#### Transcript Measurement Theory Principles

```5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design
5.5. Fundamentals of low-noise design
1
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.1. Junction-diode noise model
5.5.1. Junction-diode noise model
2
ID
1) iD = IF - IS = IS eVD /VT - IS
2) idsh2 = 2 q ( IF + IS ) = 2 q ( ID + 2IS )  2 q ID
ID
kT
3) rd 
q ID
idsh
rd
4) idsh2 = 2 q ID = 2 k T / rd
5) edsh2 = (2 k T / rd ) rd 2 = 2 k T rd
ID
At low frequencies and ID >> IS ,
idn
2
Kf ID
= 2 q ID +
, K = 2 q ff
f
Note that dynamic resistances do not generate
any noise since them dissipate no power, vd id = 0.
rd
edsh
idf rd
idf
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.2. BJT noise model
3
5.5.2. BJT noise model
C
Noiseless
rb
B
vbt
icsh
ibf
ibsh
E
vbt2 = 4 k T rb
icsh2 = 2 q IC
ibsh2 = 2 q IB
ibf
2
Kf IB
= 2 q IB +
, Kf = 2 q ff
f
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.2. BJT noise model
4
A. Total input noise
RS
B
rb
vbt
ip
vs
? vn s
C
hfe ip
rp
ibf
ro
ic
icsh
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
2) Power spectral density of the total input noise, vn s2( f ).
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.2. BJT noise model
5
A. Total input noise
RS
vn s
B
rb
vbt
ip
vs
? vn s
C
hfe ip
rp
ibf
ro
ic
icsh
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
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
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.2. BJT noise model
6
B. Optimum collector current
RS
vn s
B
rb
vbt
ip
C
hfe ip
rp
ic
ro
vn s2 = 4 k T (rb + RS) + (ibf 2 + ibsh2)(RS + rb) 2 +icsh2
2
vn s2
RC
RS+rb+rp
hfe
rb
rb+hfeVT / IC
= 4 k T (rb + RS) + 2 q IC
+ 2 q IC
hfe
hfe
IC opt =
hfeVT
(1 + hfe )0.5 rb2
2
2
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.2. BJT noise model
7
C. vn- in noise model
RS
B
vs
en
in
rb
ip
C
hfe ip
rp
ic
ro
RC
vn s2 = 4 k T (rb + RS) + (ibf 2 + ibsh2)(RS + rb)2 + icsh2
en2 = vn s2
= 4 k T rb + (ibf 2 + ibsh2) rb2 +icsh2
Rs= 0
2
v
n
s
in2 =
Rs2
icsh2
= ibf 2 + ibsh2 + 2
hfe
Rs= 
RS+rb+rp
hfe
rb+rp
hfe
2
2
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.2. BJT noise model
8
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
B
vn
in
E
vn2 = 4 k T rb + (ibf 2 + ibsh2) rb2 +icsh2
icsh2
in2 = ibf 2 + ibsh2 + 2
hfe
rb+rp
hfe
2
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.2. BJT noise model
9
D. Optimum source resistance
RS
rb
en
B
vs
C
hfe ip
rp
in
en2 = vn s2
ip
= vbt2 + (ibf 2 + ibsh2) rb2 + icsh2
Rs= 0
2
e
n
s
in2 =
Rs2
ic
ro
rb+rp
hfe
icsh2
= ibf 2 + ibsh2 + 2
hfe
Rs= 
Rs opt
=
IC opt
vn s
= rb 2  1 +  1+hfe
in
RC
2
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
10
5.4.3. JFET noise model
D
Noiseless
G
idf
igsh
idt
S
igsh2 = 2 q IG
idt2 = 4 k T (2/3)gm
idf
2
Kf ID
=
, Kf = 2 q ff
f
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
11
A. Total input noise
RS
gmvgs
ig
G
D
id
vs
? vn s
igsh
1/gm
1) Total input noise vs. time, vn s(t).
ro
idf
idt
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
12
A. Total input noise
RS
G
igsh Rs
gmvgs
ig
D
id
vs
? vn s
igsh
1/gm
ro
idf
idt
1) Total input noise vs. time, vn s(t).
vn s(t) = vst + igsh(t) RS + [idf (t) + idt(t)]/gm
2) Power spectral density of the total input noise, vn s2( f ).
