Maxim MAX2010ETI-T 500mhz to 1100mhz adjustable rf predistorter Datasheet

19-2930; Rev 0; 8/03
500MHz to 1100MHz Adjustable
RF Predistorter
The MAX2010 comes in a 28-pin thin QFN exposed
pad (EP) package (5mm x 5mm) and is specified for
the extended (-40°C to +85°C) temperature range.
Features
♦
♦
♦
♦
♦
♦
♦
♦
♦
♦
♦
♦
♦
Up to 12dB ACPR Improvement*
Independent Gain and Phase Expansion Controls
Gain Expansion Up to 6dB
Phase Expansion Up to 21°
500MHz to 1100MHz Frequency Range
Exceptional Gain and Phase Flatness
Group Delay <2.4ns (Gain and Phase Sections
Combined)
±0.03ns Group Delay Ripple Over a 100MHz Band
Capable of Handling Input Drives Up to +23dBm
On-Chip Temperature Variation Compensation
Single +5V Supply
Low Power Consumption: 75mW (typ)
Fully Integrated into Small 28-Pin Thin QFN
Package
*Performance dependent on amplifier, bias, and modulation.
Ordering Information
PART
MAX2010ETI-T
-40°C to +85°C
28 Thin QFN-EP*
Functional Diagram/
Pin Configuration
GCS
GFS
GBP
GND*
28
27
26
25
24
23
22
1
GND*
5
OUTP
6
GND*
7
18 PBEXP
MAX2010
17 PBIN
PHASE
CONTROL
16 GND*
15 VCCP
8
9
10
11
12
13
14
PDCS2
4
PDCS1
GND*
19 PBRAW
PFS2
3
PFS1
ING
20 GND*
GND*
2
INP
GND*
21 VCCG
GAIN
CONTROL
GND*
GND*
GND*
Digital Baseband Predistortion Architectures
OUTG
Feed-Forward PA Architectures
GND*
cdma2000™, GSM/EDGE, and iDEN Base Stations
cdma2000 is a trademark of Telecommunications Industry
Assoc.
PIN-PACKAGE
*EP = Exposed paddle.
Applications
Military Applications
TEMP RANGE
*INTERNALLY CONNECTED TO EXPOSED GROUND PADDLE.
________________________________________________________________ Maxim Integrated Products
For pricing, delivery, and ordering information, please contact Maxim/Dallas Direct! at
1-888-629-4642, or visit Maxim’s website at www.maxim-ic.com.
1
MAX2010
General Description
The MAX2010 adjustable RF predistorter is designed to
improve power amplifier (PA) adjacent-channel power
rejection (ACPR) by introducing gain and phase expansion in a PA chain to compensate for the PA’s gain and
phase compression. With its +23dBm maximum input
power level and wide adjustable range, the MAX2010
can provide up to 12dB of ACPR improvement for
power amplifiers operating in the 500MHz to 1100MHz
frequency band. Higher frequencies of operation can
be achieved with this IC’s counterpart, the MAX2009.
The MAX2010 is unique in that it provides up to 6dB of
gain expansion and 21° of phase expansion as the input
power is increased. The amount of expansion is configurable through two independent sets of control: one set
adjusts the gain expansion breakpoint and slope, while
the second set controls the same parameters for phase.
With these settings in place, the linearization circuit can
be run in either a static set-and-forget mode, or a more
sophisticated closed-loop implementation can be
employed with real-time software-controlled distortion
correction. Hybrid correction modes are also possible
using simple lookup tables to compensate for factors
such as PA temperature drift or PA loading.
MAX2010
500MHz to 1100MHz Adjustable
RF Predistorter
ABSOLUTE MAXIMUM RATINGS
VCCG, VCCP to GND ..............................................-0.3V to +5.5V
ING, OUTG, GCS, GFS, GBP to GND......-0.3V to (VCCG + 0.3V)
INP, OUTP, PFS_, PDCS_, PBRAW,
PBEXP, PBIN to GND ............................-0.3V to (VCCP + 0.3V)
Input (ING, INP, OUTP, OUTG) Level ............................+23dBm
PBEXP Output Current ........................................................±1mA
Continuous Power Dissipation (TA = +70°C)
28-Pin Thin QFN-EP
(derate 21mW/°C above +70°C) ...............................1667mW
Operating Temperature Range ...........................-40°C to +85°C
Junction Temperature ......................................................+150°C
Storage Temperature Range .............................-65°C to +150°C
Lead Temperature (soldering 10s) ..................................+300°C
Stresses beyond those listed under “Absolute Maximum Ratings” may cause permanent damage to the device. These are stress ratings only, and functional
operation of the device at these or any other conditions beyond those indicated in the operational sections of the specifications is not implied. Exposure to
absolute maximum rating conditions for extended periods may affect device reliability.
DC ELECTRICAL CHARACTERISTICS
(MAX2010 EV kit; VCCG = VCCP = +4.75V to +5.25V; no RF signal applied; INP, ING, OUTP, OUTG are AC-coupled and terminated to
50Ω. VPF_S1 = open; PBEXP shorted to PBRAW; VPDCS1 = VPDCS2 = 0.8V; VPBIN = VGBP = VGCS = GND; VGFS = VCCG; TA = -40°C to
+85°C. Typical values are at VCCG = VCCP = +5.0V, TA = +25°C, unless otherwise noted.)
