Analog to Digital & Digital to Analog Converters
Need of DAC and ADC converters :-
Analog quantities are continuous and they may possess infinite values between any two given
magnitudes, e. g. Temperature, pressure, distance etc. Therefore it becomes necessary that
before processing such information by a digital system, it can be changed to an equivalent
digital form. Similarly after processing the information, it may be desirable that the final result
obtained in the digital form be converted back to the analog form.
So following are the examples where, these converters are required –
1) In a digital voltmeter, A/D converter is required to convert the analog voltage into a digital
signal.
2) A digital system can be used to display temperature, humidity, pressure etc. In this systems
these quantities are converted into electrical signals and these electrical signals is then
converted in digital form by A/D converters.
3) A digital communication system is used to transmit information in the form of electrical
signal which is converted in digital form at transmitter again. So D/A conversion is required
at receiver.
4) In microprocessor based process control system, A/D and D/A converters called as
peripherals or I/O devices are used.
Thus in many cases, A/D and D/A conversion has become necessary
Digital to Analog Converter (DAC) :-
The process of conversion of digital signal into its equivalent analog signal is referred as Digital
to Analog Converter (DAC). A D/A converter is also referred to as a decoding device.
Types of digital to analog converters are :-
1) Weighted – resistor D/A converter
2) R – 2R ladder (Binary ladder) D/A converter.
1) Weighted – resister D/A converter :-
Principle – For conversion of a digital signal into an equivalent analog signal, the n digital
voltage levels should be changed into one equivalent analog voltage. This can be done by
designing a resistive network that will change each digital level into an equivalent binary
weighted voltage or current.
Working – The resistive divider can be built to change a digital voltage into an equivalent
analog voltage. Following criteria can be applied this divider :-
1) There must be one input resistor for each digital bit.
2) Beginning with LSB, each following resistor value is one half the value of previous resistor,
e.g. R, R/2, R/4, R/8 etc.
3) The full – scale output voltage is equal to the positive voltages of the digital input signal.
4) The LSB has a weight of 1/2n – 1 , where n is the no. of input bits.
5) The change in output voltage due to a change in the LSB is equal to the V/(2n – 1) , where
V is the digital input voltage level.
6) The output voltage VA can be found by using following modified form of Millman’s theorem:
VA = Vo 20 + V1 21 + V2 22 + V3 23 + . . . . . . . . . . . . . + Vn - 1 2n – 1 found
2n – 1
Where V0, V1, V2, . . . . . . , Vn-1 are the digital input voltage levels (0 or V) and n is the no.
of input bits.
For 4 – bit resistive ladder
VA = Vo 20 + V1 21 + V2 22 + V3 23 += Vo + 2 V1 + 4 V2 + 8 V3 23
24 – 1 15
V3 V2 V1 V0
(MSB) D C B A (LSB)
R R R R
8 4 2
VA
In practice, instead RL >> R
of a high value of RL ,
an op. amp is used as
an adder
Truth Table of 4 – bit resistive ladder :-
Digital Input 1 = 15 V, 0 = 0 V
(MSB) (MSB) (MSB) (LSB) Analog output
D C B A VA
0 0 0 0 0
0 0 0 1 1
0 0 1 0 2
0 0 1 1 3
0 1 0 0 4
0 1 0 1 5
0 1 1 0 6
0 1 1 1 7
1 0 0 0 8
1 0 0 1 9
1 0 1 0 10
1 0 1 1 11
1 1 0 0 12
1 1 0 1 13
1 1 1 0 14
1 1 1 1 15
Drawbacks :-
1) Each resistor in the network has different values e.g. R0, R0/2, R0/4, R0/8, etc. The values of
these resistor should be very accurate. In absence of precision resistors, the output will not
be a faithful analog equivalent.
2) As precision resistors are used, cost is more.
3) Resistor of appropriate smaller values are not easily available and the resistance may be
affected by changes in temperature.
4) The resistor used for MSB is required to handle a much greater current than that used for
the LSB resistor.
5) It is very difficult to fabricate such a wide range of R with integrated circuit technique.
To overcome these problems an alternative circuit of R – 2R ladder has been developed.
2) 4 – bit R – 2R ladder D/A converter :-
Principle – The binary ladder is a resistive network whose output voltage is a properly
weighted sum of the digital inputs. It uses resistors of only two values, R and 2R. It has op.
amp. as a scaling circuit and MSB input towards right and LSB input with left of the circuit. A
4-bit ladder type D/A converter is shown in Fig.
R R R
VA Analog
output
2R 2R 2R 2R 2R
D C B A
(LSB) (MSB)
Let us find analog input to Op. amp. for various digital inputs.
i) Suppose digital input is ABCD = 1000 then the equivalent circuit becomes
R R R 2R
VA VA
2R 2R 2R 2R 2R = 2R
+V +V
D C B A
VA = V x 2R f= + V d
4R 2
ii) Suppose digital input is ABCD = 0100 then the equivalent circuit becomes
R R R
VA
2R 2R 2R 2R 2R
+V
D C B A
+V/2
2R R R R
VA VA
2R 2R 2R
= =
+V
By voltage divider formula
VA = V/2 x 2 R f= + V d
4R 4
In this way we can easily find the output voltage of R – 2R ladder for the digital inputs as :-
When ABCD = 0010 then VA = + V d & When ABCD = 0001 then VA = + V .
