Datasheet LM4872 Datasheet (National Semiconductor)

October 2002

LM4872

1 Watt Audio Power Amplifier in micro SMD package

LM4872 1 Watt Audio Power Amplifier micro SMD package

General Description

The LM4872 is a bridge-connected audio power amplifier
capable of delivering1Wofcontinuous average power to an
8Ω load with less than .2% (THD) from a 5V power supply.

Boomer audio power amplifiers were designed specifically to
provide high quality output power with a minimal amount of
external components. Since the LM4872 does not require
output coupling capacitors or bootstrap capacitors. It is op­timally suited for low-power portable applications.

The LM4872 features an externally controlled, low-power
consumption shutdown mode, as well as an internal thermal
shutdown protection mechanism.

The unity-gain stable LM4872 can be configured by external
gain-setting resistors.

Typical Application

Key Specifications

n Power Output at 0.2% THD 1W (typ)
n Shutdown Current 0.01µA (typ)

Features

n micro SMD package (see App. note AN-1112)
n 5V - 2V operation
n No output coupling capacitors or bootstrap capacitors.
n Unity-gain stable
n External gain configuration capability

Applications

n Cellular Phones
n Portable Computers
n Low Voltage Audio Systems

10123001

FIGURE 1. Typical Audio Amplifier Application Circuit

Boomer®is a registered trademark of National Semiconductor Corporation.

© 2002 National Semiconductor Corporation DS101230 www.national.com

Connection Diagram

LM4872

8 Bump micro SMD

Top View

Order Number LM4872IBP, LM4872IBPX

See NS Package Number BPA08B6B

10123023

www.national.com 2

LM4872

Absolute Maximum Ratings (Note 2)

If Military/Aerospace specified devices are required,
please contact the National Semiconductor Sales Office/

Soldering Information

See AN-1112 ’Micro-SMD Wafers Level Chip Scale
Package’.

Distributors for availability and specifications.

Supply Voltage 6.0V

Storage Temperature −65˚C to +150˚C

Input Voltage −0.3V to V

DD

+0.3V

Power Dissipation (Note 3) Internally Limited

Operating Ratings

Temperature Range

ESD Susceptibility (Note 4) 2500V

ESD Susceptibility (Note 5) 250V

Supply Voltage 2.0V ≤ V

Junction Temperature 150˚C

Electrical Characteristics VDD=5V (Notes 1, 2, 9)

The following specifications apply for V

Symbol Parameter Conditions

V

DD

I

DD

I

SD

V

OS

P

o

Supply Voltage 2.0 V (min)

Quiescent Power Supply Current VIN= 0V, Io= 0A 5.3 7 mA (max)

Shutdown Current V

Output Offset Voltage VIN= 0V 5 50 mV (max)

Output Power THD = 0.2% (max);f=1kHz 1 W

THD+N Total Harmonic Distortion+Noise P

PSRR Power Supply Rejection Ratio V

= 5V and 8Ω Load unless otherwise specified. Limits apply for TA= 25˚C.

DD

PIN1=VDD

= 0.25 Wrms; AVD=2;20Hz≤

o

f ≤ 20 kHz

= 4.9V to 5.1V 65 dB

DD

T

MIN

≤ TA≤ T

MAX

−40˚C ≤ TA≤ 85˚C

LM4872

Typical Limit

(Note 6) (Note 7)

5.5 V (max)

0.01 2 µA (max)

0.1 %

≤ 5.5V

DD

Units

(Limits)

Electrical Characteristics VDD= 3.3V (Notes 1, 2, 9)

The following specifications apply for V

Symbol Parameter Conditions

V

DD

I

DD

I

SD

V

OS

P

o

Supply Voltage 2.0 V (min)

Quiescent Power Supply Current VIN= 0V, Io= 0A 4 mA (max)

Shutdown Current V

Output Offset Voltage VIN= 0V 5 mV (max)

Output Power THD = 1% (max);f=1kHz .5 .45 W

THD+N Total Harmonic Distortion+Noise P

PSRR Power Supply Rejection Ratio V

= 3.3V and 8Ω Load unless otherwise specified. Limits apply for TA= 25˚C.

