AN-1094: Multiplying DACs—Fixed Reference, Waveform Generation Applications (Rev. 0) PDF

AN-1094
APPLICATION NOTE
One Technology Way • P.O. Box 9106 • Norwood, MA 02062-9106, U.S.A. • Tel: 781.329.4700 • Fax: 781.461.3113 • www.analog.com
Multiplying DACs—Fixed Reference, Waveform Generation Applications
by Liam Riordan
INTRODUCTION
BASIC THEORY
Used with an amplifier with sufficient ac performance,
a multiplying digital-to-analog converter’s (DAC) R-2R
architecture makes it ideal for low noise, low glitch, fast
settling applications. This application note details the basic
theory behind current output multiplying DACs, and why
these DACs are suitable for waveform generation from a
fixed dc input reference.
Multiplying DACs offer an ideal building block for waveform generation applications. The buffered current output
DAC architecture is based on a noninverting gain amplifier
structure. A multiplying DAC uses an R-2R architecture to
replicate the functionality of the variable RDAC resistor
shown in Figure 1. The input impedance to the DAC seen
at the VREF pin is fixed, while the output impedance is code
dependent to give the equivalent variable RDAC value. See
also, www.analog.com/MultiplyingDAC.
The terms AD55xx and AD54xx used in this application note reference the multiplying DACs listed on
www.analog.com/MultiplyingDAC.
FUNCTIONAL BLOCK DIAGRAM
DC REFERENCE
MULTIPLYING DAC
RFB
VREF
0V
A1
0V
INVERTED
OUTPUT
Figure 1. Unipolar Inverting Configuration
Rev. 0 | Page 1 of 8
09339-001
RDAC
AN-1094
Application Note
TABLE OF CONTENTS
Introduction ...................................................................................... 1
Stability Issues ................................................................................4
Basic Theory ...................................................................................... 1
Key DAC Specifications for Waveform Generation .....................5
Functional Block Diagram .............................................................. 1
Settling Time ..................................................................................5
Multiplying DACs ............................................................................. 3
Midscale Glitch ..............................................................................5
Bipolar Operation ......................................................................... 3
Digital SFDR ..................................................................................6
Positive Voltage Input/Positive Voltage Output ....................... 3
Choosing the Correct Op Amp .......................................................7
Rev. 0 | Page 2 of 8
Application Note
AN-1094
MULTIPLYING DACS
BIPOLAR OPERATION
In a multiplying DAC, current is steered to either the virtual
ground connected to the IOUT1 node or the ground node (in
some parts this is the IOUT2 node), which allows for a very low
glitch output voltage (see Figure 2).
In some applications, it may be necessary to generate a bipolar
output voltage from a fixed input reference voltage. This can be
easily achieved by adding a second amplifier and some external
resistors as shown in Figure 3.
One of the key advantages in using an IOUT DAC in this
configuration is that the integrated RFB resistor is matched
to the RDAC equivalent resistor allowing for very low gain
temperature coefficient errors.
The second amplifier basically provides a gain of 2, where biasing
the external amplifier with an offset from the reference results
in bipolar operation.
When an output amplifier is connected in unipolar mode, as
shown in Figure 2, the output voltage is given by
D
× V REF
2n
where:
D is the fractional representation of the digital word loaded to
the DAC.
D = 0 to 255 (8-bit AD5450)
= 0 to 1023 (10-bit AD5451)
= 0 to 4095 (12-bit AD5452)
= 0 to 16,383 (14-bit AD5453)
= 0 to 65536 (16-bit AD5543)
n = the number of bits.
D
VOUT =  VREF × n − 1  − VREF
2


POSITIVE VOLTAGE INPUT/POSITIVE VOLTAGE
OUTPUT
To generate a positive voltage output, an external inverting
op amp circuit can be used to provide an additional inversion
of either the input or the output. Because some multiplying
DACs include uncommitted matched resistors (with tracking
temperature coefficients), a positive output can be obtained
simply by connecting an additional op amp (A2 in Figure 4),
which could be the companion op amp within a dual device.
The output signal of a multiplying DAC is proportional to the
product of the reference input and the digital input number.
