Lecture 13
High-Gain Differential Amplifier Design
Woodward Yang
School of Engineering and Applied Sciences
Harvard University
woody@eecs.harvard.edu
1
Overview
•
Background
This lecture investigates different topologies (and their
characteristics) that can be used to implement differential amplifiers
with extremely high gain. We will again be using cascoding.
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Review of Amplifier Characteristics
• Let’s review some of the characteristics of the different (singleended) amplifier topologies that we’ve looked at so far.
– We will augment this table when we look at the frequency
response characteristics of these amplifiers
Amplifier Type
Rin
Rout
Av
Ai
Commonsource/emitter
High
High
High
High
Commongate/base
Low
High
High
·1
Commondrain/collector
High
Low
<1
High
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Multi-Stage Amplifiers (Cascading)
• We can cascade different types of amplifiers to get desired
overall characteristics. Often want:
– High input impedance
– High gain
– Low output impedance
• Mix and match cascades of different types of amplifiers to get
desired result
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Common-Emitter Emitter-Follower Cascade
•
A common configuration (for discrete BJT amplifier design) is a common-emitter
emitter-follower (common-collector) cascade
– CE stage has high voltage gain and high input impedance
– CC stage has low output impedance to drive various load conditions
– CC stage also presents a high impedance load to the CE amplifier which
enables high voltage gain for the CE stage
RC
Rs
vS
Q2
R1
Q1
Cin
R2
vO
Cout
REA
REB
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CE
RE2
RLD
5
Common-Source Source-Follower Cascade
• Similarly, cascade a common-source amplifier with a sourcefollower.
RD
M2
Rs
M1
vO
Cout
vS
IS1
CS
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IS2
RLD
6
Building Op Amps
•
Op amps are an important component of modern CMOS IC’s. They used to designed as
general purpose amplifiers that can meet a variety of requirements. The main target was
extremely high gain (>1e5), high input impedance and low output impedance (like an ideal
amplifier). This was done (to some extent) at the expense of different aspects of
performance (e.g., speed, output voltage range, power, etc.). Designs these days are much
more tailored to have (good enough) performance w.r.t. the specific needs of particular
applications. Within an IC, often use Operational Transconductance Amplifiers (OTA).
•
Some performance parameters of op amps
– Gain and Bandwidth
•
–
Output Swing
•
–
Combat non-linearity with feedback
Noise and Offset
•
–
Maximize w.r.t. power supply (but supply shrinking in modern processes)
Linearity
•
–
Want as large as possible
Can minimize by trading off other parameters
Supply Rejection
•
Strong dependence on current source output resistance
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Simple One-Stage Op Amps
•
Two differential pair amplifiers that we have already seen can be used as op
amps. The low-frequency, small-signal gain of both is gmN(roN||roP). The
capacitive loads (CL) usually determine their bandwidth.
Vb
Vout
CL
Vout
CL
CL
Vin
Vin
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Cascoded Amplifier
M7
M8
M5
M6
•
•
vo
Vbias
M3
•
M4
M1
M2
vid
Use cascoding to increase load resistance
Cascode both the active loads and the
differential pair
– Higher effective load resistance
– Higher ro for the differential pair
– Reduces Miller effect (will see later)
However, there are some limitations
– Reduced output swing (must keep all
devices in saturation)
– What is the output dynamic range?
I
•
How might one increase the output swing
range for vo?
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Use High-Swing Cascodes
•
We can use the high-swing cascode circuit as a load to achieve higher output
range in a single-ended output telescopic amp
Vb2
Vout
Vb
Vin
CL
Vout
Vb1
CL
Vin
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Cascode Op Amps
•
Amplifiers that use cascoding are often called ‘telescopic’ cascode amps. While
gain increases, the output range of these devices are limited.
Vb3
Vb2
Vout
Vb
CL
Vout
CL
Vin
Vb1
CL
Vin
– Connecting in unity-gain feedback configuration results in significant
reduction of output range
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DC Biasing for High-Gain Amplifiers
•
One of the challenges of using cascodes for high gain is appropriately setting
the DC biasing for the circuit. Let’s look at an example…
VBP
ILOAD
VBPC
IREF
vOUT
VBNC
ILOAD’
vd
VBN
ITAIL
•
What is the raitio of ILOAD vs. ITAIL?
