1. 5.5. Fundamentals of low-noise design
5. SOURCES OF ERRORS Fundamentals of low-noise design
5.5. Fundamentals of low-noise design
hgygygygo

2. 5.5.1. Junction-diode noise model
5. SOURCES OF ERRORS Fundamentals of low-noise design Junction-diode noise model
Junction-diode noise model ID
1) iD = IF - IS = IS e IS
VD /VT
2) idsh2 = 2 q ( IF + IS )
= 2 q ( ID + 2IS )
 2 q ID rd
idsh ID
3) rd 
k T
q ID
idf
idf rd
4) idsh2 = 2 q ID = 2 k T / rd rd ID
edsh
5) edsh2 = (2 k T / rd ) rd 2 = 2 k T rd
hgygygygo
At low frequencies and ID >> IS ,
idn2 = 2 q ID +
Kf ID f
, K = 2 q ff
Note that dynamic resistances do not generate any noise since them dissipate no power, vd id = 0.

3. 5.5.2. BJT noise model icsh2 = 2 q IC ibsh2 = 2 q IB vbt2 = 4 k T rb
5. SOURCES OF ERRORS Fundamentals of low-noise design BJT noise model
BJT noise model C
Noiseless rb
vbt B
icsh
ibf
ibsh E
icsh2 = 2 q IC
ibsh2 = 2 q IB
vbt2 = 4 k T rb
ibf 2 = 2 q IB +
Kf IB f
, Kf = 2 q ff
hgygygygo

4. vn s(t) = vst(t) + vbt(t) + [ibf (t) + ibsh(t)](RS + rb) + icsh(t)
5. SOURCES OF ERRORS Fundamentals of low-noise design BJT noise model
A. Total input noise vs RS rb
vbt
vbt B ip C
hfe ip ic
icsh
vn s ? rp ro
ibf
ibsh
1) Total input noise vs. time, vn s(t).
vn s(t) = vst(t) + vbt(t) + [ibf (t) + ibsh(t)](RS + rb) +
icsh(t)
RS+rb+rp
hfe
hgygygygo
2) Power spectral density of the total input noise, vn s2( f ).

5. vn s(t) = vst(t) + vbt(t) + [ibf (t) + ibsh(t)](RS + rb) + icsh(t)
5. SOURCES OF ERRORS Fundamentals of low-noise design BJT noise model
A. Total input noise
vn s RS rb
vbt
vbt B ip C
hfe ip ic vs
icsh
vn s ? rp ro
ibf
ibsh
1) Total input noise vs. time, vn s(t).
vn s(t) = vst(t) + vbt(t) + [ibf (t) + ibsh(t)](RS + rb) +
icsh(t)
RS+rb+rp
hfe
hgygygygo
2) Power spectral density of the total input noise, vn s2( f ).
vn s2 = 4 k T (rb + RS) + (ibf 2 + ibsh2)(RS + rb) 2 +
icsh2
RS+rb+rp
hfe 2

6. vn s2 = 4 k T (rb + RS) + (ibf 2 + ibsh2)(RS + rb) 2 + icsh2
5. SOURCES OF ERRORS Fundamentals of low-noise design BJT noise model
B. Optimum collector current
vn s RS rb
vbt B ip C
hfe ip ic rp ro RC
RS+rb+rp
hfe 2
vn s2 = 4 k T (rb + RS) + (ibf 2 + ibsh2)(RS + rb) 2 +
icsh2
hgygygygo
vn s2 = 4 k T (rb + RS) + 2 q IC
rb2
hfe
+ 2 q IC
rb+hfeVT / IC 2
IC opt =
hfeVT
(1 + hfe )0.5 rb2

7. vn s2 = 4 k T (rb + RS) + (ibf 2 + ibsh2)(RS + rb)2 + icsh2
5. SOURCES OF ERRORS Fundamentals of low-noise design BJT noise model
C. vn- in noise model RS en rb B ip C
hfe ip ic vs in rp ro RC
RS+rb+rp
hfe 2
vn s2 = 4 k T (rb + RS) + (ibf 2 + ibsh2)(RS + rb)2 +
icsh2
hgygygygo
en2 = vn s = 4 k T rb + (ibf 2 + ibsh2) rb2 +
icsh2
rb+rp
hfe 2
Rs= 0
in2 = = ibf 2 + ibsh2 +
vn s2
Rs2
Rs= 
icsh2
hfe2