+VE VREF
VDD
0V
C1
RFB
VREF
AD55xx
SYNC
SCLK
GENERATED
WAVEFORM
IOUT1
A1
0V
GND
SDIN
AGND
09339-002
MICROCONTROLLER
Figure 2. Multiplying DAC, VOUT = 0 V to −VREF
R3
10kΩ
R2
+VE VREF
VREF
0V
AD55xx
R1
SYNC
SCLK
GENERATED
WAVEFORM
C1
RFB
VDD
R5
10kΩ
R4
5kΩ
IOUT1
A1
A2
GND
SDIN
MICROCONTROLLER
0V
AGND
NOTES
1. R1 AND R2 USED ONLY IF GAIN ADJUSTMENT IS REQUIRED.
ADJUST R1 FOR VOUT = 0V WITH CODE HALF SCALE LOADED TO DAC.
2. MATCHING AND TRACKING IS ESSENTIAL FOR RESISTORS R3 AND R4.
Figure 3. Multiplying DAC, VOUT = −VREF to +VREF
Rev. 0 | Page 3 of 8
09339-003
VOUT = −
The transfer function of this circuit shows that both negative
and positive output voltages are created as the input data (D)
is incremented from zero scale (VOUT = −VREF) to midscale
(VOUT = 0 V ) to full scale (VOUT = +VREF).
AN-1094
Application Note
A2
C2
VREF
RCOM
ROFS
RFB
GENERATED
REFERENCE
C1
+VE VREF
R1
0V
IOUT1
VDD
AD55xx
SYNC
SCLK
SDN
A1
0V
GND
AGND
09339-004
MICROCONTROLLER
*UNCOMITTED RESISTOR VERSIONS ONLY.
Figure 4. Multiplying DAC, VOUT = 0 V to VREF
STABILITY ISSUES
An important component to take into account in achieving
the desired waveform conditioning signal is the compensation
capacitor. The internal output capacitance of the DAC introduces
a pole into the open-loop response that can cause ringing or
instability in the closed-loop ramp profiling circuit. To compensate
for this, an external feedback capacitor, C1, is usually connected
in parallel with the internal RFB of the DAC (see Figure 2). If the
value of C1 is too small, it can produce ringing at the output,
and if the value of C1 is too large, it can adversely affect the
settling time of the system. Because the internal output
capacitance of the DAC varies with code, it is difficult to fix a
precise value for C1. The value is best approximated according
to the following equation:
C1 = 2
CO
1
×
2π × R FB GBW
where:
GBW is the small signal unity gain bandwidth product of the
op amp in use.
CO is the output capacitance of the DAC.
Rev. 0 | Page 4 of 8
Application Note
AN-1094
KEY DAC SPECIFICATIONS FOR WAVEFORM GENERATION
MIDSCALE GLITCH
Provided the DAC is driven from true wideband low impedance
sources (reference voltage and grounding pins), it settles quickly.
Consequently, the slew rate and settling time of a multiplying
DAC is predominantly determined by the op amp. Among the
specifications that determine the ac performance of the op amp
are its input capacitance, which must be kept to a minimum
and the 3 dB small signal bandwidth. Note that the bandwidth
of an op amp is limited due to the large load it has to drive in
the feedback resistor of the DAC. A feedback resistor of, for
example, 10 kΩ is a significant load to drive and is the dominating pole in determining the bandwidth of the circuit
configuration.
AD5444 AND AD8065
–1.66
TA = 25°C
VREF = 3.5V
AD8038 AMP
CCOMP = 1.8pF
VDD = 5V
0x7FF TO 0x800
NRG = 2.154nVs
–1.68
VDD = 3V
0x7FF TO 0x800
NRG = 1.794nVs
–1.70
–1.72
–1.74
VDD = 3V
0x800 TO 0x7FF
–1.76
–1.78
–1.80
50
VDD = 5V
0x800 TO 0x7FF
NRG = 0.694nVs
75
100
125
150
175
TIME (ns)
Figure 6. Midscale Glitch
CH1 200mV
M 400ns
A CH1
412mV
09339-005
1
Figure 5. 100 ns Settling Time
Rev. 0 | Page 5 of 8
200
225
250
09339-006
SETTLING TIME
For an R-2R structure, the major glitch, caused by a code change,
occurs at the 1 LSB change around midscale. In a 12-bit system,
such as the AD5444, the midscale change is the 7FFH to 800H
code change or the 800H to 7FFH code change. If significant,
these glitches can have an unwanted affect in any motor/valve/
actuator control application. When the multiplying DAC tries
to change from 7FFH to 800H, the MSB switch in the DAC
switches at a slower speed then the other switches. Therefore,
for a few nanoseconds, the DAC sees 000H before the MSB
switch is set to 1. The orange trace in Figure 6 is an example
of this, where the output heads towards 0 V before the MSB
switches and brings the DAC output back to 800H.
