Transcript Document

Chapter 15
Multistage Amplifiers
Microelectronic Circuit Design
Richard C. Jaeger
Travis N. Blalock
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Chapter Goals
• Understand analysis and design of ac-coupled multistage
amplifiers including voltage gain, input and output resistances
and small signal limitations.
• Understand analysis and design of dc-coupled multistage
amplifiers.
• Discuss characteristics of Darlington configuration and cascode
amplifier.
• Explore dc and ac properties of differential amplifiers.
• Understand basic three-stage op amp.
• Explore design of class-A, class-B, class-AB output stages.
• Discuss characteristics and design of electronic current sources.
• Continue understanding the use of SPICE in circuit analysis.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
AC-coupled Amplifiers: Circuit
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
AC-coupled Amplifiers: Description
• MOSFET M1operating in C-S configuration provides high input
resistance and moderate voltage gain.
• BJT Q2 in C-E configuration, the second stage, provides high gain.
• BJT Q3, an emitter-follower gives low output resistance and buffers
the high gain stage from the relatively low load resistance.
• Bias resistors are replaced byRB2  R1 R2 RB3  R3 R4
• Input and output of overall amplifier is ac-coupled through
capacitors C1 and C6.
• Bypass capacitors C2 and C4 are used to get maximum voltage gain
from the two inverting amplifiers.
• Interstage coupling capacitors C3 and C5 transfer ac signals between
amplifiers but provide isolation at dc, and prevent Q-points of the
transistors from being affected.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
AC-coupled Amplifiers: Equivalent
Circuits
AC
Equivalent
Small-signal
Equivalent
DC
Equivalent
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Richard C. Jaeger, Travis N. Blalock
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AC-coupled Amplifiers: Input
Resistance and Voltage Gain
R R R 
L2 I 2 in3
R  620Ω 17.2kΩ  598Ω
I1
R  4.7kΩ 51.8kΩ  4.31kΩ
I2
R  3.3kΩ 250Ω  232Ω
L3
R r  (  1)R   3.54kΩ
I 2   3
o3
L3
v
A  3  g R
v2 v
m2 L2
2
 62.8mS 3.54kΩ  -222
(  1)R
vo
o3
L3  0.950
A  
v3 v r  (  1)R
3 3
o3
L3
R  R  1MΩ
R  R R  598 r 598Ω 2390Ω  478Ω
in G
L1 I1 in2
2
R
v
in  998
 Av  A A A
A  2  g R  0.01S 478Ω  -4.78
v3 v2 v1 R  R
v1 v
m1 L1
in
I
1
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AC-coupled Amplifiers: Output
Resistance
vx
R 
 R RCE
R r
I 2 out I 2 o2
th3 i
x
 4310Ω 54200Ω  3990Ω
To find output resistance, test
voltage is applied at amplifier
output.
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Richard C. Jaeger, Travis N. Blalock
ix  ir  ie 
vx

vx
3300 R
out3










R

o
3
th
3
Rout 
 3300 R
 3300


out3
ix
g
 1 
m3
o3 
 0.988
3990 

 3300 

  60.5

81 
 0.0796S
vx
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AC-coupled Amplifiers: Current and
Power Gain
Input current delivered
to amplifier from source is
v
i  9.9010 7 v
i 
i R R
i
in
I
and current delivered
load by amplifier is
Av v to
v
998v
s  3.99v
i
io  o 
s
250 250
250
3.99v
io
i
A 
 4.03106
i i
7v
9
.
90

10
i
i
Po v o io
A  
 Av A  998 4.03106  4.02 109
P P
i
s v i ii
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AC-coupled Amplifiers: Input Signal
Range
0.2(1 2)
• For first stage,v1  0.2(VGS VTN )  vi 
•
•
•
0.990
 0.202V
v
 v  A v  5mV
2
v1 1
be2
For second stage,
5mV 0.005
1.05mV
v 

 1.05mV  v 
 1.06mV
i
1 A
4.78
0.990
v1
v
A A (0.990vs )
3
 v1 v2
For third stage,vbe3 
1 g R
1 g R
m3 L3
m3 L3
1 g R
m3 L3 0.005  92.7μV
v
 5mV  v 
i A A (0.990)
be3
v1 v2
v  min(202mV,1.06mV,92.7μV)  92.7μV
i
On the whole,v  A (92.7μV)  998(92.7μV)  92.5mV
v
o
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Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
AC-coupled Amplifiers: Methods to
Improve Voltage Gain
• Gain of C-S amplifier is inversely proportional to square
root of drain current, so voltage gain could be increased by
reducing ID1 while maintaining a constant voltage drop
across RD1. Signal range could be improved by increasing
current in output stage and voltage drop across RE3.
• Q1 could be replaced with a FET. This could cause gain
loss in third stage since gain of C-D amplifier is typically
< that of a C-C stage. However, this loss could be made up
by improving gain of first and second stages.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Common-Emitter Cascade
If gain is limited by interstage resistances,
each stage has a gain of about -10VCC and
overall gain is:
n


