1 announcements 1. course assistant reception day in the next week: monday instead of sunday
DESCRIPTION
3 5. SOURCES OF ERRORS Fundamentals of low-noise design 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 BJT noise modelTRANSCRIPT
1Announcements
1. Course assistant reception day in the next week: Monday instead of Sunday.
25. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design
5.5. Fundamentals of low-noise design
35. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.2. BJT noise model
rb
icshB
E
CNoiseless
vbt
ibf ibsh
icsh2 = 2 q IC
ibsh2 = 2 q IB
vbt2 = 4 k T rb
ibf 2 Kf IB
f
NB: icf 0
ict 0
5.5.2. BJT noise model
4
igsh2 = 2 q IG
idf 2 Kf ID
f
5.4.3. JFET noise model
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
idt
G
S
D
Noiseless
igsh
idf
NB: idsh 0
idt2 = 4 k T /(3/2 gm)
5
id
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
gmvgs
ro
G Dig
Equivalent small-signal model
igsh idtidf
vgs rgs
6
id
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
1/gm
gmvgs
ro
G Dig
igsh idtidf
vgsvgs rgs
Equivalent small-signal model
75. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
~1/gm
gmvgs
ro
G Dig
igsh idtidf
vgs
Equivalent small-signal model
85. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
idvs
RS
~1/gm
gmvgs
ro
G Dig
1) Total input noise vs. time, vn s(t).
vn s?
A. Total input noise
igsh idtidf
vgs
95. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
vs
RS
~1/gm
id
gmvgs
ro
G D
1) Total input noise vs. time, vn s(t).
A. Total input noise
idtidfvn s? igsh
igsh Rs
vn s(t) vst(t) + igsh(t) RS idf (t) idt(t)](1/gm)
vgs
ig
10
vn s?
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
vs
RS
~1/gm
id
gmvgs
ro
Digsh Rs
idtidf
vn sG
A. Total input noise
1) Total input noise vs. time, vn s(t).
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 4 k T RS + igsh
2RS2
idf 2 idt
2)/gm2
vgs
ig
11
vn s?
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
B. enin noise model
en2 vn s
2 idf
2 idt2)/gm
2
RS = 0
in2
igsh2vn s
2
RS2 RS =
vs
RS
~1/gm
id
gmvgs
ro
Digsh Rs
idtidf
vn s2 4 k T RS + igsh
2RS2
idf 2 idt
2)/gm2
vn s en
in
G
vgs
ig
125. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
G
S
D
en
in
en2 idf
2 idt2)/gm
2
in2 igsh
2
JFET enin 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 M
RS = 1 M
in RS = 1.8 nV/Hz0.5
f >> ff
rb = 100
IC = 1 mA
hfe = 100
en 1.36 nV/Hz0.5
in 1.8 pA/Hz0.5
en / in 756
RS = 756
in RS = 1.4 nV/Hz0.5
BJT
13
idt2 = 4 k T /(3/2 gm)
idf 2 Kf ID
f
5.5.4. MOSFET noise model
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model
idt
G
S
D
Noiseless
idf
NB: igsh 0
idsh 0
14
id
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model
1/gm
gmvgs
ro
D
vn s(t) vst(t) idf (t) idt(t)](1/gm)
1) Total input noise vs. time, vn s(t).
2) Power spectral density of the total input noise, vn s2( f ).
vn s2 4 k T RS + idf
2 idt2)/gm
2
A. Total input noise
idtidfvn s?
vs
RSvn s
G
15
vn s
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model
B. enin noise model
en2 vn s
2 idf
2 idt2)/gm
2
RS = 0
in2
0vn s2
Rs2 RS =
1/gm
id
gmvgs
ro
D
vn s2 4 k T RS + idf
2 idt2)/gm
2
vs
RSen
in
G
165. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model
G
S
D
en
en2 idf
2 idt2)/gm
2
in 0
MOSFET enin noise model
f >> ff
Vp = 2 V
IDSS = 10 mA
en 1.8 nV/Hz0.5
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 M
RS = 1 M
in RS = 1.8 nV/Hz0.5
JFET
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
ichfe i
ro
rb C
icsh
ibf ibsh
i
vbtvbt
VCC iC
C
C
VBB
vs
RS
vs
RS B
The aim is to analyze the dependence of a transistor en and in
on frequency and the operating point.
