Transcript Lecture 12 - nuu.edu.tw

Lecture 12
BJT’s Differential Pair
Microelectronic Circuits by
Meiling CHEN
1
topics
• Ideal characteristics of differential
amplifier
–
–
–
–
Input differential resistance
Input common-mode resistance
Differential voltage gain
CMRR
• Non-ideal characteristics of differential
amplifier
– Input offset voltage
– Input biasing and offset current
• Differential Amplifier with active load
Microelectronic Circuits by
Meiling CHEN
2
Differential pair
Figure 7.12 The basic BJT differential-pair configuration.
Microelectronic Circuits by
Meiling CHEN
3
Common mode operation
 Q1  Q2
 vB1  vB 2  vCM
 iE1  iE 2
I

2
 vC1  vC 2  VCC
I
  RC
2
vC1  vC 2  0
Reject common mode input
Figure 7.13 Different modes of operation of the BJT differential pair: (a) The differential pair with a common-mode input signal vCM.
Microelectronic Circuits by
Meiling CHEN
4
The differential pair with a “large” differential input
signal
(1)VB1  VB 2
VB1  1V , VB 2  0
Q1 on  VE1  0.3V  VE 2  Q2
off
VC1  VCC  IRC , VC 2  VCC
VC1  VC 2  IRC
Figure 7.13 Different modes of operation of the BJT differential pair:. (b) The differential pair with a “large” differential input signal.
Microelectronic Circuits by
Meiling CHEN
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(2)VB1  VB 2
VB1  1V , VB 2  0
Q2

0 .7
on  VE 2  0.7V  VE 2  Q1 off
VC 2  VCC  IRC , VC1  VCC
VC1  VC 2  IRC

Figure 7.13 (Continued) (c) The differential pair with a large differential input signal of polarity opposite to that in .
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Meiling CHEN
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(3)VB1  VB 2
VB1  sm all, VB 2  0
I
I
I E1   I , I E 2   I
2
2
I
VC1  VCC   RC  IRC
2
I
VC 2  VCC   RC  IRC
2
VC1  VC 2  vo  2IRC
 vo  f (I )
Figure 7.13 (Continued) (d) The differential pair with a small differential input signal vi. Note that we have assumed the bias current source I
to be ideal (i.e., it has an infinite output resistance) and thus I remains constant with the change in vCM.
Microelectronic Circuits by
Meiling CHEN
7
Exercise 7.7
let   1, vBE  0.7V
find vE , vC1 and vC 2
I
5  0.7
 4.3mA
1k

0 .7

Microelectronic Circuits by
Meiling CHEN
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Large signal operation
iE1 
IS
e ( vB1 vE ) / VT
iE 2 
IS
e ( vB 2 vE ) / VT


iE 1
 e ( vB1 vB 2 ) / VT
iE 2
iE1
1

iE1  iE 2 1  e ( vB 2 vB1 ) / VT
iE 2
1

iE1  iE 2 1  e ( vB1 vB 2 ) / VT
iE1  iE 2  I
iE1 
iE 2
I
1  e vid / VT
I

1  e vid / VT
Microelectronic Circuits by
Meiling CHEN
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iC1
1

I 1  e vid / VT
1  e vid / VT
iC 2
I
1



vid / VT
I
1 e
1  e vid / VT
I
iE 1 
iE 2

How to enhance linear
region？
Figure 7.14 Transfer characteristics of the BJT differential pair of Fig. 7.12 assuming  . 1.
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Meiling CHEN
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Re  vE  vBE  iC 
Figure 7.15 The transfer characteristics of the BJT differential pair (a) can be linearized (b) (i.e., the linear range of
operation can be extended) by including resistances in the emitters.
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Meiling CHEN
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large signal analysis (AC+DC)
I
iC1 
 (1)
1  e vid / VT
I
iC 2 
1  e vid / VT
e vid / 2VT
Ievid / 2VT
(1)  vid / 2VT  iC1  vid / 2VT
e
e
 e vid / 2VT
let
vid  2VT
vid
)
2VT

v
v
1  id  1  id
2VT
2VT
I (1 
 iC1
 iC1 
 iC 2 
ic 
Figure 7.16 The currents and voltages in the differential amplifier when a
small differential input signal vid is applied.
I
2
I
2
I vid
2VT 2

