Datasheet AD9833 Datasheet (ANALOG DEVICES)

查询AD9833供应商

PRELIMINAR Y TECHNICAL DA T A

+2.5 V to +5.5 V, 25 MHz Low Power

=

CMOS Complete DDS

Preliminary Technical Data AD9833

FEATURES
+2.3 V to +5.5 V Power Supply
25 MHz Speed
Tiny 10-Pin

µµ

µSOIC Package

µµ

Serial Loading
Sinusoidal/Triangular DAC Output
Power-Down Option
Narrowband SFDR > 72 dB
20 mW Power Consumption at 3 V

APPLICATIONS
Digital Modulation
Portable Equipment
Test Equipment
DDS Tuning

GENERAL DESCRIPTION

This low power DDS device is a numerically controlled
oscillator employing a phase accumulator, a SIN ROM
and a 10-bit D/A converter integrated on a single
CMOS chip. Clock rates up to 25 MHz are supported

with a power supply from +2.3 V to +5.5 V.
Capability for phase modulation and frequency modula-

tion is provided. Frequency accuracy can be controlled to
one part in 0.25 billion. Modulation is effected by loading
registers through the serial interface.

The AD9833 offers a variety of output waveforms from
the VOUT pin. The SIN ROM can be bypassed so that a
linear up/down ramp is output from the DAC. If the SIN
ROM is not by-passed, a sinusoidal output is available.
Also, if a clock output is required, the MSB of the DAC
data can be output.

The digital section is internally operated at +2.5 V, irre­spective of the value of VDD, by an on board regulator
which steps down VDD to +2.5 V, when VDD exceeds
+2.5 V.

The AD9833 has a power-down function (SLEEP). This
allows sections of the device which are not being used to
be powered down, thus minimising the current consump­tion of the part e.g the DAC can be powered down when a
clock output is being generated.

The AD9833 is available in a 10-pin µSOIC package.

FUNCTIONAL BLOCK DIAGRAM

CAP/2.5V

2.5V

Phase

Accumulator

(28 Bit)

Σ

MUX

MCLK

AGND

FREQ0 REG

FREQ1 REG

FSYNC

DGND

AVDD/
DVDD

MUX

Serial Interface

&

Control Logic

SCLK

SDATA

VDD

Regulator

PHASE0 REG

PHASE1 REG

Control Register

REV PrG 02/02

Information furnished by Analog Devices is believed to be accurate and
reliable. However, no responsibility is assumed by Analog Devices for its
use, nor for any infringements of patents or other rights of third parties
which may result from its use. No license is granted by implication or
otherwise under any patent or patent rights of Analog Devices.

On-Board
Reference

FullScale

Control

12

DIV BY

2

SIN

ROM

MUX

MUX

MSB

10-Bit DAC

200

R

Ω

COMP

VOUT

AD9833

One Technology Way, P.O. Box 9106, Norwood, MA 02062-9106,U.S.A.
Tel: [phone] www.analog.com
Fax: [phone] © Analog Devices, Inc., 2002

PRELIMINAR Y TECHNICAL DA TA

AD9833

= 6.8 k

ΩΩ

Ω for

ΩΩ

SPECIFICATIONS

1

(VDD = +2.3 V to +5.5 V; AGND = DGND = 0 V; TA = T

MIN

to T

MAX

; R

SET

VOUT unless otherwise noted)

Parameter Min Typ Max Units Test Conditions/Comments

SIGNAL DAC SPECIFICATIONS

Resolution 10 Bits
Update Rate (f
Output Compliance

) 25 MSPS

MAX

2

0.8 V

DC Accuracy:

Integral Nonlinearity ±1 LSB
Differential Nonlinearity ±0.5 LSB

DDS SPECIFICATIONS
Dynamic Specifications:

Signal to Noise Ratio 50 dB f

Total Harmonic Distortion -53 dBc f

= 25 MHz, f

MCLK

= 25 MHz, f

MCLK

= 1.5 kHz

OUT

= 1.5 kHz

OUT

Spurious Free Dynamic Range (SFDR):

Wideband (± 2 MHz) 50 dBc f

55 dBc f

NarrowBand (± 50 kHz) 72 dBc f

75 dBc f

= 25 MHz, f

MCLK

= 25 MHz, f

MCLK

= 25 MHz, f

MCLK

= 25 MHz, f

MCLK

= f

OUT

= 0.5 MHz

OUT

= f

OUT

= 0.5 MHz

OUT

MCLK

MCLK

/3

/3

Clock Feedthrough –55 dBc

Wake Up Time 1 ms

OUTPUT BUFFER

Output Rise/Fall Time 20 ns Using a 15 pF Load
Output Jitter 100 ps rms When DAC data MSB is output

VOLTAGE REFERENCE

Internal Reference 1.116 1.2 1.284 V 1.2 V ± 7%

LOGIC INPUTS

V

, Input High Voltage VDD –0.9 V +3.6 V to +5.5 V Power Supply

INH

- 0.5 V +2.7 V to +3.6 V Power Supply

V

DD

2 V +2.3 V to + 2.7 V Power Supply

V

, Input Low Voltage 0.9 V +3.6 V to +5.5 V Power Supply

INL

0.5 V +2.3 V to + 3.6 V Power Supply

, Input Current 1 µA

I

INH

CIN, Input Capacitance 10 pF

POWER SUPPLIES f

VDD 2.3 5.5 V

3

I

AA

3

I

DD

I

AA

Low Power Sleep Mode

NOTES

1

Operating temperature range is as follows: B Version: –40°C to +85°C; typical specifications are at 25ⴗC

2

Guaranteed by Design.

3

Measured with the digital inputs static and equal to 0 V or DVDD.

Specifications subject to change without notice. There is 95% test coverage of the digital circuitry.

+ I

DD

3

3

1 + 0.04/MHz mA
7 10 mA 3 V Power Supply
10 15 mA 5 V Power Supply

0.25 mA DAC and Internal Clock Powered Down

5mA

= 25 MHz, f

MCLK

OUT

= f

MCLK

/7

–2– REV PrG

PRELIMINAR Y TECHNICAL DA T A

AD9833

100nF

Figure 1. Test Circuit With which Specifications are tested.

TIMING CHARACTERISTICS

Parameter Limit at T

t

1

t

2

t

3

t

4

t

5

t

6

t

7

t

8

t

9

t

10

1

Guaranteed by design, not production tested.