8 16
V
In this way each digital input is transformed into a properly weighted binary output voltage.
A
The output voltage is given by :-
VA = V .+ V .+ V .+ V .+ ………………+ V .+
2 4 8 16 2n
Where, n is total number of bits at the input.
VA = Vo 20 + V1 21 + V2 22 + V3 23 + . . . . . . . . . . . . . + Vn - 1 2n – 1 found
2n
Where V0 (LSB), V1, V2, . . . . . . , Vn-1 (MSB) are the digital input voltage levels.
Analog to Digital Converter (ADC) :-
The process of conversion of an analog signal into its equivalent digital signal is referred as an
Analog to Digital Converter (ADC). An ADC is often referred to as an encoding device, since it
is used to encode signals for entry into a digital system.
Types of analog-to-digital converters (ADC) are :-
1) Simultaneous A/D converters 3) Successive approximation A/D converters
2) Counter type A/D converters 4) Continuous A/D converters
1) Simultaneous A/D converters :-
In this method a number of comparator circuits are used. As 2n – 1 comparators are required
to convert to a digital signal that has n bits. Thus in 2 – bit simultaneous ADC 3 comparators
are used. The analog signal is one of the inputs to each comparator. The second input is a
standard reference voltage obtained by using a resistive voltage divider consisting of four
equal resistors, e.g. +V/4, +V/2, +3V/4. The analog input voltage is between 0 and +V.
+V Analog input voltage
Ref. 0 to V volts
voltage
R
C3
+3v/4
A
R
Encoding Digital
C2 Networking output
+V/2
B
R Comparator o/p
C1
+V/2
If the analog input is more than the reference voltage to any comparator then that
comparator turns ON (provides high output).
If all comparators are OFF, analog input must be between 0 and +V/4.
If C1 is high and C2 & C3 are low, the input must be between +V/4 and +V/2.
If C1 and C2 are high & C3 is low, the input must be between +V/2 and +3V/4.
If all comparators are high, the input must be between +3V/4 and +V.
Analog Input Comparator’s output Digital output
Voltage C1 C2 C3 A B
0 to +V/4 Low Low Low 0 0
+V/4 to +V/2 High Low Low 0 1
+V/2 to +3V/4 High High Low 1 0
+3V/4 to +V/4 High High High 1 1
Thus, there are four voltage ranges that can be detected. The three comparator outputs
can then be fed into a coding network to provide 2 bits which are equivalent to the input
analog voltage. The bits of the coding network are then entered into a flip flop register for
storage.
Advantages :-
1) Simple construction
2) Extremely fast conversion rate, hence called as ‘flash’ converter.
Disadvantages :-
1) It requires more no. of comparators for higher no. of bits.
2) It is very difficult to construct this ADC with discrete circuit.
3) It is bulky and very costly.
2) Counter type A/D converters :-
Principle :- This is a higher-resolution A/D converter using only one comparator. This is
possible by using a variable reference voltage. A staircase reference voltage is used as
feedback voltage to the comparator.
Start
Clock Gate and Control Counter
N lines
Comparator
Analog
input Binary ladder
voltage Ref. voltage
Working :- The counter type ADC consist of a D/A converter, one comparator, a clock and
the gate & control circuitry. First the counter is reset i.e. 000. When a convert signal
appears on the start line, the gate opens and clock pulses are allowed to pass through to
the counter. The counter advances through its normal binary sequence ( 001, 010, 011 and
so on) and staircase waveform is generated at the output of the binary ladder. Analog input
voltage and this waveform are applied to the comparator. When the reference voltage is
equal to or greater than the analog input voltage, the gate is closed. The number stored
in the counter is the digital equivalent of the analog input voltage. In this way digital
equivalent of given analog voltage can be obtained.
Advantages :-
1) It needs only one comparator.
2) High resolution.
3) It provide good method of conversion
Disadvantages :-
1) Conversion time required is longer and it is determined by the clock.
3) Successive Approximation A/D converters :-
Principle :- This converter operates by successively dividing the voltage ranges in half. If
multiplexing is necessary, the successive-approximation A/D converter is most useful.
In counter type ADC more time is require as counter passes through all the counts. The
successive approximation counter uses fast technique. In this counter, instead of
incrementing step by step here individual bit is made high and making comparison the bit is
fix or change to zero. It start checking by making MSB high then second MSB and so on. The
bit position is changed by decision for instance; if Vin 100 then counter is set to 110 and if
Vin < 100 then counter is set to 010. This action is continued till input voltage approximately
becomes equal to the register output.
The successive approximation A/D consists of a comparator, a DAC and a programmable
counter indicated by SAR (Successive Approximation Register) it is an integrated circuit.
Analog
input ( End Of
Vin Conversion )
Clock Successive EOC
Comparator Approximation
Register (SAR)
Reference Digital
voltage output
DAC
( Binary Ladder )
Successive Approximation Tree
111
111
110
110
101
101
100
Start 110
000 011
011
010
010
The successive approximation ADC is
widely used in Digital Voltmeters, 001
for interfacing analog signals with 001
computers because of its high speed 000
and better resolution.
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