vn s2 = 4 k T RS + igsh2RS2 + (idf 2+ idt2)/gm2
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
13
A. Total input noise
RS
vn s
G
igsh Rs
gmvgs
ig
D
id
vs
? vn s
1/gm
ro
idf
idt
1) Total input noise vs. time, vn s(t).
vn s(t) = vst + igsh(t) RS + [idf (t) + idt(t)]/gm
2) Power spectral density of the total input noise, vn s2( f ).
vn s2 = 4 k T RS + igsh2RS2 + (idf 2+ idt2)/gm2
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
14
B. vn- in noise model
RS
vn s
G
igshe Rs
n
gmvgs
ig
D
id
vs
? vn s
ro
1/gm
in
idf
idt
vn s2 = 4 k T RS + igsh2RS2 + (idf 2+ idt2)/gm2
en2 = vn s2
= (idf 2+ idt2)/gm2
Rs= 0
2
v
n
s
in2 =
Rs2
= igsh2
Rs= 
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.3. JFET noise model
15
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
G
vn
in
S
vn2 = (idf 2+ idt2)/gm2
in2 = igsh2
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
idt2 = 4 k T (2/3)gm
idf
2
Kf ID
=
, Kf = 2 q ff
f
16
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model
17
A. Total input noise
RS
gmvgs
G
D
id
vs
? vn s
1/gm
ro
idf
idt
1) Total input noise vs. time, vn s(t).
vn s(t) = vst(t) + [idf (t) + idt(t)]/gm
2) Power spectral density of the total input noise, vn s2( f ).
vn s2 = 4 k T RS + (idf 2+ idt2)/gm2
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model
18
A. Total input noise
RS
vn s
gmvgs
G
D
id
vs
? vn s
1/gm
ro
idf
idt
1) Total input noise vs. time, vn s(t).
vn s(t) = vst(t) + [idf (t) + idt(t)]/gm
2) Power spectral density of the total input noise, vn s2( f ).
vn s2 = 4 k T RS + (idf 2+ idt2)/gm2
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model
19
B. vn- in noise model
RS
vn s
G
gmvgs
en
D
id
vs
in
ro
1/gm
vn s2 = 4 k T RS + (idf 2 + idt2)/gm2
en2 = vn s2
= (idf 2+ idt2)/gm2
Rs= 0
2
v
n
s
in2 =
Rs2
=0
Rs= 
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.4. MOSFET noise model
MOSFET vn- in noise model
f >> ff
Vp = 2 V
IDSS = 10 mA
vn = 1.8 nV/Hz0.5
D
G
vn
S
vn2 = (idf 2+ idt2)/gm2
in = 0
20
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
21
5.5.5. Frequency response effect
The aim is to analyze the dependence of a transistor en and in
on frequency and operating point.
iC
VCC
RS
vs
VBB
Cm
RS
B
rb
vbt
C
vs
Cp
ibf
ibsh
ip
hfe ip
rp
ro
icsh
ic
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
22
A. Total input noise
Cm
RS
vs
B
rb
is
C
Cp
vn s
ip
hfe ip
rp
ic
ro
1) Transconductance gain, Ag.
iC
___
Ag 
vs
is= 1
hfe [1/j 2pf (Cp+Cm )]/[rp+1/j 2pf (Cp+Cm )]
____________________________________
=
RS + rb+rpII[1/j 2pf (Cp+Cm )]
hfe /(RS +rb+rp )
_____________
=
, t = [(RS + rb)IIrp ](Cp+Cm )
1+j 2pft
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
23
Cm
RS
B
rb
vbt
C
vs
Cp
vn s
ibf
ip
hfe ip
rp
ro
ic
icsh
ibsh
hfe /(RS +rb+rp )
_____________
Ag =
, t = [(RS + rb)IIrp ](Cp+Cm )
1+j 2pft
2) Power spectral density of the total input noise, vn s2( f ).
2
vn s2 = 4 k T (RS +rb) + (ibf 2 + ibsh2) rb2 +icsh2
RS +rb+rp
[1+ (2pft)2]
hfe
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
24
2
vn s2 = 4 k T (RS +rb) + (ibf 2 + ibsh2) (RS+rb)2 +icsh2
RS +rb+rp
[1+ (2pft)2]
hfe
3) en and in of the transistor.
