BI Technologies R2R Resistor Ladder Networks
8-Bit and 10-Bit R2R resistor ladder networks for DAC and ADC applications.
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•
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Auto calibration circuits
Slope generators
Function generators
Motor speed control
Model
BCN31Ladder
628 Ladder
2512
SO-M
10 Terminal
16 Leads
1K to 100K
1K to 100K
Operating Temperature Range oC
± 100
-40oC to +125oC
± 100
-55oC to +125oC
Ladder Accuracy
8 Bit: ± 1/2 LSB
8 Bit: ± 1/2 LSB
Body Style
Number of Leads / Terminals
Resistance
Range, Ohms
Temp. Coefficient, ppm/oC
Power Rating
Resistor Power
25mW
40mW
Package Power
400mW
8-Bit Ladder Networks in dual in line and single in line packages.
10-Bit Ladder Networks in dual in line, single in line and moulded surface mount packages. Please consult factory.
Ordering Information
BCN 31 Ladder
628 Ladder
BCN 31 Ladder
628 Ladder
Schematics
640mW
Introduction
Real world signals are analogue. Digital systems that interface with the real world do so using
analogue-to-digital converters (ADC). Conversion back to analogue is accomplished using digital-toanalogue converters (DAC). The R2R ladder network is commonly used for Digital to Analogue
conversion and Analogue to Digital conversion by successive approximations. This application note
discusses the important parameters that should be considered when implementing DAC designs using
an R2R resistor ladder.
R2R ladder functional description
A basic N bit R2R resistor ladder network is shown in Figure 1. The digital inputs or bits range from
the most significant bit (MSB) to the least significant bit (LSB). The bits are switched between either
0V or VREF and depending on the state and location of the bits VOUT will vary between 0V and VREF.
The MSB causes the greatest change in output voltage and the LSB causes the smallest. The R2R
ladder is inexpensive and relatively easy to manufacture since only two resistor values are required. It
is fast and has fixed output impedance R. The R2R ladder operates as an array of voltage dividers
whose output accuracy is solely dependent on how well each resistor is matched to the others. The
resistors in the R2R network are printed directly onto a single substrate using a single film so they
share similar electrical characteristics they are also laser trimmed to provide the necessary precision.
These monolithic networks have an inherent accuracy advantage over discrete solutions because of the
tight ratio tolerances and low temperature coefficient of resistance tracking.
LSB
MSB
Bit N
Bit N - 1
Bit N - 2
Bit 3
Bit 2
Bit 1
2R
2R
2R
2R
2R
2R
R
2R
R
R
R
R
V out
R term ination
Figure 1. N Bit R2R Resistor Ladder
The termination resistor is always connected to ground and insures that the Thevenin resistance of the
network, as measured to ground looking towards the LSB (with all bits grounded), is R. The Thevenin
resistance of an R/2R ladder is always R regardless of the number of bits in the ladder. Figure 2 shows
a common implementation of the R2R resistor ladder network as a Digital to Analogue Converter using
an op amp output.This type of DAC is know as a multiplying converter. The output voltage is linearly
proportional to the digital input and the range can be adjusted by changing the reference voltage VREF.
The source impedance as seen by the op amp is always constant and equal to R regardless of the digital
input. The value of R can be made low to charge up the op amp input capacitance quickly and achieve
V ref
D0
D2
D1
D4
D3
D7
D6
D5
Rf
2R
2R
R
2R
2R
2R
2R
R
2R
R
2R
R
2R
R
2R
V out
R
R term ination
V out
=-
Rf
R
(
D0
2
+
D1
4
+
D2
8
+
D3
16
+
D4
32
+
D5
64
+
D6
128
+
D7
256
Figure 2. Multiplying converter
)
D
= 0 or 1
the required bandwidth. As a general rule the op amp bandwidth should be as small as possible (i.e. a
low pass filter) to pass only the expected changes in the digital input, any excess bandwidth only adds
noise to the output. The op amp should have good stability against temperature changes and supply
voltage variations.
The digital input is connected to the 2R resistances sometimes by means of a high-speed analogue
switch. The digital input voltage at D7 has twice the gain of the digital input at D6, and so on. This can
be demonstrated by using a repeated application of Thevenin’s theorem as follows. Consider an input
of 1 LSB that is D7 D6 D5 D4 D3 D2 D1 D0 = 00000001 and VREF = 5V. Neglecting the source resistance
of the 5V input, Thevenin’s theorem applied to the 5V source and the bottom two 2R resistors replaces
them with a 2.5V source in series with a single (Thevenin) resistance of R as shown in Figure 3.
Repeated application of Thevenin’s theorem yields the result. The 8-bit resistor ladder network used in
this example has an output voltage of 0.0039V for a digital input of 1 LSB.
