= 1 MW in RS= 1.8 nV/Hz0.5 f >> ff rb= 100 W IC = 1 mA hfe= 100 en=1.36 nV/Hz0.5 in=1.8 pA/Hz0.5 en /in=756 W RS= 756 W in RS= 1.4 nV/Hz0.5 D G S en2= (idf 2+idt2)/gm2 in2=igsh2

  13. idt2= 4kT/(3/2gm) Kf ID f idf 2= 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model 5.5.4. MOSFET noise model D Noiseless G idt idf S NB: igsh =0 idsh =0

  14. RS id vs ? vn s vn s vn s(t)= vst(t)+[idf (t)+idt(t)](1/gm) vn s2=4kTRS +(idf 2+idt2)/gm2 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model A. Total input noise gmvgs G D ro 1/gm idf idt 1) Total input noise vs. time, vn s(t). 2) Power spectral density of the total input noise, vn s2(f).

  15. en in en2= vn s2= (idf 2+idt2)/gm2 RS = RS =0 vn s2 Rs2 in2== 0 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model B. en- in noise model vn s gmvgs RS G D id vs ro 1/gm vn s2=4kTRS +(idf 2 +idt2)/gm2

  16. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model JFET MOSFET en- in noise model f >> ff Vp = 2 V IDSS= 10 mA IG = 10 pA en=1.8 nV/Hz0.5 in=1.8 fA/Hz0.5 en /in=1 MW RS= 1 MW in RS= 1.8 nV/Hz0.5 f >> ff Vp = 2 V IDSS= 10 mA en=1.8 nV/Hz0.5 D en G S en2= (idf 2+idt2)/gm2 in= 0

  17. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect 5.5.5. Frequency response effect The aim is to analyze the dependence of a transistor en and in on frequency and the operating point. VCC iC RS vs VBB Cm vbt vbt RS rb B C hfe ip ic ip Cp vs icsh rp ro ibf ibsh

  18. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect A. Total input noise Cm RS rb is B C hfe ip ic ip Cp vs rp ro 1) Transconductance gain ic vs hfe [1/j2pf(Cp+Cm )]/[rp+1/j2pf(Cp+Cm )] RS +rb+rpII[1/j2pf(Cp+Cm )] ___ Ag = ____________________________________ is=1 hfe /(RS +rb+rp ) 1+j2pft = _____________ , t = [(RS + rb)IIrp ](Cp+Cm )

  19. vn s 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect Cm vbt vbt RS rb B C hfe ip ic ip Cp vs icsh rp ro ibf ibsh hfe /(RS +rb+rp ) 1+j2pft Ag= _____________ , t = [(RS + rb)IIrp ](Cp+Cm ) 2) Power spectral density of the total input noise, vn s2(f). RS +rb+rp hfe 2 [1+(2pft)2] icsh2 vn s2=4kT(RS +rb)+(ibf 2+ibsh2)(RS+rb)2+

  20. RS = RS =0 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect RS +rb+rp hfe 2 [1+(2pft)2] icsh2 vn s2=4kT(RS +rb)+(ibf 2+ibsh2)(RS+rb)2+ 3) en and in of the transistor. rb+rp hfe 2 en2= vn s2= 4kTrb+(ibf 2+ibsh2)rb2 + [1+(2pften)2] icsh2 ten= (rbIIrp )(Cp+Cm ) icsh2 hfe2 vn s2 RS2 = ibf 2+ibsh2 + [1+(2pftin)2] in2= tin= rp (Cp+Cm )

  21. en in 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect B. en- in noise model for high-frequencies Cm RS rb B C hfe ip ic ip Cp vs rp ro rb+rp hfe 2 en2= 4kTrb+(ibf 2+ibsh2)rb2 + [1+(2pften)2] icsh2 icsh2 hfe2 ibf 2+ibsh2 + [1+(2pftin)2] in2=

  22. 5 0 4 -20 3 2 -40 1 Ag Ag max dB 100 101 102 103 104 105 106 107 108 109 ____ 100 101 102 103 104 105 106 107 108 109 f, Hz 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect C. en(f)for differentIC rb+rp hfe 2 en2= 4kTrb+(ibf 2+ibsh2)rb2 + [1+(2pften)2] icsh2 IC opt= 24 mA IC = 0.1 mA en(f) nV/Hz0.5 rb= 100 W hfe= 100 Cm = 1 pF Cp (1 mA)= 100 pF