DD

PIN1=VDD

= 0.25 Wrms; AVD=2;20Hz≤

o

f ≤ 20 kHz

= 3.2V to 3.4V 65 dB

DD

Electrical Characteristics VDD= 2.6V (Notes 1, 2, 8, 9)

The following specifications apply for V

Symbol Parameter Conditions

V

DD

I

DD

I

SD

Supply Voltage 2.0 V (min)

Quiescent Power Supply Current VIN= 0V, Io= 0A 3.4 mA (max)

Shutdown Current V

= 2.6V and 8Ω Load unless otherwise specified. Limits apply for TA= 25˚C.

DD

PIN1=VDD

LM4872

Typical Limit

(Note 6) (Note 7)

Units

(Limits)

5.5 V (max)

0.01 µA (max)

0.15 %

LM4872

Typical Limit

(Note 6) (Note 7)

Units

(Limits)

5.5 V (max)

0.01 µA (max)

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Electrical Characteristics VDD= 2.6V (Notes 1, 2, 8, 9)

The following specifications apply for V

LM4872

25˚C. (Continued)

= 2.6V and 8Ω Load unless otherwise specified. Limits apply for TA=

DD

Symbol Parameter Conditions

V

OS

P

0

Output Offset Voltage VIN= 0V 5 mV (max)

Output Power ( 8Ω )
Output Power ( 4Ω )

THD = 0.3% (max);f=1kHzTHD
= 0.5% (max);f=1kHz

THD+N Total Harmonic Distortion+Noise Po= 0.25 Wrms; AVD=2;20Hz≤

LM4872

Typical Limit

(Note 6) (Note 7)

0.25

0.5

0.25 %

Units

(Limits)

f ≤ 20 kHz

PSRR Power Supply Rejection Ratio V

Note 1: All voltages are measured with respect to the ground pin, unless otherwise specified.

Note 2: Absolute Maximum Ratings indicate limits beyond which damage to the device may occur. Operating Ratings indicate conditions for which the device is

functional, but do not guarantee specific performance limits. Electrical Characteristics state DC and AC electrical specifications under particular test conditions which
guarantee specific performance limits. This assumes that the device is within the Operating Ratings. Specifications are not guaranteed for parameters where no limit
is given, however, the typical value is a good indication of device performance.

Note 3: The maximum power dissipation must be derated at elevated temperatures and is dictated by T
allowable power dissipation is P
The typical junction-to-ambient thermal resistance is 150˚C/W.

Note 4: Human body model, 100 pF discharged through a 1.5 kΩ resistor.

Note 5: Machine Model, 220 pF–240 pF discharged through all pins.

Note 6: Typicals are measured at 25˚C and represent the parametric norm.

Note 7: Limits are guaranteed to National’s AOQL (Average Outgoing Quality Level).

Note 8: Low Voltage Circuit - See Fig. 4

Note 9: Shutdown current is measured in a Normal Room Environment. Exposure to direct sunlight will increase I

DMAX

=(T

)/θJAor the number given in Absolute Maximum Ratings, whichever is lower. For the LM4872, T

JMAX–TA

= 2.5V to 2.7V 65 dB

DD

, θJA, and the ambient temperature TA. The maximum

JMAX

by a maximum of 2µA.

SD

JMAX

= 150˚C.

External Components Description

(Figure 1)

W
W

Components Functional Description

1. R

2. C

3. R

4. C

Inverting input resistance which sets the closed-loop gain in conjunction with Rf. This resistor also forms a

i

high pass filter with C

Input coupling capacitor which blocks the DC voltage at the amplifiers input terminals. Also creates a

i

highpass filter with R
for an explanation of how to determine the value of C

Feedback resistance which sets the closed-loop gain in conjunction with Ri.

f

Supply bypass capacitor which provides power supply filtering. Refer to the Power Supply Bypassing

S

at fC= 1/(2π RiCi).

i

at fc= 1/(2π RiCi). Refer to the section, Proper Selection of External Components,

i

.

i

section for information concerning proper placement and selection of the supply bypass capacitor.

5. C

Bypass pin capacitor which provides half-supply filtering. Refer to the section, Proper Selection of External

B

Components, for information concerning proper placement and selection of C

.