2
en2 = vn s2
= 4 k T rb + (ibf 2 + ibsh2) rb2 +icsh2
Rs= 0
rb+rp
[1+ (2pften)2]
hfe
ten = (rbIIrp )(Cp+Cm )
2
v
n
s
in2 =
Rs2
2
i
csh
2]
= ibf 2 + ibsh2 +
[1+
(2pf
t
)
in
hfe2
R =
s
tin = rp (Cp+Cm )
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
25
B. vn- in noise model for high-frequencies
Cm
RS
en
B
vs
rb
C
Cp
in
vn s
ip
hfe ip
ic
rp
ro
2
en2 = vn s2
= 4 k T rb+ (ibf 2 + ibsh2) rb2 +icsh2
Rs= 0
2
v
n
s
in2 =
Rs2
rb+rp
[1+ (2pften)2]
hfe
2
i
csh
= ibf 2 + ibsh2 +
[1+ (2pftin)2]
2
hfe
R =
s
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
26
C. en( f ) for different IC
2
en2 = vn s2
= 4 k T rb+ (ibf 2 + ibsh2) rb2 +icsh2
Rs= 0
rb+rp
[1+ (2pften)2]
hfe
5
IC opt = 24 mA
4
IC = 0.1 mA
en( f )
nV/Hz0.5
3
2
1
100
0
Ag
____
Ag max
101
102
103
104
105
106
107
108
109
rb = 100 W
hfe = 100
Cm = 1 pF
Cp (1 mA) = 100 pF
-20
dB
-40
100
101
102
103
104
105
f, Hz
106
107
108
109
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
27
D. in( f ) for different IC
2
v
n
s
in2 =
Rs2
2
i
csh
2]
= ibf 2 + ibsh2 +
[1+
(2pf
t
)
in
hfe2
R =
s
8
IC opt = 24 mA
6
IC = 0.1 mA
in ( f )
pA/Hz0.5
4
2
0
100
0
Ag
____
Ag max
101
102
103
104
105
106
107
108
109
rb = 100 W
hfe = 100
Cm = 1 pF
Cp (1 mA) = 100 pF
-20
dB
-40
100
101
102
103
104
105
f, Hz
106
107
108
109
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
E. Noise simulation in PSPICE
R2
Out1
30
5k
R1
Q7
2N2 222A/ZTX
V1
100
20
V5
10V dc
1Va c
0Vd c
0.628Vdc
10
V2
0
0
0
0
1.0Hz
10KHz
100MHz
1.0THz
V(INOISE)*1G V(Out1)/V(V1:+)/10 V(ONOISE)*1G/10
Frequency
28
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.6. Comparison of the BJT, JFET and MOSFET
29
5.5.6. Comparison of the BJT, JFET and MOSFET
rb = 40 W
hfe = 500
ro = 
IC = 1 mA
IDSS = 2 mA
Vp = 2 V
ro = 
ID = 1 mA
vn s2 = 4 k T (rb + RS) + (ibf 2 + ibsh2)(RS + rb)2 + icsh2
vn s2 = 4 k T RS + igsh2RS2 + (idf 2+ idt2)/gm2
vn s2 = 4 k T RS + (idf 2+ idt2)/gm2
RS+rb+rp
hfe
2
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.6. Comparison of the BJT, JFET and MOSFET
30
100
Power spectral density of
the total input noise vn s2
as a function of RS
vn s
nV/Hz0.5
5
The 1/f noise is
neglected.
IC opt
The JFET gate current
is neglected.
1
102
103
104
RS, W
105
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.6. Comparison of the BJT, JFET and MOSFET
31
Guide for selection of the preamplifier
MOSFET
JFET
IC
amplifiers
BJT
Transformer
coupling
1
10
100
1k
10 k
100 k
1M
10 M
100 M
1G
10 G
100 G
Source resistance, RS
Reference: [9]
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.5. Frequency response effect
32
Example: Comparison of an BJT and JFET in PSPICE
Rs = 100 W
R2
Out1
Rs = 10 kW
40
40
30
30
20
20
10
10
5k
Q7
R1
2N2 222A/ZTX
V1
100
V5
10V dc
1Va c
0Vd c
0.628Vdc
V2
0
0
0
R12
Out11
0
1.0Hz
V(INOISE)*1G
10KHz
100MHz
1.0THz
V(Out1)/V(V1:+)/10
V(ONOISE)*1G/40
Frequency
0
1.0Hz
V(INOISE)*1G
10KHz
100MHz
1.0THz
V(Out1)/V(V1:+)/10
V(ONOISE)*1G/40
Frequency
40
40
30
30
20
20
10
10
0
1.0Hz
10KHz
100MHz
1.0THz
V(INOISE)*1G
V(Out11)/V(V11:+)
V(ONOISE)*1G/20
Frequency
0
1.0Hz
10KHz
100MHz
1.0THz
V(INOISE)*1G
V(Out11)/V(V11:+)
V(ONOISE)*1G/20
Frequency
5k
R11
V11
10k
J1
V15
10V dc
FN4 393
1Va c
0Vd c
1.75Vdc
V12
0
0
0
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
33
5.5.7 Noise analysis of a CE amplifier
VCC
RC
RS
vs
RE
VBB
B
rb
ro  
vbt
hfe ip
ip
rp
vst
RS
vs
ibf
ro
C
icsh
io
ibsh
E
vet
vet
RE
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
34
Our final aim is to find and minimize the total input noise vn s.