PARAMETER
Supply Voltage
Supply Current
Analog Input Voltage Range
CONDITIONS
VCCG, VCCP
UNITS
5.25
V
5.8
7
10
12.1
PBIN, PBRAW
0
VCCP
GBP, GFS, GCS
0
VCCG
-2
+2
VGBP = 0 to +5V
-100
+170
VPBIN = 0 to +5V
-100
+220
PDCS1, PDCS2 (Note 1)
Logic-Input Low Voltage
PDCS1, PDCS2 (Note 1)
2
MAX
VCCG
Logic-Input High Voltage
Logic Input Current
TYP
VCCP
VGFS = VGCS = VPBRAW = 0V
Analog Input Current
MIN
4.75
2.0
-2
_______________________________________________________________________________________
mA
V
µA
V
0.8
V
+2
µA
500MHz to 1100MHz Adjustable
RF Predistorter
(MAX2010 EV kit, VCCG = VCCP = +4.75V to +5.25V, 50Ω environment, PIN = -20dBm, fIN = 500MHz to 1100MHz, VGCS = +1.0V,
VGFS = +5.0V, VGBP = +1.2V, VPBIN = VPDCS1 = VPDCS2 = 0V, VPF_S1 = +5V, VPBRAW = VPBEXP, TA = -40°C to +85°C. Typical values are at fIN = 880MHz, VCCG = VCCP = +5V, TA = +25°C, unless otherwise noted.) (Notes 1, 2)
PARAMETER
CONDITIONS
Operating Frequency Range
VSWR
MIN
TYP
500
ING, INP, OUTG, OUTP
MAX
UNITS
1100
MHz
1.3:1
PHASE CONTROL SECTION
Nominal Gain
-5.5
dB
Gain Variation Over Temperature
TA = -40°C to +85°C
-1.7
dB
Gain Flatness
Over a 100MHz band
±0.1
dB
Phase-Expansion Breakpoint
Maximum
VPBIN = +5V
23
dBm
Phase-Expansion Breakpoint
Minimum
VPBIN = 0V
0.7
dBm
Phase-Expansion Breakpoint
Variation Over Temperature
TA = -40°C to +85°C
±1.5
dB
VPF_S1 = +5V,
VPDCS1 = VPDCS2 = 0V,
PIN = -20 dBm to +23 dBm
21
VPDCS1 = 5V,
VPDCS2 = 0V,
VPF_S1 = +1.5V
16
Degrees
Phase Expansion
VPDCS1 = 0V,
VPDCS2 = 5V,
VPF_S1 = +1.5V
14
VPF_S1 = 0V,
VPDCS1 = VPDCS2 = +5V,
PIN = -20dBm to +23dBm
6
Phase-Expansion Slope
Maximum
PIN = +9dBm
1.4
Degrees
/dB
Phase-Expansion Slope Minimum
VPF_S1 = 0V,
VPDCS1 = VPDCS2 = +5V,
PIN = +9dBm
0.6
Degrees
/dB
Phase-Slope Variation Over
Temperature
PIN = +9dBm, TA = -40°C to +85°C
0.05
Degrees
/dB
Phase Ripple
Over a 100MHz band, deviation from linear phase
±0.02
Degrees
5.5
dB
1.3
ns
Noise Figure
Absolute Group Delay
Interconnects de-embedded
Group Delay Ripple
Over a 100MHz band
±0.01
ns
Parasitic Gain Expansion
PIN = -20dBm to +23dBm
+0.4
dB
_______________________________________________________________________________________
3
MAX2010
AC ELECTRICAL CHARACTERISTICS
MAX2010
500MHz to 1100MHz Adjustable
RF Predistorter
AC ELECTRICAL CHARACTERISTICS (continued)
(MAX2010 EV kit, VCCG = VCCP = +4.75V to +5.25V, 50Ω environment, PIN = -20dBm, fIN = 500MHz to 1100MHz, VGCS = +1.0V,
VGFS = +5.0V, VGBP = +1.2V, VPBIN = VPDCS1 = VPDCS2 = 0V, VPF_S1 = +5V, VPBRAW = VPBEXP, TA = -40°C to +85°C. Typical values are at fIN = 880MHz, VCCG = VCCP = +5V, TA = +25°C, unless otherwise noted.) (Notes 1, 2)
PARAMETER
CONDITIONS
MIN
TYP
MAX
UNITS
GAIN CONTROL SECTION
-14.9
Nominal Gain
dB
VGCS = 0V, VGFS = +5V
-24.3
VGCS = +5V, VGFS = 0V
-7.6
Gain Variation Over Temperature
TA = -40°C to +85°C
-1.4
dB
Gain Flatness
Over a 100MHz band
±0.2
dB
Gain-Expansion Breakpoint
Maximum
VGBP = +5V
23
dBm
Gain-Expansion Breakpoint
Minimum
VGBP = +0.5V
-2.5
dBm
Gain-Expansion Breakpoint
Variation Over Temperature
TA = -40°C to +85°C
-0.5
dB
VGFS = +5V, PIN = -20dBm to +23dBm
5.3
VGFS = 0V, PIN = -20dBm to +23dBm
3.1
VGFS = +5V, PIN = +15dBm
0.43
VGFS = +0V, PIN = +15dBm
0.23
PIN = +15dBm, TA = -40°C to +85°C
-0.01
dB/dB
Gain-Expansion
Gain-Expansion Slope
Gain-Slope Variation Over
Temperature
Noise Figure
dB
dB/dB
14.9
dB
Absolute Group Delay
Interconnects de-embedded
1.12
ns
Group Delay Ripple
Over a 100MHz band
±0.02
ns
Phase Ripple
Over a 100MHz band, deviation from linear phase
±0.09
Degrees
Parasitic Phase Expansion
PIN = -20dBm to +23dBm
+3
Degrees
Note 1: Guaranteed by design and characterization.
Note 2: All limits reflect losses and characteristics of external components shown in the Typical Application Circuit, unless otherwise
noted.
4
_______________________________________________________________________________________
500MHz to 1100MHz Adjustable
RF Predistorter
Phase Control Section
(MAX2010 EV kit, VCCP = +5.0V, PIN = -20dBm, VPBIN = 0V, VPF_S1 = +5.0V, VPDCS1 = VPDCS2 = 0V, fIN = 880MHz, TA = +25°C
unless otherwise noted.)