I vid
2VT 2


I vid
2VT 2
gm
vid
2
vBE
Q1  VBE 
vid
2
vBE
Q2
 VBE 
vid
2
Microelectronic Circuits by
Meiling CHEN
Taylor
series
 IC 
I C vid
VT 2
 IC 
I C vid
VT 2
AC
12
Small signal analysis (AC)
g m  I C / VT 
vid
2re
ic  ie 
ie 
VT
VT
I /2
re  VT / I E 
ie 
I / 2
vid
2re
 gm
vid
2re
ie
ie
RC

Figure 7.17 A simple technique for determining the signal currents in a
differential amplifier excited by a differential voltage signal vid; dc quantities
are not shown.
vid
2
ie
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Meiling CHEN
re
id
vid
RC

ie
re
13
vc1
vo  vc1  vc 2
vc2
RC
RC
g m v


v

Rid 
re
id
vid
g m v


v

re
vid
2reie

 2(1   )re Input differential resistance
i
id
e
1 
vid
I
I

2
gm  C  E 
VT
VT
re
vid
v C 2   g m RC
2
vc1  vc 2
Ad 
  g m RC Differential voltage gain
vid
Microelectronic Circuits by
v C1   g m RC
Meiling CHEN
14
Common mode
vc1
vo  vc1  vc 2
vc2
ie 2
ie1
RC
g m v

v

RC
g m v
ib1
ie1
re
DC
vicm ib 2

ie 2
v

re
vc1  ie1 RC
if
vc 2  ie2 RC
RC1  RC 2  vo  0
vo  vc1  vc 2  Rc (ie1  ie2 )
 ie1  ie2  0  vo  Rc (ie1  ie2 )  o
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Meiling CHEN
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External emitter resistance
vc1
RC1
vo  vc1  vc 2
ie
g m v
ie
re
RE
vc2
vid
ib

vid
2re  2 RE
ie
v /(2re  2 RE )
 id
 1
 1
v
Rid  id  (   1)(2re  2 RE )
ib
ib 
RC 2
ie

ie 
g m v
Input differential resistance
re
v C1   RCie
RE
RE
Differential voltage gain
RE  Rid 
RE  Ad 
v C 2   RCie
vid
ie 
2( re  RE )
vc1  vc 2
RC
Ad 
 
vid
( re  RE )
Microelectronic Circuits by
Meiling CHEN
16
Bartlett Bisection theorem



v1
v2
v1


N

I
1
N
2

1
N
2

2. v1  v2  V  0
Common Mode
Differential Mode


v1


I=0 open circuit
Common-mode

V
1. v1  v2  I  0
1
N
2
v2
v1

1
N
2

V=0 short circuit
Differential-mode
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Meiling CHEN
17
Differential Mode
Common Mode
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Meiling CHEN
18
Equivalence of the differential amplifier to a CE amplifier
Figure 7.19 Equivalence of the BJT differential amplifier in (a) to the two common-emitter amplifiers in (b). This equivalence applies
only for differential input signals. Either of the two common-emitter amplifiers in (b) can be used to find the differential gain,
differential input resistance, frequency response, and so on, of the differential amplifier.
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Meiling CHEN
19
vc1
gm

(ro // Rc )
vid
2
vc 2 g m

(ro // Rc )
vid
2
Ad 
vc1 vc 2 vc1  vc 2


  g m ( RC // ro )
vid vid
vid
Differential half-circuit
i 
V
r
Vid
 V
2(1   )re
2
V
2V
Rid  id 
 2r
V
i

r
Figure 7.21 (a) The differential half-circuit and (b) its equivalent circuit model.
Input differential resistance
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Meiling CHEN
20
Common mode gain et CMRR (I=0 open circuit)
vc1  ie Rc
vicm  ie (re  2 REE )
Acm 1  
2
RC
(re  2 REE )