Avn   10V 
CC 

To achieve maximum gain, several If gain is limited by input resistance of
C-E stages can be cascaded.
transistors, it is given by:
v v
v
I
Av  1 2 ... o  A A A
n
v3 v2 v1
Avn   1 C1   ...on 10V 
v v v
o2 o3
CC 

n -1
I
i 1
Cn
For the final stage,
Normally ICn  IC1 as signal and power
Avn   gmn R  10V
L
CC
levels usually increase in each successive
For all other stages,
stage of most amplifiers. Since o< 10VCC ,
A  g (R r
)
vi
mi Li i 1
this case often represents the actual limit.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Direct-coupled Amplifiers: Circuit
• Bypass capacitors- C2 and C4
affect gain at low frequencies
but don’t inherently prevent the
amplifier from operating at dc.
• Coupling capacitors in series with signal pathC1, C3, C5, and C6 are eliminated as they prevent
the amplifier from providing gain at dc or very
low frequencies.
• Additional bias resistors in individual stages
are also removed, making design less expensive.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
• Symmetrical power supplies
are used to set Q-point voltages
at input and output to about
zero.
•Alternating pnp or p-channel
and npn or n-channel transistors
are used from stage to stage to
take maximum advantage of
available power supply voltage.
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Direct-coupled Amplifiers: DC Analysis
2
Kn 
2 0.01 





 0  (7.5 1600I
2
V
I 
V  



D
TN 
 GS
D




2
2
So, ID = 6.66. mA (which would produce 10.7
V drop across RS1 and cut off FET) or ID =5.29
mA (correct value).
IB2 << ID, VD  7.5  620I D  4.22V
V
DS
 4.22  0.964  3.26V
which is enough to pinch off M1.
7.5 V V
Voltage at drain of M1 provides base
D EB2 1.84mA
I 
bias for Q2 and voltage at collector of
E2
1400
Q2 provides base bias for Q3. All
F2 =150, so IC2 =1.83 mA and IB2 = 12.2 mA.
transistors operate in active region
IB3 << IC2, V  4700I  7.5V 1.10V
C2
C2
irrespective of direct connection
V
V V
V  3.82V
EC2 D1 EB2 C2
between stages.
which < 0.7 V , so Q2 is in active region.
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Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Direct-coupled Amplifiers: DC Analysis
(contd.)
Vo V V
 1.10V - 0.7V  0.4V
C2 BE3
V  7.5V Vo
I I I  o

 3.99mA
E3 3 L 3300 250
F3 = 80, so IC3 =3.94 mA and IB3 = 49.3 mA
V
 7.5 V  7.5- 0.40V  7.10V
CE3
E3
thus Q3 is in active region.
There is an offset voltage of 0.4 V at output and a nonzero dc current exists in
250 W load resistor. In an ideal design, offset voltage would be zero and no dc
current would appear in load.
Based on Q-point values, small-signal parameters can be calculated.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Direct-coupled Amplifiers: AC Analysis
• Values of interstage capacitors
are higher than those in accoupled amplifier due to
absence of bias resistors.
• Overall characteristics are
similar to those in ac-coupled
amplifier as Q-points and
small-signal parameters of
transistors are similar
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
• Dc coupling requires
fewer components than
ac-coupling but Q-points
of various stages become
interdependent.
• If Q-point of one stage
shifts, Q-points of all
other stages might also
shift.
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Direct-coupled Amplifiers: Darlington
Circuit
AC Analysis: For the composite transistor,




r '  y
11




1
 2 r
o1  2
y 0
12
Darlington circuit behaves similar to
the single transistor but has a current
gain given by the product of current
gains of individual transistors.
DC Analysis: For F1, F2 >>1,
I I I   I
C C1 C2
F1 F2 B
VBE of composite transistor = 2 diode
voltage drops. So VCE >(VBE1 + VBE2) .
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Richard C. Jaeger, Travis N. Blalock
y
gm '  y  g / 2
21 m2
1




ro'   y   (2 / 3)r
o2
 22 
o'  21
 
o1 o2
y
11 v  0
2
v
m ' 2
 m /3
f v
f2
1 i 0
2
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Direct-coupled Amplifiers: Cascode
Circuit
AC Analysis: For the composite transistor,




r '  y
11




1
r
1
y 0
12
Cascode circuit is cascade connection
of C-E and C-B amplifiers, used in
high gain amplifiers and high output
resistance current sources.
DC Analysis: For a high current gain,
I  I  I  I
F C1 C1
C C2
For forward-active operation of Q2,
V
V V
V
V
 2V
BB
BE
CE1 BB BE2
BE1
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y
o '  21
gm '  y  g
21 m1
1




ro'   y    r
o2 o2
 22 

o1
y
11 v  0
2
v
m ' 2
 m
o2 f 2
f v
1 i 0
2
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Differential Amplifiers
• Differential amplifiers,also
considered the C-C/C-B
cascade, eliminate the bypass
capacitors as well as the
external coupling capacitors at
the input and output of directcoupled amplifiers.
• Each circuit has two inputs.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
• Differential-mode output
voltage is the voltage
difference between
collectors, drains of the
two transistors.Ground
referenced outputs can
also be taken from
collector/drain.
• Ideal differential
amplifier uses perfectly
matched transistors.
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Bipolar Differential Amplifiers: DC
Analysis
Terminal currents are also equal.
I I I
C1 C2 C
V
V
EE
BE
I 
E
2R
EE
I
E1
I
V
BE1
V
BE2
V
I
E
I
B1
I
B2
I
B
I
I  I
F E
C
V V V
I R
C1 C2 CC C C
Both inputs are set to zero,
emitters are connected together.
E2
I  C
B 
F
V
V
CE1 CE2
V
V V  0V
OD C1 C2
BE
If transistors are matched, VC1 VC2 VC
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Richard C. Jaeger, Travis N. Blalock
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Small-Signal Transfer Characteristic
The current switch is a digital application of the differential amplifier.
Large-signal transfer characteristic of differential amplifier is given by:







