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

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

3. 3 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.2. BJT noise model rbrb i csh B E C Noiseless v bt i bf i bsh i csh 2 = 2 q I C i bsh 2 = 2 q I B v bt 2 = 4 k T r b i bf 2  K f I B f NB: i cf   0 i ct   0 5.5.2. BJT noise model

4. 4 i gsh 2 = 2 q I G i df 2  K f I D f 5.4.3. JFET noise model 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model i dt G S D Noiseless i gsh i df NB: i dsh   0 i dt 2 = 4 k T /(3/2 g m )

5. 5 idid 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model g m v gs roro GD igig Equivalent small-signal model i gsh i dt i df v gs r gs

6. 6 idid 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model 1/g m g m v gs roro GD igig i gsh i dt i df v gs r gs Equivalent small-signal model

7. 7 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model ~1/g m g m v gs roro GD igig i gsh i dt i df v gs Equivalent small-signal model

8. 8 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model idid vsvs RSRS ~1/g m g m v gs roro GD igig 1) Total input noise vs. time, v n s (t). v n s ? A. Total input noise i gsh i dt i df v gs

9. 9 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model vsvs RSRS ~1/g m idid g m v gs roro GD 1) Total input noise vs. time, v n s (t). A. Total input noise i dt i df v n s ? i gsh i gsh R s v n s (t)  v st (t) + i gsh (t) R S   i df (t)  i dt (t)](1/g m ) v gs igig

10. 10 v n s ? 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model vsvs RSRS ~1/g m idid g m v gs roro D i gsh R s i dt i df v n s G A. Total input noise 1) Total input noise vs. time, v n s (t). v n s (t)  v st (t) + i gsh (t) R S   i df (t)  i dt (t)](1/g m ) 2) Power spectral density of the total input noise, v n s 2 ( f ). v n s 2  4 k T R S + i gsh 2 R S 2   i df 2  i dt 2 )/g m 2 v gs igig

11. 11 v n s ? 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model B. e n  i n noise model e n 2  v n s 2  i df 2  i dt 2 )/g m 2 R S = 0 i n 2   i gsh 2 v n s 2 R S 2 R S =  vsvs RSRS ~1/g m idid g m v gs roro D i gsh R s i dt i df v n s 2  4 k T R S + i gsh 2 R S 2   i df 2  i dt 2 )/g m 2 v n s enen inin G v gs igig

12. 12 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model G S D enen inin e n 2  i df 2  i dt 2 )/g m 2 i n 2  i gsh 2 JFET e n  i n noise model f >> f f V p = 2 V I DSS = 10 mA I G = 10 pA e n  1.8 nV/Hz 0.5 i n  1.8 fA/Hz 0.5 e n /i n   1 M  R S = 1 M  i n R S = 1.8 nV/Hz 0.5 f >> f f r b = 100  I C = 1 mA h fe = 100 e n  1.36 nV/Hz 0.5 i n  1.8 pA/Hz 0.5 e n / i n   756  R S = 756  i n R S = 1.4 nV/Hz 0.5 BJT

13. 13 i dt 2 = 4 k T /(3/2 g m ) i df 2  K f I D f 5.5.4. MOSFET noise model 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model i dt G S D Noiseless i df NB: i gsh   0 i dsh   0

14. 14 idid 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model 1/g m g m v gs roro D v n s (t)  v st (t)   i df (t)  i dt (t)](1/g m ) 1) Total input noise vs. time, v n s (t). 2) Power spectral density of the total input noise, v n s 2 ( f ). v n s 2  4 k T R S +  i df 2  i dt 2 )/g m 2 A. Total input noise i dt i df v n s ? vsvs RSRS G

15. 15 v n s 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model B. e n  i n noise model e n 2  v n s 2  i df 2  i dt 2 )/g m 2 R S = 0 i n 2   0 v n s 2 R s 2 R S =  1/g m idid g m v gs roro D v n s 2  4 k T R S +  i df 2  i dt 2 )/g m 2 vsvs RSRS enen inin G

16. 16 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model G S D enen e n 2  i df 2  i dt 2 )/g m 2 i n  0 MOSFET e n  i n noise model f >> f f V p = 2 V I DSS = 10 mA e n  1.8 nV/Hz 0.5 f >> f f V p = 2 V I DSS = 10 mA I G = 10 pA e n  1.8 nV/Hz 0.5 i n  1.8 fA/Hz 0.5 e n /i n   1 M  R S = 1 M  i n R S = 1.8 nV/Hz 0.5 JFET

17. 17 5.5.5. Frequency response effect 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect rr icic h fe i  roro rbrb C i csh i bf i bsh ii v bt V CC i C C  C  V BB v s RSRS vsvs RSRS B The aim is to analyze the dependence of a transistor e n and i n on frequency and the operating point.

