EUR | USD

MAX40200 Datasheet

Maxim Integrated

Download PDF Datasheet

Datasheet

General Description
The MAX40200 is an ideal diode current-switch that drops
so little voltage that it approaches an order of magnitude
better than Schottky diodes.
When forward-biased and enabled, the MAX40200
conducts with as little as 85mV of voltage drop while carrying
currents as high as 1A. Typical voltage drop is 43mV at
500mA, with the voltage drop increasing linearly at higher
currents. The MAX40200 thermally protects itself, and any
downstream circuitry, from overtemperature conditions.
When disabled (EN = low) the MAX40200 blocks voltages
up to 6V in either direction, making it suitable for most
low-voltage, portable electronic devices. The MAX40200
operates from a supply voltage of 1.5V to 5.5V.
The MAX40200 is available in a tiny, 0.73mm X 0.73mm,
4-bump wafer-level package (WLP), with a 0.35mm bump
pitch and only 0.5mm high and 5-pin SOT-23 package.
The MAX40200 operates over the extended -40°C to
+125°C temperature range.
Applications
Notebook and Tablet Computers
Portable Media Players
Cellular Phones
Portable/Wearable Medical Devices
Electronic Toys
USB-Powered Peripherals
Benefits and Features
Save Critical Voltage Drop in Portable Application
Drops Less Than 43mV at 500mA; 85mV at 1A
Longer Battery Life
Low Leakage When Reverse-Biased : 70nA (Typ),
1.5µA (Max)
Low Supply Quiescent Current: 7µA (Typ), 18µA (Max)
Saves Space Over Larger Schottky Diodes
Tiny 0.73mm x 0.73mm 4-bump WLP
SOT23-5 Package
Supply Voltage Range 1.5V to 5.5V
Thermally Self-Protecting
-40°C to +125°C Temperature Range
Ordering Information appears at end of data sheet.
19-8728; Rev 1; 4/17
GND
EN
OUT
V
DD
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
Functional Diagram and Package
Any Pin to GND .......................................................-0.3V to +6V
Continuous Current Into EN ...............................................10mA
Continuous Current Flowing Between VDD and OUT
(WLP Package) ................................................................1.2A
Continuous current flowing between VDD and OUT
(SOT23-5 Package) ..........................................................1.0A
Maximum Power Dissipation
WLP, Derate 9.58mW/°C above +70°C ....................... 766mW
SOT, Derate 3.90mW/°C above +70°C ..................312.60mW
4 WLP
Thermal Resistance (Multi-Layer Board)
Junction to Ambient (θJA) ......................................... 104.41°C/W
5 SOT-23
Thermal Resistance (Multi-Layer Board)
Junction to Ambient (θJA) ......................................... 255.90°C/W
Junction to Case JC) ....................................................81°C/W
Operating Temperature Range ........................ -40°C to +125°C
Junction Temperature ...................................................... +150°C
Storage Temperature Range ............................ -65°C to +150°C
Reflow Soldering Peak Temperature (Pb-free) ............... +260°C