40 ns min MCLK Period
16 ns min MCLK High Duration
16 ns min MCLK Low Duration
25 ns min SCLK Period
10 ns min SCLK High Duration
10 ns min SCLK Low Duration
5 ns min FSYNC to SCLK Falling Edge Setup Time
10 ns min FSYNC to SCLK Hold Time

- 5 ns max

t

4

5 ns min Data Setup Time
3 ns min Data Hold Time

MIN

to T

MAX

VDD

10nF

CAP/2.5V

REGULATOR

12

SIN

ROM

COMP

10-BIT DAC

VOUT

20pF

AD9833

1

(VDD = +2.3 V to +5.5 V; AGND = DGND = 0 V, unless otherwise noted)

Units Test Conditions/Comments

t

1

MCLK

t

2

t

3

Figure 2. Master Clock

t

t

5

4

SCLK

FSYNC

SDATA

t

7

D15 D14 D2 D1 D0 D15 D14

t

6

t

10

t

9

t

8

Figure 3. Serial Timing

CAUTION

ESD (electrostatic discharge) sensitive device. Electrostatic charges as high as 4000 V readily
accumulate on the human body and test equipment and can discharge without detection.
Although the AD9833 features proprietary ESD protection circuitry, permanent damage may
occur on devices subjected to high energy electrostatic discharges. Therefore, proper ESD
precautions are recommended to avoid performance degradation or loss of functionality.

REV PrG

–3–

PRELIMINAR Y TECHNICAL DA TA

AD9833

ABSOLUTE MAXIMUM RATINGS*

(TA = +25°C unless otherwise noted)

VDD to AGND . . . . . . . . . . . . . . . . . . . . . –0.3 V to +6 V

VDD to DGND . . . . . . . . . . . . . . . . . . . . . –0.3 V to +6 V

AGND to DGND. . . . . . . . . . . . . . . . . . –0.3 V to +0.3 V

CAP/2.5V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.75 V

Digital I/O Voltage to DGND . –0.3 V to VDD + 0.3 V
Analog I/O Voltage to AGND . –0.3 V to VDD + 0.3 V
Operating Temperature Range

Industrial (B Version) . . . . . . . . . . . . . .–40°C to +85°C

Maximum Junction Temperature . . . . . . . . . . . . . . 150°C

µSOIC Package

Thermal Impedance . . . . . . . . . . . . . . . . . . .206°C/W

θ

JA

θ

Thermal Impedance . . . . . . . . . . . . . . . . . . .44°C/W

JC

Lead Temperature, Soldering (10 sec) . . . . . . . . . 300°C

IR Reflow, Peak Temperature . . . . . . . . . . . . . . . 220°C

*Stresses above those listed under “Absolute Maximum Ratings” may cause permanent

damage to the device. This is a stress rating only and functional operation of the device
at these or any other conditions above those listed in the operational sections of this
specification is not implied. Exposure to absolute maximum rating conditions for
extended periods may affect device reliability.

Storage Temperature Range . . . . . . . . .–65°C to +150°C

ORDERING GUIDE

Model Temperature Range Package Description Package Option

AD9833BRM –40°C to +85°C 14-Pin µSOIC (

Micro Small Outline IC

) RM-10

EVAL-AD9833EB Evaluation Board

PIN CONFIGURATION

COMP

VDD

CAP/2.5V

DGND

MCLK

1
2

AD9833

3

TOP VIEW

(Notto Scale)

4

5

10

VOUT

9

AGND

8

FSYNC

7

SCLK

6

SDATA

PIN DESCRIPTION

Pin # Mnemonic Function

POWER SUPPLY

2 VDD Positive power supply for the analog section and the digital interface sections. The on board 2.5 V

regulator is also supplied from VDD. VDD can have a value from +2.3 V to +5.5 V. A 0.1 µF and
10 µF decoupling capacitor should be connected between VDD and AGND.

3 CAP/2.5V The digital circuitry operates from a +2.5 V power supply. This +2.5 V is generated from VDD

using an on board regulator (when VDD exceeds +2.7 V). The regulator requires a decoupling
capacitor of typically 100 nF, which is connected from CAP/2.5V to DGND. If VDD is equal to

or less than +2.7 V, CAP/2.5V should be tied directly to VDD.
4 DGND Digital Ground.
9 AGND Analog Ground.

ANALOG SIGNAL AND REFERENCE

1 COMP A DAC Bias Pin. This pin is used for de-coupling the DAC bias voltage.
10 VOUT Voltage Output. The analog and digital output from the AD9833 is available at this pin. An

external load resistor is not required as the device has a 200W resistor on board.

DIGITAL INTERFACE AND CONTROL

5 MCLK Digital Clock Input. DDS output frequencies are expressed as a binary fraction of the frequency of

MCLK. The output frequency accuracy and phase noise are determined by this clock.

6 SDATA Serial Data Input. The 16-bit serial data word is applied to this input.

7 SCLK Serial Clock Input. Data is clocked into the AD9833 on each falling SCLK edge.
8 FSYNC Active Low Control Input. This is the frame synchronisation signal for the input data. When

FSYNC is taken low, the internal logic is informed that a new word is being loaded into the

device.

–4– REV PrG

PRELIMINAR Y TECHNICAL DA T A

Typical Performance Characteristics

AD9833

TBD

TPC 1. Typical Current Consumption

vs. MCLK Frequency

TBD

TPC 4. Wide Band SFDR vs. f

for Various MCLK Frequencies

OUT/fMCLK

TBD

TPC 2. Narrow Band SFDR vs. MCLK

Frequency

TBD

TPC 5. SNR vs. MCLK Frequency

TBD

TPC 3. Wide Band SFDR vs. MCLK

Frequency

TBD

TPC 6. SNR vs. f
Various MCLK Frequencies

OUT/fMCLK

for

TPC 7. Wake-Up Time vs.