18. 18 vsvs RSRS Ag Ag  1) Transconductance gain 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect rr icic h fe i  roro rbrb BC ii C  C  icvsicvs  is= 1is= 1 h fe [1/j  2  f  (C  +C  )]/[r  +1/j  2  f  (C  +C  )] R S + r b + r  II [1/j  2  f  (C  +C  )]   h fe /(R S +r b +r  ) 1+j  2  f      [(R S + r b ) II r  ](C  +C  ) isis A. Total input noise

19. 19 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect rr icic h fe i  roro rbrb C i csh i bf i bsh ii v bt C  C  2) Power spectral density of the total input noise, v n s 2 ( f ). v n s 2  4 k T (R S +r b )   i bf 2  i bsh 2 ) (R S +r b ) 2  i csh 2 R S +r b +r  h fe 2 [1    2  f  ) 2 ] vsvs RSRS B v n s h fe /(R S +r b +r  ) 1+j  2  f  A g     [(R S + r b ) II r  ](C  +C  )

20. 20 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect 3) e n and i n of the transistor. v n s 2  4 k T (R S +r b )   i bf 2  i bsh 2 ) (R S +r b ) 2  i csh 2 R S +r b +r  h fe 2 [1    2  f  ) 2 ] e n 2  v n s 2  4 k T r b   i bf 2  i bsh 2 ) r b 2  R S = 0 in2 in2  v n s 2 R S 2 R S =  i csh 2 r b +r  h fe 2 [1    2  f  en ) 2 ]  i bf 2  i bsh 2  [1    2  f  in ) 2 ] i csh 2 h fe 2  en  (r b II r  )(C  +C  )  in  r  (C  +C  )

21. 21 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect rr icic h fe i  roro rbrb C ii C  C  vsvs RSRS B e n 2  4 k T r b   i bf 2  i bsh 2 ) r b 2  in2 in2  i csh 2 r b +r  h fe 2 [1    2  f  en ) 2 ] i bf 2  i bsh 2  [1    2  f  in ) 2 ] i csh 2 h fe 2 enen inin B. e n  i n noise model for high-frequencies

22. 22 I C opt = 24 mA I C = 0.1 mA 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect e n ( f ) nV/Hz 0.5 A g A g max dB  10 1 10 3 10 5 10 8 10 0 10 2 10 4 10 6 10 9 10 7 -40 -20 0 10 1 10 3 10 5 10 8 10 0 10 2 10 4 10 6 10 9 10 7 2 4 1 3 5 f, Hz C. e n ( f ) for different I C r b   100  h fe   100 C   1 pF C  (1 mA)   100 pF r b   100  h fe   100 C   1 pF C  (1 mA)   100 pF e n 2  4 k T r b   i bf 2  i bsh 2 ) r b 2  i csh 2 r b +r  h fe 2 [1    2  f  en ) 2 ]

23. 23 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect D. i n ( f ) for different I C I C opt = 24 mA I C = 0.1 mA i n ( f ) pA/Hz 0.5 A g A g max dB  10 1 10 3 10 5 10 8 10 0 10 2 10 4 10 6 10 9 10 7 -40 -20 0 10 1 10 3 10 5 10 8 10 0 10 2 10 4 10 6 10 9 10 7 2 6 0 4 8 f, Hz r b   100  h fe   100 C   1 pF C  (1 mA)   100 pF r b   100  h fe   100 C   1 pF C  (1 mA)   100 pF in2 in2  i bf 2  i bsh 2  [1    2  f  in ) 2 ] i csh 2 h fe 2

24. 24 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect E. Noise simulation in PSPICE Frequency 1.0Hz10KHz100MHz1.0THz 0 10 20 30 V(ONOISE)*1G/10 V(Out1)/V(V1:+)/10 V(INOISE)*1G

25. 25 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 r b   40  h fe   500 r o   I C  1 mA r b   40  h fe   500 r o   I C  1 mA I DSS   2 mA V p   2 V r o   I D  1 mA v n s 2  4 k T R S + i gsh 2 R S 2   i df 2  i dt 2 )/g m 2 v n s 2  4 k T (r b  R S )   i bf 2  i bsh 2 )(R S  r b ) 2  i csh 2 R S +r b +r  h fe 2 v n s 2  4 k T R S +  i df 2  i dt 2 )/g m 2

26. 26 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.6. Comparison of the BJT, JFET and MOSFET 1 5 100 10 2 10 3 10 4 10 5 R S,  v n s nV/Hz 0.5 Power spectral density of the total input noise v n s as a function of R S I C opt The 1/f noise is neglected. The JFET gate current is neglected.