VDD = 3.3V, GND = 0V, EN = VDD, TA = -40°C to +125°C, unless otherwise noted. Typical values are at +25°C (Note 2)
PARAMETER SYMBOL CONDITIONS MIN TYP MAX UNITS
Supply Voltage Range VDD Guaranteed by DVON_FRWD 1.5 5.5 V
Quiescent Current IDD
EN = VDD, IFORWARD = 0 mA 7 18 µA
EN = VGND, IFORWARD = 0 mA 0.7 2.5
Quiescent Current in Reverse
Operation
Current drawn from VDD; VOUT - VDD = 0.1V -1.5 0.072 1.5 µA
Current drawn from OUT; VOUT - VDD = 0.1V 1.2 3.5
VDD Leakage Current Current sourced into VDD; VDD = 0V,
VOUT = 5.5V -5.5 -0.55 +2.5 µA
Forward Turn-On Threshold
Voltage VON_FRWD
Voltage between VDD and OUT (VDD more
positive than OUT) IFORWARD = 1mA 18 40 mV
Forward Turn-On Threshold
Voltage Change Over Supply
Voltage
DVON_FRWD VDD = 1.5V to 5.5V -3 +0.2 +3 mV
Reverse Turn-Off Threshold VOFF_REV Voltage between VDD and VOUT 20 mV
Forward Voltage
(VDD – VOUT) (WLP Only) VFWD
IFORWARD = 100mA 21 52
mV
IFORWARD =
200mA
VDD = 1.5V 45 89
VDD = 3.3V 24 57
IFORWARD = 500mA 43 89
IFORWARD = 1A 85 175
Forward Voltage (VDD – VOUT)
(SOT Only) VFWD
IFORWARD = 100mA 32 65
mV
IFORWARD =
200mA
VDD = 1.5V 63 110
VDD = 3.3V 46 90
IFORWARD = 500mA 97 175
IFORWARD = 1A (Note 3) 197 350
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
www.maximintegrated.com Maxim Integrated
2
Note 1: Package thermal resistances were obtained using the method described in JEDEC specification JESD51-7, using a four-layer
board. For detailed information on package thermal considerations, refer to www.maximintegrated.com/thermal-tutorial.
Absolute Maximum Ratings
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.
Electrical Characteristics
VDD = 3.3V, GND = 0V, EN = VDD, TA = -40°C to +125°C, unless otherwise noted. Typical values are at +25°C (Note 2)
Note 2: All devices are production tested at TA = + 25°C. Specifications over temperature are guaranteed by design
Note 3: 1A pulsed current in duty cycle used for this test to make sure the device’s self heating is negligible. For more information,
see Thermal Performance and Power Dissipation Information section.
PARAMETER SYMBOL CONDITIONS MIN TYP MAX UNITS
Capacitive Load Range COUT Stable for all load currents 0.3 - 100 µF
Thermal Protection Threshold 154 °C
Thermal Protection Hysteresis 10 °C
ENABLE (EN) CHARACTERISTICS
Low-Level Input Current EN = 0V -1 -0.1 +0.1 µA
Low-Level Voltage Level LOW 0.6 V
High Input Voltage Level HIGH 1.2 V
High Level Input Current EN = VDD 0.5 2.5 µA
Enable Input Hysteresis 50 mV
Enable Time
IFORWARD reaching 90% of its final value
with a resistive load (ROUT) = 33Ω and 4.7µF,
enable input toggled from 0V to 3.3V
65 µs
Disable Time
IFORWARD prior to disable = 100mA,
IFORWARD reaching ≤ 1mA resistive load
(ROUT) = 33Ω and 4.7µF, enable input
toggled from 0V to 3.3V
1.6 ms
Power-Up Delay Time 65 µs
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
www.maximintegrated.com Maxim Integrated
3
Electrical Characteristics (continued)
VDD = 3.3V, GND = 0V, EN = VDD, 100mA load or IFORWARD and 10µF COUT on OUT, TA = -40°C to +125°C, unless otherwise noted.
Typical values are at +25°C.