B

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Typical Performance Characteristics

LM4872

THD+N vs Frequency

at 5V and 8Ω

THD+N vs Frequency

at 2.6V and 8Ω

THD+N vs Frequency

at 3.3V and 8Ω

10123003 10123006

THD+N vs Frequency

at 2.6V and 4Ω

THD+N vs Output Power

@

VDD=5V

10123005 10123004

THD+N vs Output Power

@

VDD= 3.3V

10123007 10123008

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Typical Performance Characteristics (Continued)

LM4872

THD+N vs

Output Power

2.6V at 8Ω

Output Power vs

Supply Voltage

THD+N vs

Output Power

2.6V at 4Ω

10123009 10123010

Output Power vs
Load Resistance

Power Derating Curve

10123011 10123012

Power Dissipation vs

Output Power

=5V

V

DD

10123014 10123026

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Typical Performance Characteristics (Continued)

LM4872

Power Dissipation vs

Output Power

= 3.3V

V

DD

Clipping Voltage vs

Supply Voltage

10123027

Power Dissipation vs

Output Power

VDD= 2.6V

10123028

Supply Current vs
Shutdown Voltage

10123015

10123020

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Typical Performance Characteristics (Continued)

LM4872

Frequency Response vs

Input Capacitor Size

10123017

Power Supply

Rejection Ratio

Open Loop

Frequency Response Noise Floor

10123018

10123019 10123016

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Application Information

BRIDGE CONFIGURATION EXPLANATION

As shown in Figure 1, the LM4872 has two operational
amplifiers internally, allowing for a few different amplifier
configurations. The first amplifier’s gain is externally config­urable, while the second amplifier is internally fixed in a
unity-gain, inverting configuration. The closed-loop gain of
the first amplifier is set by selecting the ratio of R
the second amplifier’s gain is fixed by the two internal 10 kΩ
resistors. Figure 1 shows that the output of amplifier one
serves as the input to amplifier two which results in both
amplifiers producing signals identical in magnitude, but out
of phase by 180˚. Consequently, the differential gain for the
IC is

= 2 *(Rf/Ri)

A

VD

By driving the load differentially through outputs Vo1 and
Vo2, an amplifier configuration commonly referred to as
“bridged mode” is established. Bridged mode operation is
different from the classical single-ended amplifier configura­tion where one side of its load is connected to ground.

A bridge amplifier design has a few distinct advantages over
the single-ended configuration, as it provides differential
drive to the load, thus doubling output swing for a specified
supply voltage. Four times the output power is possible as
compared to a single-ended amplifier under the same con­ditions. This increase in attainable output power assumes
that the amplifier is not current limited or clipped. In order to
choose an amplifier’s closed-loop gain without causing ex­cessive clipping, please refer to the Audio Power Amplifier
Design section.

A bridge configuration, such as the one used in LM4872,
also creates a second advantage over single-ended amplifi­ers. Since the differential outputs, Vo1 and Vo2, are biased
at half-supply, no net DC voltage exists across the load. This
eliminates the need for an output coupling capacitor which is
required in a single supply, single-ended amplifier configura­tion. Without an output coupling capacitor, the half-supply
bias across the load would result in both increased internal
IC power dissipation and also possible loudspeaker damage.

POWER DISSIPATION

Power dissipation is a major concern when designing a
successful amplifier, whether the amplifier is bridged or
single-ended. A direct consequence of the increased power
delivered to the load by a bridge amplifier is an increase in
internal power dissipation. Since the LM4872 has two opera­tional amplifiers in one package, the maximum internal
power dissipation is 4 times that of a single-ended amplifier.
The maximum power dissipation for a given application can
be derived from the power dissipation graphs or from Equa­tion 1.

= 4*(VDD)2/(2π2RL) (1)

P

DMAX

It is critical that the maximum junction temperature T
150˚C is not exceeded. T
power derating curves by using P

can be determined from the

JMAX

and the PC board foil

DMAX

area. By adding additional copper foil, the thermal resistance
of the application can be reduced from a free air value of
150˚C/W, resulting in higher P

. Additional copper foil

DMAX

can be added to any of the leads connected to the LM4872.
It is especially effective when connected to V
the output pins. Refer to the application information on the
LM4872 reference design board for an example of good heat
sinking. If T

still exceeds 150˚C, then additional

JMAX

changes must be made. These changes can include re-

to Riwhile

f

DD,GND

JMAX

, and

LM4872

duced supply voltage, higher load impedance, or reduced
ambient temperature. The National Reference Design board
using a 5V supply and an 8 ohm load will run in a 110˚C
ambient environement without exceeding T
power dissipation is a function of output power. Refer to the
Typical Performance Characteristics curves for power dis­sipation information for different output powers and output
loading.