RC
(2 REE )
1
g m RC
2
A
CMRR 1  d  g m REE
2
Acm
Ad
1
2

Common-mode half-circuit
Figure 7.22 (a) The differential amplifier fed by a common-mode voltage signal vicm. (b) Equivalent “halfcircuits” for common-mode calculations.
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Meiling CHEN
21
Common mode gain at CMRR ( Asymmetric case)
vc1  ie RC
vc 2  ie ( RC  RC )
Last page
vo  vc1  vc 2  ie RC
RC
vc1  vicm
vicm  ie (2 REE  re )
 RC
RC
RC RC
Acm 


2 REE  re 2 REE
2 REE RC
vc 2  vicm
<<
Acm 1  
v1  v2
vicm 
2
vid  v1  v2
2
RC
2 REE
RC
2 REE
RC
2 REE
1
g m RC
1
2
2
A
CMRR  d  g m REE
Acm
Ad
v1  v2
vo  Ad (v1  v2 )  Acm (
)
2
2 REE  re
 vicm
Microelectronic Circuits by
Meiling CHEN

22
Common-mode input resistance
V  ie (re  2 REE )
ie
I  ib 
1 
2 Ricm  (   1)(2 REE // ro )
ro
Ricm  (   1)(REE // )
2
g m v
I
ro

v

RC
re
2 REE
Figure 7.23 (a) Definition of the input common-mode resistance
Ricm. (b) The equivalent common-mode half-circuit.
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Meiling CHEN
23
ie
ie  i  ie
Ricm
g m v
ib
ro

ie v
re

i
2 Ricm
RC
ro
 (   1)( REE // )
2
2 REE
ie  i
2 Ricm 
V
,
ib
V  reie  2 REE i
2 REE i  ro (ie  i )  Rc (ie  i  ie )
 (2 REE  ro  Rc )i  roie  Rc (ie  ie )  roib (1   )  Rc ib
i
roib (1   )  Rc ib
2 REE  ro  Rc
V  reie  2 REE i  reib (1   )  2 REE
2 Ricm 
roib (1   )  Rc ib
2 REE  ro  Rc
2 REE ro
2 REE Rc
V
 re (1   )  (1   )

ib
2 REE  ro  Rc 2 REE  ro  Rc
2Ricm  (   1)(2REE // ro )
Microelectronic Circuits by
Meiling CHEN
24
Example 7.1
1. Input differential resistance
  100
re1  re 2 
VA  100
VT 25m V

 50
I E 0.5m A
Rid  2(   1)(re  RE )  40k
2. Differential voltage gain
Ad 
vo vid
Rid
 g m RC
 40
vid vs
Rs  Rid
3. Common-mode gain in worst case
Acm 
4. Input common-mode resistance
RC
RC
2 REE  (re  RE ) RC
RC  0.02RC
VA
4
ro 
 200k
A

5

10
cm
I /2
1
A
Ricm  (   1)(2 REE // ro )  6.7 M
CMRR  20 log d  98dB
2
A
25
Microelectronic Circuits by
Meiling CHEN
cm
Differential mode
vo
vo
RS
vs
2
RC
ie
RC
vs
2
RS
g m v
RE
re re 
Rid 1  (1   )(50  150)
RE
2
VT 25m

 50
I E 0.5m
150
Rid  2(1   )(50  150)  40k
v c1
 ie Rc
  (1   )ib10k
Ad 


vs
Rs ib  0.2ie 5kib  0.2k (1   )ib
2
v c1 1   (1   )10k

vs 2 5k  0.2k (1   )
v c1 v c 2
v
  (1   )10k
 2 c1 
 40
vs
vs 5k  0.2k (1   )
Rid
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Meiling CHEN
26
Common mode
vo
RS
vicm
vo
RS
RC
vicm
ie
ie
ib
0.05k
re
g m v
0.15k
RE
ro 
rO
RC 10k
RE
2 Ricm
2 REE
2 Ricm
ie
400 k
if
VA VA