v














v
BE1
BE2
I  I  2 I tanh
 2 I tanh id
C1 C2
C
C
2V
2V
T
T








v
3
 v  1 v 
v
2
 2I  id    id    id
C  2V  3  2V  15  2V
 T  T
 T
5

v
17
 
 id
 315  2V

 T








7



  ...






Even-order distortion terms are eliminated.This increases signal-handling
capability of differential pair. For small-signal operation, liner term must
be dominant. Hence, we set the third-order term to be one-tenth the linear
term.
v  2V 0.3  v  27mV
id
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Richard C. Jaeger, Travis N. Blalock
T
id
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Bipolar Differential Amplifiers: DC
Analysis (Example)
• Problem: Find Q-points of transistors in the differential
amplifier.
• Given data: VCC=VEE=15 V, REE=RC=75k, F =100
15  0.7 V
V
V

EE
BE
• Analysis:
I 
 
 95.3mA
E
2R
EE
2(75103)
100
I  I 
I  94.4mA
F E 101 E
C
I
94.4mA
I  C 
 0.944mA
B 
100
F
V 15 I R  7.92V
C
C C
V V V  7.92V - (-0.7V)  8.62V
CE C E
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Richard C. Jaeger, Travis N. Blalock
Due to symmetry, both
transistors are biased at Qpoint (94.4 mA, 8.62V)
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Bipolar Differential Amplifiers: AC
Analysis
v
v  v  id
1 ic 2
v
v  v  id
2 ic 2
Add = differential-mode gain
Acd = common-mode to differential-mode
conversion gain
Acc = common-mode gain
Adc = differential mode to common-mode
conversion gain
Circuit analysis is done by
superposition of differential-mode
For ideal symmetrical amplifier, Acd = Adc = 0.
and common-mode signal portions.

 v
v v
voc  c1 c2
2
v
 A
A  v 
 od    dd cd   id 



 
v
A

 v 
A
 oc 
cc   ic 
 dc
v  v v
od c1 c2
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Richard C. Jaeger, Travis N. Blalock
v  A
0  id 

od

 dd
voc   0 A  v 
cc  ic 





Purely differential-mode input gives purely
differential-mode output and vice versa.
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Bipolar Differential Amplifiers: Differential-mode
Gain and Input Resistance
v
v
v  id  ve v   id  ve
3 2
4
2
( gm  g )(v  v )  G ve
EE
3 4
ve(G  2g  2gm)  0  ve  0
EE
Emitter node in differential amplifier represents
virtual ground for differential-mode input signals.
v
v
v   id
v  id
4
2
3 2
Output signal voltages are:
v
v
v   gm R id
v   gmR id
c2
C 2
c1
C 2
v
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od
  gm R v
C id
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Bipolar Differential Amplifiers: Differential-mode
Gain and Input Resistance (contd.)
Differential-mode gain for balanced output, vod  vc1  vc2 is:
v
A  od
  gm R
C
dd v
id v  0
ic
If either vc1 or vc2 is used alone as output, output is said to be single-ended.
A
A
v
gm R
v
gm R
c1
C
dd
c2
C
A 


A


  dd
dd1 v
dd 2 v
2
2
2
2
id v  0
id v  0
ic
ic
Differential-mode input resistance is small-signal resistance presented to
differential-mode input voltage between the two transistor bases.
(v / 2)
R  v / i  2r
i  id
id
id b1
b1
r
If vid =0, R  2( R r )  2R . For single-ended outputs, R  RC
od
C o
C
od
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Richard C. Jaeger, Travis N. Blalock
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Bipolar Differential Amplifiers: Common-mode
Gain and Input Resistance
Both arms of differential amplifier are symmetrical.
So terminal currents and collector voltages are equal.
Characteristics of differential pair with commonmode input are similar to those of a C-E (or C-S)
amplifier with large emitter (or source) resistor.
v
ic
i 
b r  2(  1)R

o
EE
Output voltages are:
 o R
C
v  v  oi R 
v
c1 c2
b C r  2(  1)R
ic

o
EE
ve  2( o 1)i R
b EE
2( o 1)R
EE v  v

ic ic
r  2( o 1)R
EE
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Bipolar Differential Amplifiers: Common-mode
Gain and Input Resistance (contd.)
Common-mode gain is given by:
o R
R
V
v oc
C
C
Acc 


 C
v
r  2( o 1)R
2R
2V
EE
EE
EE
ic v  0
id
For symmetrical power supplies, common-mode gain =0.5. Thus, commonmode output voltage and Acc is 0 if REE is infinite. This result is obtained since
output resistances of transistors are neglected. A more accurate expression is:














1
1

o ro 2R
EE
v  v  v  0 Therefore, common-mode conversion gain is found to be 0.
od c1 c2
v
r  2( o 1)R
ic
EE  r  (  1)R
R 

o
ic 2i
EE
2
2
b
Acc  R
C
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Common-Mode Rejection ratio (CMRR)
• Represents ability of amplifier to amplify desired differential-mode input
signal and reject undesired common-mode input signal.
• For differential output, common-mode gain of balanced amplifier is zero,
CMRR is infinite. For single-ended output,
A
A /2
CMRR  dm  dd

Acm
Acc
1








1 
1

2
om f 2 gm REE 

• For infinite REE , CMRR is limited by omf . If term containing REE is
dominant CMRR  gm REE  40IC REE  20VEE
Thus for differential pair biased by resistor REE , CMRR is limited by
available negative power supply.