0
10
20
30
40
50
60
70
0200 400 600 800 1000
GROUND CURRENT (μA)
FORWARD/LOAD CURRENT(mA)
GROUND CURRENT
vs. FORWARD/LOAD CURRENT toc02a
Refer to Figure 1 for Test Setup Conditions
VDD = 1.5V
TA= 25°C
TA= 125°C
TA= -40°C
TA= 85°C
0
25
50
75
0200 400 600 800 1000
GROUND CURRENT (μA)
FORWARD/LOAD CURRENT(mA)
GROUND CURRENT
vs. FORWARD/LOAD CURRENT toc02b
VDD = 3.3V
Refer to Figure 1 for Test Setup Conditions
VDD = 3.3V
TA= 25°C
TA= 125°C
TA= -40°C
TA= 85°C
0
4
8
12
16
20
24
0123456
QUIESCENT SUPPLY CURRENT (
μA)
SUPPLY INPUT VOLTAGE (V)
QUIESCENT SUPPLY CURRENT
vs. SUPPLY INPUT VOLTAGE toc01
TA= 25°C
TA= 125°C
TA= -40°C
TA= 85°C
Refer to Figure 1 for Test Setup Conditions
IFWD/LOAD = 0mA
0
25
50
75
100
0200 400 600 800 1000
GROUND CURRENT (µA)
FORWARD/LOAD CURRENT(mA)
GROUND CURRENT
vs. FORWARD/LOAD CURRENT toc02c
Refer to Figure 1 for Test Setup Conditions
VDD = 5.5V
TA= 25°C
TA= 125°C
TA= -40°C
TA= 85°C
0
100
200
300
400
0250 500 750 1000
FORWARD VOLTAGE (mV)
FORWARD CURRENT (mA)
FORWARD VOLTAGE vs. FORWARD CURRENT
(WLP) toc03a
VDD = 1.5V
TA= -40°C
TA= 25°C
Refer to Figure 1 for Test Setup Conditions
VDD = 1.5V
TA= 85°C
TA= 125°C
Thermal Limit Reached
0
100
200
300
400
500
600
700
0250 500 750 1000
FORWARD VOLTAGE (mV)
FORWARD CURRENT (mA)
FORWARD VOLTAGE vs. FORWARD CURRENT
(SOT) toc03b
VDD = 1.5V
TA= -40°C
TA= 25°C
TA= 85°C
TA= 125°C
Themal Limit Reached
Refer to Figure 1 for Test Setup Conditions
0
25
50
75
100
125
150
0250 500 750 1000
FORWARD VOLTAGE (mV)
FORWARD CURRENT (mA)
FORWARD VOLTAGE vs. FORWARD CURRENT
(WLP) toc03c
VDD = 3.3V
Refer to Figure 1 for Test Setup Conditions
VDD = 3.3V
TA= -40°C
TA= 25°C
TA= 85°C
TA= 125°C
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
Maxim Integrated
4
www.maximintegrated.com
Typical Operating Characteristics
VDD = 3.3V, GND = 0V, EN = VDD, 100mA load or IFORWARD and 10µF COUT on OUT, TA = -40°C to +125°C, unless otherwise noted.
Typical values are at +25°C.
Typical Operating Characteristics (continued)
0
25
50
75
100
0250 500 750 1000
FORWARD VOLTAGE (mV)
FORWARD CURRENT (mA)
FORWARD VOLTAGE vs. FORWARD CURRENT
(WLP) toc03e
VDD = 5.5V
Refer to Figure 1 for Test Setup Conditions
VDD = 5.5V
TA= -40°C
TA= 25°C
TA= 85°C
TA= 125°C
0
50
100
150
200
250
0250 500 750 1000
FORWARD VOLTAGE (mV)
FORWARD CURRENT (mA)
FORWARD VOLTAGE vs. FORWARD CURRENT
(SOT) toc03f
VDD = 5.5V
TA= -40°C
TA= 25°C
TA= 85°C
TA= 125°C
Thermal Limit Reached
Refer to Figure 1 for Test Setup Conditions
VDD = 5.5V
0
50
100
150
200
250
300
0250 500 750 1000
FORWARD VOLTAGE (mV)
FORWARD CURRENT (mA)
FORWARD VOLTAGE vs. FORWARD CURRENT
(SOT) toc03d
VDD = 3.3V
Refer to Figure 1 for Test Setup Conditions
VDD = 3.3V
TA= -40°C
TA= 25°C
TA= 85°C
TA= 125°C
Themal Limit Reached
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0123456
CATHODE CURRENT (µA)
VOUT (V)
CATHODE CURRENT
AT REVERSE OPERATION
toc04
VDD = 0V ICATHODE
TA= -40°C
TA= 25°C
TA= 85°C
TA= 125°C
Refer to Figure 2 for Test Setup Conditions
-0.5
0
0.5
1
1.5
2
2.5
3
0123456
ANODE CURRENT (μA)
VOUT (V)
ANODE CURRENT
AT REVERSE OPERATION toc05
VDD = 0V IANODE
TA= -40°C
TA= 25°C
TA= 85°C
TA= 125°C
Refer to Figure 2 for Test Setup Conditions
