Differential and Multistage
Amplifiers
1
7.1 MOS Differential Pair
Single transistor vs. Differential Pair
Where is I/P signal applied for the single transistor amplifier?
Where is I/P signal applied for the differential amplifier?
Why it is called differential amplifier?
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright  2004 by Oxford University Press, Inc.
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7.1 MOS Differential Pair
Differential Pair advantages:
• less sensitive to noise.
• Amplifier stages can be coupled without bypass/coupling capacitors
Differential I/P: difference between the signals at the two I/P terminals and can have several forms
(input signal at one terminal with the other terminal grounded, or opposite-polarity input signals
applied).
Microelectronic
Circuits - I/P:
Fifth Edition
Copyright
 2004
by Oxford University Press, Inc.
Common-mode
If the Sedra/Smith
same input is applied
to both
inputs.
3
I/P signals: AC (vid , vicm) & DC (VCM)
+vicm
+vicm
diff. I/P
DC Biasing
diff. I/P
Common I/P
(noise, interference)
DC Biasing
Copyright  2004 by Oxford University Press, Inc.
Common I/P
(noise, interference)
4
Biasing the MOS differential amplifier:
• To do amplification, transistors have to be in saturation mode
• To have perfect elimination (subtraction) for
noise/interference: transistors pair have to be matched &
biased equally (common-mode input VCM )
Saturation mode condition:
VGS ≥ Vt
(1)
VG -VD ≤ Vt
(2)
+
VCS
-
To maintain Q1 & Q2 in Saturation mode:
VCMmax =Vt +VDD - 0.5 I RD
(3)
Vov =VGS -Vt
VCMmin =-VSS +VCS + Vt + ?? = -VSS +V
CS
+
V
t
+
V
OV
(4)
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5
Common Mode I/P:
DC Biasing
Calculate: ID1 , ID2 , VGS , VS
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6
Use Slide Show
Example:
For VG=1V,
What are the mode of operation for Q1& Q2?
Calculate VS
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7
Use Slide Show
Example:
What are the mode of operation for Q1& Q2?
Calculate VS
𝐼𝐷1 = 0.5 ∗ 4𝑚 (𝑉𝐺𝑆1 − 0.5) 2
0.4𝑚 = 2𝑚 (𝑉𝐺𝑆1 − 0.5) 2
VGS1=0.95V , Vs = -0.35V , VGS2=0.35V
ID1=0.4mA , ID2=0 , Q1 in Saturation & Q2 off
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Use Slide Show
7.1.2 The MOS differential pair with a differential input signal vid
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9
7.1.3 Large Signal Operation: I-V Non-linear relation
As vid increasing gradually more portion of I passing in Q1 and less current passing in Q2.
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10
7.1.3 Large Signal Operation: I-V Non-linear relation
Vov =VGS -Vt
I-V linear range
How can we make the diff. amplifier have linear relation vid << 2VOV
between its I/P and its O/P ?
Copyright  2004 by Oxford University Press, Inc.
Small Signal Operation
Large Signal Operation
I-V linear range proportional to VOV value
,
𝑔𝑚 =
2𝑘𝑛′
𝑤
𝐼𝐷
𝑙
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12
7.2 Small-signal operation of the MOS differential amplifier
Small-signal condition: vid << 2VOV
Small-signal I/P: vid , vicm
diff. I/P
Common
I/P
+vicm
+vicm
DC Biasing
noise
DC Biasing
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noise
13
Small-signal analysis of the MOS differential amplifier
Differential I/P: vid
Differential Gain: vo/vid = Ad
Small-signal Analysis
Ad =vo/vid = gm RD
Including ro effect:
Copyright
by Oxford
Ad =vo/vid =
gm R2004
D//r
o University Press, Inc.
14
Differential Gain: Ad = vo/vid
By Half Circuit Technique:
Ad1 =vo1/vid = -0.5 gm RD//ro
Ad2 =vo2/vid = 0.5 gm RD//ro
Ad = vo/vid = (vo2 – vo1)/vid= gm RD//ro
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15
Common-Mode Gain: ACM
Common-Mode I/P: vicm
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright  2004 by Oxford University Press, Inc.
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Common-Mode Gain: Acm =vo/vicm
Half Circuit Technique
Acm1 =vo1/vicm = -RD/(2RSS+1/gm)
Acm1 =vo2/vicm = -RD/(2RSS+1/gm)
by Oxford University Press, Inc.