OUTPUT VOLTAGE (V)
Some of the key selected ac specifications that must be
taken into account when generating a waveform from
a fixed reference input voltage include settling time,
midscale glitch, and digital SFDR.
AN-1094
Application Note
DIGITAL SFDR
For Figure 7, a 12-bit AD5444 is used to generate a 20 kHz
sine wave with an update rate of 1 MHz. This gives 50 sample
points per period. The AD5444 has a maximum update rate of
2.7 MSPS. To generate a waveform with more sample points a
faster update rate is required. A parallel interfaced AD5445 has
an update rate of 20 MSPS.
0
TA = 25°C
VDD = 5V
VREF = 3.5V
AD8038 AMPLIFIER
–20
where:
N = number of sample points.
Clock = update rate of DAC.
fOUT = output frequency of a generated waveform.
–40
SFDR (dB)
An ideal sine wave has an infinite number of points per cycle.
However, a digitally created sine wave is limited by the fixed
update rate and resolution of a DAC. The number of points
per cycle is given by
Clock
N=
f OUT
–60
–80
–100
–120
0
100
200
300
400
FREQUENCY (kHz)
Figure 7. Wideband SFDR, fOUT = 20 kHz, Clock = 1 MHz
Rev. 0 | Page 6 of 8
500
09339-007
Spurious-free dynamic range (SFDR) is the usable dynamic
range of a DAC before spurious noise interferes or distorts
the fundamental signal. SFDR is the measure of difference
in amplitude between the fundamental and the largest
harmonically or nonharmonically related spur from dc
to full Nyquist bandwidth (half the DAC sampling rate).
Narrow-band SFDR is a measure of SFDR over an arbitrary
window size.
Application Note
AN-1094
CHOOSING THE CORRECT OP AMP
Multiplying DAC circuit performance is strongly dependent
on the ability of the selected op amp to maintain the voltage
null at the ladder output and perform the current-to-voltage
conversion. For best dc accuracy, it is important to select an
operational amplifier with low offset voltage and bias current
to keep errors commensurate with the resolution of the DAC.
Detailed op amp specifications are included in device data
sheets.
For applications where a digital waveform is to be generated from
a fixed dc reference, a high slew rate, high bandwidth, low noise
op amp is required. This is to ensure that the output voltage settles
accurately and quickly enough before the next DAC code change.
The gain bandwidth of an op amp circuit is limited by
the impedance level of the feedback network and the gain
configuration. To determine what GBW is required, a useful
guideline is to select an op amp with a –3 dB bandwidth that
is 10 times the frequency of the reference signal.
If the slew rate of the op amp is not given careful consideration,
it can limit the multiplying DAC. As a rule for the AD54xx and
AD55xx parts, an op amp with a slew rate of 100 V/µs is generally sufficient.
Table 1 is a selection of operational amplifiers that can be used
for multiplying applications.
Table 1. Selection of Suitable Analog Devices High Speed Op Amps
Part No.
AD8065
AD8066
AD8021
AD8038
Supply Voltage (V)
5 to 24
5 to 24
5 to 24
3 to 12
BW @ ACL (MHz)
145
145
490
350
Slew Rate (V/µs)
180
180
120
425
VOS (Maximum) (µV)
1500
1500
1000
3000
IB (Maximum) (nA)
0.006
0.006
10,500
750
ADA4899
AD8057
AD8058
AD8061
AD8062
AD9631
5 to 12
3 to 12
3 to 12
2.7 to 8
2.7 to 8
±3 to ±6
600
325
325
320
320
320
310
850
850
650
650
1300
35
5000
5000
6000
6000
10,000
100
500
500
350
350
7000
Rev. 0 | Page 7 of 8
Packages
SOIC-8, SOT-23-5
SOIC-8, MSOP-8
SOIC-8, MSOP-8
SOIC-8, SC70-5,
SOT-23-5
LFCSP-8, SOIC-8
SOT-23-5, SOIC-8
SOIC-8, MSOP-8
SOT-23-5, SOIC-8
SOIC-8, MSOP-8
SOIC-8, PDIP-8
AN-1094
Application Note
NOTES
©2010 Analog Devices, Inc. All rights reserved. Trademarks and
registered trademarks are the property of their respective owners.
AN09339-0-9/10(0)
Rev. 0 | Page 8 of 8
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