 200k
I
IC
2
2 REE
RC1  Rc  1%  RC 2  Rc  1%
vc1    ib ( RC )
vc 2    ib ( RC  RC )
2 Ricm  (1   )(400k // 200k )
RC  RC  0.02
Ricm 
1
(1   )(400k // 200k )  6.7 M
2
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Meiling CHEN
27
vicm  5kib  (1   )ib (400.2k )
Acm 
vc1  vc 2
 (RC )

vicm
5k  (1   )(400.2k )
7-4.2 Input offset voltage
Vos 
V
o vi  0
Ad
Solution : Add a -Vos

 Vos
Ad
Vo  Vos Ad  (Vos ) Ad  0

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Meiling CHEN
28
7-4.2 Input offset voltage
let
RC1  RC 2 , Q1  Q2
RC
2
R
RC 2  RC  C
2
R
I
VC1  VCC  ( )(RC  C )
2
2
R
I
VC 2  VCC  ( )(RC  C )
2
2
I
Vo  VC1  VC 2 
RC
2
I
I
RC
RC
Vo
Vos 
 2
 2
IE
Ad
g m RC
RC
VT
RC1  RC 
Case 1 : different RC
Case 2 : different Q
Vos  VT
RC
RC
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Meiling CHEN
29
consider Q1  Q2  I S 1  I S 2
VBE
IC  I S e
VT
I S
2
I S
IS2  IS 
2
VBE1  VBE 2
internal
I S1  I S 
 I E1 
 IE2
Consider Q and RC
Vos  (VT
RC 2
I
)  (VT S ) 2
RC
IS
Solution : Add a -Vos
I S
I
(1 
)
2
2I S
I S
I
 (1 
)
2
2I S
I I S
 VO  
RC
2 IS
Vos  VT (
I S
)
IS
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Meiling CHEN
30
Input offset current
I /2
 sym m etric case
 1
let 1   2  I B1  I B 2
I B1  I B 2 
I os  I B1  I B 2


, 2   
2
2
I E1
I
1
I 1

 I B1 


(1 
)
(1  1 ) 2   1   / 2 2   1
2
let 1   
 I B2 
I os 
IE2
I
1
I 1



(1 
)
(1   2 ) 2   1   / 2 2   1
2
I
(

)
2(   1) 
I I
I
 I B  B1 B 2 
2
2(   1)

 I os  I B ( )

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31
7-5.5 Differential amplifier with active load
Active load
Small-signal
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Meiling CHEN
32
Active load Q3 Q4
Passive load RC
Ad   g m (ro 4 // ro 2 )
Ad   g m RC
RC
Acm  
2 REE
CMRR  g m REE
Rid  (1   )(2re  2 RE )  2r  2(1   ) RE
r
Ricm  (1   )(REE // 0 )
2
Ro  RC // r0
1
2
Acm 1
2
ro 4

 3 REE
CMRR  g m (ro // ro 4 )
 3 REE
ro 4
Rid  2r
Ricm 
Ro  ro 4 // ro 2
Improving: 1. Differential gain
2. Common-mode gain and CMRR
Defect: Vos
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Meiling CHEN
33
Differential amplifier with active load equivalent-circuit
Differential-mode
vo
Q1
v B1 
vid
2
Q4
Q3
Q2
vB2  
vid
2
0v
Vid
2
Vo

r 1 V 1

Rid 

gm1V 1 ro1 re3 // ro3V 4 r 4

Ro  ro 4 // ro 2

Vid
2

g m4V 4 ro 4
ro 2 gm2V 2 r 2 V 2

vid
I
vid
 Ir  Rid  2r
2
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Meiling CHEN
34
vid
v
)(re 3 // ro 3 // ro1 // r 4 )   g m1re 3 ( id )
2
2
v id
 vb 4  vb 3  g m 4 vb 4   g m 4 g m1re3 ( )
2
v
vo  ( g m v 4  g m v 2 )(r04 // ro 2 )
io  g m 2 ( id )  g m 4 vb 4
2
vid
v