rb
B
vbt
C
hfe ip
ip
rp
vst
ibf
io
ibsh
E
RS
vs
icsh
?
vn s
vet
vet
RE
RC
Let us first find vn s by applying superposition.
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
35
1) Signal gain As for vs, vst, vbt, and vet.
B
rb
vbt
C
hfe ip
ip
vst
RS
vs
io
rp
E
vet
RE
io
AOL
___
_______
As 
= Gs
+ Gs bs fwd
vs
1+AOLb
hfe
1
____________________
___________
As =
+0
RS+rb+rp+RE 1+hfe RE/(RE +RS+rb+rp)
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
36
2) Noise gain Abf for ibf and ibsh.
B
rb
C
hfe ip
ip
io
rp
ibf
RS
ibsh
E
vs
RE
io
AOL
___
_______
Abf 
= Gibf
+ Gbf bbf fwd
ibf
1+AOLb
RS+rb+RE ____________________
hfe
___________
Abf =
+0
RS+rb+RE +rp 1+hfe RE/(RE +RS+rb+rp)
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
37
3) Noise gain Acsh for icsh.
B
rb
C
hfe ip
ip
rp
RS
icsh
io
E
vs
RE
io
AOL
___
_______
Acsh 
= Gcsh
+ Gcsh bcsh fwd
icsh
1+AOLb
hfe
RE
____________________
___________
Acsh = +1
RE +RS+rb+rp 1+hfe RE/(RE +RS+rb+rp)
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
38
4) Noise gain Act for icsh.
B
rb
C
hfe ip
ip
io
rp
RS
E
vet
vs
RE
io
AOL
___
_______
Act 
= Gcsh
+ Gct bct fwd
ict
1+AOLb
1
___
Acsh =
RC
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.7. Example circuit
39
5) Total input noise vs. time, vn s.
B
rb
C
hfe ip
ip
io
rp
RS
E
vn s
vs
RSbE =RS+rb+RE
RE
RC
(ibf +ibsh) Abf _______
icsh Acsh
vct Act
__________
_____
vn s(t) = vst +vbt +vet+
+
+
As
As
As
2
(R
+r
)
1
SbE
p
________
_____
2
2
2
2
2
+ 4kT
vn s ( f ) = 4kT RSbE+(ibf +ibsh ) RSbE + icsh
hfe2
RC As2
0
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
40
6) Vn- In noise model.
vn
B
rb
C
hfe ip
ip
in
rp
ic
RC
E
RS
vs
RbE = rb + RE
en2 = en s2
(1+h
R
E fe) RE
2
(R
+r
)
bE
p
= 4 k T RbE + (ibf 2 + ibsh2) RbE 2 +icsh2
hfe2
Rs= 0
2
e
n
s
in2 =
Rs2
2
i
csh
= ibf 2 + ibsh2 +
hfe2
Rs= 
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
41
7) Minimizing CE noise.