27. 27 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.6. Comparison of the BJT, JFET and MOSFET Reference: [9] Guide for selection of the preamplifier 1101001 k10 k100 k1 M10 M100 M1 G10 G100 G MOSFET Transformer coupling IC amplifiers BJT Source resistance, R S JFET

28. 28 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 R S = 10 k  R S = 100 

29. 29 5.5.7 Noise analysis of a CE amplifier RSRS R C R E V CC V BB v s 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit rr ioio h fe i  roro rbrb RERE RCRC B E C i csh vsvs RSRS i bf i bsh ii v et v bt v st v ct ro  ro  

30. 30 Our final aim is to find and minimize the total input noise v n s. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit rr ioio h fe i  rbrb RERE RCRC B E C i csh vsvs RSRS i bf i bsh ii v et v bt v st v n s ? v ct Let us first find v n s by applying superposition.

31. 31 A s  G s  G s  s fwd A OL 1  A OL   iovsiovs  1) Signal gain A s for v s, v st, v bt, and v et. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit rr ioio h fe i  rbrb RERE RCRC B E C vsvs RSRS ii A s  1RSrbrRE1RSrbrRE  h fe 1  h fe R E /(R E  R S  r b  r  )  00 v et v bt v st

32. 32 A bf  G ibf  G bf  bf fwd A OL 1  A OL   i o i bf  2) Noise gain A bf for i bf and i bsh. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit rr ioio h fe i  rbrb RERE RCRC B E C vsvs RSRS i bf i bsh ii A bf  R S  r b  R E R S  r b  R E  r   h fe 1  h fe R E /(R E  R S  r b  r  )  00

33. 33 A csh  G csh  G csh  csh fwd A OL 1  A OL   i o i csh  rr ioio h fe i  rbrb RERE RCRC B E C i csh vsvs RSRS ii 3) Noise gain A csh for i csh. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit A csh  R E R E  R S  r b  r    h fe 1  h fe R E /(R E  R S  r b  r  )  11

34. 34 A ct  G ct  G ct  ct fwd A OL 1  A OL   i o i ct  4) Noise gain A ct for i csh. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit rr ioio h fe i  RERE RCRC B E C vsvs RSRS ii v ct /R C rbrb A csh  1RC1RC 

35. 35 5) Total input noise vs. time, v n s. 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit rr ioio h fe i  RERE RCRC B E C vsvs RSRS ii v n s v n s (t)  v st  v bt  v et (i bf  i bsh ) A bf A s   i csh A csh A s   v ct A ct A s   rbrb v n s 2 ( f )  4kT R SbE +(i bf 2  i bsh 2 ) R SbE 2 (R SbE  r  ) 2 h fe 2    i csh 2  4kT 1 R C A s 2   0 0 R SbE   R S  r b  R E

36. 36 rr icic h fe i  RCRC BC rbrb vsvs RSRS (1+h fe ) R E E RERE E 6) e n  i n noise model. enen inin i n 2   i bf 2  i bsh 2  i csh 2 h fe 2 e n s 2 R S 2 R S =  e n 2  e n s 2  4 k T R bE   i bf 2  i bsh 2 ) R bE 2  i csh 2 (R bE +r  ) 2 h fe 2 R S = 0 ii R bE  r b  R E 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit

37. 37 R SbE 2 h fe I C opt  h fe V T    h fe  0.5  R SbE r b = 100 R S = 200 R E = 200 i bf 2 = 0 v bt 2 = 4 k T r b v et 2 = 4 k T R E i bsh 2 = 2 q I C /  i csh 2 = 2 q I C 7) Minimizing CE noise. v n s min 2   4 k T R SbE (1 + h fe ) 0.5 (1 + h fe ) 0.5  1 v n s 2  4 k T R SbE  2 q I C 2 q IC2 q IC R SbE +h fe V T /I C h fe 2 10 2 -0.5 -0.4 -0.3 -0.2 -0.1 0 10 3 10 4 e n s norm. dB h fe 0.1 0 0.2 0.4 0.8 1.4 10 h fe =10 4 h fe =10 2 h fe =10 3 I C / I C opt e n s norm. dB 1.0 0.6 1.2 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit Reference: [7]