SMALL-SIGNAL INPUT RETURN LOSS
vs. FREQUENCY
TA = +25°C
6.1
6.0
5.9
TA = -40°C
5.8
20
C
30
D
40
5.7
4.95
5.05
5.15
5.25
0.9
1.0
0.8
FREQUENCY (GHz)
A = VPDCS1 = VPDCS2 = VPF_S1 = 0V
B = VPDCS1 = VPDCS2 = 0V, VPF_S1 = 5V
C = VPDCS1 = VPDCS2 = 5V, VPF_S1 = 0V
D = VPDCS1 = VPDCS2 = VPF_S1 = 5V
SUPPLY VOLTAGE (V)
0.6
0.7
MAX2010 toc04
0
OUTPUT RETURN LOSS (dB)
INPUT RETURN LOSS (dB)
10
A
D
B
A
20
30
D
40
C
40
1.1
0.5
0.6
0.9
1.0
0.8
FREQUENCY (GHz)
A = VPDCS1 = VPDCS2 = VPF_S1 = 0V
B = VPDCS1 = VPDCS2 = 0V, VPF_S1 = 5V
C = VPDCS1 = VPDCS2 = 5V, VPF_S1 = 0V
D = VPDCS1 = VPDCS2 = VPF_S1 = 5V
10
B
D
1.1
-4.0
-4.5
A
20
30
0.7
SMALL-SIGNAL GAIN
vs. FREQUENCY
LARGE-SIGNAL OUTPUT RETURN LOSS
vs. FREQUENCY
LARGE-SIGNAL INPUT RETURN LOSS
vs. FREQUENCY
0
30
50
0.5
GAIN (dB)
4.85
MAX2010 toc05
4.75
B
20
A
B
50
5.6
10
MAX2010 toc06
TA = +85°C
OUTPUT RETURN LOSS (dB)
6.3
6.2
10
INPUT RETURN LOSS (dB)
6.4
0
MAX2010 toc02
6.5
SUPPLY CURRENT (mA)
0
MAX2010 toc01
6.6
SMALL-SIGNAL OUTPUT RETURN LOSS
vs. FREQUENCY
MAX2010 toc03
SUPPLY CURRENT
vs. SUPPLY VOLTAGE
C
40
-5.0
TA = -40°C
-5.5
TA = +25°C
-6.0
TA = +85°C
-6.5
C
-7.0
50
50
0.5
0.6
0.7
0.9
0.8
FREQUENCY (GHz)
PIN = +15dBm
A = VPDCS1 = VPDCS2 = VPF_S1 = 0V
B = VPDCS1 = VPDCS2 = 0V, VPF_S1 = 5V
C = VPDCS1 = VPDCS2 = 5V, VPF_S1 = 0V
D = VPDCS1 = VPDCS2 = VPF_S1 = 5V
1.0
1.1
0.5
0.6
0.7
0.9
0.8
FREQUENCY (GHz)
1.0
1.1
0.5
0.6
0.7
0.8
0.9
FREQUENCY (GHz)
1.0
1.1
PIN = +15dBm
A = VPDCS1 = VPDCS2 = VPF_S1 = 0V
B = VPDCS1 = VPDCS2 = 0V, VPF_S1 = 5V
C = VPDCS1 = VPDCS2 = 5V, VPF_S1 = 0V
D = VPDCS1 = VPDCS2 = VPF_S1 = 5V
_______________________________________________________________________________________
5
MAX2010
Typical Operating Characteristics
Typical Operating Characteristics (continued)
Phase Control Section (continued)
(MAX2010 EV kit, VCCP = +5.0V, PIN = -20dBm, VPBIN = 0V, VPF_S1 = +5.0V, VPDCS1 = VPDCS2 = 0V, fIN = 880MHz, TA = +25°C
unless otherwise noted.)
SMALL-SIGNAL GAIN
vs. COARSE SLOPE
VPF_S1 = 1.5V
-5.0
GAIN (dB)
VCCP = 4.75V, 5.0V, 5.25V
-5.5
-5.5
VPF_S1 = 5V
-6.0
-6.5
-6.5
-6.5
1.0
-7.0
PDCS1 = 0
PDCS2 = 0
1.1
GROUP DELAY vs. FREQUENCY
1.40
1.35
A
1.30
C
6.4
6.2
D
5.8
B
5.6
0.5
0.6
0.7
0.8
B
0.9
FREQUENCY (GHz)
A = VPDCS1 = VPDCS2 = VPF_S1 = 0V
B = VPDCS1 = VPDCS2 = 0V, VPF_S1 = 5V
C = VPDCS1 = VPDCS2 = 5V, VPF_S1 = 0V
D = VPDCS1 = VPDCS2 = VPF_S1 = 5V
INTERCONNECTS DE-EMBEDDED
1.0
B
5.90
C
5.85
D
A
5.80
E
A
C
5.0
1.1
5.95
5.75
5.2
D
1.20
6.00
MAX2010 toc11
6.6
5.4
1.25
6
6.8
6.0
PDCS1 = 5
PDCS2 = 5
PDCS1 = 5
PDCS1 = 0
PDCS2 = 0
PDCS2 = 5
COARSE SLOPE (V)
SUPPLY CURRENT vs. INPUT POWER
NOISE FIGURE vs. FREQUENCY
NOISE FIGURE (dB)
1.45
-7.0
PDCS1 = 0
PDCS2 = 0
PDCS1 = 5
PDCS2 = 5
7.0
MAX2010 toc10
1.50
PDCS1 = 5
PDCS1 = 0
PDCS2 = 0
PDCS2 = 5
COARSE SLOPE (V)
MAX2010 toc12
0.7
0.8
0.9
FREQUENCY (GHz)
SUPPLY CURRENT (mA)
0.6
TA = +85°C
-5.5
-6.0
0.5
TA = +25°C
-5.0
-6.0
-7.0
TA = -40°C
-4.5
GAIN (dB)
-5.0
VPF_S1 = 0V
-4.5
-4.0
MAX2010 toc08
-4.5
GAIN (dB)
-4.0
MAX2010 toc07
-4.0
SMALL-SIGNAL GAIN
vs. COARSE SLOPE
MAX2010 toc09
SMALL-SIGNAL GAIN
vs. FREQUENCY
DELAY (ns)
MAX2010
500MHz to 1100MHz Adjustable
RF Predistorter
0.5
1.0
0.7
0.8
0.9
FREQUENCY (GHz)
A = VPDCS1 = VPDCS2 = VPF_S1 = 0V
B = VPDCS1 = VPDCS2 = 0V, VPF_S1 = 5V
C = VPDCS1 = VPDCS2 = 5V, VPF_S1 = 0V
D = VPDCS1 = VPDCS2 = VPF_S1 = 5V
0.6
1.1
5.70
0
4
8
12
16
INPUT POWER (dBm)
D = VPBIN = 1.5V
A = VPBIN = 0V
E = VPBIN = 3.0V
B = VPBIN = 0.5V
C = VPBIN = 1.0V
_______________________________________________________________________________________
20
24
500MHz to 1100MHz Adjustable
RF Predistorter
Phase Control Section (continued)
(MAX2010 EV kit, VCCP = +5.0V, PIN = -20dBm, VPBIN = 0V, VPF_S1 = +5.0V, VPDCS1 = VPDCS2 = 0V, fIN = 880MHz, TA = +25°C
unless otherwise noted.)