18
vs
RS
Ag
1) Transconductance gain
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
r
ichfe i
ro
rbB C
i C
C
ic
vs
is= 1
hfe [1/j2f(C+C)]/[r+1/j2f(C+C)]
RS + rb+ rII[1/j2f(C+C)]
hfe /(RS +rb+r)
1+j2f[(RS + rb)IIr](C+C)
is
A. Total input noise
195. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
r
ichfe i
ro
rb C
icsh
ibf ibsh
i
vbtvbt
C
C
2) Power spectral density of the total input noise, vn s2( f ).
vn s2 4 k T (RS +rb) ibf
2 ibsh
2) (RS+rb)2 icsh2 RS +rb+r
hfe
2
]12f)2[
vs
RS B
vn s
hfe /(RS +rb+r)
1+j2fAg [(RS + rb)IIr](C+C)
205. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
3) en and in of the transistor.
vn s2 4 k T (RS +rb) ibf
2 ibsh
2) (RS+rb)2 icsh2 RS +rb+r
hfe
2
]12f)2[
en2 vn s
2 4 k T rb ibf
2 ibsh
2) rb2
RS = 0
in2 vn s
2
RS2 RS =
icsh2 rb+r
hfe
2
]12fen)2[
ibf 2
ibsh2 ]12fin)2[icsh
2
hfe2
en(rbIIr)(C+C)
inr(C+C)
215. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
r
ichfe i
ro
rb C
i C
C
vs
RS B
en2 4 k T rb ibf
2 ibsh
2) rb2
in2
icsh2 rb+r
hfe
2
]12fen)2[
ibf 2
ibsh2 ]12fin)2[icsh
2
hfe2
en
in
B. enin noise model for high-frequencies
22
IC opt = 24 mA
IC = 0.1 mA
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
en( f )
nV/Hz0.5
Ag
Ag max
dB
101 103 105 108100 102 104 106 109107
-40
-20
0101 103 105 108100 102 104 106 109107
2
4
1
3
5
f, Hz
C. en( f ) for different IC
rb100
hfe100
C1 pF
C(1 mA)100 pF
en2 4 k T rb ibf
2 ibsh
2) rb2 icsh
2 rb+r
hfe
2
]12fen)2[
235. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
D. in( f ) for different IC
IC opt = 24 mA
IC = 0.1 mAin( f )
pA/Hz0.5
Ag
Ag max
dB
101 103 105 108100 102 104 106 109107
-40
-20
0101 103 105 108100 102 104 106 109107
2
6
0
4
8
f, Hz
rb100
hfe100
C1 pF
C(1 mA)100 pF
in2 ibf
2 ibsh
2 ]12fin)2[icsh2
hfe2
245. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
E. Noise simulation in PSPICE
V11Vac0Vdc
V510Vdc
0
Out1
0
R2
5k
0
V20.628Vdc
R1
100
Q7
2N2222A/ZTX
Frequency
1.0Hz 10KHz 100MHz 1.0THz0
10
20
30
V(ONOISE)*1G/10V(Out1)/V(V1:+)/10V(INOISE)*1G
255. 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
rb40
hfe500
ro
IC 1 mA
IDSS2 mA
Vp2 V
ro
ID 1 mA
vn s2 4 k T RS + igsh
2RS2
idf 2 idt
2)/gm2
vn s2 4 k T (rb RS) ibf
2 ibsh
2)(RS rb)2 icsh2 RS+rb+r
hfe
2
vn s2 4 k T RS + idf
2 idt2)/gm
2
265. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.6. Comparison of the BJT, JFET and MOSFET
1
5
100
102 103 104 105
RS,
vn s
nV/Hz0.5
Power spectral density of
the total input noise vn s
as a function of RS
IC opt
The 1/f noise is neglected.
The JFET gate currentis neglected.