POWER SUPPLY BYPASSING

As with any amplifier, proper supply bypassing is critical for
low noise performance and high power supply rejection. The
capacitor location on both the bypass and power supply pins
should be as close to the device as possible. Typical appli­cations employ a 5V regulator with 10 µF Tantalum or elec­trolytic capacitor and a 0.1 µF bypass capacitor which aid in
supply stability. This does not eliminate the need for bypass­ing the supply nodes of the LM4872. The selection of bypass
capacitor, especially C

, is dependent upon PSRR require-

B

ments, click and pop performance as explained in the sec­tion, Proper Selection of External Components, system
cost, and size constraints.

SHUTDOWN FUNCTION

In order to reduce power consumption while not in use, the
LM4872 contains a shutdown pin to externally turn off the
amplifier’s bias circuitry. This shutdown feature turns the
amplifier off when a logic high is placed on the shutdown pin.
The trigger point between a logic low and logic high level is
typically half- supply. It is best to switch between ground and
supply to provide maximum device performance. By switch­ing the shutdown pin to V

, the LM4872 supply current

DD

draw will be minimized in idle mode. While the device will be
disabled with shutdown pin voltages less than V
current may be greater than the typical value of 0.01 µA. In
either case, the shutdown pin should be tied to a stable
voltage to avoid unwanted state changes.

In many applications, a microcontroller or microprocessor
output is used to control the shutdown circuitry which pro­vides a quick, smooth transition into shutdown. Another so­lution is to use a single-pole, single-throw switch in conjunc­tion with an external pull-up resistor. When the switch is
closed, the shutdown pin is connected to ground and en­ables the amplifier. If the switch is open, then the external
pull-up resistor will disable the LM4872. This scheme guar­antees that the shutdown pin will not float thus preventing
unwanted state changes.

PROPER SELECTION OF EXTERNAL COMPONENTS

Proper selection of external components in applications us­ing integrated power amplifiers is critical to optimize device
and system performance. While the LM4872 is tolerant of
external component combinations, consideration to compo­nent values must be used to maximize overall system qual-

of

ity.
The LM4872 is unity-gain stable which gives a designer

maximum system flexibility. The LM4872 should be used in
low gain configurations to minimize THD+N values, and
maximize the signal to noise ratio. Low gain configurations
require large input signals to obtain a given output power.
Input signals equal to or greater than 1 Vrms are available
from sources such as audio codecs. Please refer to the
section, Audio Power Amplifier Design, for a more com­plete explanation of proper gain selection.

Besides gain, one of the major considerations is the closed­loop bandwidth of the amplifier. To a large extent, the band-

JMAX

. Internal

, the idle

DD

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Application Information (Continued)

width is dictated by the choice of external components

LM4872

shown in Figure 1. The input coupling capacitor, C
first order high pass filter which limits low frequency re­sponse. This value should be chosen based on needed
frequency response for a few distinct reasons.

Selection Of Input Capacitor Size

Large input capacitors are both expensive and space hungry
for portable designs. Clearly, a certain sized capacitor is
needed to couple in low frequencies without severe attenu­ation. But in many cases the speakers used in portable
systems, whether internal or external, have little ability to
reproduce signals below 100 Hz to 150 Hz. Thus, using a
large input capacitor may not increase actual system perfor­mance.

In addition to system cost and size, click and pop perfor­mance is effected by the size of the input coupling capacitor,

A larger input coupling capacitor requires more charge to

C

i.

reach its quiescent DC voltage (nominally 1/2 V
charge comes from the output via the feedback and is apt to
create pops upon device enable. Thus, by minimizing the
capacitor size based on necessary low frequency response,
turn-on pops can be minimized.

Besides minimizing the input capacitor size, careful consid­eration should be paid to the bypass capacitor value. Bypass
capacitor, C
turn-on pops since it determines how fast the LM4872 turns
on. The slower the LM4872’s outputs ramp to their quiescent
DC voltage (nominally 1/2 V
Choosing C
(in the range of 0.1 µF to 0.39 µF), should produce a virtually
clickless and popless shutdown function. While the device
will function properly, (no oscillations or motorboating), with

equal to 0.1 µF, the device will be much more susceptible

C

B

to turn-on clicks and pops. Thus, a value of C

1.0 µF is recommended in all but the most cost sensitive
designs.