8. vn2 = 4 k T rb + (ibf 2 + ibsh2) rb2 + icsh2
5. SOURCES OF ERRORS Fundamentals of low-noise design BJT noise model
BJT vn- in noise model
f >> ff
rb = 100 W
IC = 1 mA
hfe = 100
vn = 1.36 nV/Hz0.5
in = 1.8 pA/Hz0.5
vn / in = 756 W C vn in B E
hgygygygo
rb+rp
hfe 2
vn2 = 4 k T rb + (ibf 2 + ibsh2) rb2 +
icsh2
icsh2
hfe2
in2 = ibf 2 + ibsh2 +

9. en2 = vn s2 = vbt2 + (ibf 2 + ibsh2) rb2 + icsh2
5. SOURCES OF ERRORS Fundamentals of low-noise design BJT noise model
D. Optimum source resistance RS en rb B ip C
hfe ip ic vs rp ro RC in
rb+rp
hfe 2
en2 = vn s = vbt2 + (ibf 2 + ibsh2) rb2 +
icsh2
Rs= 0
en s2
Rs2
icsh2
hfe2
hgygygygo
Rs= 
in2 = = ibf 2 + ibsh2 +
Rs opt =
vn s in
IC opt
= rb 2  1 +  1+hfe

10. 5.4.3. JFET noise model igsh2 = 2 q IG idt2 = 4 k T (2/3)gm idf 2 =
5. SOURCES OF ERRORS Fundamentals of low-noise design JFET noise model
JFET noise model D
Noiseless G
idf
idt
igsh S
igsh2 = 2 q IG
idt2 = 4 k T (2/3)gm
idf 2 =
Kf ID f
, Kf = 2 q ff
hgygygygo

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

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

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

14. vn s2 = 4 k T RS + igsh2RS2 + (idf 2+ idt2)/gm2
5. SOURCES OF ERRORS Fundamentals of low-noise design JFET noise model
B. vn- in noise model
vn s
gmvgs en in RS
igsh Rs G ig D id vs
vn s ? ro RC
1/gm
idf
idt
vn s2 = 4 k T RS + igsh2RS2 + (idf 2+ idt2)/gm2
en2 = vn s = (idf 2+ idt2)/gm2
Rs= 0
hgygygygo
in2 = = igsh2
vn s2
Rs2
Rs= 

15. vn2 = (idf 2+ idt2)/gm2 in2 = igsh2 JFET vn- in noise model
5. SOURCES OF ERRORS Fundamentals of low-noise design JFET noise model
JFET vn- in noise model
f >> ff
Vp = 2 V
IDSS = 10 mA
IG = 10 pA
vn = 1.8 nV/Hz0.5
in = 1.8 fA/Hz0.5
vn /in = 1 MW
RS = 1 MW
in RS = 1.8 nV/Hz0.5 D vn in G S
hgygygygo
vn2 = (idf 2+ idt2)/gm2
in2 = igsh2

16. 5.5.4. MOSFET noise model idt2 = 4 k T (2/3)gm Kf ID f idf 2 =
5. SOURCES OF ERRORS Fundamentals of low-noise design MOSFET noise model
MOSFET noise model D
Noiseless G
idt
idf S
idt2 = 4 k T (2/3)gm
idf 2 =
Kf ID f
, Kf = 2 q ff
hgygygygo

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

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

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

20. MOSFET vn- in noise model
5. SOURCES OF ERRORS Fundamentals of low-noise design MOSFET noise model
MOSFET vn- in noise model
f >> ff
Vp = 2 V
IDSS = 10 mA
vn = 1.8 nV/Hz0.5 D vn G S
vn2 = (idf 2+ idt2)/gm2
hgygygygo
in = 0