275. 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
1 10 100 1 k 10 k 100 k 1 M 10 M 100 M 1 G 10 G 100 G
MOSFET
Transformer coupling
IC amplifiers
BJT
Source resistance, RS
JFET
285. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
Frequency
1.0Hz 10KHz 100MHz 1.0THzV(INOISE)*1G V(Out11)/V(V11:+) V(ONOISE)*1G/20
0
10
20
30
40
Example: Comparison of an BJT and JFET in PSPICE
Frequency
1.0Hz 10KHz 100MHz 1.0THzV(INOISE)*1G V(Out1)/V(V1:+)/10 V(ONOISE)*1G/40
0
10
20
30
40
RS = 10 kRS = 100
Frequency
1.0Hz 10KHz 100MHz 1.0THzV(INOISE)*1G V(Out1)/V(V1:+)/10 V(ONOISE)*1G/40
0
10
20
30
40
V11Vac0Vdc
V510Vdc
0
Out1
0
R2
5k
0
V20.628Vdc
R1
100
Q7
2N2222A/ZTX
Frequency
1.0Hz 10KHz 100MHz 1.0THzV(INOISE)*1G V(Out11)/V(V11:+) V(ONOISE)*1G/20
0
10
20
30
40
V121.75Vdc
0
Out11
V111Vac0Vdc
R12
5k
V1510Vdc
J1
FN4393
00
R11
10k
29
5.5.7 Noise analysis of a CE amplifier
RS
RC
RE
VCC
VBB
vs
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
r
iohfe i
ro
rb
RE RC
B
E
C
icsh
vs
RS
ibf ibsh
i
vet
vbt
vst
vct
ro
30
Our final aim is to find and minimize the total input noise vn s.
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
r
iohfe i
rb
RE RC
B
E
C
icsh
vs
RS
ibf ibsh
i
vet
vbt
vst
vn s
?vct
Let us first find vn s by applying superposition.
31
As Gs Gs s fwd AOL
1AOL
io
vs
1) Signal gain As for vs, vst, vbt, and vet.
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
r
iohfe i
rb
RE RC
B
E
C
vs
RS
i
As 1
RSrbrRE
hfe
1hfe RE/(RE RSrbr) 0
vet
vbt
vst
32
Abf Gibf Gbf bf fwd AOL
1AOL
io
ibf
2) Noise gain Abf for ibf and ibsh.
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
r
iohfe i
rb
RE RC
B
E
C
vs
RS
ibf ibsh
i
Abf RSrbRE
RSrbRE r
hfe
1hfe RE/(RE RSrbr) 0
33
Acsh Gcsh Gcsh csh fwd AOL
1AOL
io
icsh
r
iohfe i
rb
RE RC
B
E
C
icsh
vs
RS
i
3) Noise gain Acsh for icsh.
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
Acsh RE
RE RSrbr
hfe
1hfe RE/(RE RSrbr) 1
34
Act Gct Gct ct fwd AOL
1AOL
io
ict
4) Noise gain Act for icsh.
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
r
io
hfe i
RE RC
B
E
C
vs
RS
i
vct /RC
rb
Acsh 1
RC
35
5) Total input noise vs. time, vn s.
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
r
iohfe i
RE RC
B
E
C
vs
RS
i
vn s
vn s(t) vst vbt vet
)ibf ibsh( Abf
As
icsh Acsh
As
vct Act
As
rb
vn s2( f ) 4kT RSbE+(ibf
2ibsh2) RSbE
2)RSbEr(2
hfe2
icsh2 4kT
1 RC As
2
0
RSbE RS rbRE
36
r
ichfe i
RC
B Crb
vs
RS
)1+hfe( RE
E
RE
E
6) enin noise model.
en
in
in2 ibf
2 ibsh
2 icsh2
hfe2
en s2
RS2 RS =
en2 en s
2 4 k T RbE ibf
2 ibsh
2) RbE 2 icsh
2 )RbE+r(2
hfe2
RS = 0
i
RbE rb RE
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
37
RSbE2
hfe
IC opt hfeVT
hfe 0.5RSbE
rb = 100
RS = 200
RE = 200
ibf 2 = 0
vbt2 = 4 k T rb
vet2 = 4 k T RE
ibsh2 = 2 q IC /
icsh2 = 2 q IC
7) Minimizing CE noise.