REV PrG

TBD

Temperature

–5–

PRELIMINAR Y TECHNICAL DA TA

AD9833

Typical Performance Characteristics

TBD

TPC 9. f

Frequency Word = 000FBA9

= 10 MHz; f

MCLK

OUT

TBD

TPC 12. f

Frequency Word =

= 25 MHz; f

MCLK

= 2.4 kHz;

= 6 kHz;

OUT

000FBA9

TBD

TPC 10. f

Frequency Word = 2492492

= 10 MHz; f

MCLK

= f

MCLK

/7 ;

TBD

TPC 13. f

Frequency Word =

= 25 MHz; f

MCLK

= 1.43 kHz

OUT

= 60 kHz;

OUT

009D495

TBD

TPC 11. f

Frequency Word = 5555555

= 10 MHz; f

MCLK

= f

MCLK

/3 ;

TBD

TPC 14. f

Frequency Word =

= 25 MHz; f

MCLK

= 3.33 kHz

OUT

= 600 kHz;

OUT

0624DD3

TBD

TPC 15. f

f

Frequency Word =

OUT

= 25 MHz;

MCLK

= 2.4 MHz;

189374D

TBD

TPC 16. f

f

= 3.857 MHz = f

OUT

Frequency Word = 277EE4F

= 25 MHz;

MCLK

–6– REV PrG

MCLK

/7 ;

TBD

TPC 17. f

f

= 8.333 MHz = f

OUT

Frequency Word = 555475C

= 25 MHz;

MCLK

MCLK

/3 ;

PRELIMINAR Y TECHNICAL DA T A

AD9833

TERMINOLOGY
Integral Nonlinearity

This is the maximum deviation of any code from a
straight line passing through the endpoints of the transfer
function. The endpoints of the transfer function are zero
scale, a point 0.5 LSB below the first code transition
(000 . . . 00 to 000 . . . 01) and full scale, a point 0.5 LSB
above the last code transition (111 . . . 10 to 111 . . . 11).
The error is expressed in LSBs.

Differential Nonlinearity

This is the difference between the measured and ideal 1
LSB change between two adjacent codes in the DAC. A
specified differential nonlinearity of

monotonicity.

Output Compliance

The output compliance refers to the maximum voltage
that can be generated at the output of the DAC to meet
the specifications. When voltages greater than that speci­fied for the output compliance are generated, the AD9833
may not meet the specifications listed in the data sheet.

Spurious Free Dynamic Range

Along with the frequency of interest, harmonics of the
fundamental frequency and images of the these frequencies
are present at the output of a DDS device. The spurious
free dynamic range (SFDR) refers to the largest spur or
harmonic which is present in the band of interest. The
wide band SFDR gives the magnitude of the largest har­monic or spur relative to the magnitude of the fundamental
frequency in the 0 to Nyquist bandwidth. The narrow band
SFDR gives the attenuation of the largest spur or harmonic
in a bandwidth of ±200 kHz about the fundamental fre­quency.

Total Harmonic Distortion

Total Harmonic Distortion (THD) is the ratio of the rms
sum of harmonics to the rms value of the fundameltal. For
the AD9834, THD is defined as:

THD = 20 log√(V

2

+ V

2

2

3

where V1 is the rms amplitude of the fundamental and V2,
V

, V4, V5 and V6 are the rms amplitudes of the second

3

through thre sixth harmonic.

Signal-to-Noise Ratio (SNR)

S/N is the ratio of the rms value of the measured output
signal to the rms sum of all other spectral components
below the Nyquist frequency, excluding the first six har­monics and dc. The value for SNR is expressed in
decibels.

Clock Feedthrough

There will be feedthrough from the MCLK input to the
analog output. Clock feedthrough refers to the magnitude
of the MCLK signal relative to the fundamental frequency
in the AD9834’s output spectrum.

±1 LSB maximium ensures

2

2

+ V

4

+ V

5

+ V

2

6

)/V

1

THEORY OF OPERATION

Sine waves are typically thought of in terms of their
magnitude form a(t) = sin (ωt). However, these are
nonlinear and not easy to generate except through piece
wise construction. On the other hand, the angular
information is linear in nature. That is, the phase angle
rotates through a fixed angle for each unit of time. The
angular rate depends on the frequency of the signal by the
traditional rate of ω = 2πf.

+1

0

-1

π

2

0

MAGNITUDE

PHASE

Figure 4. Sine Wave

Knowing that the phase of a sine wave is linear and given
a reference interval (clock period), the phase rotation for
that period can be determined.

∆Phase = ωδt

Solving for ω

ω = ∆Phase/δt = 2πf

Solving for f and substituting the reference clock
frequency for the reference period (1/f

f = ∆Phase x f

MCLK

MCLK

/2π

= δt)

The AD9833 builds the output based on this simple
equation. A simple DDS chip can implement this
equation with three major subcircuits:

Numerical Controlled Oscillator + Phase Modulator
SIN ROM
Digital- to- Analog Convertor.

Each of these sub-circuits are discussed in the following
section.

REV PrG

–7–

PRELIMINAR Y TECHNICAL DA TA

AD9833

CIRCUIT DESCRIPTION

The AD9833 is a fully integrated Direct Digital Synthesis
(DDS) chip. The chip requires one reference clock, one
low precision resistor and decoupling capacitors to pro­vide digitally created sine waves up to 12.5 MHz. In
addition to the generation of this RF signal, the chip is
fully capable of a broad range of simple and complex
modulation schemes. These modulation schemes are fully
implemented in the digital domain allowing accurate and
simple realization of complex modulation algorithms us­ing DSP techniques.
The internal circuitry of the AD9833 consists of the fol­lowing main sections: a Numerical Controlled Oscillator
(NCO), Frequency and Phase Modulators, SIN ROM, a
Digital-to-Analog Converter, and a Regulator.

Numerical Controlled Oscillator + Phase Modulator

This consists of two frequency select registers, a phase
accumulator, two phase offset registers and a phase offset
adder. The main component of the NCO is a 28-bit phase
accumulator which assembles the phase component of the
output signal. Continuous time signals have a phase range
of 0 to 2␲. Outside this range of numbers, the sinusoid
functions repeat themselves in a periodic manner. The
digital implementation is no different. The accumulator
simply scales the range of phase numbers into a multibit
digital word. The phase accumulator in the AD9833 is
implemented with 28 bits. Therefore, in the AD9833, 2␲

28

. Likewise, the ∆Phase term is scaled into this range

= 2
of numbers 0 < ∆Phase < 2

28

– 1. Making these substitu-

tions into the equation above

f = ∆Phase x f

where 0 < ∆Phase < 2

28

- 1.

MCLK

/2

28

The input to the phase accumulator (i.e., the phase step)
can be selected either from the FREQ0 Register or
FREQ1 Register and this is controlled by the FSELECT
bit. NCOs inherently generate continuous phase signals,
thus avoiding any output discontinuity when switching
between frequencies.

