Lecture 26
Differential Amplifiers (I)
DIFFERENTIAL AMPLIFIERS
Outline
1.
2.
3.
Introduction
Incremental analysis of differential
amplifier
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
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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
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1. Introduction
Two problems found in single-transistor amplifier stages
are:
•
Bias and gain sensitivity to device parameters (µCox,
V T)
– 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.
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Introduction (contd.)
Solution : represent relevant signal by the difference
between two voltages
Differential Amplifier:
• Amplifies difference between two voltages
• Rejects components common to both voltages
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MOSFET Differential Amplifier
Basic 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 ⇒ vO
unchanged.
•
Need precise device matching
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Differential-mode and Common-mode signals
Distinguish between common-mode and differential-mode:
v I1 = v IC +
v ID
,
2
v I 2 = v IC −
Then:
v ID = v I1 − v I 2 ,
v IC =
v ID
2
v I1 + v I 2
2
Similarly at the output:
v O1 = v OC +
v OD
,
2
v O 2 = v OC −
v OD
2
Then:
v OD = v O1 − v O 2 ,
6.012 Electronic Devices and Circuits-Fall 2000
v OC =
v O1 + v O 2
2
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2. Incremental analysis of differential amplifier
Consider generic differential amplifier:
Figures of Merit:
Differential-mode voltage gain (want it high):
adm =
v od
v id
Common-mode voltage gain (want it small):
acm =
v oc
v ic
Common-mode rejection ratio (want it very high):
CMRR =
6.012 Electronic Devices and Circuits-Fall 2000
a dm
a cm
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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”.
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Incremental analysis of differential amplifier
Differential-mode Analysis
No voltage relative to ground along axis of symmetry ⇒
circuit identical to:
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Incremental analysis of differential amplifier
Differential-mode Analysis (contd.)
Need to solve:
Differential-mode voltage gain:
a dm
v od v o 2 − v o1
=
=
v id
v i 2 − v i1
In differential –mode:
v i1 = − v i 2 =
v id
2
and v o1 = − v o 2
Then:
a dm
2 v o1 v o1
=
=
v id
v id
2
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Incremental analysis of differential amplifier
Common-mode Analysis
No current across wires connecting the two half-circuits
⇒ circuit is identical to:
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Incremental analysis of differential amplifier
Common-mode Analysis (contd.)
Common-mode voltage gain:
a cm
v o 2 + v o1
v oc
2
=
=
v ic
v ic
In common–mode, vo1 = vo2, then:
a cm
6.012 Electronic Devices and Circuits-Fall 2000
v o1
=
v ic
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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:
VIC, max = VO1 + VT = VT + VDD − R D
I BIAS
2
• Lower limit to VI1 and VI2: set by circuit that
implements IBIAS.
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Common-source differential amplifier
(small-signal equivalent circuit model)
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Common-source differential amplifier
Differential-mode half circuit
v id
v o1 = −g m1R D
2
Then the differential mode gain is
a dm =
v o1
= −g m1R D
v id
2
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Common-source differential amplifier
Common-mode half circuit
g m1R D
v o1 = −
• v ic
1 + 2g m1rob
Then the common-mode gain is
a cm
v o1
g m1R D
=
=−
v ic
1+ 2g m1rob
Common-mode Rejection Ratio (CMRR):
CMMR =
adm
− g m1R D
= 1 + 2g m1rob
=
a cm − g m1R D
1 + 2g m1rob
To get good CMRR, need good current source.
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Large-signal response of differential
amplifier
Examine large-signal transfer function:
•
•
•
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 ⇒
v O1 = v O1,min = VDD − I BAIS R D ,
v O 2 = v O1,max = VDD
v OD,min = −I BAIS R D
•
Symmetric behavior for vI1 < vI2 and vI1 << vI2
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Large-signal response of differential amplifier
(contd.)
Saturating behavior for large differential input signals:
vID that leads to amplifier saturation (vI1 >> vI2 ):
v ID,sat = v GS1 − v GS 2
With:
v GS1 = VT +
I BAIS
W
µCox
2L
v GS 2 = VT
Then:
v ID,sat =
6.012 Electronic Devices and Circuits-Fall 2000
I BAIS
W
µCox
2L
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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)
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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
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Wrap-up of 6.012
6.012: Introductory subject to microelectronic devices
and circuits
•
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): fτ ↑ and gm ↑ as L ↓:
however, Avomax ↓ as L ↓
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
6.012 Electronic Devices and Circuits-Fall 2000
Lecture 26
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