vn s min2 4 k T RSbE
)1 + hfe (0.5
)1 + hfe (0.51
vn s2 4 k T RSbE 2 q IC 2 q IC
RSbE+hfeVT /IC
hfe
2
102-0.5
-0.4
-0.3
-0.2
-0.1
0
103 104
en s
norm.dB
hfe 0.10
0.2
0.4
0.8
1.4
10 10
hfe=104
hfe=102
hfe=103
IC / IC opt
en 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]
38Next lecture
Appendix: Noise analysis of the CE without applications of superposition
Reference: [7]
395. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
Noise analysis of a CE amplifier
r
ichfe i
ro
rb
RE
RC
B
E
C
icsh
vn s
?
vs
RS
ibf ibsh
i
vet
vbst
RS
RC
RE
VCC
VBB
vs
40
r
iichfe i
ro
rb
RE
RC
B
E
C
icsh
vn s
?
vs
RS
vet
vbst
1) Disconnecting ibf and ibsh sources.
ibf ibsh
ibf ibsh
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
41
ibf ibsh
ibf ibsh
r
iichfe i
ro RC
C
icsh
RE
E
rbB
vn s
vs
RS
?
vetvne = vet (ibf + ibsh) RE
1) Disconnecting ibf and ibsh sources.
vbst
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
42
r
ichfe i
ro
rb
RE
RC
B
E
C
icsh
vet
vn s
?
vs
RS
ibf ibsh
vne = vet (ibf + ibsh) RE
1) Disconnecting ibf and ibsh sources.
i
ivbstvbst (ibf ibsh) (Rs rb)
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
43
r
ichfe i
ro
rb
RE
RC
B Cro
icsh
vet
E
vn s
?
vs
RS
vne = vet (ibf + ibsh) RE
2) Disconnecting ibf and ibsh sources.
vbst (ibf ibsh) (Rs rb)
i
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
44
r
ichfe i
rb
RC
B C
RE
icsh
vet
E
vn s
?
vs
RS
vne = vet (ibf + ibsh) RE
2) Disconnecting ibf and ibsh sources.
vbst (ibf ibsh) (Rs rb)
i
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
45
vet
r
ichfe i
rb
RC
B C
RE )1+hfe( RE
icsh
E
vn s
?
vs
RS
vne = vet (ibf + ibsh) RE
2) Disconnecting ibf and ibsh sources.
vbst (ibf ibsh) (Rs rb)
vne = vet (ibf + ibsh) RE + icsh RE
i
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
46
r
ichfe i
rb
RC
B C
icsh
vne = vet (ibf + ibsh) RE + icsh RE
E
)1+hfe( RE
vn s
?
vn s(t) ic(t)
RS+rb+r+(1+hfe)RE
hfe
vs
RS
3) Reflecting ibf and ibsh to vn s.
vbst (ibf ibsh) (Rs rb)
vn s(t) vbst(t) vet(t) ibf (t) ibsh(t)] R* ?
i
R* RS rb RE
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
47
2( ic hfe
RS+rb+r+(1+hfe)RE
icsh (t)icsh (t) RE
r
ic
rb
RC
B C
icsh
)1+hfe( RE
icsc RE
E
vn s
?
vs
RS
hfe i
1( vn s ic(t),
RS+rb+r+(1+hfe)RE
hfe
3( vn s icsh (t) RE icsh (t)RS+rb+r+(1+hfe)RE
hfe
icsh (t)R* + r
hfe
3) Reflecting icsh to vn s.
i
R* RS rb RE
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
48
r
ichfe i
rb
RC
B C
)1+hfe( RE
E
vn s
vs
RS
4) Total input noise vs. time, vn s(t).
i
vn s(t) vbst(t) vet(t) ibf (t) ibsh(t)] R* icsh (t)R*+ r
hfe
R* RS rb RE
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
49
r
ichfe i
rb
RC
B C
vn s
vs
RS
vn s(t) vbst(t) vet(t) ibf (t) ibsh(t)] R* icsh (t)R*+ r
hfe
vn s2 4 k T R* ibf
2 ibsh
2) R* 2 icsh2 R*+ r
hfe
2
)1+hfe( RE
E
RE
E
5) Power spectral density of the total input noise, vn s2.
i
R* RS rb RE
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
50Next lecture
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