Lecture 26 - MITweb.mit.edu/6.012/FALL00/www/handouts/lec26.pdf · 6.012 Electronic Devices and...
Transcript of Lecture 26 - MITweb.mit.edu/6.012/FALL00/www/handouts/lec26.pdf · 6.012 Electronic Devices and...
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 1
Lecture 26Differential Amplifiers (I)DIFFERENTIAL AMPLIFIERS
Outline
1. Introduction
2. Incremental analysis of differential amplifier
3. Common-source differential amplifier
Reading Assignment:Howe and Sodini, Chapter 11, Sections 11-1-11.3, 11.6
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 2
Summary of Key Concepts
• In differential amplifiers, signals are represented by difference between two voltages
• Differential amplifier amplifies the difference between two voltages but rejects “common mode” signals– ⇒ Improved noise immunity
• Using “half-circuit” technique, small-signal operation of differential amplifiers is analyzed by breaking the problem into two simpler ones– Differential mode problem– Common mode problem
• Common-mode rejection ratio (CMRR) is an important figure of merit for differential amplifiers
• Differential amplifiers require good device matching
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 3
1. Introduction
• Bias and gain sensitivity to device parameters (µCox, VT)– Sensitivity can be mitigated but often at a price in
terms of performance or cost (gain, power, device area, etc.)
• Vulnerability to ground and power supply noise– In dense IC’s there is cross-talk, 60 Hz coupling,
substrate noise, etc.
Two problems found in single-transistor amplifier stages are:
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 4
Introduction (contd.)
Solution : represent relevant signal by the difference between two voltages
• Amplifies difference between two voltages• Rejects components common to both voltages
Differential Amplifier:
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 5
MOSFET Differential AmplifierBasic Configuration
• vO responds to difference between vI’s– If vI1 = vI2 ⇒ symmetry ⇒ vO1 = vO2 ⇒ vO = 0
– If vI1 > vI2 ⇒ M1 conducts more than M2 ⇒ i1 > i2⇒ vO1 < vO2 ⇒ vO < 0
• vO insensitive to common mode signals:– If both vO1 and vO2 move in sync, symmetry is
preserved ⇒ vO unchanged
– If ground VDD or VSS have noise, symmetry preserved ⇒ vO unchanged
– If VT or µCox change, symmetry preserved ⇒ vOunchanged.
• Need precise device matching
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 6
Differential-mode and Common-mode signals
Distinguish between common-mode and differential-mode:
2,
2 21ID
ICIID
ICI
vvv
vvv −=+=
Then:
2, 21
21II
ICIIID
vvvvvv
+=−=
Similarly at the output:
2,
2 21OD
OCOOD
OCO
vvv
vvv −=+=
Then:
2, 21
21OO
OCOOOD
vvvvvv
+=−=
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 7
2. Incremental analysis of differential amplifierConsider generic differential amplifier:
Figures of Merit:
id
oddm v
va =
Differential-mode voltage gain (want it high):
ic
occm v
va =
Common-mode voltage gain (want it small):
cm
dm
aa
CMRR =
Common-mode rejection ratio (want it very high):
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 8
Incremental analysis of differential amplifier (contd.)Two steps to simplify the problem:
1. Use superposition and break the problem into two:
2. Exploit symmetry:
Circuit broken into two “half circuits”.
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 9
Incremental analysis of differential amplifier Differential-mode Analysis
No voltage relative to ground along axis of symmetry ⇒circuit identical to:
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 10
Incremental analysis of differential amplifier Differential-mode Analysis (contd.)
Need to solve:
Differential-mode voltage gain:
12
12
ii
oo
id
oddm vv
vvvv
a−−
==
In differential –mode:
and 2 2121 ooid
ii vvv
vv −==−=
Then:
2
2 11
id
o
id
odm v
vvv
a ==
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 11
Incremental analysis of differential amplifier Common-mode Analysis
No current across wires connecting the two half-circuits ⇒ circuit is identical to:
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 12
Incremental analysis of differential amplifier Common-mode Analysis (contd.)