2( g  g )
 g  g
CMRR

g
R
 g 1 g 2 gives fractional
,
• Due to mismatches,
m EE 
g

1 2
 g 
mismatch between small-signal device parameters in the two arms of
differential pair. Hence gmREE product is maximized.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Analysis of Differential Amplifiers
Using Half-Circuits
• Half-circuits are constructed by first
drawing the differential amplifier in a
fully symmetrical form- power supplies
are split into two equal halves in parallel,
emitter resistor is separated into two
equal resistors in parallel.
• None of the currents or voltages in the
circuit are changed.
• For differential mode signals, points on
the line of symmetry are virtual grounds
connected to ground for ac analysis
• For common-mode signals, points on line
of symmetry are replaced by open
circuits.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Bipolar Differential-mode Half-circuits
Direct analysis of the half-circuits yield:
v
  gmR id
c1
C 2
v
v   gm R id
c2
C 2
v
vo  v
Applying rules for drawing halfcircuits, the two power supply
lines and emitter become ac
grounds. The half-circuit
represents a C-E amplifier stage.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
c1
v
c2
  gm R v
C id
R  v / i  2r
id
id b1
R  2( R ro )
C
od
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Bipolar Common-mode Half-circuits
• All points on line of symmetry become open circuits.
• DC circuit with VIC set to zero is used to find amplifier’s
Q-point.
• Last circuit is used for for common-mode signal analysis
and represents the C-E amplifier with emitter resistor 2REE.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Bipolar Common-mode Input Voltage
Range
V V
 I R V  0
CB CC C C IC
V V
V
BE
EE
IC
I 
F
C
2R
EE

V
V 
R

C  EE BE 
1
F 2R
V
EE
CC
V V
IC CC
R
C
1 
F 2R
EE
For symmetrical power supplies, VEE >> VBE, and RC = REE,
V
V  CC
IC
3
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Biasing with Electronic Current Sources
• Differential amplifiers are biased using electronic
current sources to stabilize the operating point and
increase effective value of REE to improve CMRR
• Electronic current source has a Q-point current of ISS
and an output resistance of RSS as shown.
• DC model of the electronic current source is a dc
current source, ISS while ac model is a resistance RSS.
SPICE model includes both ac
and dc models.
V
I
I  0
DC SS R
SS
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
MOSFET Differential Amplifiers: DC
Analysis
K
2
 n V V 
D
GS TN 
2 
I
2I
D
V V 
V  SS
TN
GS TN
Kn
Kn
I
V V
V
I R
and Vo  0
Op amps with MOSFET inputs have a D1 D2 DD D D
high input resistance and much higher
V
V V V
 I R V
D S
DD D D GS
DS
slew rate that those with bipolar input
stages.
Using half-circuit analysis method, we
see that IS = ISS /2.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Small-Signal Transfer Characteristic
MOS differential amplifier gives improved linear input signal range and
distortion characteristics over that of a single transistor.
Kn 

2
2
v

I I 
V
v
V
 GS1

D1 D2
TN
TN
GS2
2

 

For symmetrical differential amplifier with purely differential-mode input
v
v
id
v
V 
v
V  id
GS1 GS 2
GS2 GS 2
I
D1
I
 Kn V V v  gmv
TN  id
D2
id
 GS
Second-order distortion product is eliminated and distortion is greatly
reduced. However some distortion prevails as MOSFETs are nor perfect
square law devices and some distortion arises through voltage dependence
of output impedances of the transistors.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
MOSFET Differential Amplifiers: DC
Analysis
(Example)
• Problem: Find Q-points of transistors in the differential
•
•
amplifier.
Given data: VDD=VSS=12 V, ISS =200 mA, RSS = 500 k, RD =
62 k, l = 0.0133
V-1, Kn = 5 mA/ V2, VTN =1V
I
I  SS 100mA
Analysis: D 2
V
 1
GS
200mA
 1.20V
2
5mA/V
 12V - (100mA)(62k ) 1.2V  7V
DS
To maintain pinch-off operation of M1 for nonzero VIC ,
V
V
V - V
- I R  V
GD IC  DD D D  TN
V V
- I R V
 6.8V
IC DD D D TN
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
MOSFET Differential Amplifiers: Differentialmode Input Signals
Source node in differential amplifier represents virtual ground
Differential-mode gain for balanced output is
v
A  od
dd v
id v
ic
0
  gm R
D
Gain for single-ended output is
v
v
  gm R id
D 2
d1
v
v   gm R id
D 2
d2
v
v
od
  gm R v
D id
A
 d1
dd1 v
id v
ic
0
A
gm R
D

 dd
2
2
A
gm R
d2
D   dd
A


dd 2 v
2
2
id v  0
ic
R  2R
R 
D
od
id
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
v
Copyright © 2005 – The McGraw-Hill Companies srl
MOSFET Differential Amplifiers: Commonmode Input Signals
Electronic current source is modeled by twice its smallsignal output resistance representing output resistance of the
current source.
Acc 
v oc
v
ic v
id
Common-mode half-circuit is similar to inverting amplifier
with 2RSS as source resistor.
2 gm R
 gm R
SS v  v
D v
v v 
vs 
d1 d2 1 2g R
ic
ic ic
1