, is the most critical component to minimize

B

), the smaller the turn-on pop.

equal to 1.0 µF along with a small value of C

B

DD

, forms a

i

). This

DD

equal to

B

AUDIO POWER AMPLIFIER DESIGN

A 1W/8Ω AUDIO AMPLIFIER

Given:

Power Output 1 Wrms

Load Impedance 8Ω

Input Level 1 Vrms

Input Impedance 20 kΩ

Bandwidth 100 Hz– 20 kHz

±

0.25 dB

A designer must first determine the minimum supply rail to
obtain the specified output power. By extrapolating from the
Output Power vs Supply Voltage graphs in the Typical Per-
formance Characteristics section, the supply rail can be
easily found. A second way to determine the minimum sup­ply rail is to calculate the required V

using Equation 2

opeak

and add the output voltage. Using this method, the minimum
supply voltage would be (V

and V

V

OD

BOT

age vs Supply Voltage curve in the Typical Performance

are extrapolated from the Dropout Volt-

OD

TOP

opeak

+(V

OD

TOP

+V

OD

)), where

BOT

Characteristics section.

(2)

Using the Output Power vs Supply Voltage graph for an 8Ω
load, the minimum supply rail is 4.6V. But since 5V is a
standard voltage in most applications, it is chosen for the
supply rail. Extra supply voltage creates headroom that al­lows the LM4872 to reproduce peaks in excess of 1W with-

i

out producing audible distortion. At this time, the designer
must make sure that the power supply choice along with the
output impedance does not violate the conditions explained
in the Power Dissipation section.

Once the power dissipation equations have been addressed,
the required differential gain can be determined from Equa­tion 3.

LOW VOLTAGE APPLICATIONS ( BELOW 3.0 V

)

DD

The Lm4872 will function at voltages below 3 volts but this
mode of operation requires the addition of a 1kΩ resistor
from each of the differential output pins ( pins 8 and 4 )
directly to ground. The addition of the pair of 1kΩ resistors (
R4 & R5 ) assures stable operation below 3 Volt Vdd opera­tion. The addition of the two resistors will however increase
the idle current by as much as 5mA. This is because at 0v
input both of the outputs of the LM4872’s 2 internal opamps
go to 1/2 V

( 2.5 volts for a 5v power supply ), causing

DD

current to flow through the 1K resistors from output to
ground. See fig 4.

Jumper options have been included on the reference design,
Fig. 4, to accommodate the low voltage application. J2 & J3
connect R4 and R5 to the outputs. J1 operates the shutdown
function. J1 must be installed to operate the part. A switch
may be installed in place of J1 for easier evaluation of the
shutdown function.

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(3)

R

f/Ri=AVD

From Equation 3, the minimum A

/2

is 2.83; use AVD=3.

VD

Since the desired input impedance was 20 kΩ, and with a

impedance of 2, a ratio of 1.5:1 of Rfto Riresults in an

A

VD

allocation of R

=20kΩ and Rf=30kΩ. The final design step

i

is to address the bandwidth requirements which must be
stated as a pair of −3 dB frequency points. Five times away
from a −3 dB point is 0.17 dB down from passband response

±

which is better than the required

= 100 Hz/5 = 20 Hz

f

L

f

=20kHz*5=100kHz

H

As stated in the External Components section, R
junction with C

≥ 1/(2π*20 kΩ*20 Hz) = 0.397 µF; use 0.39 µF

C

i

create a highpass filter.

i

0.25 dB specified.

in con-

i

The high frequency pole is determined by the product of the
desired frequency pole, f
With a A

= 3 and fH= 100 kHz, the resulting GBWP =

VD

, and the differential gain, AVD.

H

150 kHz which is much smaller than the LM4872 GBWP of
4 MHz. This figure displays that if a designer has a need to
design an amplifier with a higher differential gain, the
LM4872 can still be used without running into bandwidth
limitations.