-0.5
0
0.5
1
1.5
2
2.5
0123456
GROUND CURRENT (µA)
VOUT (V)
GROUND CURRENT
AT REVERSE OPERATION toc06
VDD = 0V IGND
TA= -40°C
TA= 25°C
TA= 85°C
TA= 125°C
Refer to Figure 2 for Test Setup Conditions -0.1
-0.05
0
0.05
0.1
0.15
0.2
-40 -25 -10 520 35 50 65 80 95 110 125
INPUT CURRENT INTO VIN (µA)
TEMPERATURE (°C)
ANODE CURRENT
AT REVERSE OPERATION toc07
VDD = 3.3V
VOUT-VDD = 0.1V
Refer to Figure 2 for Test Setup Conditions
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
Maxim Integrated
5
www.maximintegrated.com
VDD = 3.3V, GND = 0V, EN = VDD, 100mA load or IFORWARD and 10µF COUT on OUT, TA = -40°C to +125°C, unless otherwise noted.
Typical values are at +25°C.
0
0.5
1
1.5
2
2.5
3
-40 -25 -10 520 35 50 65 80 95 110 125
OUTPUT CURRENT FROM VOUT (µA)
TEMPERATURE (°C)
CATHODE CURRENT
AT REVERSE OPERATION toc08
VDD = 0V
VOUT = 5.5V
Refer to Figure 2 for Test Setup Conditions
ENABLE TRANSIENT
IFWD = 1A
2V/div
1V/div
10µs/div
V(EN)
VOUT
3.3V
CLOAD = 4.7µF
3.3V
toc10a
DISABLE TRANSIENT
IFWD = 1A
2V/div
1V/div
100µs/div
V(EN)
VOUT
3.3V
CLOAD = 4.7µF
3.3V
toc11a
POWER-UP DELAY
2V/div
1V/div
20µs/div
VDD
VOUT
3.3V
RLOAD = 3.3k
3.3V
toc9
ENABLE TRANSIENT
IFWD = 100mA
2V/div
1V/div
10µs/div
V(EN)
VOUT
3.3V
CLOAD = 4.7µF
3.3V
toc10b
DISABLE TRANSIENT
IFWD = 100mA
2V/div
1V/div
400µs/div
V(EN)
VOUT
3.3V
CLOAD = 4.7µF
3.3V
toc11b
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
Maxim Integrated
6
www.maximintegrated.com
Typical Operating Characteristics (continued)
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
www.maximintegrated.com Maxim Integrated
7
Test Setup
WLP 5 SOT-23 NAME FUNCTION
A1 1 VDD Supply Input or Anode.
A2 5 OUT Ideal Diode Output or Cathode.
B1 3 EN Enable Input. Pull high to enable the device and pull low to disable the
device. Active pullup.
B24 2 GND Circuit Ground and Substrate Connection.
4 N.C. No Connect. Internally not connected.
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
www.maximintegrated.com Maxim Integrated
8
Pin Description
Pin Configurations
Detailed Description
The MAX40200 mimics a near-ideal diode. The device
blocks reverse-voltages and passes current when forward-
biased just as a normal diode. The improvements are that
instead of a cut-in voltage around 500mV and a logarithmic
voltage-current transfer curve, the MAX40200 has a near
constant voltage drop independent of the magnitude of
the forward current flowing through it. This voltage drop is
around 45mV at 500mA of forward or load current.
The constant forward voltage drop significantly helps with
supply regulation; a normal diode typically drops an additional
60mV for every 10 times change in current through it.
Similar to a normal diode, the MAX40200 also becomes
resistive as the forward current exceeds the specified
limit (see Figure 1). Unlike a normal diode, should the
MAX40200 exceed the specified temperature, it will turn
off in order to protect itself and the circuitry connected to
it. Like a normal diode MAX40200 will turn-off when it is
reverse biased. The turn-on and turn-off times for enable
and disable responses are similar to those of forward and
reverse bias conditions.