  23. 8 0 6 -20 4 2 -40 0 Ag Ag max dB ____ 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect D. in(f)for differentIC icsh2 hfe2 ibf 2+ibsh2 + [1+(2pftin)2] in2= IC opt= 24 mA IC = 0.1 mA in(f) pA/Hz0.5 100 101 102 103 104 105 106 107 108 109 rb= 100 W hfe= 100 Cm = 1 pF Cp (1 mA)= 100 pF 100 101 102 103 104 105 106 107 108 109 f, Hz

  24. V(INOISE)*1G V(Out1)/V(V1:+)/10 V(ONOISE)*1G/10 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect E. Noise simulation inPSPICE 30 20 10 0 1.0Hz 10KHz 100MHz 1.0THz Frequency

  25. rb= 40 W hfe= 500 ro = IC = 1 mA IDSS= 2 mA Vp= 2 V ro = ID = 1 mA RS+rb+rp hfe 2 icsh2 vn s2=4kT(rb+ RS) +(ibf 2+ibsh2)(RS+rb)2+ vn s2=4kTRS +igsh2RS2+(idf 2+idt2)/gm2 vn s2=4kTRS +(idf 2+idt2)/gm2 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.6. Comparison of the BJT, JFET and MOSFET 5.5.6. Comparison of the BJT, JFET and MOSFET

  26. IC opt 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.6. Comparison of the BJT, JFET and MOSFET 100 Power spectral density of the total input noise vn s as a function of RS vn s nV/Hz0.5 5 The 1/f noise is neglected. The JFET gate current is neglected. 1 102 103 104 105 RS, W

  27. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.6. Comparison of the BJT, JFET and MOSFET MOSFET Guide for selection of the preamplifier JFET IC amplifiers BJT Transformer coupling 1 10 100 1 k 10 k 100 k 1 M 10 M 100 M 1 G 10 G 100 G Source resistance, RS Reference: [9]

  28. RS = 100 W RS = 10 kW 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect Example: Comparison of an BJT and JFET in PSPICE

  29. vbt rb B C hfe ip ip io icsh rp ro vst ibf ibsh E RS vct vet vs RE RC 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit 5.5.7 Noise analysis of a CE amplifier VCC RC RS vs RE VBB ro

  30. ? vn s 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit • Our final aim is to find and minimize the total input noise vn s. vbt rb B C hfe ip ip io icsh rp vst ibf ibsh E RS vet vct vs RE RC • Let us first find vn s by applying superposition.

  31. io vs AOL 1+AOLb As =Gs + Gs bs fwd ___ _______ hfe 1+hfe RE/(RE +RS+rb+rp) 1 RS+rb+rp+RE As= +0 ____________________ ___________ 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit • 1) Signal gain As for vs, vst, vbt, and vet. vbt rb B C hfe ip ip io rp vst E RS vet vs RE RC

  32. io ibf AOL 1+AOLb Abf =Gibf + Gbf bbf fwd ___ _______ RS+rb+RE RS+rb+RE +rp hfe 1+hfe RE/(RE +RS+rb+rp) Abf= +0 ____________________ ___________ 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit • 2) Noise gain Abf for ibf and ibsh. rb B C hfe ip ip io rp ibf ibsh E RS vs RE RC

  33. io icsh AOL 1+AOLb Acsh =Gcsh + Gcsh bcsh fwd ___ _______ hfe 1+hfe RE/(RE +RS+rb+rp) RE RE +RS+rb+rp Acsh= +1 ____________________ - ___________ 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit • 3) Noise gain Acsh for icsh. rb B C hfe ip ip io icsh rp E RS vs RE RC

  34. io ict AOL 1+AOLb Act =Gct + Gct bct fwd ___ _______ 1 RC Acsh= ___ 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit • 4) Noise gain Act for icsh. rb B C hfe ip ip rp E RS io vs vct /RC RE RC

  35. vn s (ibf +ibsh)Abf As icsh Acsh As vct Act As vn s(t) = vst +vbt +vet + + + __________ _______ _____ (RSbE+rp)2 hfe2 1 RC As2 +icsh2 + 4kT ________ _____ vn s2(f) = 4kTRSbE+(ibf 2+ibsh2)RSbE2 0 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit • 5) Total input noise vs. time, vn s. rb B C hfe ip ip io rp RS E vs RE RC RSbE =RS +rb+RE

  36. rb en in E RE (RbE+rp)2 hfe2 en2 =en s2 =4kTRbE+(ibf 2+ibsh2) RbE2+ icsh2 RS = RS =0 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit 6) en- in noise model. B C hfe ip ic ip rp RC E RS vs (1+hfe)RE RbE= rb +RE icsh2 hfe2 en s2 RS2 in2 ==ibf 2+ibsh2+