Application Information (Continued)

LM4872

FIGURE 2. Higher Gain Audio Amplifier

The LM4872 is unity-gain stable and requires no external
components besides gain-setting resistors, an input coupling
capacitor, and proper supply bypassing in the typical appli­cation. However, if a closed-loop differential gain of greater
than 10 is required, a feedback capacitor may be needed as
shown in Figure 2 to bandwidth limit the amplifier. This
feedback capacitor creates a low pass filter that eliminates
possible high frequency oscillations. Care should be taken

10123024

when calculating the -3dB frequency in that an incorrect
combination of R

and C4will cause rolloff before 20kHz. A

3

typical combination of feedback resistor and capacitor that
will not produce audio band high frequency rolloff is R
20kΩ and C

= 25pf. These components result in a -3dB

4

3

point of approximately 320 kHz. It is not recommended that
the feedback resistor and capacitor be used to implement a
band limiting filter below 100kHZ.

=

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Application Information (Continued)

LM4872

10123029

FIGURE 3. Differential Amplifier Configuration for LM4872

Mono LM4872 Reference Design Board - Assembly Part Number: 980011207-100 Revision: A Bill of Material

Item Part Number Part Description Qty Ref Designator

1 551011208-001 LM4872 Mono Reference Design Board PCB etch 001 1

10 482911183-001 LM4872 Audio AMP micro SMD 8 Bumps 1 U1

20 151911207-001 Cer Cap 0.1uF 50V +80/-20% 1206 1 C1

21 151911207-002 Cer Cap 0.39uF 50V Z5U 20% 1210 1 C2

25 152911207-001 Tant Cap 1uF 16V 10% Size=A 3216 1 C3

30 472911207-001 Res 20K Ohm 1/10W 5% 0805 3 R1, R2, R3

31 472911207-002 Res 1K Ohm 1/10W 5% 0805 2 R4, R5,

35 210007039-002 Jumper Header Vertical Mount 2X1 0.100 3 J1, J2, J3

36 210007582-001 Jumper Shunt 2 position 0.100 3

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Application Information (Continued)

Silk Screen Top Layer

LM4872

10123030

Bottom Layer Inner Layer V

10123032

Inner Layer Ground

10123031

DD

10123033

10123034

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Application Information (Continued)

LM4872

Reference Design Board and PCB Layout Guidelines

10123025

FIGURE 4. Reference Design Board

PCB Layout Guidelines

This section provides practical guidelines for mixed signal
PCB layout that involves various digital/analog power and
ground traces. Designers should note that these are only
’rule-of-thumb’ recommendations and the actual results will
depend heavily on the final layout.

General Mixed Signal Layout Recommendation

Power and Ground Circuits

For 2 layer mixed signal design, it is important to isolate the
digital power and ground trace paths from the analog power
and ground trace paths. Star trace routing techniques (bring­ing individual traces back to a central point rather than daisy
chaining traces together in a serial manner) can have a
major impact on low level signal performance. Star trace
routing refers to using individual traces to feed power and
ground to each circuit or even device. This technique will
take require a greater amount of design time but will not
increase the final price of the board. The only extra parts
required will be some jumpers.

Single-Point Power / Ground Connections

The analog power traces should be connected to the digital
traces through a single point (link). A ’Pi-filter’ can be helpful
in minimizing High Frequency noise coupling between the
analog and digital sections. It is further recommended to put
digital and analog power traces over the corresponding digi­tal and analog ground traces to minimize noise coupling.

Placement of Digital and Analog Components

All digital components and high-speed digital signals traces
should be located as far away as possible from analog
components and circuit traces.

Avoiding Typical Design / Layout Problems

Avoid ground loops or running digital and analog traces
parallel to each other (side-by-side) on the same PCB layer.
When traces must cross over each other do it at 90 degrees.
Running digital and analog traces at 90 degrees to each
other from the top to the bottom side as much as possible will
minimize capacitive noise coupling and cross talk.

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Physical Dimensions inches (millimeters) unless otherwise noted

LM4872 1 Watt Audio Power Amplifier micro SMD package

Note: Unless otherwise specified.

1. Epoxy coating.

2. 63Sn/37Pb eutectic bump.

3. Recommend non-solder mask defined landing pad.

4. Pin 1 is established by lower left corner with respect to text orientation pins are numbered counterclockwise.

5. Reference JEDEC registration MO-211, variation BC.

8-Bump micro SMD

Order Number LM4872IBP, LM4872IBPX

NS Package Number BPA08B6B

±

X1 = 1.31

0.03 X2 = 1.97±0.03 X3 = 0.850±0.10

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