Following the NCO, a phase offset can be added to
perform phase modulation using the 12-bit Phase
Registers. The contents of one of these phase registers is
added to the most significant bits of the NCO. The
AD9833 has two Phase registers, the resolution of these
registers being 2π/4096.

SIN ROM

To make the output from the NCO useful, it must be
converted from phase information into a sinusoidal value.
Since phase information maps directly into amplitude, the
SIN ROM uses the digital phase information as an ad­dress to a look-up table, and converts the phase
information into amplitude. Although the NCO contains a
28-bit phase accumulator, the output of the NCO is trun­cated to 12 bits. Using the full resolution of the phase
accumulator is impractical and unnecessary as this would
require a look-up table of 2

28

entries. It is necessary only
to have sufficient phase resolution such that the errors due
to truncation are smaller than the resolution of the 10-bit
DAC. This requires the SIN ROM to have two bits of

phase resolution more than the 10-bit DAC.
The SIN ROM is enabled using the MODE bit (D1) in
the control register. This is explained further in Table 11.

Digital-to-Analog Converter

The AD9833 includes a high impedance current source
10-bit DAC. The DAC receives the digital words from
the SIN ROM and converts them into the corresponding
analog voltages.
The DAC is configured for single-ended operation. An
external load resistor is not required as the device has a
200 Ω resistor on board. The DAC generates an output
voltage of typically 0.6 Vpp.

Regulator

VDD provides the power supply required for the analog
section and the digital section of the AD9833. This supply
can have a value of +2.3V to +5.5V
The internal digital section of the AD9833 is operated at

2.5 V. An on-board regulator steps down the voltage ap­plied at VDD to 2.5 V. When the applied voltage at the
VDD pin of the AD9833 is equal to or less than 2.7 V,
the pins CAP/2.5V and VDD should be tied together, thus
by-passing the on-board regulator.

–8– REV PrG

PRELIMINAR Y TECHNICAL DA T A

AD9833

FUNCTIONAL DESCRIPTION
Serial Interface

The AD9833 has a standard 3-wire serial interface, which
is compatible with SPI, QSPI, MICROWIRE and DSP
interface standards.
Data is loaded into the device as a 16-bit word under the
control of a serial clock input, SCLK. The timing dia­gram for this operation is given in Figure 3.
The FSYNC input is a level triggered input that acts as a
frame synchronisation and chip enable. Data can only be
transferred into the device when FSYNC is low. To start
the serial data transfer, FSYNC should be taken low, ob­serving the minimum FSYNC to SCLK falling edge setup
time, t
into the device's input shift register on the falling edges of
SCLK for 16 clock pulses. FSYNC may be taken high
after the sixteenth falling edge of SCLK, observing the
minimum SCLK falling edge to FSYNC rising edge time,
t
16 SCLK pulses, and then brought high at the end of the
data transfer. In this way, a continuous stream of 16 bit
words can be loaded while FSYNC is held low, FSYNC
only going high after the 16th SCLK falling edge of the
last word loaded.
The SCLK can be continuous or, alternatively, the SCLK
can idle high or low between write operations.

Powering up the AD9833

The flow chart in Figure 6 shows the operating routine for
the AD9833. When the AD9833 is powered up, the part
should be reset. This will reset appropriate internal regis­ters to zero to provide an analog output of midscale. To
avoid spurious DAC outputs while the AD9833 is being
initialized, the RESET bit should be set to 1 until the part
is ready to begin generating an output. RESET does not

. After FSYNC goes low, serial data will be shifted

7

. Alternatively, FSYNC can be kept low for a multiple of

8

reset the phase, frequency or control registers. These reg­isters will contain invalid data and, therefore, should be set
to a known value by the user. The RESET bit should then
be set to 0 to begin generating an output. A signal will
appear at the DAC output 7 MCLK cycles after RESET is
set to 0.

Latency

Associated with each asynchronous write operation in the
AD9833 is a latency. If a selected frequency/phase register
is loaded with a new word there is a delay of 7 to 8 MCLK
cycles before the analog output will change. (There is an
uncertainty of one MCLK cycle as it depends on the posi­tion of the MCLK rising edge when the data is loaded into
the destination register.)

The Control Register

The AD9833 contains a 16-bit control register which sets
up the AD9833 as the user wishes to operate it. All control
bits, except MODE, are sampled on the internal negative
edge of MCLK.
Table 2, on the following page, describes the individual
bits of the control register. The different functions and the
various output options from the AD9833 are described in
more detail in the section following Table 2.
To inform the AD9833 that you wish to alter the contents
of the Control register, D15 and D14 must be set to '0' as
shown below.

Table 1. Control Register

D15 D14 D13 D0

0 0 CONTROL BITS

REV PrG

SLEEP12

SLEEP1

RESET

MODE + OPBITEN

DIV2

OPBITEN

DB15 DB14 DB13 DB12 DB11 DB10 DB9 DB8 DB7 DB6 DB5 DB4 DB3 DB2 DB1 DB0

0 0 B28 HLB FSELECT PSELECT 0 RESET SLEEP1 SLEEP12 OPBITEN 0 DIV2 0 MODE 0

Phase

Accumulator

(28 Bit)

SIN

ROM

0

MUX

1

DIV B Y

2

1
MUX

0

(Low Pow er)

10-Bit DAC

AD 9833

DIGITAL
OUTPUT

(enable)

VOUT

Figure 5. Function of Control Bits

–9–

PRELIMINAR Y TECHNICAL DA TA

AD9833

Table 2. Description of bits in the Control Register

Bit Name Function

D13 B28 Two write operations are required to load a complete word into either of the Frequency registers.

B28 = '1' allows a complete word to be loaded into a frequency register in two consecutive
writes. The first write contains the 14 LSBs of the frequency word and the next write will
contain the 14 MSBs. The first two bits of each sixteen-bit word define the frequency register to
which the word is loaded, and should therefore be the same for both of the consecutive writes.
Refer to table 6 for the appropriate addresses. The write to the frequency register occurs after both
words have been loaded, so the register never holds an intermediate value. An example of a com­plete 28-bit write is shown in table 5.
When B28 = '0' the 28-bit frequency register operates as 2 14-bit registers, one containing the 14
MSBs and the other containing the 14 LSBs. This means that the 14 MSBs of the frequency
word can be altered independent of the 14 LSBs and vice versa. To alter the 14 MSBs or the 14
LSBs, a single write is made to the appropriate Frequency address. The control bit D12 (HLB)
informs the AD9833 whether the bits to be altered are the 14 MSBs or 14 LSBs.