[

g
v

g
(

)](r04 // ro 2 )
vid
vid
o
m 4
m
2
 io  g m 2 ( )  g m 4 g m1re 3
2
2
v
v 4   g m v 1 ( r01 // re 3 // ro 3 // r 4 )   g m id re 3
 g m1  g m 2  g m 4  g m
2
vb 3   g m1 (
I /2
gm 
VT
re 3   3 / g m 3  1 / g m
 GM 
io
 gm
vid
vid
)(r04 // ro 2 )[g m (r01 // re 3 // ro 3 // r 4 )  1]
2
v
vo  g m ( id )(r04 // ro 2 )[g m re 3  1]
2
1
vo
1
Ad 
 g m ( )(r04 // ro 2 )[g m re 3  1]
vid
2
vo  g m (
Ad 
vo
 g m (r04 // ro 2 )
vid
Microelectronic Circuits by
Meiling CHEN
35
Since four transistors have the same
parameters
i
vx
v
 x
Ro 2 2ro 2
ix  2i 
vx vx vx


ro 4 ro 2 ro 4
 Ro 
vx
 ro 2 // ro 4
ix
Ad 
vo
 GM Ro  g m (ro 2 // ro 4 )
vid
 ro 2  ro 4  ro
Ad  g m
ro
2
Rid  2r
Microelectronic Circuits by
Meiling CHEN
36
Common-mode gain at CMRR
Differential amplifier with active load
equivalent-circuit Common-mode
i1
Vicm
ie1
ro1
vb3
Vo

1
r 3 //
// ro3 r V
4
4
gm3

g m4V 4
re1
i1
ro 4 i2 ro 2
ie 2
re 2
2 REE
2 REE
Microelectronic Circuits by
Meiling CHEN
Vicm
i2
37
i1  i2 
vicm
2 REE
vb 3  i1 (
1
// r 3 // ro 3 // r 4 )
g m3
Q3
ic 4  g m 4 vb 3
vo  ( g m 4 vb 3  i2 )ro 4
Acm 

let
vo
r
1
 o4 [ gm4 (
// r 3 // ro 3 // r 4 )  1]
vicm 2 REE
g m3
ro 4
2 REE
1
1
1


r 3 r 4 ro 3
1
1
1
g m3 


r 3 r 4 ro 3

v

r
g m v
ro
1
gm
ro
g m3  g m 4 , r 3  r 4 , ro 3  r 3 , ro 3  r 4
Acm 
1
r 3
vo
r
r
r
2
  o4
  o4
   o4
vicm
2 REE g  1
2 REE  3
 3 REE
m3
r 3
CMRR 
Ad
Acm
 g m (ro 2 // ro 4 )(
 3 REE
ro 4
)

v

r
when ro 2  ro 4  ro
CMRR 
1
 3 g m REE
2
Microelectronic Circuits by
Meiling CHEN
38
Input offset voltage (systematic problem)
I 3  2 I B  I 4 I
 I3  2
I3
  I 4 I
let I 3   I
I3
IB
I4
2
I4
1

  P  3   4
I3 1  2 /  P
I / 2
I4 
1 2 / P
I
I / 2
I 2 /  P
I
i 



2 1 2 / P
2 1 2 / P P
i
I /  P
2VT
Vos  


GM
I / 2VT
P
Microelectronic Circuits by
Meiling CHEN
39
Exercise 7-13
 VCC
 VCC
Q3
v1
Q4
v2
Q1
Ro  ro
Q2
Ro  ro
 VCC
I
I
Q5
Q6
g m v
ro

v


r
v

r
g m v
ro
 VEE
Microelectronic Circuits by
Meiling CHEN
40