0
1.4
1.2
-0.1
en s
norm.
dB
en s
norm.
dB
-0.2
-0.3
-0.4
-0.5
102
1.0
0.8
0.6
0.4
hfe=104
hfe=103
hfe=102
0.2
103
104
0
0.1
vet2 = 4 k T RE
ibsh2 = 2 q IC /b
icsh2 = 2 q IC
2
vn s2
10
IC / IC opt
hfe
rb = 100
RS = 200
RE = 200
ibf 2 = 0
vbt2 = 4 k T rb
10
RSbE
RSbE +hfeVT / IC
= 4 k T RSbE + 2 q IC
+ 2 q IC
hfe
hfe
hfeVT
IC opt =
(1 + hfe )0.5 R*2
0.5
(1
+
h
)
fe
vn s min2 = 4 k T RSbE
(1 + hfe )0.5-1
2
Next lecture
42
Appendix: Noise analysis of the CE without
applications of superposition
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
43
Noise analysis of a CE amplifier
VCC
RC
RS
vs
RE
VBB
B
rb
vbst
ip
?
vn s
RS
vs
C
hfe ip
rp
ibf
ibsh
E
vet
RE
ro
icsh
ic
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
44
1) Disconnecting ibf and ibsh sources.
B
rb
vbst
ip
?
vn s
RS
vs
C
hfe ip
rp
ibf
ibsh
ibf
ibsh
E
vet
RE
ro
icsh
ic
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
45
1) Disconnecting ibf and ibsh sources.
B
rb
vbst
ip
?
vn s
RS
vs
ibf
ibsh
ibf
ibsh
C
hfe ip
rp
ro
icsh
E
vetne = vet - (ibf + ibsh) RE
RE
ic
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
46
1) Disconnecting ibf and ibsh sources.
B
rb
?
vn s
RS
vs
vbst + (ibf + ibsh) (Rs + rb)
ip
hfe ip
ip
rp
ibf ibsh
C
ro
icsh
E
vne
et = vet - (ibf + ibsh) RE
RE
ic
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
47
2) Disconnecting ibf and ibsh sources.
B
rb
vn s
vs
ro  
hfe ip
ip
?
RS
vbst + (ibf + ibsh) (Rs + rb)
rp
ro
C
icsh
E
vne
et = vet - (ibf + ibsh) RE
RE
ic
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
48
2) Disconnecting ibf and ibsh sources.
B
rb
vn s
vs
hfe ip
ip
?
RS
vbst + (ibf + ibsh) (Rs + rb)
rp
C
icsh
E
vne
et = vet - (ibf + ibsh) RE
RE
ic
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
49
2) Disconnecting ibf and ibsh sources.
B
rb
vn s
vs
hfe ip
ip
?
RS
vbst + (ibf + ibsh) (Rs + rb)
rp
C
icsh
ic
E
vne
et = vet - (ibf + ibsh) RE + icsh RE
(1+h
RE fe) RE
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
50
3) Reflecting ibf and ibsh to vn s.
B
rb
vbst + (ibf + ibsh) (Rs + rb)
hfe ip
ip
?
vn s
C
rp
icsh
ic
E
RS
vne = vet - (ibf + ibsh) RE + icsh RE
vs
R* = RS + rb + RE
(1+hfe) RE
RS+rb+rp+(1+hfe)RE
vn s(t) = ic(t)
hfe
vn s(t) = vbst(t) - vet(t) + [ibf (t) + ibsh(t)] R* + ?
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
51
3) Reflecting icsh to vn s.
B
rb
C
hfe ip
ip
?
vn s
rp
icsh
ic
RC
E
RS
icsc RE
vs
R* = RS + rb + RE
(1+hfe) RE
RS+rb+rp+(1+hfe)RE
hfe
, 2) ic = - icsh (t) RE
1) vn s = - ic(t)
+ i (t)
hfe
RS+rb+rp+(1+hfe)RE csh
RS+rb+rp+(1+hfe)RE
R* + rp
= icsh (t)
3) vn s = - icsh (t) RE + icsh (t)
hfe
hfe
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
52
4) Total input noise vs. time, vn s(t).
B
rb
C
hfe ip
ip
rp
vn s
E
RS
vs
R* = RS + rb + RE
(1+hfe) RE
*+ r
R
p
vn s(t) = vbst(t) - vet(t) + [ibf (t) + ibsh(t)] R* +icsh (t)
hfe
ic
RC
5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. Appendix: conventional noise analysis
53
5) Power spectral density of the total input noise, vn s2.
rb
B
C
hfe ip
ip
ic
rp
vn s
RC
E
RS
vs
R* = RS + rb + RE
(1+h
R
E fe) RE
*+ r
R
p
vn s(t) = vbst(t) - vet(t) + [ibf (t) + ibsh(t)] R* +icsh (t)
hfe
vn s2 = 4 k T R* + (ibf 2 + ibsh2) R* 2 + icsh2
R*+ rp
hfe
2
Next lecture
54
Next lecture:
```