Acm Copyright
=vo/2004
vicm
= (vo2 – vo1)/vid= 0
17
Common-Mode Rejection Ratio:
CMRR = │Ad/Acm│
Ad1 =vo1/vid = -0.5 gm RD
Ad2 =vo2/vid = 0.5 gm RD
Ad = vo/vid = (vo2 – vo1)/vid= gm RD
Acm1 =vo1/vicm = -RD/(2RSS+1/gm)
Acm2 =vo2/vicm = -RD/(2RSS+1/gm)
Acm =vo/vicm = (vo2 – vo1)/vid= 0
CMRR1 = │Ad1/Acm1│ = 0.5 gm (2RSS+1/gm)
CMRR = │Ad/Acm│ = ∞
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18
Small-signal analysis of the MOS differential amplifier
Differential I/P: vid
Differential Gain: vo/vid = Ad
Small-signal Analysis
Voltage Gain from gate to drain=
total resistance at drain / total resistance at source
Ad =vo/vid = (2 RD //RL)/(2RS+2/ gm )
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19
7.3 BJT Differential Amplifier
Differential I/P (vid) + Common mode I/P (DC biasing VCM, noise vicm)
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20
Common-mode input signal VCM
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21
Large Signal Operation (AC analysis)
Linear relation: (small signal condition):
Vid << 2VT ;
Vid ≤ 0.5 VT
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22
Large Signal Operation
Rs : Extend the linear range at the expense of the gain
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright  2004 by Oxford University Press, Inc.
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7.3.4 Small Signal Operation
Small signal condition: Vid ≤ 0.5 VT
gm= IC/VT
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re= VT/IE
24
Small-signal analysis of the BJT differential amplifier
Differential Gain: Ad = vo/vid
DC
Small signal
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright  2004 by Oxford University Press, Inc.
25
Small-signal analysis of the BJT differential amplifier
Differential Gain: Ad = vo/vid
Ad1 =vo1/vid = 0.5 gm RC
Ad2 =vo2/vid = -0.5 gm RC
Ad = vo/vid = (vo2 – vo1)/vid= -gm RC
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright  2004 by Oxford University Press, Inc.
26
Small-signal analysis of the BJT differential amplifier
Differential Gain (in terms of re) : Ad = vo/vid
𝛼𝑅𝐶
2𝑟𝑒
𝛼𝑅𝐶
id = −
2𝑟𝑒
Ad1 =vo1/vid =
Ad2 =vo2/v
Ad = vo/vid = (vo2 – vo1)/vid= −
Microelectronic Circuits - Fifth Edition
Sedra/Smith
𝛼𝑅𝐶
𝑟𝑒
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27
Small-signal analysis of the BJT differential amplifier
Differential Gain (with Re)
𝛼𝑅𝐶
2𝑅𝑒 +2𝑟𝑒
𝛼𝑅𝐶
id = −
2𝑅𝑒 +2𝑟𝑒
Ad1 =vo1/vid =
Ad2 =vo2/v
Ad = vo/vid = (vo2 – vo1)/vid= −
𝛼𝑅𝐶
𝑅𝑒 +𝑟𝑒
Another approach:
Voltage Gain from Base to Collector =
-total resistance at Collector / total resistance at Emitter
Differential Input Resistance:
𝑅𝑖𝑑 = (β + 1)(2𝑅𝑒 + 2𝑟𝑒 )
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright  2004 by Oxford University Press, Inc.
28
Differential-Mode Gain Ad = vo/vid
Half Circuit Technique
Voltage Gain from Base to Collector =
-total resistance at Collector / total resistance at Emitter =
𝛼𝑅𝐶
2𝑟𝑒
𝛼𝑅𝐶
id =
2𝑟𝑒
Ad1 =vc1/vid = −
𝑣𝑐1
𝑅𝐶
=−
0.5𝑣𝑖𝑑
𝑟𝑒
Ad2 =vo2/v
Ad = vo/vid = (vc2 – vc1)/vid=
Microelectronic Circuits - Fifth Edition Sedra/Smith
𝛼𝑅𝐶
𝑟𝑒
Copyright  2004 by Oxford University Press, Inc.
29
Common-Mode Gain: Acm = vo/vicm
Half Circuit Technique
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright  2004 by Oxford University Press, Inc.
30
Common-Mode I/P Resistance
Half Circuit Technique
vo 1
Microelectronic Circuits - Fifth Edition
Sedra/Smith
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Example 7.4
Microelectronic Circuits - Fifth Edition
Sedra/Smith
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7.5 The Active-loaded MOS differential pair
Small-signal analysis (differential I/P)
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright  2004 by Oxford University Press, Inc.
33
Small-signal analysis (differential I/P)
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright  2004 by Oxford University Press, Inc.
34
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35
7.5 The Active-loaded MOS differential pair
Small-signal analysis (differential I/P)
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright  2004 by Oxford University Press, Inc.
36
Active-loaded BJT differential pair
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37