D12 H LB This control bit allows the user to continuously load the MSBs or LSBs of a frequency register

while ignoring the remaining 14 bits. This is useful if the complete 28 bit resolution is not re­quired. HLB is used in conjunction with D13 (B28). This control bit indicates whether the 14 bits
being loaded are being transferred to the 14 MSBs or 14 LSBs of the addressed frequency regis­ter. D13 (B28) must be set to '0' to be able to change the MSBs and LSBs of a frequency word
seperately. When D13 (B28) = '1', this control bit is ignored.
HLB = '1' allows a write to the 14 MSBs of the addressed frequency register.
HLB = '0' allows a write to the 14 LSBs of the addressed frequency register.

D11 FSELECT The FSELECT bit defines whether the FREQ0 register or the FREQ1 register is used in the

phase accumulator.

D10 PSELECT The PSELECT bit defines whether the PHASE0 register or the PHASE1 register data is added to

the output of the phase accumulator.
D9 Reserved This bit should be set to 0.
D8 RESET RESET = '1' resets internal registers to zero, which corresponds to an analog output of midscale.

RESET = '0' disables Reset. This function is explained further in Table 9.
D7 SLEEP1 When SLEEP1 = '1', the internal MCLK clock is disabled. The DAC output will remain at its

present value as the NCO is no longer accumulating.

When SLEEP1 = '0' MCLK is enabled. This function is explained further in Table 10.
D6 SLEEP12 SLEEP12 = '1' powers down the on-chip DAC. This is useful when the AD9833 is used to output

the MSB of the DAC data.

SLEEP12 = '0' implies that the DAC is active. This function is explained further in Table 10.
D5 OPBITEN The function of this bit, in association with D1 (MODE), is to control what is output at the

VOUT pin. This is explained further in Table 11.

When OPBITEN = '1' the output of the DAC is no longer available at the VOUT pin. Instead,

the MSB (or MSB/2) of the DAC data is connected to the VOUT pin. This is useful as a coarse

clock source. The bit DIV2 controls whether it is the MSB or MSB/2 that is ouput.

When OPBITEN equals 0, the DAC is connected to VOUT. The MODE bit determines whether

it is a sinusoidal or a ramp output that is available.
D4 Reserved This bit must be set to 0.
D3 DIV2 DIV2 is used in association with D5 (OPBITEN). This is explained further in Table 11.

When DIV2 = '1', the MSB of the DAC data is passed directly to the VOUT pin.

When DIV2 = '0', the MSB/2 of the DAC data is output at the VOUT pin.
D2 Reserved This bit must always be set to 0.
D1 MODE This bit is used in association with OPBITEN (D5). The function of this bit is to control what is

output at the VOUT pin when the on-chip DAC is connected to VOUT. This bit should be

set to '0' if the control bit OPBITEN = '1'. This is explained further in Table 11.

When MODE = '1', the SIN ROM is bypassed, resulting in a ramp output from the DAC.

When MODE = '0' the SIN ROM is used to convert the phase information into amplitude infor-

mation which results in a sinusoidal signal at the output.
D0 Reserved This bit must always be set to 0.

–10– REV PrG

PRELIMINAR Y TECHNICAL DA T A

AD9833

The Frequency and Phase Resisters

The AD9833 contains 2 frequency registers and 2 phase
registers. These are described in Table 3 below.

Table 5: Writing 3FFF0000 to FREQ0 REG

SDATA input Result of input word

Table 3. Frequency/Phase Registers

Register Size Description

FREQ0 28 Bits Frequency Register 0. When the

FSELECT bit = 0, this register
defines the output frequency as a
fraction of the MCLK frequency.

FREQ1 28 Bits Frequency Register 1. When the

FSELECT bit = 1, this register
defines the output frequency as a
fraction of the MCLK frequency.

PHASE0 12 Bits Phase Offset Register 0. When the

PSELECT bit = 0, the contents of
this register are added to the output
of the phase accumulator.

PHASE1 12 Bits Phase Offset Register 1. When the

PSELECT bit = 1, the contents of
this register are added to the output
of the phase accumulator.

The analog output from the AD9833 is

f

MCLK

28

/2

x FREQREG
where FREQREG is the value loaded into the selected
frequency register. This signal will be phase shifted by

2π/4096 x PHASEREG

where PHASEREG is the value contained in the selected
phase register.

The flow chart in Figure 8 shows the routine for writing
to the frequency and phase registers of the AD9833.

0010 0000 0000 0000 Control word write (D15, D14 = 00);

B28 (D13) = 1; HLB (D12) = X

0100 0000 0000 0000 FREQ0 REG write (D15, D14 = 01);

14 LSBs = 0000

0111 1111 1111 1111 FREQ0 REG write (D15, D14 = 01);

14 MSBs = 3FFF

In some applications, the user does not need to alter all 28
bits of the frequency register. With coarse tuning, only
the 14 MSBs are altered while with fine tuning, only the
14 LSBs are altered. By setting the control bit B28 (D13)
to 0, the 28-bit frequency register operates as 2 14-bit
registers, one containing the 14 MSBs and the other con­taining the 14 LSBs. This means that the 14 MSBs of the
frequency word can be altered independent of the 14 LSBs
and vice versa. Bit HLB (D12) in the control register
identifies which 14 bits are being altered. Examples of this
are shown below.

Table 6: Writing 3FFF to the 14 LSBs of FREQ1 REG

SDATA input Result of input word

0000 0000 0000 0000 Control word write (D15, D14 = 00);

B28 (D13) = 0; HLB (D12) = 0, i.e. LSBs

1011 1111 1111 1111 FREQ1 REG write (D15, D14 = 10);

14 LSBs = 3FFF

Table 7: Writing 3FFF to the 14 MSBs of FREQ0 REG

SDATA input Result of Input word

Writing to a Frequency Register:

When writing to a frequency register, bits D15 and D14
give the address of the frequency register.