  37. 0 1.4 1.2 -0.1 en s norm. dB en s norm. dB 1.0 hfe=104 -0.2 0.8 hfe=103 0.6 hfe=102 -0.3 0.4 -0.4 0.2 0 -0.5 102 103 104 0.1 10 10 IC /IC opt hfe hfeVT (1+ hfe )0.5RSbE IC opt= (1+hfe )0.5 (1+hfe )0.5-1 vn s min2=4kTRSbE 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit 7) Minimizing CE noise. rb= 100 RS= 200 RE= 200 ibf 2= 0 vbt2= 4kTrb vet2= 4kTRE ibsh2= 2qIC /bicsh2= 2qIC 2 RSbE2 hfe RSbE+hfeVT /IC hfe vn s2= 4kTRSbE+ 2qIC +2qIC Reference: [7]

  38. Next lecture Appendix: Noise analysis of the CE without applications of superposition Reference: [7]

  39. vbst rb B ip C hfe ip ic icsh ? rp ro RC vn s ibf ibsh E RS vet vs RE 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis Noise analysis of a CE amplifier VCC RC RS vs RE VBB

  40. ibf ibsh ibf ibsh 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis 1) Disconnecting ibf and ibsh sources. vbst rb B ip C hfe ip ic icsh ? rp ro RC vn s E RS vet vs RE

  41. vbst ibf ibf ibsh ibsh vne= vet -(ibf + ibsh)RE 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis 1) Disconnecting ibf and ibsh sources. rb B ip C hfe ip ic icsh ? rp ro RC vn s E RS vet vs RE

  42. vbst +(ibf + ibsh)(Rs + rb) vbst ibf ibsh vne= vet -(ibf + ibsh)RE 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis 1) Disconnecting ibf and ibsh sources. rb B ip C hfe ip ic ip icsh ? rp ro RC vn s E RS vet vs RE

  43. vbst +(ibf + ibsh)(Rs + rb) 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis 2) Disconnecting ibf and ibsh sources. rb ro B C hfe ip ic ip icsh ? rp ro RC vn s E RS vne= vet -(ibf + ibsh)RE vet vs RE

  44. vbst +(ibf + ibsh)(Rs + rb) 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis 2) Disconnecting ibf and ibsh sources. rb B C hfe ip ic ip icsh ? rp RC vn s E RS vne= vet -(ibf + ibsh)RE vet vs RE

  45. vbst +(ibf + ibsh)(Rs + rb) 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis 2) Disconnecting ibf and ibsh sources. rb B C hfe ip ic ip icsh ? rp RC vn s E RS vne= vet -(ibf + ibsh)RE vne= vet -(ibf + ibsh)RE +icsh RE vet vs (1+hfe)RE RE

  46. vbst +(ibf + ibsh)(Rs + rb) RS+rb+rp+(1+hfe)RE hfe vn s(t)= ic(t) vn s(t)=vbst(t)-vet(t)+[ibf (t)+ibsh(t)] R*+ ? 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis 3) Reflecting ibf and ibsh to vn s. rb B C hfe ip ic ip icsh ? rp RC vn s E RS vne= vet -(ibf + ibsh)RE +icsh RE vs (1+hfe)RE R*= RS +rb +RE

  47. RS+rb+rp+(1+hfe)RE hfe hfe RS+rb+rp+(1+hfe)RE - ic(t) , 1) vn s= - icsh (t)RE +icsh (t) 2) ic= R*+ rp hfe RS+rb+rp+(1+hfe)RE hfe = icsh (t) - icsh (t)RE+icsh (t) 3) vn s= 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis 3) Reflecting icsh to vn s. rb B C hfe ip ic ip icsh ? rp RC vn s E RS icsc RE vs (1+hfe)RE R*= RS +rb +RE

  48. R*+rp hfe vn s(t)=vbst(t)-vet(t)+[ibf (t)+ibsh(t)] R*+ icsh (t) 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis 4) Total input noise vs. time, vn s(t). rb B C hfe ip ic ip rp RC vn s E RS vs (1+hfe)RE R*= RS +rb +RE

  49. E RE R*+rp hfe 2 vn s2 =4kTR*+(ibf 2+ibsh2) R*2+ icsh2 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis 5) Power spectral density of the total input noise, vn s2. rb B C hfe ip ic ip rp RC vn s E RS vs (1+hfe)RE R*= RS +rb +RE R*+rp hfe vn s(t)=vbst(t)-vet(t)+[ibf (t)+ibsh(t)] R*+ icsh (t)

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