PHASE EXPANSION vs. INPUT POWER
C
-5.1
B
-5.3
C
-4.9
B
0
A
-5
3
8
13
18
-7
INPUT POWER (dBm)
D = VPBIN = 1.5V
A = VPBIN = 0V
E = VPBIN = 2.0V
B = VPBIN = 0.5V
C = VPBIN = 1.0V F = VPBIN = 2.5V
MAX2010 toc16
13
18
10
B
E
0
D
-5
-10
8
13
INPUT POWER (dBm)
E = VPF_S1 = 2.0V
A = VPF_S1 = 0V
B = VPF_S1 = 0.5V F = VPF_S1 = 5.0V
C = VPF_S1 = 1.0V VPDCS1 = 5.0V
D = VPF_S1 = 1.5V
18
23
13
18
23
15
10
5
B
0
A
-5
D
C
-15
-20
3
8
A
B
C
A
-2
3
INPUT POWER (dBm)
C = VPDCS1 = 0V, VPDCS2 = 5V
A = VPDCS1 = VPDCS2 = 0V
B = VPDCS1 = 5V, VPDCS2 = 0V D = VPDCS1 = VPDCS2 = 5V
-10
-15
-5.7
-2
PHASE EXPANSION vs. INPUT POWER
5
F
-7
-7
23
F
PHASE (DEGREES)
-5.1
E
8
15
-4.8
-5.4
3
PHASE EXPANSION vs. INPUT POWER
GAIN EXPANSION vs. INPUT POWER
D
-2
INPUT POWER (dBm)
D = VPBIN = 1.5V
A = VPBIN = 0V
E = VPBIN = 2.0V
B = VPBIN = 0.5V
C = VPBIN = 1.0V F = VPBIN = 2.5V
-4.5
C
-5.7
-20
23
PHASE (DEGREES)
-2
MAX2010 toc17
-7
C
-5.5
F
-5.7
-5.1
D
E
-15
B
A
-5.3
D
-5.5
GAIN (dB)
-4.7
5
-10
A
MAX2010 toc15
MAX2010 toc14
10
PHASE (DEGREES)
GAIN (dB)
-4.9
GAIN EXPANSION vs. INPUT POWER
-4.5
GAIN (dB)
F
E
MAX2010 toc13
D
-4.7
15
MAX2010 toc18
GAIN EXPANSION vs. INPUT POWER
-4.5
-20
-7
-2
3
8
13
INPUT POWER (dBm)
D = VPF_S1 = 1.5V
A = VPF_S1 = 0V
B = VPF_S1 = 0.5V E = VPF_S1 = 2.0V
C = VPF_S1 = 1.0V F = VPF_S1 = 5.0V
VPDCS1 = 5.0V
18
23
-7
-2
3
8
13
18
23
INPUT POWER (dBm)
A = VPDCS1 = VPDCS2 = 0V
B = VPDCS1 = 5V, VPDCS2 = 0V
C = VPDCS1 = 0V, VPDCS2 = 5V
D = VPDCS1 = VPDCS2 = 5V
_______________________________________________________________________________________
7
MAX2010
Typical Operating Characteristics (continued)
Typical Operating Characteristics (continued)
Phase Control Section (continued)
(MAX2010 EV kit, VCCP = +5.0V, PIN = -20dBm, VPBIN = 0V, VPF_S1 = +5.0V, VPDCS1 = VPDCS2 = 0V, fIN = 880MHz, TA = +25°C
unless otherwise noted.)
GAIN EXPANSION vs. INPUT POWER
GAIN (dB)
-4.6
TA = -40°C
-4.8
-5.0
VPDCS1 = 5.0, VPF_S1 = 1.5V
-5
PHASE (DEGREES)
-4.4
MAX2010 toc20
VPDCS1 = 5.0, VPF_S1 = 1.5V
-4.2
PHASE EXPANSION vs. INPUT POWER
0
MAX2010 toc19
-4.0
TA = +25°C
-5.2
-10
TA = +25°C
-15
TA = +85°C
-5.4
TA = -40°C
-20
TA = +85°C
-5.6
-5.8
-25
-7
-2
3
8
13
18
23
-7
-2
INPUT POWER (dBm)
3
8
13
18
23
INPUT POWER (dBm)
Typical Operating Characteristics
Gain Control Section
(MAX2010 EV kit, VCCG = +5.0V, PIN = -20dBm, VGBP = +1.2V, VGFS = +5.0V, VGCS = +1.0V, fIN = 880MHz, TA = +25°C, unless
otherwise noted.)
SMALL-SIGNAL INPUT RETURN LOSS
vs. FREQUENCY
6.3
TA = +85°C
6.2
6.1
TA = +25°C
6.0
TA = -40°C
5.9
5.8
0
10
OUTPUT RETURN LOSS (dB)
6.4
INPUT RETURN LOSS (dB)
6.5
MAX2010 toc22
0
MAX2010 toc21
6.6
SMALL-SIGNAL OUTPUT RETURN LOSS
vs. FREQUENCY
C, D
20
A, B
30
40
MAX2010 toc23
SUPPLY CURRENT vs. SUPPLY VOLTAGE
SUPPLY CURRENT (mA)
MAX2010
500MHz to 1100MHz Adjustable
RF Predistorter
10
C, D
20
30
A, B
40
5.7
5.6
50
4.75
4.85
4.95
5.05
SUPPLY VOLTAGE (V)
8
5.15
5.25
50
0.5
0.6
0.7
0.8
0.9
1.0
1.1
FREQUENCY (GHz)
A = VGCS = 0V, VGFS = 0V C = VGCS = 5V, VGFS = 0V
B = VGCS = 0V, VGFS = 5V D = VGCS = 5V, VGFS = 5V
0.5
0.6
0.7
0.8
0.9
1.0
1.1
FREQUENCY (GHz)
A = VGCS = 0V, VGFS = 0V C = VGCS = 5V, VGFS = 0V
B = VGCS = 0V, VGFS = 5V D = VGCS = 5V, VGFS = 5V
_______________________________________________________________________________________
500MHz to 1100MHz Adjustable
RF Predistorter
Gain Control Section (continued)
(MAX2010 EV kit, VCCP = +5.0V, PIN = -20dBm, VPBIN = 0V, VPF_S1 = +5.0V, VPDCS1 = VPDCS2 = 0V, fIN = 880MHz, TA = +25°C
unless otherwise noted.)