Table 4. Frequency Register Bits

D15 D14 D13 D0

0 1 MSB 14 FREQ0 REG BITS LSB
1 0 MSB 14 FREQ1 REG BITS LSB

If the user wishes to alter the entire contents of a fre­quency register, two consecutive writes to the same
address must be performed, as the frequency registers are
28 bits wide. The first write will contain the 14 LSBs
while the second write will contain the 14 MSBs. For this
mode of operation, the control bit B28 (D13) should be
set to 1. An example of a 28-bit write is shown in Table 5.

0001 0000 0000 0000 Control word write (D15, D14 = 00);

B28 (D13) = 0; HLB (D12) = 1, i.e. MSBs

0111 1111 1111 1111 FREQ0 REG write (D15, D14 = 01);

14 MSBs = 3FFF

Writing to a Phase Register:

When writing to a phase register, bits D15 and D14 are
set to 11. Bit D13 identifies which phase register is being
loaded.

Table 8. Phase Register Bits

D15 D14 D13 D12 D11 D0

1 1 0 X MSB 12 PHASE0 BITS LSB
1 1 1 X MSB 12 PHASE1 BITS LSB

The RESET Function

The RESET function resets appropriate internal registers
to zero to provide an analog output of midscale. RESET
does not reset the phase, frequency or control registers.
When the AD9833 is powered up, the part should be re­set. To reset the AD9833, set the RESET bit to 1. To
take the part out of reset, set the bit to 0. A signal will

REV PrG

–11–

PRELIMINAR Y TECHNICAL DA TA

AD9833

appear at the DAC output 7 MCLK cycles after RESET is
set to 0.

Table 9: Applying RESET

RESET bit Result

0 No Reset Applied
1 Internal Registers Reset

The Sleep Function

Sections of the AD9833 which are not in use can be pow­ered down to minimise power consumption. This is done
using the Sleep Function. The parts of the chip that can
be powered down are the Internal clock and the DAC.
The bits required for the Sleep Function are outlined in
Table 10.

Table 10: Applying the SLEEP Function

SLEEP1 SLEEP12 Result
bit bit

0 0 No powerdown

0 1 DAC Powered Down
1 0 Internal Clock disabled
1 1 Both the DAC powered down and

the Internal Clock disabled

This square wave can also be divided by 2 before being
output. The bit DIV2 (D3) in the control register controls
the frequency of this output from the VOUT pin.

Sinusoidal Output: The SIN ROM is used to convert the
phase information from the frequency and phase registers
into amplitude information which results in a sinusoidal
signal at the output. To have a sinusoidal output from the
VOUT pin, set the bit MODE (D1) = 0 and the
OPBITEN (D5) bit to 0.

Up/Down Ramp Output: The SIN ROM can be bypassed
so that the truncated digital output from the NCO is sent
to the DAC. In this case, the output is no longer sinusoi­dal. The DAC will produce a ramp up/down function. To
have a ramp output from the VOUT pin set the bit
MODE (D1) = 1.

Note that the SLEEP12 bit must be 0 (i.e. the DAC is
enabled) when using this pin.

Table 11: Various Outputs from VOUT

OPBITEN MODE DIV2 VOUT

bit bit bit Pin

0 0 X Sinusoid
0 1 X Up/Down Ramp
1 0 0 DAC data MSB / 2
1 0 1 DAC data MSB
1 1 X Reserved

DAC Powered Down: This is useful when the AD9833 is
used to output the MSB of the DAC data only. In this
case, the DAC is not required so it can be powered down
to reduce power consumption.

Internal Clock disabled: When the internal clock of the
AD9833 is disabled the DAC output will remain at its
present value as the NCO is no longer accumulating. New
frequency, phase and control words can be written to the
part when the SLEEP1 control bit is active. The
synchronising clock is still active which means that the
selected frequency and phase registers can also be changed
using the control bits. Setting the SLEEP1 bit equal to 0
enables the MCLK. Any changes made to the registers
while SLEEP1 was active will be seen at the output after a
certain latency.

The VOUT Pin

The AD9833 offers a variety of outputs from the chip, all
of which are available from the VOUT pin. The choice of
outputs are:

The MSB of the DAC data,
A sinusoidal output or

A ramp output.
The bits OPBITEN (D5) and MODE (D1) in the control
register are used to decide which output is available from
the AD9833. This is explained further below and also in
Table 11.

MSB of the DAC data: The MSB of the DAC data can be
output from the AD9833. By setting the OPBITEN (D5)
control bit to 1, the MSB of the DAC data is available at
the VOUT pin. This is useful as a coarse clock source.

–12– REV PrG

PRELIMINAR Y TECHNICAL DA T A

AD9833

APPLICATIONS

Because of the various output options available from the
part, the AD9833 can be configured to suit a wide variety
of applications.

One of the areas where the AD9833 is suitable is in modu­lation applications. The part can be used to perform
simple modulation such as FSK. More complex modula­tion schemes such as GMSK and QPSK can also be
implemented using the AD9833.
In an FSK application, the two frequency registers of the
AD9833 are loaded with different values; one frequency
will represent the space frequency while the other will
represent the mark frequency. Using the FSELECT bit in
the control register of the AD9833, the user can modulate
the carrier frequency between the two values.
The AD9833 has two phase registers; this enables the part
to perform PSK. With phase shift keying, the carrier fre­quency is phase shifted, the phase being altered by an
amount which is related to the bit stream being input to
the modulator.

The AD9833 is also suitable for signal generator applica­tions. Because the MSB of the DAC data is available at
the VOUT pin, the device can be used to generate a
square wave.

With its low current consumption, the part is suitable for
applications in which it can be used as a local oscillator.

GROUNDING AND LAYOUT

The printed circuit board that houses the AD9833 should
be designed so that the analog and digital sections are
separated and confined to certain areas of the board. This
facilitates the use of ground planes which can be separated
easily. A minimum etch technique is generally best for
ground planes as it gives the best shielding. Digital and
analog ground planes should only be joined in one place.
If the AD9833 is the only device requiring an AGND to
DGND connection, then the ground planes should be
connected at the AGND and DGND pins of the AD9833.
If the AD9833 is in a system where multiple devices re­quire AGND to DGND connections, the connection
should be made at one point only, a star ground point that
should be established as close as possible to the AD9833.