21. 5.5.5. Frequency response effect
5. SOURCES OF ERRORS Fundamentals of low-noise design Frequency response effect
Frequency response effect
The aim is to analyze the dependence of a transistor en and in on frequency and operating point.
VCC iC RS vs
VBB Cm
hgygygygo RS rb
vbt
vbt B C
hfe ip ic vs Cp ip
icsh rp ro
ibf
ibsh

22. ___ iC vs hfe [1/j 2pf (Cp+Cm )]/[rp+1/j 2pf (Cp+Cm )]
5. SOURCES OF ERRORS Fundamentals of low-noise design Frequency response effect
A. Total input noise Cm RS rb B is C
vn s
hfe ip ic vs Cp ip rp ro
1) Transconductance gain, Ag.
hgygygygo iC vs
hfe [1/j 2pf (Cp+Cm )]/[rp+1/j 2pf (Cp+Cm )]
RS + rb+rpII[1/j 2pf (Cp+Cm )]
Ag 
___
= ____________________________________
is= 1
hfe /(RS +rb+rp )
1+j 2pft
= _____________ ,
t = [(RS + rb)IIrp ](Cp+Cm )

23. t = [(RS + rb)IIrp ](Cp+Cm )
5. SOURCES OF ERRORS Fundamentals of low-noise design Frequency response effect Cm RS rb
vbt
vbt B C
hfe ip ic vs Cp ip
icsh
vn s rp ro
ibf
ibsh
hfe /(RS +rb+rp )
1+j 2pft
Ag = _____________ ,
t = [(RS + rb)IIrp ](Cp+Cm )
2) Power spectral density of the total input noise, vn s2( f ).
hgygygygo
RS +rb+rp
hfe 2
vn s2 = 4 k T (RS +rb) + (ibf 2 + ibsh2) rb2 +
icsh2
[1+ (2pft)2]

24. vn s2 = 4 k T (RS +rb) + (ibf 2 + ibsh2) (RS+rb)2 + icsh2 [1+ (2pft)2]
5. SOURCES OF ERRORS Fundamentals of low-noise design Frequency response effect
RS +rb+rp
hfe 2
vn s2 = 4 k T (RS +rb) + (ibf 2 + ibsh2) (RS+rb)2 +
icsh2
[1+ (2pft)2]
3) en and in of the transistor.
rb+rp
hfe 2
en2 = vn s = 4 k T rb + (ibf 2 + ibsh2) rb2 +
icsh2
[1+ (2pften)2]
Rs= 0
ten = (rbIIrp )(Cp+Cm )
hgygygygo
vn s2
Rs2
icsh2
hfe2
Rs= 
in2 =
= ibf 2 + ibsh2 +
[1+ (2pftin)2]
tin = rp (Cp+Cm )

25. en2 = vn s2 = 4 k T rb+ (ibf 2 + ibsh2) rb2 + icsh2 [1+ (2pften)2]
5. SOURCES OF ERRORS Fundamentals of low-noise design Frequency response effect
B. vn- in noise model for high-frequencies Cm RS en in rb B C
hfe ip ic vs Cp ip
vn s rp ro
rb+rp
hfe 2
en2 = vn s = 4 k T rb+ (ibf 2 + ibsh2) rb2 +
icsh2
[1+ (2pften)2]
Rs= 0
hgygygygo
vn s2
Rs2
icsh2
hfe2
Rs= 
in2 =
= ibf 2 + ibsh2 +
[1+ (2pftin)2]

26. ____ rb+rp hfe 2 en2 = vn s2 = 4 k T rb+ (ibf 2 + ibsh2) rb2 + icsh2
5. SOURCES OF ERRORS Fundamentals of low-noise design Frequency response effect
C. en( f ) for different IC
rb+rp
hfe 2
en2 = vn s = 4 k T rb+ (ibf 2 + ibsh2) rb2 +
icsh2
[1+ (2pften)2]
Rs= 0
101
103
105
108
100
102
104
106
109
107
-40
-20 2 4 1 3 5
f, Hz
IC opt = 24 mA
IC = 0.1 mA
en( f )
nV/Hz0.5
hgygygygo
rb = 100 W
hfe = 100
Cm = 1 pF
Cp (1 mA) = 100 pF Ag
Ag max dB
____