LARGE-SIGNAL OUTPUT RETURN LOSS
vs. FREQUENCY
D
20
C
A
30
PIN = +15dBm
10
D
TA = -40°C
-13
C
-14
20
A
30
TA = +25°C
-15
TA = +85°C
-16
-17
B
-18
40
B
40
MAX2010 toc25
10
SMALL-SIGNAL GAIN vs. FREQUENCY
-12
GAIN (dB)
INPUT RETURN LOSS (dB)
PIN = +15dBm
0
OUTPUT RETURN LOSS (dB)
MAX2010 toc24
0
MAX2010 toc26
LARGE-SIGNAL INPUT RETURN LOSS
vs. FREQUENCY
-19
50
0.6
0.7
0.8
0.9
1.0
-20
0.5
1.1
0.9
1.0
1.1
0.5
0.6
0.7
0.8
0.9
1.0
1.1
FREQUENCY (GHz)
SMALL-SIGNAL GAIN vs. VGCS
0
MAX2010 toc27
VCCG = 4.75V, 5.0V, 5.25V
0.8
SMALL-SIGNAL GAIN vs. VGCS
SMALL-SIGNAL GAIN vs. FREQUENCY
-13
0.7
FREQUENCY (GHz)
A = VGCS = 0V, VGFS = 0V C = VGCS = 5V, VGFS = 0V
B = VGCS = 0V, VGFS = 5V D = VGCS = 5V, VGFS = 5V
FREQUENCY (GHz)
A = VGCS = 0V, VGFS = 0V C = VGCS = 5V, VGFS = 0V
B = VGCS = 0V, VGFS = 5V D = VGCS = 5V, VGFS = 5V
-12
0.6
0
MAX2010 toc28
0.5
VGFS = 0V, 1.5V, 5.0V
-5
MAX2010 toc29
50
TA = -40°C
-5
-14
-10
-16
-17
GAIN (dB)
GAIN (dB)
GAIN (dB)
-10
-15
-15
-15
-20
-20
-25
-25
-30
-30
TA = +25°C
TA = +85°C
-18
-19
VGFS = +1.5V
-20
0.5
0.6
0.7
0.8
0.9
FREQUENCY (GHz)
1.0
1.1
0
1
2
3
VGCS (V)
4
5
0
1
2
3
4
5
VGCS (V)
_______________________________________________________________________________________
9
MAX2010
Typical Operating Characteristics (continued)
Typical Operating Characteristics (continued)
Gain Control Section (continued)
(MAX2010 EV kit, VCCP = +5.0V, PIN = -20dBm, VPBIN = 0V, VPF_S1 = +5.0V, VPDCS1 = VPDCS2 = 0V, fIN = 880MHz, TA = +25°C
unless otherwise noted.)
NOISE FIGURE vs. FREQUENCY
1.1
A
25
SUPPLY CURRENT (mA)
C, D
1.2
A
25
NOISE FIGURE (dB)
1.3
30
MAX2010 toc31
MAX2010 toc30
1.4
SUPPLY CURRENT vs. INPUT POWER
30
B
20
C
15
1.0
10
B
0.6
0.7
0.8
0.9
1.0
0.5
C
-14
-17
F
G H
12
16
20
24
8
INPUT POWER (dBm)
A = VGBP = 0V
D = VGBP = 1.5V
B = VGBP = 0.5V
E = VGBP = 3.0V
C = VGBP = 1.0V
B
-9
C
-11
D
F
-13
H
G
E
-15
-20
-7
10
-7
A
E
PHASE (DEGREES)
GAIN (dB)
D
4
-5
MAX2010 toc33
B
-8
0
PHASE EXPANSION vs. INPUT POWER
GAIN EXPANSION vs. INPUT POWER
A
5
0.6
-5
-11
E
1.1
0.7
0.8
0.9
1.0
FREQUENCY (GHz)
D = VGCS = 5V, VGFS = 0V
A = VGCS = 0V, VGFS = 0V
E = VGCS = 5V, VGFS = 5V
B = VGCS = 0V, VGFS = 5V
C = VGCS = 1.5V, VGFS = 5V
1.1
FREQUENCY (GHz)
A = VGCS = 0V, VGFS = 0V C = VGCS = 5V, VGFS = 0V
B = VGCS = 0V, VGFS = 5V D = VGCS = 5V, VGFS = 5V
INTERCONNECTS DE-EMBEDDED
C
15
MAX2010 toc34
0.5
A
20
D
D
5
0.8
B
10
E
0.9
MAX2010 toc32
GROUP DELAY vs. FREQUENCY
1.5
DELAY (ns)
MAX2010
500MHz to 1100MHz Adjustable
RF Predistorter
-2
8
13
18
23
3
INPUT POWER (dBm)
A = VGBP = 0V
E = VGBP = 2.0V
B = VGBP = 0.5V
F = VGBP = 2.5V
C = VGBP = 1.0V
G = VGBP = 3.5V
D = VGBP = 1.5V
H = VGBP = 5.0V
-7
-2
8
13
18
23
3
INPUT POWER (dBm)
A = VGBP = 0V
E = VGBP = 2.0V
B = VGBP = 0.5V
F = VGBP = 2.5V
C = VGBP = 1.0V
G = VGBP = 3.5V
D = VGBP = 1.5V
H = VGBP = 5.0V
______________________________________________________________________________________
500MHz to 1100MHz Adjustable
RF Predistorter
Gain Control Section (continued)
(MAX2010 EV kit, VCCP = +5.0V, PIN = -20dBm, VPBIN = 0V, VPF_S1 = +5.0V, VPDCS1 = VPDCS2 = 0V, fIN = 880MHz, TA = +25°C
unless otherwise noted.)