2
g
R
m SS
m SS
v  v  v  0 Thus, common-mode conversion gain= 0
od d1 d2
gm R
R
Due to infinite current gain of
D
D


FET, ro can be neglected.
1 2 g m R
2R
SS
SS
0
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
R 
ic
Copyright © 2005 – The McGraw-Hill Companies srl
Common-Mode Rejection ratio (CMRR)
• For purely common-mode input signal, output of balanced MOS
amplifier is zero, CMRR is infinite. For single-ended output,
Adm Add / 2  ( gm RD ) / 2
CMRR 


 gmR
SS
Acm
Acc
 R /(2R )
D
SS
• RSS (which is much > REE and thus provides more Q-point stability)
should be maximized.
• To compare MOS amplifier directly to BJT amplifier, assume that
MOS amplifier is biased by
V V
2I R
I R
(V V )
SS
GS
D
SS
SS
SS
SS GS
R 

CMRR



SS
I
V V
V V
V V
SS
GS TN
GS TN
GS TN
• From given data in example, MOS amplifier’s CMRR=54 or 35 dB
(almost 10 dB worse than BJT amplifier).To increase CMRR in BJT
and FET amplifiers, current sources with higher RSS or REE are used.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Two-port model for Differential
Amplifiers
i  gmv
dm
dm
gm
vcm
icm 
vcm 
1 2 g m R
2R
EE
EE
R  2ro
od
Roc  2m R
f EE
Two-port model simplifies circuit analysis of differential
amplifiers.
Expressions for FET are obtained by substituting RSS for
REE.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Differential Amplifier Design (Example)
• Problem: Find Q-points of transistors in the differential amplifier.
• Given data: Adm=40 dB, Rid >250 k, single-ended CMRR> 80 dB, VIC
at least ±5V, MOSFETs with: l = 0.0133 V-1, Kn’ = 50 mA/ V2, VTN =1V,
BJTs with : F =100, VA =75V, IS =0.5 fA
• Assumptions: Active-region operation, symmetrical power supplies, o =
F, vid maximum of ±30 mV.
• Analysis:
Adm=40 dB =100. To achieve this gain with resistively loaded amplifier, we
use BJT. For Adm = gm RC =40 IC RC , required gain can be obtained with
voltage drop of 2.5 V across RC.
For bipolar differential amplifier, Rid =2r, so, r =125 k.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
oV
T  20μA
I 
C
r
Copyright © 2005 – The McGraw-Hill Companies srl
Differential Amplifier Design (Example
contd.)
Choose IC = 15 mA to provide safety margin. So RC =2.5 V/15 mA =167 k.
Choose RC = 180 k as the nearest value with 5% toleranceand alos to
compensate for neglecting ro in the analysis.
VIC of 5V requires collector voltage to be at least 5 V at all times. We also
know that vid can be a maximum of ±30 mV for linearity. So ac
component of differential output will not be greater than 100(0.03 V)=3V,
half of which appears at each collector. Thus dc signal across RC won’t
exceed 4 V( 2.5 V dc + 1.5 V ac) and positive power supply must fulfill
V V  4V  (5  4)V  9V
CC IC
Choose VCC =10 V to dive desired margin of 1 V, For symmetrical supplies,
VEE = -10 V. Single-ended CMRR of 80 dB needs
CMRR
104
Choose current source with IEE
R 

 16.7MΩ
EE
=30 mA and REE > 20 M
gm
(40 / V)(15μA)
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Two-stage Prototype of an Op Amp
• For higher gain, pnp C-E amplifier is
connected at output of the input stage
differential amplifier.
• Virtual ground at emitter node allows
input stage to achieve full inverting
amplifier gain without needing emitter
bypass capacitor.
• Pnp transistor permits direct coupling
between stages, allows emitter of pnp
to be connected to ac ground and
Differential amplifier provides
provides required voltage level shift to
desired differential input,CMRR
bring output back to zero.
and ground referenced output as
• Bypass and coupling capacitors are
the input stage of op amp.
thus eliminated.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Two-stage Op Amp: DC Analysis
This circuit requires a resistance in
From dc equivalent circuit, IE1= IE2 = I1 /2. If
series with emitter of Q3 to stabilize Q- base current of Q3 is neglected and C-B
point (as collector current of Q3 is
current gains are one,
I R
V
V
V
 1 C V
exponentially dependent on baseBE
CE1 CE2 CC
2
emitter voltage), at the expense of
As both inputs are zero, output also=0
voltage gain loss.
I V / R
V
V
C3 EE
EC3