Avoid running digital lines under the device as these will
couple noise onto the die. The analog ground plane should
be allowed to run under the AD9833 to avoid noise cou­pling. The power supply lines to the AD9833 should use
as large a track as is possible to provide low impedance
paths and reduce the effects of glitches on the power sup­ply line. Fast switching signals such as clocks should be
shielded with digital ground to avoid radiating noise to
other sections of the board. Avoid crossover of digital and
analog signals. Traces on opposite sides of the board
should run at right angles to each other. This will reduce
the effects of feedthrough through the board. A microstrip
technique is by far the best but is not always possible with
a double-sided board. In this technique, the component
side of the board is dedicated to ground planes while sig­nals are placed on the other side.

Good decoupling is important. The AD9833 should have
supply bypassing of 0.1 µF ceramic capacitors in parallel
with 10 µF tantalum capacitors. To achieve the best from
the decoupling capacitors, they should be placed as close
as possible to the device, ideally right up against the de­vice.

REV PrG

–13–

PRELIMINAR Y TECHNICAL DA TA

AD9833

DATA WRITE

See Figure 8 below

SELECT DATA

SOURCES

WAIT 7/8 MCLK

CYCLES

DAC OUTPUT

V

= V

OUT

REF

* 18 * R

LOAD/RSET *

(1+ (SIN(2p(FREQREG * F

MCLK *

INITIALISATION

See Figure 7 below

28 +

t/2

PHASEREG/212)))

CHANGE PHASE?

YES

NO

YES

YES

CHANGE

FSELECT?

NO

CHANGE FREQ

REGISTER?

CONTROL

REGISTER

WRITE

(see Tab le 11)

YES

CHANGE FREQUENCY?

CHANGE DAC OUTPUT

FROM SIN TO RAMP?

YES

CHANGE OUTPUT TO

A DIGITAL SIGNAL?

YES

CHANGE PHASE

NO

NO

NO

Figure 6. Flow Chart for AD9833 Initialisation and Operation

INITIALISATION

APPLY RESET

(CONTROL REGISTER WRITE)

RESET = 1

CHANGE

PSELECT?

NO

REGISTER?

YES

YES

WRITE TO FREQUENCY AND PHASE REGISTERS

FREQ0 REG = F
FREQ1 REG = F

PHASE 0 & PHASE1 REG = (PhaseShift * 212) / 2p

(See Figure 8)

SET RESET = 0

SELECT FREQUENCY REGISTERS

SELECT PHASE REGISTERS

(CONTROL REGISTER WRITE)

FSELECT = Selected Freq Register

PSELECT = Selected Phase Register

RESET bit = 0

OUT0
OUT1

/ f
/ f

MCLK
MCLK

* 2
* 2

28
28

Figure 7. Initialisation

–14– REV PrG

PRELIMINAR Y TECHNICAL DA T A

AD9833

DA T A WRITE

WRITE A FULL 28-BIT WORD

TO A FREQUENCY REGISTER?

(CONTROL REGISTER WRITE)

B28 (D13) = 1

WRITE 2 CONSECUTIVE

16-BIT WORDS

(See Table 5 for Example)

YES

WRITE ANOTHER FULL

28 BITS TO A

FREQUENCY REGISTER?

NO

YES

NO

WRITE 14 MSBs OR LSBs

TO A FREQUENCY REGISTER?

YES

(CONTROL REGISTER WRITE)

B28 (D13) = 0

HLB (D12) = 0 / 1

WRITE A 16-BIT WORD

(See Tables 6 & 7 for

examples)

WRITE 14 MSBs OR LSBs

TO A

FREQUENCY REGISTER?

NO

Figure 8. Data Writes

YES

NO

WRITE TO PHASE

REGISTER?

(16 - Bit Write)

D15, D14 = 11
D13 = 0/1 (chooses the

phase register)
D12 = X
D11 ... D0 = Phase Data

WRITE TO ANOTHER

PHASE REGISTER?

YES

YES

NO

INTERFACING TO MICROPROCESSORS

The AD9833 has a standard serial interface which allows
the part to interface directly with several microprocessors.
The device uses an external serial clock to write the data/
control information into the device. The serial clock can
have a frequency of 40 MHz maximum. The serial clock
can be continuous or, it can idle high or low between
write operations. When data/control information is being
written to the AD9833, FSYNC is taken low and is held
low while the 16 bits of data are being written into the
AD9833. The FSYNC signal frames the 16 bits of infor­mation being loaded into the AD9833.

AD9833 to ADSP-21xx Interface

Figure 9 shows the serial interface between the AD9833
and the ADSP-21xx. The ADSP-21xx should be set up to
operate in the SPORT Transmit Alternate Framing Mode
(TFSW = 1). The ADSP-21xx is programmed through
the SPORT control register and should be configured as
follows:

Internal clock operation (ISCLK = 1)
Active low framing (INVTFS = 1)
16-bit word length (SLEN = 15)
Internal frame sync signal (ITFS = 1)
Generate a frame sync for each write (TFSR = 1).

Transmission is initiated by writing a word to the Tx reg-

ister after the SPORT has been enabled. The data is
clocked out on each rising edge of the serial clock and
clocked into the AD9833 on the SCLK falling edge.

ADSP-2101/
ADSP-2103*

TFS

DT

SCLK

* ADDITIONAL PINS OMITTED FOR CLARITY

AD9833*

FSYNC
SDAT A

SCLK

Figure 9. ADSP2101/ADSP2103 to AD9833 Interface

AD9833 to 68HC11/68L11 Interface

Figure 10 shows the serial interface between the AD9833
and the 68HC11/68L11 microcontroller. The
microcontroller is configured as the master by setting bit
MSTR in the SPCR to 1 and, this provides a serial clock
on SCK while the MOSI output drives the serial data line
SDATA. Since the microcontroller does not have a dedi­cated frame sync pin, the FSYNC signal is derived from a
port line (PC7). The set up conditions for correct opera­tion of the interface are as follows:

REV PrG

–15–

PRELIMINAR Y TECHNICAL DA TA

AD9833

SCK idles high between write operations (CPOL = 0)

data is valid on the SCK falling edge (CPHA = 1).
When data is being transmitted to the AD9833, the
FSYNC line is taken low (PC7). Serial data from the
68HC11/68L11 is transmitted in 8-bit bytes with only 8
falling clock edges occuring in the transmit cycle. Data is
transmitted MSB first. In order to load data into the
AD9833, PC7 is held low after the first 8 bits are trans­ferred and a second serial write operation is performed to
the AD9833. Only after the second 8 bits have been trans­ferred should FSYNC be taken high again.