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

39. 39 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis Noise analysis of a CE amplifier rr icic h fe i  roro rbrb RERE RCRC B E C i csh v n s ? vsvs RSRS i bf i bsh ii v et v bst RSRS R C R E V CC V BB v s

40. 40 rr ii icic h fe i  roro rbrb RERE RCRC B E C i csh v n s ? vsvs RSRS v et v bst 1) Disconnecting i bf and i bsh sources. i bf i bsh i bf i bsh 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis

41. 41 i bf i bsh i bf i bsh rr ii icic h fe i  roro RCRC C i csh RERE E rbrb B v n s vsvs RSRS ? v et v ne = v et  (i bf + i bsh ) R E 1) Disconnecting i bf and i bsh sources. v bst 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis

42. 42 rr icic h fe i  roro rbrb RERE RCRC B E C i csh v et v n s ? vsvs RSRS i bf i bsh v ne = v et  (i bf + i bsh ) R E 1) Disconnecting i bf and i bsh sources. ii ii v bst v bst  (i bf  i bsh ) (R s  r b ) 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis

43. 43 rr icic h fe i  roro rbrb RERE RCRC BC ro  ro   i csh v et E v n s ? vsvs RSRS v ne = v et  (i bf + i bsh ) R E 2) Disconnecting i bf and i bsh sources. v bst  (i bf  i bsh ) (R s  r b ) ii 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis

44. 44 rr icic h fe i  rbrb RCRC BC RERE i csh v et E v n s ? vsvs RSRS v ne = v et  (i bf + i bsh ) R E 2) Disconnecting i bf and i bsh sources. v bst  (i bf  i bsh ) (R s  r b ) ii 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis

45. 45 v et rr icic h fe i  rbrb RCRC BC RERE (1+h fe ) R E i csh E v n s ? vsvs RSRS v ne = v et  (i bf + i bsh ) R E 2) Disconnecting i bf and i bsh sources. v bst  (i bf  i bsh ) (R s  r b ) v ne = v et  (i bf + i bsh ) R E + i csh R E ii 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis

46. 46 rr icic h fe i  rbrb RCRC BC i csh v ne = v et  (i bf + i bsh ) R E + i csh R E E (1+h fe ) R E v n s ? v n s (t)  i c (t) R S +r b +r  +(1+h fe )R E h fe vsvs RSRS 3) Reflecting i bf and i bsh to v n s. v bst  (i bf  i bsh ) (R s  r b ) v n s (t)  v bst (t)  v et (t)   i bf (t)  i bsh (t)] R *  ? ii R *  R S  r b  R E 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis

47. 47 2) i c  h fe R S +r b +r  +(1+h fe )R E  i csh (t)  i csh (t) R E rr icic rbrb RCRC BC i csh (1+h fe ) R E i csc R E E v n s ? vsvs RSRS h fe i  1) v n s   i c (t), R S +r b +r  +(1+h fe )R E h fe 3) v n s   i csh (t) R E   i csh (t) R S +r b +r  +(1+h fe )R E h fe  i csh (t) R * + r  h fe 3) Reflecting i csh to v n s. ii R *  R S  r b  R E 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis

48. 48 rr icic h fe i  rbrb RCRC BC (1+h fe ) R E E v n s vsvs RSRS 4) Total input noise vs. time, v n s (t). ii v n s (t)  v bst (t)  v et (t)   i bf (t)  i bsh (t)] R *  i csh (t) R * + r  h fe R *  R S  r b  R E 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis

49. 49 rr icic h fe i  rbrb RCRC BC v n s vsvs RSRS v n s (t)  v bst (t)  v et (t)   i bf (t)  i bsh (t)] R *  i csh (t) R * + r  h fe v n s 2  4 k T R *   i bf 2  i bsh 2 ) R * 2  i csh 2 R * + r  h fe 2 (1+h fe ) R E E RERE E 5) Power spectral density of the total input noise, v n s 2. ii R *  R S  r b  R E 5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis

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