LINEARIZATION TECHNIQUES FOR
PUSH-PULL AMPLIFIERS
Rinaldo Castello
Department of Electronics
University of Pavia, Pavia Italy.
Outline of the presentation
•  Motivation and relevant applications
•  OL distortion and how to minimize it
•  Output stage (push-pull) distortion
•  Injected distortion independent of frequency response/topology
•  CL distortion prop. to output conductance at distortion frequency
•  Distortion vs. topology for same output stage/frequency
response
•  Input stage distortion
•  Injected distortion depends on gain at the signal frequency
•  Different topologies for low Input/output distortion
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Typical wireless transceivers
Large number
of standards
Large number
of bands
Large number
of receiver paths
Large number of Components and Complex Board
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Saw-Less Transceiver
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Full Duplex Transceiver
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Baseband Requirements
Baseband
Stages
Transmitter Side
Receiver Side
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Linearity Signal Definitions
At signal
frequency
Dist. frequency
At distortion frequency
RX
Side
Signal frequency
TX
Side
Signal frequency
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Dist. frequency
6
Overall Amplifiers Linearization
Consider push-pull output stage
•  Minimize open loop distortion not
implicit in the push push operation
Via topology optimization
•  Minimize closed loop distortion
Via topology and bandwidth optimization
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Push-Pull Output Stages
Sources of OL distortion
•  Output devices moving from linear to
saturation region during signal period
•  Crossover distortion
Can be reduced e.g. preventing all transistors
from shutting-off completely or turning-on on
the wrong phase during transients
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Push-Pull Output Stages
Cross Over Condition
Vout
M1
Iout
Load
Vout
M1
t
M2
Cross-Over
Vout
M1
Load
Vout
M2
Iout
M2
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t
9
Push-Pull Output Stages
Sources of open loop Distortion
Shutting-off completely some devices
caused by: circuit structure
VDD
VX
VDD
I
M2
X
VDD - Vth
M1
t
Vout
Vin
Vout
M3
t
ΔT
(a)
(b)
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Push-Pull Output Stages
Causes of open loop distortion
Shutting-off completely some devices
caused by: capacive coupling
VDD
VX
VDD
Cp
M2
VDD - Vth
M1
X
t
Cc
Vin
Vout
Vout
M3
t
ΔT
(a)
(b)
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Push-Pull Output Stages
Eliminating Distortion
Complete devices shut-off can be prevented by
clamping the critical nodes:
VDD
VX
VDD - Vth
I
M2
Vbias
X
t
Cc
MC
Vin
M1
Vout
Vout
M3
(a)
t
MC normally off goes
on when X starts to rise
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(b)
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Push-Pull Output Stages
Causes of distortion
Turning-on some devices during the wrong phase
VDD
I
I
M1
X
I
Cc
Vin
M3
t
Vout
Vout
t
M2
(a)
Vss
(b)
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Push-Pull Output Stages
Eliminating distortion
VDD
M3
Vin+
M1
M4
M2
Vin-
Cc
Turning-on can be
prevented by driving off
the critical nodes with a
large current
Vout
I
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Minimization of CL Distortion
due to Push-Pull Output Stage
•  Injected distortion depends only on output stage
OL gain at signal frequency doesn’t affect distortion
•  Critical parameter for closed loop distortion
output impedance at distortion frequency
OL gain at distortion frequency
affects distortion
For given output stage
and OL gain
topology affects CL
distortion
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Closed loop distortion for Miller vs.
Nested and Multi-Nested Miller
1
Cm2
Simple
Miller
-
VIN
Unity gain buffer
configuration
VOUT
A
++
VA
H(jω)
gm2
distortion
@ 3fIN
Mout
2
Cm2
Cm1
Nested
Miller
VIN
-1
-
VOUT
A
++
VA
H(jω)
gm2
Multiply open loop
distortion by
closed loop output
impedance.
distortion
@ 3fIN
Mout
3
Double
Nested
Miller
Cm2
Cm0
Cm1
VIN
-
-1
-1
++
VOUT
A
VA
H(jω)
gm2
distortion
@ 3fIN
Mout
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Is topology affecting distortion?
To verify if this is true make this experiment
•  Chose the same output stage for all configurations
•  Choose gain and bandwidth of the n stages such
that the overall frequency response is the same
independently of number of stages
Open Loop Gain [dB]
80
4s
3 s tage
s
2 s tages
tag
es
60
40
20
0
-20
10k
100k
1M
10M
100M
1G
Frequency [Hz]
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Closed Loop YOUT
YOUT = closed loop Output Admittance
0
-10
-30
20dB/dec
-40
ges
Yout [dBS]
ag
es
ta
4s
es
tag
st
3s
2
-20
-50
40dB/dec
-60
-70
60dB/dec
-80
10k
100k
1M
10M
Frequency [Hz]
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100M
1G
18
Grounded-Out Gain (GOG)
Compute output conductance injecting
voltage and measuring current
Critical parameter is GOG
60
VIN
A
gm2
VA
Grounded Output Gain =
Mout
20
10
0
40dB/dec
-10
60dB/dec
-20
-30
10k
VA
20dB/dec
ges
-1
st
ag
es
30
ta
4s
es
tag
Cm1
2
40
3s
Cm2
Cm0
Grounded-Out Gain [dB]
50
100k
1M
10M
100M
1G
Frequency [Hz]
VIN
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Closed Loop YOUT vs Grounded-Out Gain
60
0
ag
es
-30
20dB/dec
-40
s
-50
40dB/dec
-60
-70
60dB/dec
-80
10k
100k
1M
10M
Frequency [Hz]
100M
40
30
20
0
40dB/dec
-10
60dB/dec
-20
-30
1G
20dB/dec
10
10k
100k
1M
10M
Frequency [Hz]
100M
1G
0
-10
2
st
ag
es
-30
20dB/dec
-40
e
tag
4s
es
ta g
-20
3s
s
Yout and NormalizedGOG [dB]
Yout [dBS]
st
e
ta g
4s
es
tag
-20
3s
2
Grounded-Out Gain [dB]
50
-10
-50
40dB/dec
-60
-70
60dB/dec
-80
10k
100k
1M
10M
Frequency [Hz]
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100M
1G
20
Closed Loop Linearity
HD3 = Third Harmonic Tone at 3fIN for an input tone at fIN
Consistent with output conductance plot.