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DC Biasing Cont’d
• Strategy for setting up DC bias
– All transistors should be saturation
– Set VBNC so that differential input pair in saturation
• Want to set it to the edge with sufficient saturation margin
(~300mV)
– Set VBP so that ILOAD = ITAIL/2
– Set VBPC so that pMOS currnet source loads are close to
edge of saturation
– Need to set VBP and VBPC carefully to keep devices in
saturation and the DC common mode of the output nodes to
be in the middle of the output swing range
• This can be challenging to do due to the high output resistance
at the output.
• Would be nice if there was a way to automatically set the
biasing…
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Common-Mode Feedback Biasing
•
Use an amplifier to set the pMOS current source with respect to some
desired output common-mode voltage (VREF).
VBP
ILOAD
VREF
VBPC
IREF
vOUT
VBNC
vd
VBN
ITAIL
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CM FB Biasing
• Here’s how it works:
– Use large resistors to find the average (common-mode)
output voltage
– An amplifier compares VREF to VOUT,CM and sets VBP such that
VOUT,CM = VREF
• Let’s understand how it works
– What happens to VBP if VREF increases?
– What happens to VBP if VOUT,CM increases?
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Folded Cascode Circuit
•
•
In order to alleviate some of the
drawbacks of telescopic op amps (limited
output range), a “folded cascode” can be
used
– M1 is common-source
transconductance amp and M2 is
common-gate transimpedance amp
– Advantage is M2 no longer stacks on
top of M1
– Possible for either pMOS or nMOS
cascodes
The output resistance for cascode and
folded cascode are roughly equivalent
(gmro2)
Vout
Vb
M2
Vin
M1
Vin
M1
Vb
M2
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Vin
Vout
Vb
M1
M2
Vout
Vin
M1
Vb
Vout
M2
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Folded Cascode Amplifier
•
Turn a differential telescopic cascode amplifier into a folded cascode amplifier
Vout
Vb
Vout
Vin
Vb
Vin
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Full circuit Implementation
of Folded Cascode Amplifier
Vbp2
IREF1
Vout
Vin
Vbn2
•
•
IREF2
IREF3
– Reference current sources are set: I REF3  I REF2  I REF1 2
A version with nMOS differential pair inputs also possible (flip upside down)
What sets output common mode?
– Depends on relative output resistances looking up and down
– Can vary with process and reference current mismatches
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Gain of a Folded-Cascode Amplifier
•
Calculate gain using the differential half-circuit. Gain
can be calculated as GmRout where Gm is the shortcircuit transconductance of the overall circuit and Rout
is the output resistance.
– Short out Vout to ground and solve for Iout/Vin = Gm
– Solve for the output resistance
Vin
M1
Vbp1
M5
Vbp2
M4
ro45
Vout
Vbn2
M3
Vbn1
M2
Vout
-gm3Vx
-Vx
ro3
ro45
gm1Vin
Vin
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ro1||ro2
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Common-Mode Feedback
•
Use feedback to set the output common mode of a folded cascode amplifier,
called common-mode feedback
– Sense the average (common-mode) voltage at the output, compare to a
desired reference voltage (Vref), and use it to set the current source
IREF1
IREF2
IREF2
Vout
Vin
Vb
CM
Sense
IFB
•
Vref
For Vin=0, feedback sets IFB=IREF2+IREF1/2 and common-mode voltage = Vref
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Two-Stage Op Amps
•
•
In order to implement amplifiers with high gain and high swing, we must resort to
two-stage amplifier designs
High-Gain
High-Swing
– First stage used to generate high gain
Vin
Vout
Stage
Stage
– Second stage to generate high swing
Use any high-gain first stage and high-swing second stage
– two simple examples (differential and single-ended output amplifiers)
Vbp
Vout1
Vin
Vbp
Vout2
Vin
Vout
Vbn
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