68HC11/68L11*

PC7

MOSI

SCK

* ADDITIONAL PINS OMITTED FOR CLARITY

AD9833*

FSYNC
SDATA

SCLK

Figure 10. 68HC11/68L11 to AD9833 Interface

AD9833 to 80C51/80L51 Interface

Figure 11 shows the serial interface between the AD9833
and the 80C51/80L51 microcontroller. The
microcontroller is operated in mode 0 so that TXD of the
80C51/80L51 drives SCLK of the AD9833 while RXD
drives the serial data line SDATA. The FSYNC signal is
again derived from a bit programmable pin on the port
(P3.3 being used in the diagram). When data is to be
transmitted to the AD9833, P3.3 is taken low. The
80C51/80L51 transmits data in 8 bit bytes thus, only 8
falling SCLK edges occur in each cycle. To load the re­maining 8 bits to the AD9833, P3.3 is held low after the
first 8 bits have been transmitted and a second write op­eration is initiated to transmit the second byte of data.
P3.3 is taken high following the completion of the second
write operation. SCLK should idle high between the two
write operations. The 80C51/80L51 outputs the serial
data in a format which has the LSB first. The AD9833
accepts the MSB first (the 4 MSBs being the control in­formation, the next 4 bits being the address while the 8
LSBs contain the data when writing to a destination regis­ter). Therefore, the transmit routine of the 80C51/80L51
must take this into account and re-arrange the bits so that
the MSB is output first.

80C51/80L51*

P3.3
RXD

TXD

* ADDITIONAL PINS OMITTED FOR CLARITY

AD9833*

FSYNC
SDATA

SCLK

Figure 11. 80C51/80L51 to AD9833 Interface

AD9833 to DSP56002 Interface

Figure 12 shows the interface between the AD9833 and
the DSP56002. The DSP56002 is configured for normal
mode asynchronous operation with a Gated internal clock
(SYN = 0, GCK = 1, SCKD = 1). The frame sync pin is
generated internally (SC2 = 1), the transfers are 16 bits
wide (WL1 = 1, WL0 = 0) and the frame sync signal will
frame the 16 bits (FSL = 0). The frame sync signal is
available on pin SC2 but, it needs to be inverted before
being applied to the AD9833. The interface to the
DSP56000/DSP56001 is similar to that of the DSP56002.

DSP56002*

SC2

STD

SCK

* ADDITIONAL PINS OMITTED FOR CLARITY

AD9833*

FSYNC

SDATA

SCLK

Figure 12. AD9833 to DSP56002 Interface

AD9833 EVALUATION BOARD

The AD9833 Evaluation Board allows designers to evalu­ate the high performance AD9833 DDS modulator with
minimum of effort.

To prove that this device will meet the user's waveform
synthesis requirements, the user only require's a power­supply, an IBM-compatible PC and a spectrum analyser
along with the evaluation board.

The DDS evaluation kit includes a populated, tested
AD9833 printed circuit board. The evaluation board in­terfaces to the parallel port of an IBM compatible PC.
Software is available with the evaluation board which al­lows the user to easily program the AD9833. A schematic
of the Evaluation board is shown in Figure 13. The soft­ware will run on any IBM compatible PC which has
Microsoft Windows95, Windows98 or Windows ME 2000
NT™ installed.

Using the AD9833 Evaluation Board

The AD9833 Evaluation kit is a test system designed to
simplify the evaluation of the AD9833. An application
note is also available with the evaluation board and gives
full information on operating the evaluation board.

Prototyping Area

An area is available on the evaluation board for the user to
add additional circuits to the evaluation test set. Users
may want to build custom analog filters for the output or
add buffers and operational amplifiers to be used in the

–16– REV PrG

PRELIMINAR Y TECHNICAL DA T A

AD9833

final application.

XO vs. External Clock

The AD9833 can operate with master clocks up to 25
MHz. A 25 MHz oscillator is included on the evaluation
board. However, this oscillator can be removed and, if
required, an external CMOS clock connected to the part.

1
2

SCLK

3

SDATA

4

FSYNC

5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36

MCLK

R1

50R

0.1mF

DVDD

C6

DVDD

0.1mF

J1

SCLK

SDATA

FSYNC

C5

DVDD

U3

DGND

DVDD

C6

0.1mF

LK2

OUT

1

2
4

18
16

6

14

U2

7
6
8

5

C11
10mF

SCLK
SDATA
FSYNC

MCLK

C1

0.1mF

Power Supply

Power to the AD9833 Evaluation Board must be provided
externally through pin connections. The power leads
should be twisted to reduce ground loops.

VDD

CAP

C2

2

VDD

0.1mF

COMP

C8

10mF

VDD

1

C3

0.01mF

LK1

3

DVDD

C7

0.1mF

J2 J3

0.1mF

VDD

C9

C10
10mF

U1

AD9833

VOUT

C4

DGND AGND

4

10

VOUT

9

Figure 13. AD9833 Evaluation Board Layout

Integrated Circuits

U1 AD9833BRU
U2 74HCT244
U3 OSC XTAL 25 MHz

Capacitors

C1 C2 100nF Ceramic Capacitor 0805
C5 C6 C7 C9 100nF Ceramic Capacitor
C3 10nF ceramic Capacitor
C8 C10 C11 10uF Tantalum Capacitor
C4 Option for extra decoupling capacitor

Resistor

R1 51 Ω Resistor

REV PrG

Links

Lk1 Lk2 2 pin sil header

Sockets

MCLK VOUT Sub Minature BNC Connector

Connectors

J1 36-Pin Edge Connector
J2, J3 PCB Mounting Terminal Block

–17–

PRELIMINAR Y TECHNICAL DA TA

AD9833

OUTLINE DIMENSIONS

Dimensions shown in inches and (mm).

10-Lead mSOIC Package

(RM-10)

0.122 (3.10)

0.114 (2.90)

1

6

0.037
(0.94)

0.031
(0.78)

0.122 (3.10)

0.114 (2.90)

PIN 1

0.006 (0.15)

0.002 (0.05)

0

0.0197 (0.50) BSC

0.120 (3.05)

0.112 (2.85)

51

0.012 (0.30)

0.006 (0.15)

0.199 (5.05)

0.187 (4.75)

0.043 (1.10)
MAX

SEATING
PLANE

0.009 (0.23)

0.005 (0.13)

0.120 (3.05)

0.112 (2.85)

o

6

o

0

0.028 (0.70)

0.016 (0.40)

–18– REV PrG