Common-mode voltage gain:
ic
oo
ic
occm v
vv
vv
a 212 +
==
In common–mode, vo1 = vo2, then:
ic
ocm v
va 1=
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 13
3. Common-source differential amplifier (source-coupled pair)
Biasing Issues: must keep MOSFET’s in saturation
• Upper limit to VI1 and VI2: MI and M2 driven into linear regime:
21max,BIAS
DDDTTOIC
IRVVVVV −+=+=
• Lower limit to VI1 and VI2: set by circuit that implements IBIAS.
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 14
Common-source differential amplifier (small-signal equivalent circuit model)
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 15
Common-source differential amplifier Differential-mode half circuit
211id
Dmo
vRgv −=
Then the differential mode gain is
Dmid
odm Rg
vv
a 11
2
−==
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 16
Common-source differential amplifier Common-mode half circuit
icobm
Dmo v
rgRg
v •+
−=1
11 21
Then the common-mode gain is
obm
obm
Dm
Dm
cm
dm rg
rgRgRg
aa
CMMR 1
1
1
1 21
21
+=
+−
−==
obm
Dm
ic
ocm rg
Rgvv
a1
11
21+−==
Common-mode Rejection Ratio (CMRR):
To get good CMRR, need good current source.
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 17
Large-signal response of differential amplifier
• If vI1 = vI2 ⇒ vO1 = vO2 ⇒ vO = 0
• If vI1 > vI2 ⇒ M1 conducts more than M2 ⇒ i1 > i2⇒ vO1 < vO2 ⇒ vO < 0
• If vI1 >> vI2 ⇒ M1 conducts strongly, M2 turns off
⇒ i1 ≈ IBIAS, i2 ≈ 0 ⇒
• Symmetric behavior for vI1 < vI2 and vI1 << vI2
Examine large-signal transfer function:
DBAISOD
DDOODBAISDDOO
RIv
VvvRIVvv
−=
==−==
min,
max,12min,11 ,
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 18
Large-signal response of differential amplifier (contd.)
Saturating behavior for large differential input signals:
vID that leads to amplifier saturation (vI1 >> vI2 ):
21, GSGSsatID vvv −=
With:
TGS
ox
BAISTGS
Vv
CL
WI
Vv
=
+=
2
1
2µµ
ox
BAISsatID
CL
WI
vµµ
2
, =
Then:
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 19
Large-signal response of differential amplifier (contd.)
• For small vID, vO is linear in vI ⇒ differential amplifier
• For large vID, vO saturates: once vID is large enough, vO independent of vID ⇒ logic inverter
Can do logic with this:
• Logic 0 = -VID,sat, logic 1 = VID,sat
• Regenerative if VO (swing) >VID,sat
• Used in some MOSFET logic styles
• Used with Si BJTs: Emitter-Coupled Logic (ECL)
• And GaAs FETs: Source-Coupled FET Logic (SCFL)
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 20
What did we learn today?
Summary of Key Concepts
• In differential amplifiers, signals are represented by difference between two voltages
• Differential amplifier amplifies the difference between two voltages but rejects “common mode” signals– ⇒ Improved noise immunity
• Using “half-circuit” technique, small-signal operation of differential amplifiers is analyzed by breaking the problem into two simpler ones– Differential mode problem
– Common mode problem
• Common-mode rejection ratio (CMRR) is an important figure of merit for differential amplifiers
• Differential amplifiers require good device matching
6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 21
Wrap-up of 6.012
• MICROELECTRONIC DEVICES– Semiconductor physics: electrons / holes and drift /
diffusion– Metal-oxide-semiconductor field-effect transistors
(MOSFETs): drift of carriers in inversion layer– Bipolar junction transistors (BJTs): minority carrier
diffusion• MICROELECTRONIC CIRCUITS
– Digital circuits (mainly CMOS): no static power dissipation; power ↓↓, delay ↓↓ & density ↑↑ as W & L ↓↓
– Analog circuits (BJT and CMOS): fττ ↑↑ and gm ↑↑ as L ↓↓: however, Avomax ↓↓ as L ↓↓
6.012: Introductory subject to microelectronic devices and circuits
Follow-on Courses
• 6.152J — Microelectronics Processing Technology• 6.720J — Integrated Microelectronic Devices• 6.301 — Solid State Circuits• 6.371 — Introduction to VLSI Systems• 6.374 — Analysis and Design of Digital ICs• 6.775 — Design of Analog MOS LSI