27. ____ vn s2 icsh2 Rs2 hfe2 in2 = = ibf 2 + ibsh2 + [1+ (2pftin)2]
5. SOURCES OF ERRORS Fundamentals of low-noise design Frequency response effect
D. in( f ) for different IC
vn s2
Rs2
icsh2
hfe2
Rs= 
in2 =
= ibf 2 + ibsh2 +
[1+ (2pftin)2] 2 6 4 8
IC opt = 24 mA
IC = 0.1 mA
in( f )
pA/Hz0.5
hgygygygo
100
101
102
103
104
105
106
107
108
109
-40
-20
rb = 100 W
hfe = 100
Cm = 1 pF
Cp (1 mA) = 100 pF Ag
Ag max dB
____
100
101
102
103
104
105
106
107
108
109
f, Hz

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

29. 5.5.6. Comparison of the BJT, JFET and MOSFET
5. SOURCES OF ERRORS Fundamentals of low-noise design Comparison of the BJT, JFET and MOSFET
Comparison of the BJT, JFET and MOSFET
rb = 40 W
hfe = 500
ro = 
IC = 1 mA
IDSS = 2 mA
Vp = 2 V
ID = 1 mA
vn s2 = 4 k T RS + igsh2RS2 + (idf 2+ idt2)/gm2
vn s2 = 4 k T (rb + RS) + (ibf 2 + ibsh2)(RS + rb)2 +
icsh2
RS+rb+rp
hfe 2
vn s2 = 4 k T RS + (idf 2+ idt2)/gm2
hgygygygo

30. Power spectral density of the total input noise vn s2
5. SOURCES OF ERRORS Fundamentals of low-noise design Comparison of the BJT, JFET and MOSFET
100
Power spectral density of the total input noise vn s2
as a function of RS
IC opt
vn s
nV/Hz0.5 5
The 1/f noise is
neglected.
hgygygygo
The JFET gate current
is neglected. 1
102
103
104
105
RS, W

31. Guide for selection of the preamplifier
5. SOURCES OF ERRORS Fundamentals of low-noise design Comparison of the BJT, JFET and MOSFET
MOSFET
Guide for selection of the preamplifier
JFET IC
amplifiers
BJT
Transformer
coupling
hgygygygo 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]

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

33. 5.5.7 Noise analysis of a CE amplifier
5. SOURCES OF ERRORS Fundamentals of low-noise design Example circuit
5.5.7 Noise analysis of a CE amplifier
VCC RC RS vs RE
VBB rp io
hfe ip ro rb RE RC B E C
icsh vs RS
ibf
ibsh ip
vet
vbt
vst
ro  
hgygygygo

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

35. 1+hfe RE/(RE +RS+rb+rp)
5. SOURCES OF ERRORS Fundamentals of low-noise design Example circuit
1) Signal gain As for vs, vst, vbt, and vet. rb
vbt B C
hfe ip ip io rp
vst RS E
vet vs RE RC
hgygygygo
As  = Gs Gs bs fwd
AOL
1+AOLb
_______ io vs
___
As = 1
RS+rb+rp+RE
___________
hfe
1+hfe RE/(RE +RS+rb+rp)
____________________
+ 0

36. 1+hfe RE/(RE +RS+rb+rp)
5. SOURCES OF ERRORS Fundamentals of low-noise design Example circuit
2) Noise gain Abf for ibf and ibsh. rb B C
hfe ip ip io rp
ibf
ibsh RS E vs RE RC
hgygygygo
Abf  = Gibf Gbf bbf fwd
AOL
1+AOLb
_______ io
ibf
___
Abf =
RS+rb+RE
RS+rb+RE +rp
___________
hfe
1+hfe RE/(RE +RS+rb+rp)
____________________
+ 0