D7
2R
D6
2R
D5
2R
D4
2R
D3
2R
D2
2R
D1
2R
D0
2R
2R
R
R
2R
R
R
R
R
R
R
R
R
R
R
2R
R
0.625V
2R
R
2R
R
R
2R
2R
2R
R
R
2R
2R
2R
R
2R
2R
2R
R
2R
2R
2R
R
5V
2R
R
2R
R
2R
R
2R
2.5V
2.5V
Figure 3. Repeated application of Thevenin’s theorem
Resolution
Resolution is the smallest standard incremental change in output voltage of a DAC. An n-bit DAC can
decode 1 part in 2n, therefore the LSB carries a weight of 2-n. For example, a DAC with 10-bit
resolution can resolve 1 part in 210 or 0.097% of the full-scale output voltage when the binary input
code is incremented by one LSB.
Accuracy
The accuracy of an R2R ladder is the percentage error in the output voltage and is usually expressed in
terms of least significant bits. For example, a +/- ½ LSB.specification on an 8-bit ladder is the same as
+/- 0.195% full scale accuracy. We define output error as the deviation from an ideal output voltage
that would be provided by a perfect reference and DAC. We address absolute accuracy in this
application note, this means that everything is referenced to an ideal DAC output-voltage range. For
example, a 10 bit DAC code 1023 should produce an output of 1.023V with a reference voltage of
1.024V and any deviation from this is an error.
1. Automatic Circuit Calibration DAC – Air pressure sensor
Electronic air pressure sensors are
Microprocessor
CH1
available at very reasonable cost and are
D4
D2
D6
D7
D0
D5
D1
D3
used
in
numerous
commercial
Error Adjustment
Test Point
applications. Air pressure sensors are
sensitive strain gauges configured as
resistor bridges. One leg of the bridge is a
Resistor Ladder Network
diaphragm that compresses and expands
with fluctuations in air pressure resulting
in small resistance changes. Since the
resistance change is small the system is
required to have a very large gain. For
Instrumentation Amplifier
systems with a single power supply the
instrumentation amplifier configuration
provides good common-mode rejection Resistor
Bridge
ratio CMRR and minimises the number of
passive components required to set the
gain. The gain is set so that it provides
maximum output voltage swing while
avoiding amplifier saturation. System
errors such as temperature drift and sensor
offset can cause the output voltage to
saturate and as a result it is necessary to
provide a calibration mechanism. Calibration can be realised using potentiometers however they are undesirable in
production designs. The part cost is higher than a fixed resistor and a pot requires human intervention thus it is
preferable for adjustments to be made in software. Provided the current air pressure is known, then it is possible for
the microprocessor to determine the calibration constants automatically and store them to memory. An R2R resistor
ladder network controlled by the microprocessor forms a DAC that adjusts for the errors as shown in this example.
20K
20K
20K
20K
20K
20K
20K
20K
10K
10K
10K
10K
20K
10K
10K
10K
R 14
R 15
R 13
R 12
R1
R6
R3
20K
R7
C1
20K
R 11
R4
20K
20K
R5
R 10
C2
R8
R9
R2
2. LCD Backlight Dimmer – Slope generator DAC
V CC
Bright
100K
UP / DOWN
Push Button Control
To Brightness
Adjust
1 = UP
0 = DOWN
Dim
CLK
P3
U/D
C O UT
200K
Q3
100K
100K
200K
P2
Q2
100K
100K
M.S.B
P1
P0
R
CLOCK
100K
CLK
P3
Q1
UP / DOWN Counter
100K
MC14516B
PE
U/D
100K
Q0
200K
C IN
100K
200K
Ladder
Network
100K
200K
C O UT
100K
200K
100K
P2
Q2
100K
200K
100K
P1
R
Q1
UP / DOWN Counter
P0
MC14516B
100K
200K
Q3
L.S.B
Backlighting is a key element in many liquid
crystal display (LCD) applications. Due to the
relatively low overall transmission of a typical
LCD, the backlight is sometimes required to have
extreme brightness. It should also possess a wide
dimming range to facilitate use, depending on the
amount of ambient light. LCD backlight controller
IC’s require a brightness adjustment signal in the
form of a linear control voltage. There are several
ways of generating the “Brightness Adjust”
voltage. The simplest is by using a potentiometer.
Another method, shown in this example, is by
using a digital UP/DOWN counter. In this method
two push button switches are used to generate a
logic level 1 for an “UP count” and a logic level 0
for a “DOWN count”. The UP/DOWN counters
provide a digital output signal that is converted into
an analogue signal using the R2R resistor ladder
network. There are 256 brightness levels and
setting the UP/DOWN counters pre-set inputs
configures the brightness level at turn on.
