1 5. sources of errors. 5.5. fundamentals of low-noise design 5.5. fundamentals of low-noise design

15. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design

5.5. Fundamentals of low-noise design

2

rd

ID

edsh

rd

idsh

ID

5. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.1. Junction-diode noise model

4) idsh2 = 2 q ID = 2 k T / rd

3) rd k T

q ID

5) edsh2 = )2 k T / rd ) rd

2 = 2 k T rd

2) idsh2 2 q ) IF+IS ) 2 q ) ID+2IS ) 2 q ID

5.5.1. Junction-diode noise model

1) ID IS e IS IFISVD /VT

ID

At low frequencies and ID >> IS ,

idn2 = 2 q ID

Kf ID

f, Kf = 2 q ff

Note that dynamic resistances do not generate any thermal

noise since them dissipate no power, vd id = 0.

idf

idf rd

35. SOURCES OF ERRORS. 5.5. Fundamentals of low-noise design. 5.5.2. BJT noise model

5.5.2. BJT noise model

rb

icsh

B

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

4

vs

RS

r

ichfe i

ro

rbB C

icsh


A. Total input noise

ibf ibsh

ivbt

vn s)t) vst)t) vbt)t) ibf )t) ibsh)t)])RS rb) icsh)t)RS+rb+r

hfe

1) Total input noise vs. time, vn s)t).

2) Power spectral density of the total input noise, vn s2) f ).

vbt

vn s?

5

vs

RS

r

ichfe i

ro

C

icsh



ibf ibsh

i

vn s)t) vst)t) vbt)t) ibf )t) ibsh)t)])RS rb) icsh)t)RS+rb+r

hfe



vn s2 4 k T )rb RS) ibf

2 ibsh

2))RS rb)2 icsh2

RS+rb+r

hfe

2

vn s?

rbvbtvbt

vn sB

6

vn s2 4 k T )rb RS) +2 q IC

)RS rb)2

hfe

2 q IC

RS+rb+hfeVT / IC

hfe

2

vn s


B. Optimum collector current

IC opt hfeVT

hfe 0.5)RS rb)

r

ichfe i

ro

rbB Civbt

vn s2 4 k T )rb RS) ibsh

2 )RS rb)2 icsh2

RS+rb+r

hfe

2

RS

ibf 0

Reference: [7]


C. enin noise model

en2 vn s

2 4 k T rb ibf

2 ibsh

2) rb2 icsh

2 rb+r

hfe

2

RS= 0

in2

ibf 2 ibsh

2 vn s

2

RS2 RS=

icsh2

hfe2

vs

RS

r

ichfe i

ro

rbB Cien

in


2 ibsh

2))RS rb)2 icsh2

RS+rb+r

hfe

2


B

E

C

en2 4 k T rb ibf

2 ibsh

2) rb2 icsh

2 rb+r

hfe

2

in2 ibf

2 ibsh2

icsh2

hfe2

en

in

BJT enin noise model

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


D. Optimum source resistance at IC opt

vs

RS

r

ichfe i

ro

rbB Ci

Rs opt en

in IC opt

rb 2 1 + 1+hfe

en

in

IC opt

10

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)

11

id


gmvgs

ro

G Dig

Equivalent small-signal model

igsh idtidf

vgs rgs

12

id


1/gm

gmvgs

ro

G Dig

igsh idtidf

vgsvgs rgs



~1/gm

gmvgs

ro

G Dig

igsh idtidf

vgs



idvs

RS

~1/gm

gmvgs

ro

G Dig


vn s?


igsh idtidf

vgs


vs

RS

~1/gm

id

gmvgs

ro

G D



idtidfvn s? igsh

igsh Rs

vn s)t) vst)t) + igsh)t) RS idf )t) idt)t)])1/gm)

vgs

ig

16

vn s?


vs

RS

~1/gm

id

gmvgs

ro

Digsh Rs

idtidf

vn sG



vn s)t) vst)t) + igsh)t) RS idf )t) idt)t)])1/gm)


vn s2 4 k T RS + igsh

2RS2

idf 2 idt

2)/gm2

vgs

ig

17

vn s?


B. enin noise model

en2 vn s

2 idf

2 idt2)/gm

2

RS = 0

in2

igsh2

vn s2

RS2 RS =

vs

RS

~1/gm

id

gmvgs

ro

Digsh Rs

idtidf


2RS2

idf 2 idt

2)/gm2

vn s en

in

G

vgs

ig


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


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


BJT

19

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

20

id


1/gm

gmvgs

ro

D

vn s)t) vst)t) idf )t) idt)t)])1/gm)



vn s2 4 k T RS + idf

2 idt2)/gm

2


idtidfvn s?

vs

RSvn s

G

21

vn s


B. enin noise model

en2 vn s

2 idf

2 idt2)/gm

2

RS = 0

in2

0vn s

2

Rs2 RS =

1/gm

id

gmvgs

ro

D


2 idt2)/gm

2

vs

RSen

in

G


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


JFET

23

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.