GAIN EXPANSION vs. INPUT POWER
E
-9
F
-11
-14
C
D
A, B
-13
D
-15
-17
C
-19
A, B
10
E
0
C
D
A, B
-21
-17
20
PHASE (DEGREES)
-11
GAIN (dB)
GAIN (dB)
F
-7
PHASE EXPANSION vs. INPUT POWER
30
MAX2010 toc37
-8
MAX2010 toc35
E
-5
MAX2010 toc36
GAIN EXPANSION vs. INPUT POWER
-5
-10
-23
-25
8
13
18
23
3
INPUT POWER (dBm)
A = VGFS = 0V
D = VGFS = 1.5V
B = VGFS = 0.5V
E = VGFS = 2.0V
C = VGFS = 1.0V
F = VGFS = 5.0V
-10
-8
-10
D
-12
C
A, B
-13
-12
-13
TA = -40°C
-14
TA = +25°C
-15
-14
-16
-15
-17
-7
-2
8
13
18
23
3
INPUT POWER (dBm)
A = VGFS = 0V
D = VGFS = 1.5V
B = VGFS = 0.5V
E = VGFS = 2.0V
C = VGFS = 1.0V
F = VGFS = 5.0V
-2
8
13
18
23
3
INPUT POWER (dBm)
A = VGCS = 0V
D = VGCS = 1.5V
B = VGCS = 0.5V
E = VGCS = 2.0V
C = VGCS = 1.0V
F = VGCS = 5.0V
PHASE EXPANSION vs. INPUT POWER
-11
-9
GAIN (dB)
PHASE (DEGREES)
-9
E
-11
-7
-5
MAX2010 toc39
F
8
13
18
23
3
INPUT POWER (dBm)
A = VGCS = 0V
D = VGCS = 1.5V
B = VGCS = 0.5V
E = VGCS = 2.0V
C = VGCS = 1.0V
F = VGCS = 2.5V
-8
MAX2010 toc38
-6
-7
-2
GAIN EXPANSION vs. INPUT POWER
PHASE EXPANSION vs. INPUT POWER
-5
F
-20
-7
-2
-6
-7
PHASE (DEGREES)
-7
MAX2010 toc40
-20
-8
-9
TA = -40°C
-10
TA = +25°C
-11
-12
TA = +85°C
-13
TA = +85°C
-14
-15
-7
-2
8
13
3
INPUT POWER (dBm)
18
23
-7
-2
8
13
3
INPUT POWER (dBm)
18
______________________________________________________________________________________
23
11
MAX2010
Typical Operating Characteristics (continued)
MAX2010
500MHz to 1100MHz Adjustable
RF Predistorter
Pin Description
PIN
NAME
FUNCTION
1, 2, 4, 5, 7,
8, 10, 16, 20,
22, 26, 28
GND
Ground. Internally connected to the exposed paddle.
3
ING
RF Gain Input. Connect ING to a coupling capacitor if it is not connected to OUTP. ING is
interchangeable with OUTG.
6
OUTP
RF Phase Output. Connect OUTP to a coupling capacitor if it is not connected to INP. OUTP is
interchangeable with INP.
9
INP
RF Phase Input. Connect INP to a coupling capacitor. This pin is interchangeable with OUTP.
11
PFS1
Fine Phase-Slope Control Input 1. See the Typical Application Circuit.
12
PFS2
Fine Phase-Slope Control Input 2. See the Typical Application Circuit.
13
PDCS1
Digital Coarse Phase-Slope Control Range Input 1. Set to logical zero for the steepest slope.
14
PDCS2
Digital Coarse Phase-Slope Control Range Input 2. Set to logical zero for the steepest slope.
15
VCCP
Phase-Control Supply Voltage. Bypass with a 0.01µF capacitor to ground as close to the device as
possible. Phase section can operate without VCCG.
17
PBIN
Phase Breakpoint Control Input
18
PBEXP
Phase Expansion Output. Connect PBEXP to PBRAW to use PBIN as the breakpoint control voltage.
19
PBRAW
Uncompensated Phase Breakpoint Input
21
VCCG
Gain-Control Supply Voltage. Bypass with a 0.01µF capacitor to ground as close to the device as
possible. Gain section can operate without VCCP.
23
GBP
Gain Breakpoint Control Input
24
GFS
Fine Gain-Slope Control Input
25
GCS
Coarse Gain-Slope Control Input
27
OUTG
EP
GND
RF Gain Output. Connect OUTG to a coupling capacitor. OUTG is interchangeable with ING.
Exposed Ground Paddle. Solder EP to the ground plane.
Detailed Description
The MAX2010 adjustable predistorter can provide up to
12dB of ACPR improvement for high-power amplifiers
by introducing gain and phase expansion to compensate for the PA’s gain and phase compression. The
MAX2010 enables real-time software-controlled distortion correction, as well as set-and-forget tuning through
the adjustment of the expansion starting point (breakpoint) and the rate of expansion (slope). The gain and
12
phase breakpoints can be set over a 20dB input power
range. The phase expansion slope is variable from
0.3°/dB to 2.0°/dB and can be adjusted for a maximum
of 21° of phase expansion. The gain expansion slope is
variable from 0.1dB/dB to 0.53dB/dB and can be
adjusted for a maximum of 6dB gain expansion.
The following sections describe the tuning methodology
best implemented with a class A amplifier. Other classes
of operation may require significantly different settings.
______________________________________________________________________________________
500MHz to 1100MHz Adjustable
RF Predistorter
Phase Expansion Breakpoint
The phase expansion breakpoint is typically controlled
by a digital-to-analog converter (DAC) connected
through the PBIN pin. The PBIN input voltage range of
0V to VCC corresponds to a breakpoint input power
range of 0.7dBm to 23dBm. To achieve optimal performance, the phase expansion breakpoint of the
MAX2010 must be set to equal the phase compression
breakpoint of the PA.
Phase Expansion Slope
The phase expansion slope of the MAX2010 must also
be adjusted to equal the opposite slope of the PA’s
phase compression curve. The phase expansion slope
of the MAX2010 is controlled by the PFS1, PFS2, PDCS1,
and PDCS2 pins. With pins PFS1 and PFS2 AC-coupled
and connected to a variable capacitor or varactor diode,
PA PHASE
COMPRESSION
IMPROVED
PHASE DISTORTION
COMBINED PHASE (DEGREES)
SLOPE
MAX2010 PHASE (DEGREES)
PA PHASE (DEGREES)
Gain Expansion Circuitry
In addition to phase compression, the PA also suffers
from gain compression (AM-AM) distortion, as shown in
Figure 3. The PA gain curve remains flat for input powers below the breakpoint level, and begins to compress
at a given rate (slope) for input powers greater than the
breakpoint level. To compensate for such gain compression, the MAX2010 generates a gain expansion,
which occurs at the same breakpoint level with the
opposite slope. The overall result is a flat gain response
at the PA output.
MAX2010
PHASE EXPANSION
BREAKPOINT
PIN (dBm)
the PFS1 and PFS2 pins perform the task of fine tuning
the phase expansion slope. Since off-chip varactor
diodes are recommended for this function, they must
be closely matched and identically biased. A minimum
effective capacitance of 2pF to 6pF is required
to achieve the full phase slope range as specified in
the Electrical Characteristics tables.