PE
Q0
C IN
200K
3. Sine and DTMF Waveform Generation - Function generator DAC
Many embedded applications require the generation of analogue
signals. For example the generation of multiplexed frequencies
(DTMF) for telephone dialling, controlling the speed of a motor,
the generation of sound and complex waveforms as well as the
generation of variable voltages in power supplies. Although
separate digital to analogue converter IC’s exist the extra
expense makes them prohibitive in cost sensitive designs. The
example shown here demonstrates a DAC design using an R2R
ladder and a microcontroller. To generate a single sine wave, the
user creates a lookup table with the correct number of sample
points. The software steps through each sample point and moves
this value to the I/O port. The R2R ladder converts the digital
signal to an analogue one. It is important that every sample point
uses the same timing interval. Many telecomm applications,
such as auto diallers, telephone keypads and security systems
require DTMF for dialling and data transfer. Using the R2R
ladder and seven sine lookup tables an entire 12-key keypad of
DTMF patterns can be generated using a 3.579545 crystal.
3.57945 MHz
22pF
C2
22pF
C1
X1
Analogue Output
OSC 1
V DD
OSC 2
200K
V DD
RB
MCLR
RB
RA
RB
7
100K
200K
6
100K
3
PIC16C620
RA
2
PIC Microcontroller
200K
5
100K
200K
RB
4
100K
200K
RA
RB
1
Ladder
Network
3
100K
200K
RA
RB
0
2
100K
200K
TOCLI
RB
1
100K
200K
GND
RB
0
200K
4. Non-Linear Digital Dimmer - ADC
The digital dimmer box is intended for stage
illumination in theatres. It is simple and inexpensive
to implement using a microcontroller and an R2R
ladder. It is compatible with older analogue dimmer
boxes and supports 4400-Watt loads. In stage
illumination, dimming of each incandescent lamp is
controlled by an analogue voltage (ranging from 0 to
10 volts) and is supplied by a remote console. To
achieve linear perception, a dimmer box should
exhibit a non-linear response to the control voltage.
Older dimmer boxes employ analogue processing for
the task of compensation. The digital approach uses a
simple software look-up table concept to implement
response compensation. As a result, a dedicated
external analogue circuit is not required. The system
control uses a microcontroller running at 12MHz and
an 8-bit R2R resistor ladder network on port 2 as a
digital to analogue converter. The R2R output
provides a reference voltage (pin 33) for the analogue
comparator on port P3. The analogue control voltage is connected to another comparator input (pin 31) and the
analogue to digital conversion is completed by software using a successive approximation technique. The
counter/timer generates a time delay between the zero crossing of the line voltage and the TRIAC’s trigger pulse. As a
result, power is delivered to the load. At 12 MHz, it is possible to achieve delays from 0 to 8.33ms with the correct
settings of the counter/timer prescaler, which corresponds to the phase-triggering range for an AC line frequency of
60Hz.
V cc
Control Voltage
0 to 10V
R1
20k
D1
1N 4148
R6
20k
D2
1N 4148
12.0000 MHz
100nF
C3
22pF
C2
X1
7
R7
1k
11
22pF
C1
6
XTAL2
P 00
15
20K
20K
P 20
LOAD
10K
LED
12
V cc
4400 W
P 21
P 01
R 11
330R
6
Q1
P 22
P 02
20K
18
20K
1
10K
P 23
U1
MAC
224A10
20K
17
10K
13
R 10
180R
16
10K
4 2
MO C 3020N
P 24
1
20K
10K
6+6V/100mA
R 14
18k
8
P 25
P 31
2
20K
3
20K
10K
R 19
10k
230VAC
D6
1N 4007
78L05
V1
100nF
C5
10uF
C4
D5
1N 4007
V0
G
1000uF
C6
9
D4
1N 4148
D3
1N 4148
P 32
10
P 33
Microprocessor
Z86E0812PSC
AC LINE
P 26
10K
P 27
4
20K
Resistor
Ladder
Network
5. R2R Analogue to Digital Converter - ADC
This is an example of an 8-bit analogue to
digital converter built using two cascaded
binary up/down counters an op-amp and an
R2R resistor ladder network. The analogue
signal that needs to be converted into a digital
signal is fed into the inverting input of the opamp. The op-amp output drives the up/down or
“direction” pin of the binary counters until the
R2R ladder output on the non-inverting opamp input equals the analogue input, at that
point the counter state represents the digital
equivalent of the analogue input. Adjusting the
clock frequency sets the system resolution.
P0
P1
P0
P3
P2
R
PE
U/D
UP / DOWN Counter
Q1
Q2
P2
P3
CLK
MC14516B
L.S.B
C IN
Q0
P1
R
CLK
MC14516B
M.S.B
PE
UP / DOWN Counter
C O UT
Q3
C IN
Q0
Q1
Q2
U/D
C O UT
Q3
D0
D1
D2
Digital
Output
D3
D4
Analogue Input
D5
D6
D7
200K
200K
200K
100K
200K
100K
200K
100K
200K
100K
200K
100K
Resistor Ladder Network
200K
100K
200K
100K