37. 1+hfe RE/(RE +RS+rb+rp)
5. SOURCES OF ERRORS Fundamentals of low-noise design Example circuit
3) Noise gain Acsh for icsh. rb B C
hfe ip ip io
icsh rp RS E vs RE RC
hgygygygo
Acsh  = Gcsh Gcsh bcsh fwd
AOL
1+AOLb
_______ io
icsh
___
Acsh = RE
RE +RS+rb+rp
- ___________
hfe
1+hfe RE/(RE +RS+rb+rp)
____________________
+ 1

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

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

40. en2 = en s2 = 4 k T RbE + (ibf 2 + ibsh2) RbE 2 + icsh2 (RbE+rp)2 hfe2
5. SOURCES OF ERRORS Fundamentals of low-noise design. Appendix: conventional noise analysis
6) Vn- In noise model. vn in rb B C
hfe ip ic ip rp RC RE E RS E vs
(1+hfe) RE
RbE = rb + RE
hgygygygo
en2 = en s2 = 4 k T RbE + (ibf 2 + ibsh2) RbE 2 +
icsh2
(RbE+rp)2
hfe2
Rs= 0
in2 = = ibf 2 + ibsh2 +
icsh2
hfe2
en s2
Rs2
Rs= 

41. RSbE2 hfe RSbE +hfeVT / IC hfe 2 vn s2 = 4 k T RSbE + 2 q IC + 2 q IC
5. SOURCES OF ERRORS Fundamentals of low-noise design. Appendix: conventional noise analysis
7) Minimizing CE noise.
102
-0.5
-0.4
-0.3
-0.2
-0.1
103
104
en s
norm. dB
hfe
0.1
0.2
0.4
0.8
1.4 10
hfe=104
hfe=102
hfe=103
IC / IC opt
en s
norm. dB
1.0
0.6
1.2
rb = 100
RS = 200
RE = 200
ibf 2 = 0
vbt2 = 4 k T rb
vet2 = 4 k T RE
ibsh2 = 2 q IC /b icsh2 = 2 q IC
RSbE2
hfe
RSbE +hfeVT / IC
hfe 2
vn s2 = 4 k T RSbE + 2 q IC
+ 2 q IC
hgygygygo
IC opt =
hfeVT
(1 + hfe )0.5 R*2
vn s min2 = 4 k T RSbE
(1 + hfe )0.5
(1 + hfe )0.5-1

42. Next lecture
Appendix: Noise analysis of the CE without applications of superposition

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

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

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

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

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

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

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

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

51. R* = RS + rb + RE 1) vn s = - ic(t) , RS+rb+rp+(1+hfe)RE hfe 2) ic =
5. SOURCES OF ERRORS 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 RS E
icsc RE vs
(1+hfe) RE
R* = RS + rb + RE
hgygygygo
1) vn s =
- ic(t) ,
RS+rb+rp+(1+hfe)RE
hfe
2) ic =
hfe
RS+rb+rp+(1+hfe)RE
+ icsh (t)
- icsh (t) RE
3) vn s =
- icsh (t) RE + icsh (t)
RS+rb+rp+(1+hfe)RE
hfe
= icsh (t)
R* + rp
hfe

52. vn s(t) = vbst(t) - vet(t) + [ibf (t) + ibsh(t)] R* + icsh (t) R*+ rp
5. SOURCES OF ERRORS 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 RS E vs
(1+hfe) RE
R* = RS + rb + RE
hgygygygo
vn s(t) = vbst(t) - vet(t) + [ibf (t) + ibsh(t)] R* +
icsh (t)
R*+ rp
hfe

53. vn s(t) = vbst(t) - vet(t) + [ibf (t) + ibsh(t)] R* + icsh (t)
5. SOURCES OF ERRORS 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 RE E RS E vs
(1+hfe) RE
R* = RS + rb + RE
hgygygygo
R*+ rp
hfe
vn s(t) = vbst(t) - vet(t) + [ibf (t) + ibsh(t)] R* +
icsh (t)
vn s2 = 4 k T R* + (ibf 2 + ibsh2) R* 2 +
icsh2
R*+ rp
hfe 2

54. Next lecture
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