MAX40200 has an enable function feature. Unlike a normal
diode the device can be turned off when not required.
When turned off, it blocks voltages on either side to
a maximum of 6V above ground. This feature allows
MAX40200 to be used, to switch supply sources, or to
control which sub-systems are to be powered up.
It should be noted, however, that, unlike normal diodes,
this “ideal diode” is not suited to rectifying AC. In applications
where the supply is inductively coupled, conventional
diodes should be used for the rectification part of the
circuitry. MAX40200 is designed to be used in applications
to switch between different DC sources.
Principle of Operation
The MAX40200 features an internal pMOSFET to pass
the current from the VDD input to the OUT output. The
internal MOSFET is controlled by circuitry that:
1) Creates the 18mV constant forward drop when the
MAX40200 is forward-biased.
2) Turns the MOSFET off when the part is reverse-biased.
3) Turns the MOSFET off if the enable input is pulled low.
4) Turns the device off when the device temperature
exceeds the thermal protection threshold.
This control circuitry consumes 7µA typical current and
this limits the rate at which the internal MOSFET can be
turned on/off.
To ensure the control loop remains stable for all output
current levels, there should always be a minimum of
0.33µF connected to the OUT output and likewise, a minimum
of 0.33µF on the VDD input.
These capacitors also improve the surge capability of
power supply. In general for higher Output Capacitive
Loads [e.g., COUT = 10µF], then CIN should be kept to
COUT/10 (µF) for optimum transient response.
Applications Information
The simplest application would be as shown in Figure 2,
where the battery has to be disconnected from the load
when the wall-supply is connected. Often, the wall-supply
can handle the additional losses of a normal diode, so it
would use a regular diode to prevent battery power from
flowing back into it.
The battery, on the other hand, benefits significantly by
only losing 30mV when powering the load, thus increasing
the battery life between charging cycles.
For systems that require more than the 500mA that the
MAX40200 is specified for, it may be convenient to split
the load up into various sections that could also benefit
from the individual power enabling that the MAX40200’s
Enable pins offer.
This also suggests that any integrated circuit without built-
in power-down capability can have it added by powering it
through a MAX40200.
This allows many parts to be used in portable and other
power-sensitive products.
Figure 1. Forward Voltage vs. Forward Current (WLP)
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
www.maximintegrated.com Maxim Integrated
9
Figure 3. Diode ORing Circuit 2
Figure 2. Diode ORing Circuit 1
LOAD-A
EN
MAX40200
EN
LOAD-B
MAX40200
BATTERY
FROM WALL ADAPTER
IDEAL DIODE (1)
IDEAL DIODE (2)
DIODE (D2)
DIODE (D1)
LOAD
EN
MAX40200
BATTERY
FROM WALL ADAPTER DIODE (D1)
IDEAL DIODE
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
www.maximintegrated.com Maxim Integrated
10
Thermal Performance and Power
Dissipation Information
Although the device is guaranteed for TA = -40°C to
125°C, care must be taken when using heavy loads
(e.g., IFWD above 500mA to 1A) where the forward
current across the ideal diode is large. The forward voltage
drop across the VDD and OUT pins increases linearly
with forward current. The device’s power dissipation is
directly proportional to the voltage drop across the device.
The power dissipation is going to be the differential
voltage (VFWD) multiplied by the current passed
by the device (IFWD). The quiescent current of the
device is negligible for these calculations. The ambient
temperature is essentially the PCB temperature, since
this is where all the heat is sunk to. Therefore, the
parts temperature rise is [VFWD x IFWD x θ
JA] + TA,
where TA is the temperature of the board or ambient
temperature. From this exercise, we observe that the
internal temperature from power dissipation will be higher
than the ambient temperature. The device has an internal
thermal shutdown temperature of about +154°C and,
typically, 12°C hysteresis.