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Multi-stage topology Unity Gain Bandwidth
Increasing number of stage generally forces to use smaller
bandwidth for power consumption and stability reasons
GOPG
GOPG
N=4
N=4
N=3
N=3
N=2
N=2
f
(a)
f
(b)
b) is the typical situation and the distortion
advantage is partially lost
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Output Stage Distortion Conclusions
•  Injected distortion depends only on output stage
•  Critical parameter for closed loop distortion is
GOG at frequency of distortion
Shape and bandwidth of GOG are critical
GOG for Multi-Miller has:
•  20( N -1) dB/dec slope with N = # of stages
•  same unity gain frequency as OL gain
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CL distortion due to input stage
For a given input and output stage
•  OL gain at signal freq. affects injected distortion
•  OL gain at distortion frequency has no effect
To minimize distortion from input stage
Maximize open loop gain in front of the
output stage at the frequency of the signal
Via topology and bandwidth optimization
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OL response/GOG effect on distortion
•  OL bandwidth
Affects CL distortion due to both
input and output stage
•  Shape of OL response/GOG
GOG at frequency of distortion affects
output stage generated distortion
OL gain at frequency of signal affects
first stage distortion injection
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Extending GOG for same OL response
Two Stage Amplifier cascode Miller compensated
Miller capacitance returned to low impedance node
GOG behavior is the same but bandwidth is larger
than simple Miller by a factor CM/Cgs1
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Extending OL bandwidth
Three Stage nested Miller Amplifier with DC Feedforward
C2
Vin
A1
A2
A3
Vout
Open Loop Gain [dB]
C1
C1 halved
Af
distorsion
f
Af
(a)
(b)
Multipath nested Miller
Can control very accurately the doublet
separation, is only limited by matching
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Frequency Response Shaping
C2
Vin
A1
A2
A3
Vout
C1
Open Loop Gain [dB]
Two Stage Amplifier with Pole-Zero in First Stage
-40dB/dec
Af
f
Signal BW
Af
(a)
(b)
Slope of two in overall FR
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Frequency Response Shaping
Miller amplifier with high pass feedback
Slope of two in overall FR
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Frequency Response Shaping
C2
Vin
A1
A2
A3
Vout
C1
Open Loop Gain [dB]
Three Stage Miller Amplifier with DC Feedforward
-40dB/dec
Af
f
Signal BW
Af
(a)
-40dB/dec
Slope of two in
overall FR
(b)
wUGBW=
wZ=
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gM4 gM51
gM52 CZ
gM52
CM3
-20dB/dec
30
Frequency Response Shaping
Three Stage Amplifier with Pole-Zero in First Stage
Slope of two in overall FR
Top circuit equivalent to the
one below but implemented
with 1 less transconductor
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Frequency Response Shaping
Three Stage Amplifier with 2 Pole-Zero Stages
Slope of three in overall FR
No Complex Zeros
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Bandwidth for Different Loads
•  Push-pull operation makes output gain
smaller than one at peak voltage swing
Both effects can degrade stability forcing
small bandwidth
•  Returning the compensation capacitance to
different nodes drastically changes behavior
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Miller with different (R, C) load
•  Unity gain Bandwidth reduced
for small resistive load
•  Output pole enters in band for
large capacitive load
typ
Magnitude [dB]
80
RL low
60
P1 ≈
40
gmp
gmp
P2 ≈
Z1 ≈ CL
CA
GAIN = gm2 • gmp • R2 • RL
20
0
-20
1E+3
1
R2 • (C 2 + gmp • CA • CL + CA)
1E+4
1E+5
1E+6
Frequency [Hz]
1E+7
1E+8
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GBW ≈
gm2
C2 + CA
CA +
gmp • RL
34
Cascoded Miller with different (R,C) load
Compensation out
of signal path
•  Bandwidth constant with load
•  Second pole out of band for
large capacitive load
•  LHZ in frequency response
Magnitude [dB]
80
typ
RL low
60
gm2
GBW ≈
CA
40
20
0
-20
1E+3
1E+4
1E+5
1E+6
Frequency [Hz]
1E+7
1E+8
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gma
Z1 ≈
CA
35
Three Stage Nested Miller topology
Behavior for Varying Loads (R)
Effect on stability of changing the input node of C2
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Frequency Stability
Three Stage inner Miller compensation
typ
RL low
Vout [V]
1.5
1.0
0.5
0.0
9.95E-061.01E-051.02E-051.03E-051.04E-051.05E-05
Time [s]
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Frequency Stability
3 stage inner cascode Miller compensation
typ
RL low
1.2
Vout [V]
1.0
0.8
0.6
0.4
0.2
0.0
9.95E-061.01E-051.02E-051.03E-051.04E-051.05E-05
Time [s]
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