24

vs

RS

Ag

1) Transconductance gain


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



r

ichfe i

ro

rb C

icsh

ibf ibsh

i

vbtvbt

C

C


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)


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 s2

RS2 RS =

icsh2

rb+r

hfe

2

]12fen)2[

ibf 2

ibsh2 ]12fin)2[

icsh2

hfe2

en)rbIIr))C+C)

inr)C+C)


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[

icsh2

hfe2

en

in

B. enin noise model for high-frequencies

28

IC opt = 24 mAIC opt = 24 mA

IC = 0.1 mAIC = 0.1 mA


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

rb 100

hfe100

CpF 1

C)mA 1)pF 100

rb100

hfe100

C1 pF

C)1 mA)100 pF

en2 4 k T rb ibf

2 ibsh

2) rb2 icsh

2rb+r

hfe

2

]12fen)2[


D. in) f ) for different IC

IC opt = 24 mAIC opt = 24 mA

IC = 0.1 mAIC = 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

rb 100

hfe100

CpF 1

C)mA 1)pF 100

rb100

hfe100

C1 pF

C)1 mA)100 pF

in2 ibf

2 ibsh

2 ]12fin)2[icsh

2

hfe2


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

315. 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

rb 40

hfe500

r o

I CmA 1

rb40

hfe500

ro

IC 1 mA

IDSS2 mA

Vp2 V

ro

ID 1 mA


2RS2

idf 2 idt

2)/gm2


2 ibsh

2))RS rb)2 icsh2

RS+rb+r

hfe

2


2 idt2)/gm

2


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 current

is neglected.


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


Reference: [9]

Conclusion: 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

35

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

io

hfe i

ro

rb

RE RC

B

E

C

icsh

vs

RS

ibf ibsh

i

vet

vbt

vst

vct

ro

36

Our final aim is to find and minimize the total input noise vn s.


r

io

hfe 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.

37

As Gs Gs s fwd AOL

1AOL

io

vs

1) Signal gain As for vs, vst, vbt, and vet.


r

io

hfe i

rb

RE RC

B

E

C

vs

RS

i

As 1

RSrbrRE

hfe

1hfe RE/)RE RSrbr) 0

vet

vbt

vst

38

Abf Gibf Gbf bf fwd AOL

1AOL

io

ibf

2) Noise gain Abf for ibf and ibsh.


r

io

hfe i

rb

RE RC

B

E

C

vs

RS

ibf ibsh

i

Abf RSrbRE

RSrbRE r

hfe


39

Acsh Gcsh Gcsh csh fwd AOL

1AOL

io

icsh

r

io

hfe i

rb

RE RC

B

E

C

icsh

vs

RS

i

3) Noise gain Acsh for icsh.


Acsh RE

RE RSrbr

hfe


40

Act Gct Gct ct fwd AOL

1AOL

io

ict

4) Noise gain Act for icsh.


r

io

hfe i

RE RC

B

E

C

vs

RS

i

vct /RC

rb

Acsh 1

RC

41

5) Total input noise vs. time, vn s.


r

io

hfe 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 As2

0

RSbE RS rbRE

42

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


43

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


Reference: [7]

44Next lecture

Appendix: Noise analysis of the CE without applications of superposition

Reference: [7]

455. 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

46

r

iic

hfe 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


47

ibf ibsh

ibf ibsh

r

iic

hfe i

ro RC

C

icsh

RE

E

rbB

vn s

vs

RS

?

vetvne = vet )ibf + ibsh) RE


vbst


48

r

ichfe i

ro

rb

RE

RC

B

E

C

icsh

vet

vn s

?

vs

RS

ibf ibsh

vne = vet )ibf + ibsh) RE


i

ivbstvbst )ibf ibsh) )Rs rb)


49

r

ichfe i

ro

rb

RE

RC

B Cro

icsh

vet

E

vn s

?

vs

RS



vbst )ibf ibsh) )Rs rb)

i


50

r

ichfe i

rb

RC

B C

RE

icsh

vet

E

vn s

?

vs

RS




i


51

vet

r

ichfe i

rb

RC

B C

RE )1+hfe) RE

icsh

E

vn s

?

vs

RS




vne = vet )ibf + ibsh) RE + icsh RE

i


52

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.


vn s)t) vbst)t) vet)t) ibf )t) ibsh)t)] R* ?

i

R* RS rb RE


53

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


54

r

ichfe i

rb

RC

B C

)1+hfe) RE

E

vn s

vs

RS


i

vn s)t) vbst)t) vet)t) ibf )t) ibsh)t)] R* icsh )t)R*+ r

hfe

R* RS rb RE


55

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


56Next lecture

Next lecture:

1 5. sources of errors. 5.5. fundamentals of low-noise design 5.5. fundamentals of low-noise design

Documents

noise design5

jfet noise model5

jfet noise modelb

bjt noise model5

bjt noise modela

bjt noise modelbecen2

bjt noise modelc

bjt noise modeld