As shown in Figure 2, the varactors connected to PFS1
and PFS2 are in series with three internal capacitors on
each pin. By connecting and disconnecting these internal capacitors, a larger change in phase expansion
slope can be achieved through the logic levels presented at the PDCS1 and PDCS2 pins. The phase expansion slope is at its maximum when both VPDCS1 and
V PDCS2 equal 0V. The phase tuning has a minimal
effect on the small-signal gain.
PIN (dBm)
PIN (dBm)
Figure 1. PA Phase Compression Canceled by MAX2010 Phase Expansion
______________________________________________________________________________________
13
MAX2010
Phase Expansion Circuitry
Figure 1 shows a typical PA’s phase behavior with
respect to input power. For input powers less than the
breakpoint level, the phase remains relatively constant.
As the input power becomes greater than the breakpoint level, the phase begins to compress and deteriorate the power amplifier’s linearity. To compensate for
this AM-PM distortion, the MAX2010 provides phase
expansion, which occurs at the same breakpoint level
but with the opposite slope. The overall result is a flat
phase response.
MAX2010
500MHz to 1100MHz Adjustable
RF Predistorter
PFS1
PF_S1
PHASE-CONTROL
CIRCUITRY
PFS2
2
PDCS1
PDCS2
SWITCH
CONTROL
MAX2010
Figure 2. Simplified Phase Slope Internal Circuitry
PA GAIN
COMPRESSION
MAX2010
GAIN EXPANSION
IMPROVED
GAIN DISTORTION
PIN (dBm)
COMBINED GAIN (dB)
SLOPE
MAX2010 GAIN (dB)
PA GAIN (dB)
BREAKPOINT
PIN (dBm)
PIN (dBm)
Figure 3. PA Gain Compression Canceled by MAX2010 Gain Expansion
14
______________________________________________________________________________________
500MHz to 1100MHz Adjustable
RF Predistorter
Gain Expansion Slope
In addition to properly setting the breakpoint, the gain
expansion slope of the MAX2010 must also be adjusted
to compensate for the PA’s gain compression. The
slope should be set using the following equation:
MAX2010 _ SLOPE =
−PA _ SLOPE
1 + PA _ SLOPE
where:
MAX2010_SLOPE = MAX2010 gain section’s slope in
dB/dB.
PA_SLOPE = PA’s gain slope in dB/dB, a negative
number for compressive behavior.
To modify the gain expansion slope, two adjustments
must be made to the biases applied on pins GCS and
GFS. Both GCS and GFS have an input voltage range of
0V to VCC, corresponding to a slope of approximately
0.1dB/dB to 0.53dB/dB. The slope is set to maximum
when VGCS = 0V and VGFS = +5V, and the slope is at its
minimum when VGCS = +5V and VGFS = 0V.
Unlike the GBP pin, modifying the gain expansion slope
bias on the GCS pin causes a change in the part’s insertion loss and noise figure. For example, a smaller slope
caused by GCS results in a better insertion loss and
lower noise figure. The GFS does not affect the insertion
loss. It can provide up to -30% or +30% total slope variation around the nominal slope set by GCS.
Large amounts of GCS bias adjustment can also lead to
an undesired (or residual) phase expansion/compression behavior. There exists an optimal bias voltage that
minimizes this parasitic behavior (typically GCS = 1.0V).
Control voltages higher than the optimal result in parasitic phase expansion, lower control voltages result in
phase compression. GFS does not contribute to the
phase behavior and is preferred for slope control.
Applications Information
The following section describes the tuning methodology
best implemented with a class A amplifier. Other classes
of operation may require significantly different settings.
Gain and Phase Expansion Optimization
The best approach to improve the ACPR of a PA is to
first optimize the AM-PM response of the phase section. For most high-frequency LDMOS amplifiers,
improving the AM-PM response provides the bulk of the
ACPR improvement. Figure 4 shows a typical configuration of the phase tuning circuit. A power sweep on a
network analyzer allows quick real-time tuning of the
AM-PM response. First, tune PBIN to achieve the phase
expansion starting point (breakpoint) at the same point
where the PA’s phase compression begins. Next, use
control pins PF_S1, PDCS1, and PDCS2 to obtain the
optimal AM-PM response. The typical values for these
pins are shown in Figure 4.
To further improve the ACPR, connect the phase output to the gain input through a preamplifier. The preamplifier is used to compensate for the high insertion
loss of the gain section. Figure 5 shows a typical application circuit of the MAX2010 with the phase section
cascaded to the gain section for further ACPR optimization. Similar to tuning the phase section, first tune
the gain expansion breakpoint through the GBP pin
and adjust for the desired gain expansion with pins
GCS and GFS. To minimize the effect of GCS on the
parasitic phase response, minimize the control voltage
to around 1V. Some retuning of the AM-PM response
may be necessary.
Layout Considerations
A properly designed PC board is an essential part of any
high-frequency circuit. In order to minimize external components, the PC board can be designed to incorporate
small values of inductance and capacitance to optimize
the input and output VSWR (refer to the MAX2009/
MAX2010 EV Kit). The phase section’s PFS1 and PFS2
pins are sensitive to external parasitics. Minimize trace
lengths and keep varactor diodes close to the pins.
Remove the ground plane underneath the traces can further help reduce the parasitic capacitance. For best performance, route the ground pin traces directly to the
grounded EP underneath the package. Solder the EP on
the bottom of the device package evenly to the board
ground plane to provide a heat transfer path along with
signal grounding.
______________________________________________________________________________________
15
MAX2010
Gain Expansion Breakpoint
The gain expansion breakpoint is usually controlled by
a DAC connected through the GBP pin. The GBP input
voltage range of 0.5V to 5V corresponds to a breakpoint input power range of -2.5dBm to 23dBm. To
achieve the optimal performance, the gain expansion
breakpoint of the MAX2010 must be set to equal the
gain compression point of the PA. The GBP control has
a minimal effect on the small-signal gain when operated from 0.5V to 5V.
