The document discusses R-2R ladder type digital to analog converters (DACs). It describes how DACs are used to convert digital signals to analog formats for applications like process control systems. Specifically, it explains that R-2R ladder DACs use only two resistor values in a ladder network to produce analog voltages corresponding to digital inputs. Some key advantages of R-2R ladder DACs are that they require only two accurate resistor values and allow for expanded resolution by adding more sections to the ladder.

1. LECTURE NOTES
ON
R-2R Ladder Type
Digital to Analog Converter
By
Mrs. S.S. Biswal
Asst. Prof.,
Department of EEE, ITER
Sikha ‘O’ Anusandhan
(Deemed to be University) Bhubaneswar, Odisha, India

2. The most important
digital tools for process
control systems is one
that translates digital
information to analog
and vice versa [1].
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3. The increasing use of digital computers
in measurement and control systems
and the scarcity of true digital
measuring devices lead to a need for
converters to allow analogue sensors to
communicate with computers or the
digital output of the computers to
communicate with analogue systems[2].
2

4. Basically converters are of two types [3,4].
 Digital-to-analog (DAC or D/A or D-to-A)
 Analog-to-digital (ADC or A/D or A-to-D)
A/D and D/ A converters relate analog quantities
to digital quantities and vice versa through an
appropriate code [5].
3

5. A digital to analog converter has an input of
digital signals and an output of an analog
signal[6].
A DAC is used to convert a digital signal to the
analog format.
4

6. A DAC has an input of digital signals and an
output of an analogue signal[5].
An 8-bit DAC may produce an output signal of
2.56V when the digital inputs see a word of
111111112.
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7. Resolution: The number of possible output levels
the DAC is designed to reproduce. This is usually
stated as the number of bits it uses, which is
the binary logarithm of the number of levels.
Maximum sampling rate: The maximum speed at
which the DACs circuitry can operate and still
produce correct output.
Dynamic range: A measurement of the difference
between the largest and smallest signals the DAC
can reproduce expressed in decibels. This is usually
related to resolution and noise floor.
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8. Monotonicity: This refers to the ability of a DAC's
analog output to move only in the direction that the
digital input moves (i.e., if the input increases, the
output doesn't dip before asserting the correct
output).
THD+N: This is a measurement of the distortion and
noise introduced to the signal by the DAC. It is
expressed as a percentage of the total power of
unwanted harmonic distortion and noise that
accompany the desired signal.
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9. Pulse-width modulator (PWM)DAC
 Oversampling or interpolating DAC
Binary-weighted DAC
R-2R ladder DAC
Thermometer-coded DAC
 Hybrid DAC
The segmented DAC
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10. The most common DAC structure is the R-
2R resistor ladder network.
 It uses resistors of only two different
values, and their ratio is 2:1.
An N-bit DAC requires 2N resistors, and
they are quite easily trimmed.
9

11. As the name suggests, R-2R Ladder DAC
produces an analog output, which is almost
equal to the digital (binary) input by using
a R-2R ladder network in the inverting
adder circuit.
 A 4-bit
DAC
10

12. Vref V2V1 V3
ref ref ref ref
out 3 2 1 0
2 4 8 16
V V V V
V R b b b b
R R R R
 
     
 
11 A 4 bit R-2R ladder network with output equation

13. A practical circuit implementation of a R-2R ladder DAC
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14. Advantages:
 It contains only two values of resistor: R and 2R.
So, it is easy to select and design more accurate
resistors.
 Does not require high precision resistors
 Number of bits can be expanded by adding more
sections of same R/2R values.
 In inverted R/2R ladder DAC, node voltages
remain constant with changing input binary
words.
Disadvantages:
 The conversion rate is lower as compared to
binary weighted digital to analog converter.13

15. Problem 1
What is the largest value of output voltage from an 8-
bit DAC that produces 1.0V for a digital input of
00110010?
Solution 1:
001100102 = 5010
1.0 V = K× 50
Therefore,
K = 20 mV
The largest output will occur for an input of
111111112 = 25510
VOUT(max) = 20mV×255 = 5.10 V
14

16. Problem 2
A 5-bit D/A converter produces VOUT = 0.2 V for a
digital input of 0001. Find the value of Vout for an
input of 11111.
Solution 2: Obviously, 0.2 V is the weight of the
LSB. Thus, the weights of the other bits must be
0.4 V, 0.8 V, 1.6 V, and 3.2 V respectively. For a
digital input of 11111, then, the value of VOUT will
be 3.2 V + 1.6 V+ 0.8V + 0.4V + 0.2 V = 6.2 V.
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17. Computer driven CRT displays
Computer Printers
Digital Motor Control
Digital Thermostat
Digital control of automatic process control systems
Electronic Cruise Control
Sound Equipment (e.g. CD/MP3 Players, etc.)
16

18. 1. C. D. Johnson, Process control instrumentation
technology, Prentice Hall PTR ,1999.
2. Ernest O. Doebelin, Measurement Systems-
Application and Design, TMH, 2007.
3. Joseph J.Carr, Elements of Electronics Instrumentation
and Measurement, Pearson Education, 2003.
4. Alan. S. Morris, Principles of Measurements and
Instrumentation, 2nd Edition, Prentice Hall of India,
2003.
17

19. 5. Sawhney, A. K., and P. Sawhney. "Electrical and
electronics measurements and measuring
instruments." Measurement and Measurement
Systems (2003).
6. Bolton, William. Industrial control and instrumentation.
Universities Press, 1993.
7. Albert D.Helfrick and William D.Cooper – Modern
Electronic Instrumentation and Measurement
Techniques, Pearson / Prentice Hall of India, 2007.
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20. 1.What is a DAC?
2. What function does a DAC perform?
3.What are the different types of DAC circuits?
3. What is the resolution of a DAC?
4.What is the advantage of R/2R ladder DAC over the
DAC that uses binary weighted resistors?
5. An 8-bit DAC has an output of 3.92 mA for an input of
01100010.
6.What are the DAC’s resolution and full-scale output?
7.What is the percentage resolution of an 8-bit DAC?
8.How many different output voltages can a 12-bit DAC
produce?
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