CC


I 
V
V ln 1 C3 
EB3 T  I 

S3 

IS3 is saturation current. For zero offset voltage


I 
V
T
R
ln 1 C3 

C  

I 

I
I



S3 
1  C3  

 F2 2
 

F3 

2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Two-stage Op Amp: AC Analysis
(Differential Mode) Half-circuit can be constructed from ac
equivalent circuit in spite of asymmetricity, as
voltage variations at collector of Q2 don’t
substantially alter transistor current in
forward-active operation region.
From small-signal circuit model,
v
g
g
c2
m
2
A 

R   m2 ( R r )
vt1 v
C 3
2 L1
2
id
vo
A 
 g R
vt2 v
m3
c2
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Two-stage Op Amp: AC Analysis
(Differential
Mode
contd.)
v
g
g R
 R
vo
c2
m
2
m
2
C
o3
A 

 A A 
( R r )( g R) 
vt1 vt2
C 3
m3
dm v
v v
2
2
R r
C 3
id
id c2
vo
This can be rewritten
as

g

R   R g
1
A  
dm 2
R  1  40I R    40I R 
m2 C  o3  m3    C 2 C  o3 C3 
I
g R 
2
40 C3 I R  
m3 C o3
C 2 C o3
I
C2
Base current of Q3 is neglected so, IC2RC=VBE3=0.7 V, IC3R=VEE,
Upper limit onIC2 and I1 is set by maximum dc bias
EE
current at input, lower limit on IC3 is set by minimum
A 


dm
28  IC 3  current to drive total load impedance at output.
1


  I 
o3  C 2 
560V
R  v / i  2r  2r
 2 1
id
id id
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Rout  R r  R
o3
Copyright © 2005 – The McGraw-Hill Companies srl
Two-stage Op Amp: AC Analysis
(Common Mode) From ac equivalent circuit for commonmode inputs,
 v
g v
g v
o
2
m
2
m2 ic
ic
ic
i 


g
c2 r  2(  1)R
1 2 g R
2
o2
1 1 2 m2 R1
m2 1

o2
For differential-mode inputs, collector
g
current was
i  m2 v
c2
2 id
From ac equivalent circuit, we
Thus,
2A
g R
 R
observe that circuitry beyond
m2 C
o3 
dm
collector of Q2 is same as that in
1 2 g R R  r
1 2 g R
m
2
1
C

3
m2 1
differential mode half-circuit.
A
1 2 g R
The difference in collector
m2 1  g R
CMRR  dm 
m2 1
currents causes difference in
Acm
2
output voltage.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Improving Op Amp Voltage Gain
Overall amplifier gain decreases rapidly as the
quiescent current of second stage decreases.
Voltage gain can improve if resistor in second
stage is replaced by current source with R2 >>
ro3, if R2 is neglected,
g
A  A A   m2 ( R r )( g r )
C 3
m3 o3
dm vt1 vt2
2
This expression can be reduced to
560V
A3
A 
Rout  R r  r


dm
2 o3 o3
28  IC 3 
1


  I 
o3  C 2 
Output resistance is degraded, amplifier more represents
transconductance amplifier than a true low output
resistance voltage amplifier.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Reducing Output Resistance
From ac equivalent circuit,
g
A   m2 ( R r )
v1
C 3
2
A   g (r RCC )
v2
m3 o3 in
A 
v3 r
(
4
A C-C stage is added to the
prototype to maintain voltage
gain but reduce output
resistance.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
o4
 (
1) R
 r  ( 1)R
RCC
in
L
4
o4
L
1
1) R
L
o4
v v v
A  2 3 oA A A
R  2r
vt1 vt2 vt3
dm v v v
2
id
id 2 3
R
r
1
1
th
4
Rout 


 o3
g
 1 g
 1
m4
o4
m4
o4


m


I
1 
f
3

C
4

1


g   1 I 
m4 
o4
C3 
Copyright © 2005 – The McGraw-Hill Companies srl
Three-Stage Bipolar Op Amp Analysis
•
•
•
Problem: Find differential-mode gain, CMRR, input and output
resistances.
Given data: VCC=VEE=15 V, o1 = o2 = o3 = o4 =100, VA3 =75V, I1 = 100
mA, I2 = 500 mA, I3 = 5 mA, R1 = 750 k , RL = 2 k, R2 and R3 are
infinite.
g  40I  40( I )  1.98mS
m2
C2
F2 E2
Analysis:
I
I
3  550mA
I  I  I  I  E4  I 
C3 2 B4 2  1 2  1
F4
F4
g  40I  2.2 10 2S
m3
C3

 o3  4.55k
3 g
m3
r
Voltage at node 3 is one base-emitter voltage
drop above zero. VEC3=15-0.7=14.3 V.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Three-Stage Bipolar Op Amp Analysis
(contd.)
g
V V
A   m2 ( R r )  3.50
v1
C 3
2
C3


r
  1980
A


g
(
r

(


1
)
R
)
I   I  4.95mA
 o3  4
v
2
m
3
L 
o4

C4 F4 E4
(  1)R
 V
L  0.998 1
o4
A 
r  o4 T  505
v3 r  (  1)R
4 I
L
4
o4
C4
V
A  A A A  6920
EB3  15.9k
R 
dm vt1 vt2 vt3
r
C
I
1
C3
o3 1.61kΩ
I 
R


