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Lecture 13
High-Gain Differential Amplifier Design
Woodward Yang
School of Engineering and Applied Sciences
Harvard University
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2ES154 - Lecture 13
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
Lets review some of the characteristics of the different (single-ended) amplifier topologies that weve 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
Common-
source/emitterHigh High High High
Common-
gate/base Low High High 1
Common-
drain/collectorHigh Low < 1 High
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4ES154 - Lecture 13
Multi-Stage Amplifiers (Cascading)
We can cascade different types of amplifiers to get desiredoverall 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-emitteremitter-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 whichenables high voltage gain for the CE stage
R1
R2
Rs
vS
RC
REA
REB CE
RE2
RLD
vO
Q1
Q2
Cout
Cin
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Common-Source Source-Follower Cascade
Similarly, cascade a common-source amplifier with a source-follower.
Rs
vS
RD
IS1
CS R
LD
vO
M1
M2
Cout
IS2
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Building Op Amps
Op amps are an important component of modern CMOS ICs. They used to designed asgeneral 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
Want as large as possible
Output Swing
Maximize w.r.t. power supply (but supply shrinking in modern processes)
Linearity
Combat non-linearity with feedback
Noise and Offset
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.
CL
Vout
Vin
CL
Vout
Vin
CL
Vb
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Cascoded Amplifier
Use cascoding to increase load resistance Cascode both the active loads and the
differential pair
Higher effective load resistance
Higherro 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?
How might one increase the output swing
range for vo?
vo
I
M1 M2
vid
Vbias
M4M3
M6M5
M8M7
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Use High-Swing Cascodes
We can use the high-swing cascode circuit as a load to achieve higher outputrange in a single-ended output telescopic amp
CL
Vout
Vin
Vb
CL
Vout
Vin
Vb1
Vb2
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Cascode Op Amps
Amplifiers that use cascoding are often called telescopic cascode amps. Whilegain increases, the output range of these devices are limited.
Connecting in unity-gain feedback configuration results in significantreduction of output range
CL
Vout
Vin
CL
Vout
Vin
CL
Vb3
Vb
Vb2
Vb1
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DC Biasing for High-Gain Amplifiers
One of the challenges of using cascodes for high gain is appropriately settingthe DC biasing for the circuit. Lets look at an example
What is the raitio of ILOAD vs. ITAIL?
vd
vOUT
ITAIL
ILOAD
ILOAD
IREF
VBN
VBNC
VBPC
VBP
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DC Biasing Contd
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 insaturation and the DC common mode of the output nodes tobe in the middle of the output swing range
This can be challenging to do due to the high output resistanceat the output.
Would be nice if there was a way to automatically set thebiasing
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Common-Mode Feedback Biasing
Use an amplifier to set the pMOS current source with respect to somedesired output common-mode voltage (VREF).
vd
vOUT
ITAIL
ILOAD
IREF
VBN
VBNC
VBPC
VBP
VREF
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CM FB Biasing
Heres 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
Lets 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 thedrawbacks 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 andfolded cascode are roughly equivalent
(gmro2)
Vout
Vin
Vb
M1
M2
VoutVinV
b
M1
M2
Vout
Vb
M1
M2
Vout
Vin
Vb
M1
M2
Vin
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Folded Cascode Amplifier
Turn a differential telescopic cascode amplifier into a folded cascode amplifier
Vb
Vin
Vout
Vb
Vin
Vout
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Full circuit Implementation
of Folded Cascode Amplifier
Reference current sources are set: 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
2123 REFREFREF III
Vbn2
Vin
Vout
Vbp2
IREF1
IREF2
IREF3
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Gain of a Folded-Cascode Amplifier
Calculate gain using the differential half-circuit. Gaincan be calculated as GmRoutwhere Gm is the short-
circuit 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
-Vx
ro45
ro3
-gm3Vx
gm1Vin
ro1||r
o2
Vout
M4
Vbn2
Vin
Vout
Vbp2
Vbp1
Vbn1
M1
M2
M3
M5
ro45
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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
ForVin=0, feedback sets IFB=IREF2+IREF1/2 and common-mode voltage = Vref
VbV
in
Vout
CM
Sense
Vref
IREF1
IREF2
IREF2
IFB
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Two-Stage Op Amps
In order to implement amplifiers with high gain and high swing, we must resort totwo-stage amplifier designs
First stage used to generate high gain
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)
High-Gain
Stage
High-Swing
StageV
inV
out
Vin
Vbp
Vbn
Vin
Vbp
Vout
Vout2
Vout1
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