Lecture 12 - nuu.edu.tw
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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
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Meiling CHEN
2
Differential pair
Figure 7.12 The basic BJT differential-pair configuration.
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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.
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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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(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 2IRC
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.
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Meiling CHEN
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Exercise 7.7
let 1, vBE 0.7V
find vE , vC1 and vC 2
I
5 0.7
4.3mA
1k
0 .7
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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
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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
11
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
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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
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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
15
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 RCie
RE
RE
Differential voltage gain
RE Rid
RE Ad
v C 2 RCie
vid
ie
2( re RE )
vc1 vc 2
RC
Ad
vid
( re RE )
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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.
Microelectronic Circuits by
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
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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 )
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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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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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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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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
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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
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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
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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