R

2
r

101
kΩ
C2 
out g
2
id
 1
F3
m4 o4
CMRR  g R  1490  63.5dB
m2 1
Overall gain is lower because of lower gain of first stage (since r3 << RC) and
lower gain than expected for second stage (as reflected loading of RL is of same
order as ro3).
r  A3
o3
I
EC3  162k
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
CMOS Op Amp Prototype: Circuit
• Differential amplifier (M1
and M2) followed by C-S
stage M3 and source
follower M4.
• Current sources are used
to bias differential input
and source follower
stages and as load for M3.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
CMOS Op Amp Prototype: AC Analysis









V

GS
3
A  A A (1)  m

dm vt1 vt2
f3V

V
GS 2 TN 2 




K
K
2
I


1
n2 p3 
D3 V



TP3 
l I
I
K


3 D2 D3 
p3

Design freedom is higher than in bipolar case
due to Q-point dependence of mf. Operating
A A A A 
currents should be reduced and M3 should
dm vt1 vt2 vt3


have small l to achieve higher gain. Input

R
g
 g
 m2

m 
R  m4 L 
bias current doesn’t restrict ID1 as IG =0.
f 3 2 D  1 g R 
1


Rout 
R 
m4 L 

id
g
m4
Since source follower has unity gain,
CMRR  g R
m2 1
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
BiCMOS Amplifiers
•
•
• Integrated circuit processes that offer
combination of bipolar and MOS transistors •
or bipolar transistors and JFETs are called
BiCMOS and BiFET technologies
respectively.
• Input PMOS transistors give high input
resistance, can be biased at relatively high
input currents, which can improve slew
rate.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Second gain stage uses BJT
with superior amplification
factor than FET.
RE increases voltage across
RD2 and hence the voltage
gain of first stage without
reducing amplification
factor of Q1.
Follower stage uses another
FET to maximize secondstage gain while maintaining
reasonable output resistance.
Copyright © 2005 – The McGraw-Hill Companies srl
Op Amp Output Stages
• Output stage is designed to provide low output resistance
and relatively high current drive capability.
• Followers: Class-A amplifiers- transistors conduct during
full 3600 of signal waveform, conduction angle =3600.
• Push-pull: Class-B- each of the two transistors conducts
during 1800of signal wavefrom, conduction angle =1800.
• Class-AB: Characteristics of Class-A and Class-B are
combined, most commonly used as output stage in op
amps.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Source-Follower: Class-A Output Stage
For a source-follower,difference between input and output
voltages is fixed and voltage transfer characteristic is as
shown. If load resistor is connected to output, total source
vo
i

I

0
current:
S
SS
R
L
vMIN = -ISS RL and iS=0, M1cuts off when vI = -ISS RL + VTN.
If output signal is given by:
vo V
sint
DD
Efficiency of amplifier is given by:
2
V
DD
2R
Pac
L


 25%
Pav 2 I V
SS DD
Low efficiency is due to current ISS that constantly
flows between the two supplies.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Class-B Push-Pull Output Stage
Improve efficiency by operating transistors at
zero Q-point current eliminating quiescent
power dissipation. NMOS transistor is a
source-follower for positive input signals and
NMOS transistor is a source-follower for
negative input signals.
V
2
DD
2R
Pac
L  78.5%


2
V
Pav
2 DD
R
L
Since neither transistor conducts when,
V v
V
TP GS
TN
output waveform suffers from a dead-zone or
crossover distortion.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Class-AB Amplifiers
The required bias voltage can be
developed as shown.We assume that
bias voltage splits equally between
gate-source(or base-drain) terminals.
Benefits of Class-B amplifier can be
maintained without dead zone by
biasing transistors into conduction
but at a low quiescent current level
Currents are given by
2
(<< peak ac current delivered to

K n V

 GG V

I 
load). For each transistor, 1800<


D
TN
2


2
0


conduction angle <360 .
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock







I R 
I  I exp B B 
C S
2V 
T 
Copyright © 2005 – The McGraw-Hill Companies srl
Class-AB Output Stages for Op Amps
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Short-Circuit Protection
High current, high power dissipation or direct destruction
of base-emitter junction can destroy the BJT if output of a
follower circuit is accidentally shorted to ground. Q2 is
added to protect the emitter follower.
Normally, voltage across R is <0.7 V, Q2 is cutoff. Q2 turns
on to shunt extra current away from base of Q1. IE1 is
limited to I V
/ R  0 .7 / R
E1
BE 2
For complementary output stage, similar
current-limiting circuitry is used. In
MOSFET complementary output stages,
output current is limited to
V
 2I / K
V
G n2
TN
2
GS
2
I 