For example:
WLP:
At 1A IFWD, TA = 85°C. VFWD = 110mV. Therefore,
PDIS = 110mW.
Package Derate Calculation:
For 85°C: Maximum Power Dissipation from the data
sheet: 766mW – [(85 - 70) x 9.58] = 622mW. The device is
within specification. Therefore, the junction temperature:
85°C + (104.41°C/W x 0.110W) = 85°C + 11.5°C = 96.5°C
SOT-23 (Small Outline Transistor Package):
At 1A IFWD, TA = 85°C. VFWD = 250mV. Hence,
PDIS = 250mW.
Package Derate Calculation:
For 85°C: Maximum Power Dissipation from the data
sheet: 312.6mW – [(85 - 70)°C x 3.9mW/°C] = 254.1mW.
The device is very close to the power dissipation ratings
provided in the absolute maximum specification.
Hence the device’s junction temperature: 85°C +
(255.90°C/W x 0.2541W) = 85°C + 65.02°C = 150.02°C
As the above example shows, the thermal performance of
the WLP exceeds the SOT package.
When the device’s junction temperature rises to 154°C
thermal trip is triggered, the thermal cycle for the WLP
and SOT packages are shown in Figure 5 and Figure 6.
Figure 4. Typical Application Circuit
SUB
CIRCUIT-N
EN
MAX40200
SUB
CIRCUIT 1
SUB
CIRCUIT 2
BATTERY
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
www.maximintegrated.com Maxim Integrated
11
Figure 5. Thermal Protection (WLP) Figure 6. Thermal Protection (SOT)
TA = 125°C TA = 125°C
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
www.maximintegrated.com Maxim Integrated
12
+Denotes a lead(Pb)-free/RoHS-compliant package.
PART TEMP RANGE PIN-PACKAGE
MAX40200ANS+ -40°C to +125°C 4 WLP
MAX40200AUK+ -40°C to +125°C 5 SOT23
PACKAGE
TYPE
PACKAGE
CODE OUTLINE NO. LAND
PATTERN NO.
4 WLP N40C0+1 21-100103 Refer to
App Note 1891
5 SOT23 U5+1 21-0057 90-0174
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
www.maximintegrated.com Maxim Integrated
13
Ordering Information Chip Information
PROCESS: BiCMOS
Package Information
For the latest package outline information and land patterns
(footprints), go to www.maximintegrated.com/packages. Note
that a “+”, “#”, or “-” in the package code indicates RoHS status
only. Package drawings may show a different suffix character, but
the drawing pertains to the package regardless of RoHS status.
REVISION
NUMBER
REVISION
DATE DESCRIPTION PAGES
CHANGED
0 12/16 Initial release
1 4/17
Updated Electrical Characteristics table, correct typos in Applications and
Detailed Description sections, added TOC, and removed future product asterisk
from SOT version
1–3, 9, 13
Maxim Integrated cannot assume responsibility for use of any circuitry other than circuitry entirely embodied in a Maxim Integrated product. No circuit patent licenses
are implied. Maxim Integrated reserves the right to change the circuitry and specifications without notice at any time. The parametric values (min and max limits)
shown in the Electrical Characteristics table are guaranteed. Other parametric values quoted in this data sheet are provided for guidance.
Maxim Integrated and the Maxim Integrated logo are trademarks of Maxim Integrated Products, Inc.
MAX40200 Ultra-Tiny Micropower, 1A Ideal Diode
with Ultra-Low Voltage Drop
© 2017 Maxim Integrated Products, Inc.
14
Revision History
For pricing, delivery, and ordering information, please contact Maxim Direct at 1-888-629-4642, or visit Maxim Integrated’s website at www.maximintegrated.com.

Products

IC DIODE CURRENT SWITCH 4WLP
Available Quantity19511
Unit Price0.83
EVAL BOARD FOR MAX40200
Available Quantity12
Unit Price49.97
IC DIODE CURRENT SWITCH SOT23-5
Available Quantity0
Unit Price0.82