MAX2010
500MHz to 1100MHz Adjustable
RF Predistorter
POWER
AMPLIFIER
POUT = 7dBm
6
OUTP
3
ING
MAX2010
PREAMPLIFIER
9 INP
OUTG 27
PIN = 14dBm
11 PFS1
GBP 23
VPF_S1 = 1.5V
12 PFS2
PHASE
CONTROL
19 PBRAW
18 PBEXP
VPBIN = 0.8V
GAIN
CONTROL
PBIN PDCS1 PDCS2
GCS
17
25
13
14
GFS 24
VPDCS1 = 0V
VPDCS2 = 5V
Figure 4. AM-PM Response Tuning Circuit
Power-Supply Bypassing
Bypass each VCC pin with a 0.01µF capacitor.
Table 1. Suggested Components of
Typical Application Circuit
Exposed Pad RF
The exposed paddle (EP) of the MAX2010’s 28-pin thin
QFN-EP package provides a low inductance path to
ground. It is important that the EP be soldered to the
ground plane on the PC board, either directly or
through an array of plated via holes.
16
DESIGNATION
VALUE
TYPE
C1, C2, C3, C10
100pF ±5%
C4, C5
0.01µF ±10%
0603 ceramic capacitors
C6, C8
15pF ±5%
0402 ceramic capacitors
C11, C12
2.2pF ±0.1pF
0402 ceramic capacitors
L1, L2
5.6nH ±0.3nH
R1, R2
1kΩ ±5%
VR1, VR2
Skyworks
SMV1232-079
0402 ceramic capacitors
0402 ceramic inductors
0402 resistors
Hyperabrupt varactor
diodes
______________________________________________________________________________________
500MHz to 1100MHz Adjustable
RF Predistorter
MAX2010
PREAMPLIFIER
GAIN = 7dB
6
3
OUTP
ING
MAX2010
POWER
AMPLIFIER
PREAMPLIFIER
9 INP
OUTG 27
PIN = 14dBm
11 PFS1
GBP 23
VPF_S1 = 1.5V
12 PFS2
PHASE
CONTROL
19 PBRAW
18 PBEXP
VPBIN = 0.8V
GAIN
CONTROL
PBIN PDCS1 PDCS2
GCS
17
25
13
14
GFS 24
VGBP = 1V
VPDCS1 = 0V
VGFS = 1.5V
VPDCS2 = 5V
VGCS = 1V
Figure 5. MAX2010 Phase and Gain Optimization Circuit
______________________________________________________________________________________
17
500MHz to 1100MHz Adjustable
RF Predistorter
MAX2010
Typical Application Circuit
28
GND*
GND*
L2
C10
PREAMPLIFER
OUTP
GND*
C12
GND*
GBP
GFS
GCS
21
GAIN
CONTROL
2
20
3
19
4
18
MAX2010
5
17
PHASE
CONTROL
6
16
7
15
9
INP
GND*
PREAMPLIFER
22
1
8
10
L1
C1
23
11
C2
12
13
14
VCCG
GND*
C5
PBRAW
PBEXP
PBIN
CONTROL
UNIT
GND*
VCCP
C4
PDCS2
ING
24
PDCS1
C8
25
PFS2
GND*
26
PFS1
OPTIONAL MATCH COMPENSATION
27
GND*
GND*
GND*
GND*
POWER
AMPLIFER
OUTG
C6
C3
R2
C11
R1
*INTERNALLY CONNECTED TO EXPOSED GROUND PADDLE.
VR1
VR2
Chip Information
TRANSISTOR COUNT:
Bipolar: 160
CMOS: 240
PROCESS: BiCMOS
18
______________________________________________________________________________________
500MHz to 1100MHz Adjustable
RF Predistorter
b
CL
0.10 M C A B
D2/2
D/2
PIN # 1
I.D.
QFN THIN.EPS
D2
0.15 C A
D
k
0.15 C B
PIN # 1 I.D.
0.35x45
E/2
E2/2
CL
(NE-1) X e
E
E2
k
L
DETAIL A
e
(ND-1) X e
CL
CL
L
L
e
e
0.10 C
A
C
0.08 C
A1 A3
PROPRIETARY INFORMATION
TITLE:
PACKAGE OUTLINE
16, 20, 28, 32L, QFN THIN, 5x5x0.8 mm
APPROVAL
COMMON DIMENSIONS
DOCUMENT CONTROL NO.
REV.
21-0140
C
1
2
EXPOSED PAD VARIATIONS
NOTES:
1. DIMENSIONING & TOLERANCING CONFORM TO ASME Y14.5M-1994.
2. ALL DIMENSIONS ARE IN MILLIMETERS. ANGLES ARE IN DEGREES.
3. N IS THE TOTAL NUMBER OF TERMINALS.
4. THE TERMINAL #1 IDENTIFIER AND TERMINAL NUMBERING CONVENTION SHALL CONFORM TO JESD 95-1
SPP-012. DETAILS OF TERMINAL #1 IDENTIFIER ARE OPTIONAL, BUT MUST BE LOCATED WITHIN THE
ZONE INDICATED. THE TERMINAL #1 IDENTIFIER MAY BE EITHER A MOLD OR MARKED FEATURE.
5. DIMENSION b APPLIES TO METALLIZED TERMINAL AND IS MEASURED BETWEEN 0.25 mm AND 0.30 mm
FROM TERMINAL TIP.
6. ND AND NE REFER TO THE NUMBER OF TERMINALS ON EACH D AND E SIDE RESPECTIVELY.
7. DEPOPULATION IS POSSIBLE IN A SYMMETRICAL FASHION.
8. COPLANARITY APPLIES TO THE EXPOSED HEAT SINK SLUG AS WELL AS THE TERMINALS.
9. DRAWING CONFORMS TO JEDEC MO220.
10. WARPAGE SHALL NOT EXCEED 0.10 mm.
PROPRIETARY INFORMATION
TITLE:
PACKAGE OUTLINE
16, 20, 28, 32L, QFN THIN, 5x5x0.8 mm
APPROVAL
DOCUMENT CONTROL NO.
REV.
21-0140
C
2
2
Maxim cannot assume responsibility for use of any circuitry other than circuitry entirely embodied in a Maxim product. No circuit patent licenses are
implied. Maxim reserves the right to change the circuitry and specifications without notice at any time.
Maxim Integrated Products, 120 San Gabriel Drive, Sunnyvale, CA 94086 408-737-7600 ____________________ 19
© 2003 Maxim Integrated Products
Printed USA
is a registered trademark of Maxim Integrated Products.
MAX2010
Package Information
(The package drawing(s) in this data sheet may not reflect the most current specifications. For the latest package outline information
go to www.maxim-ic.com/packages.)
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