S1
R
R
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Transformer Coupling: Follower
Transformer coupling is used in
amplifiers to achieve high voltage gain
and efficiency while delivering power
to low impedance loads.
Coupling capacitor blocks dc path
through primary of transformer.
v  nv
1
2
i  ni
2
1
Z  n2Z
L
1
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Transformer provides impedance
transformation by n2 . From ac
equivalent circuit,transistor must
drive R
 n2 R
L
EQ
v
vo  1
n
Transformer restricts operation to
frequencies >dc.
Copyright © 2005 – The McGraw-Hill Companies srl
Transformer Coupling: Inverting
Amplifier and Class-B Output Stage
Inductance permits signal voltage to swing
symmetrically above and below VDD.
As both quiescent
At dc, transformer is a short circuit,
operating currents
quiescent operating current is supplied
= 0, emitters can be
through transformer primary. At signal
directly connected
2
frequency load n RL is presented to
to transformer
transistor.
primary.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Electronic Current Sources: Introduction
• Current through ideal current
source is independent of
voltage across its terminals and
the output resistance is infinite.
• In electronic current sources,
current depends on voltage
across the terminals and they
have a finite output resistance.
Current
source
Current
sink
Single-transistor current sources operate in only one quadrant of i-v space but
realize very high output resistances.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Current Sources: Figure of Merit
V  Io Rout
CS
is used as a figure of merit for comparing different current sources.
For a given Q-point current, VCS represents the equivalent
voltage that will be needed across a resistor to achieve same
output resistance as given current source.
For resistor:
For BJT:
For MOSFET:
V
V  Io Rout  EE R V
EE
CS
R
V V
V  Io Rout  I ro  I A CE V V V
CS
C
C
A CE A
I
C
1
V
V  Io Rout  I ro  I l DS  1 V  1
D
D I
CS
l DS l
D
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Higher Output Resistance Sources
For MOSFET:
Rout  ro (1 gm R )  m R
S
f S
V
V  m SS
CS
f 3
Output resistance of the current source
can be increased by placing a resistor
in series with the emitter or source of
the transistor.
For BJT: 
Rout  ro 1
o R







E

R R  r  R

E
1 2

V  o(V V )  oV V  o(V V )  oV
CS
A CE
A CS
A CE
A
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Multiple Output Current Sources
V V V V  0.7
E B BE B
Assume equal current gains for all BJTs.
(V  0.7) 15
I  I  I  B
B1 B2 B3
 1
F1

1
1
1 






22
k

4
.
7
k

0
.
47
k



R
1 V  3.18V
V 
BB R  R SS
1 2
RR
R  1 2  3.39k
BB R  R
1 2
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
V  15  3.18  ( I  I  I )(3390)  12V
B
B1 B2 B3
V  12  0.7  12.7V
E
V 15
I   I  E
 103μA
C1 F B1 F 22kΩ
I   I  484μA IC 3   F I B3  4.84mA
C 2 F B2
Copyright © 2005 – The McGraw-Hill Companies srl
Multiple Output Current Sources
(contd.)
Output resistances of the three current sources are given by:













Rout  ro 1
o
R R  r
1 1 2
R
E
 31.8MΩ



























72.7
100
1
I
R R  r
C
1 1 2
R
E













R
out1
R
 5.48MΩ
out2
R
 177kΩ
out3
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Bipolar Transistor Current Source
Design Example
•
•
•
Problem: Design a current source with the largest possible output
voltage range that meets the given output resistance specification.
Given data:VEE = 15 V, Io = 200 mA, IEE < 250 mA, Rout > 2 M,
BJTs available with (o, VA) = (80, 100 V) and (150, 75 V), VB
must be as low as possible.
Assumptions: Active region and small-signal operating
conditions. VBE = 0.7 V, VT = 0.025 V, choose Vo = 0 V as





R
representative output value. 

o
E
Rout  ro 1
 r
Analysis:  R R  r  R  o o

E 
1 2 

V  Io Rout  oV
CS
A
oV  IoRout  (200μA)(10MΩ)  2000V
A
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Bipolar Transistor Current Source
Design Example (contd.)
Both BJTs can satisfy these conditions. But, we choose BJT (150, 75V)
with higher oVA product.
Total current < 250 mA. As output current is 200
mA, maximum of 50 mA can be used by base bias
network. Current used by base bias network must
be 5 to 10 times base current of BJT (1.33 mA for
BJT with a current gain of 150). So bias network
current =20 mA.
Large RBB reduces output resistance and output
compliance range (increase VBB).Trading
increased operating current for wider compliance
range, choose bias network current of 40 mA.
R  R  15V  375k
1 2 40mA
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Bipolar Transistor Current Source
Design
Example
(contd.)
• Following set of equations can be used in a spreadsheet analysis
to determine design variables. Primary design variable is VBB
which can be used to determine other variables.
I
I  o
B 
F
V

V


BB
BB


R  (R  R )
 375k

1
1 2 15
 15 


R R R
BB 1 2
V V  (V V  I R )
EE
BB BE B BB
CE
V V
ro  A CE
Io
oV
T
r 
Io
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
R  ( R  R )  R  375k  R
2
1 2
1
1
V V  I R 
BB BE B BB 
R 

E F
Io















Rout  ro 1
o R
E
R R  r  R
E
1 2







Copyright © 2005 – The McGraw-Hill Companies srl
Bipolar Transistor Current Source
Design Example (contd.)
• From spreadsheet, smallest VBB for which output resistance >
10M with some safety margin is 4.5 V, resulting output
resistance is 10.7M.
• Analysis of circuit with 1% resistor values gives Io = 200 mA and
supply current = 244 mA.
• Final current source design is as shown.
• MOSFET current source design can also be analyzed in similar
manner.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl