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AD/DA CONVERTER

Connecting digital circuitry to sensor devices is simple if the sensor devices

are inherently digital themselves. Switches, relays, and encoders are easily
interfaced with gate circuits due to the on/off nature of their signals. However, when
analog devices are involved, interfacing becomes much more complex. What is
needed is a way to electronically translate analog signals into digital (binary)
quantities, and vice versa.

Figure 1 Digital signal and analog signal waveform

Together, they are often used in digital systems to provide complete interface
with analog sensors and output devices for control systems such as those used in
automotive engine controls:

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It is much easier to convert a digital signal into an analog signal than it is to do the
reverse. Therefore, we will begin with DAC circuitry and then move to ADC circuitry.

6.1 Converting digital signal to analogue signals (DAC)

6.1.1 Methods of converting digital signal to analogue signals

A DAC, on the other hand, inputs a binary number and outputs an analog
voltage or current signal. In block diagram form, it looks like this:

6.1.2 Explain the application of D/A converter

Audio

Most modern audio signals are stored in digital form (for example MP3s and CDs)
and in order to be heard through speakers they must be converted into an analog
signal. DACs are therefore found in CD players, digital music players, and PC sound
cards.

Specialist standalone DACs can also be found in high-end hi-fi systems. These
normally take the digital output of a compatible CD player or dedicated transport
(which is basically a CD player with no internal DAC) and convert the signal into
an analog line-level output that can then be fed into an amplifier to drive speakers.

Similar digital-to-analog converters can be found in digital speakers such as USB

speakers, and in sound cards.

Data transmission over the Internet is done digitally so in order for voice to be
transmitted it must be converted to digital using an Analog-to-Digital Converter

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and be converted into analog again using a DAC so the voice it can be heard on the
other end.

Video

Video signals from a digital source, such as a computer, must be converted

to analog form if they are to be displayed on an analog monitor. As of 2007, analog
inputs are more commonly used than digital, but this may change as flat panel
displays with DVI and/or HDMI connections become more widespread. A video
DAC is, however, incorporated in any digital video player with analog outputs. The
DAC is usually integrated with some memory (RAM), which contains conversion
tables for gamma correction, contrast and brightness, to make a device called a
RAMDAC.

A device that is distantly related to the DAC is the digitally controlled

potentiometer, used to control an analog signal digitally.

6.1.3 Construct the circuits to convert digital signals to analogue signals.

A digital-to-analog converter, or simply DAC, is a semiconductor device

that is used to convert a digital code into an analog signal. Digital-to-analog
conversion is the primary means by which digital equipment such as computer-
based systems are able to translate digital data into real-world signals that are
more understandable to or useable by humans, such as music, speech, pictures,
video, and the like. It also allows digital control of machines, equipment,
household appliances, and the like.

Counter 4-bit Full Scale:15V

D
C
B DAC VOUT 1V

A Resolusi
(1 V)
clock 0V
mo Bin
0000 … 1001 ………..

Figure 6.1.3: Input and Output waveform for DAC

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a) Resistive divider circuit

All resistors must be of equal value. If any of the input resistors were
different, the input voltages would have different degrees of effect on the
output, and the output voltage would not be a true sum. Let's consider,
however, intentionally setting the input resistors at different values. Suppose
we were to set the input resistor values at multiple powers of two: R, 2R, and
4R, instead of all the same value R:

Starting from V1 and going through V3, this would give each input voltage
exactly half the effect on the output as the voltage before it. In other words,
input voltage V1 has a 1:1 effect on the output voltage (gain of 1), while input
voltage V2 has half that much effect on the output (a gain of 1/2), and V3 half
of that (a gain of 1/4). If we drive the inputs of this circuit with digital gates so
that each input is either 0 volts or full supply voltage, the output voltage will be
an analog representation of the binary value of these three bits.

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If we chart the output voltages for all eight combinations of binary bits
(000 through 111) input to this circuit, we will get the following progression of
voltages (for VDD =10 volts):

| Binary | Output voltage |

| 000 | 0.00 V |
| 001 | -1.25 V |
| 010 | -2.50 V |
| 011 | -3.75 V |
| 100 | -5.00 V |
| 101 | -6.25 V |
| 110 | -7.50 V |
| 111 | -8.75 V |

And the analog signal we can see like this;

If we wish to expand the resolution of this DAC (add more bits to the
input), all we need to do is add more input resistors, holding to the same
power-of-two sequence of values:

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D C B A

3V
18.7K 37.5K 75K 150K
RF
R4 R R R
3 2 1 20K

--
VVout
o

++ V
ut

Figure 2 : 4 bit DAC circuit V

OU

Example:- T

Calculate the resistive value of R1, R2,R3 and R4 for 4 bit DAC circuit above and
find out the Vout for 0001 and 0110 input.

Resistive value:-
R 1 =150K Bit 20 (LSB)
R2 = R1 = 150K = 75k,  Bit 21
21 21
R 1 150K 150K
R3 = 2
= 2
= = 37.5k ,  Bit 2 2
2 2 4
R 1 150K
R4 = 3 = = 18.75k   Bit 2 3
2 8

Vout for 0001 and 0110 input:-

i. Binary input = 0001.

RF 20K
R1 = 150K, RF = 20K, voltan gain (AV) = = = 0.133
R1 150K
Vout = Vref X AV = 3 X 0.133 = 0.4V
ii. Binary input = 0110
R2 = 75K, R3 = 37.5K, RT = (R2 parallel with R3) = 25K
 AV = 20K/25K = 0.8, Vout = Vref X AV = 3 X 0.8 = 2.4V

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or
RIN = 1 dan Vout = Vref RF RIN, so we can find Vout with
1 1 1 1
+ + +
R 4 R 3 R 2 R1
replacing RIN, and for all sixteen combinations of binary bits (0000 through
1111) input to this circuit, we will get the following progression of voltages
(for VCC =6 volts): -

Progression voltages table

Binary Input
Decimal Vout (V)
Number D C B A

0 0 0 0 0 0
1 0 0 0 1 0.4
2 0 0 1 0 0.8
3 0 0 1 1 1.2
4 0 1 0 0 1.6
5 0 1 0 1 2.0
6 0 1 1 0 2.4
7 0 1 1 1 2.8
8 1 0 0 0 3.2
9 1 0 0 1 3.6
10 1 0 1 0 4.0
11 1 0 1 1 4.4
12 1 1 0 0 4.8
13 1 1 0 1 5.2
14 1 1 1 0 5.6
15 1 1 1 1 6.0

b) R-2R ladder circuit

An alternative to the resistive divider is the R/2R DAC, which uses

fewer unique resistor values. A disadvantage of the former DAC design was its
requirement of several different precise input resistor values: one unique
value per binary input bit. Manufacturing may be simplified if there are fewer
different resistor values to purchase, stock, and sort prior to assembly. Of

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course, we modify it to use two resistance values, by connecting resistors

together in series and it call R-2R ladder circuit.

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.

General exspression for this circuit is;

Vref Rf
Vout =  B in  ,
n
2 −1 R

n = bit number and Bin = digital input that we want to convert.

Vref R f
a) For input equal to 012 = 110, Vout = , 3 circuit below show you the
4 R
equivalent circuit
Vref
B
A

I1 Rf
I1 = Vref/2R, I2 = 0/2R = 0.
A B
2R I2
I3
2R I3 = I1 + I2 = Vref/2R
2 -
Vth1 I
R (1+2R -
+ Rth = 2R 2R = R, Vth1 = Vref/2
2R ) I2
VOUT
then,
2
R

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B
I4 = Vref/2R = 0/2R = 0.
Rf
I4
B I I5 = Vref/(2 X 2R) = Vref/(4R)
2R
2
then,
VREF/2
2R Rth = 2R 2R = R, Vth2 = Vref/4
-
I5 R R Vth
-
2
+
VOUT
2
Rf
R

I6 IO I6 = Vref/4R = -Io
-
I(1+2 R - VOUT (01) = Io X Rf = Vref/(4R) x Rf
VREF/4
) +

2R
VOUT Rf
= (Vref/4)
R

b) For 102, see figure below.

Vref R f
102 = 210, Vout =
2 R

A Vref

B
Vref
Rf
Rf B
I1 Rf
AI I4 I6
2R 2R B I IO
2R VREF/2 -
2
2 I3
0
2 I(1 R -
2R - +
Vth1 I
R (1 R - 2R -
-
+2)
+ I5 R I(1R Vt VOUT
2R +2)I2 VOUT h2
+ 2
+2)
2 VOU R
2 T I6 = Vref/2R = -Io
R VOUT (10) = Io X Rf =
R
Vref/(2R) x Rf
I1 = Vref/2R= I2 = 0/2R I4 = Vref/2R. R
= 0. I5 = 0 = (Vref/2) f
I3 = I1 + I2 = Vref/2R Rth = R, Vth2 = Vref/2 R
=0 9
Rth =2R 2R = R, Vth1 DAC circuit for R/2R for 102 bit input
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c) For 112, the circuit shown below.

3Vref R f
When input is 112 = 310, Vout =
4 R

A
Vref
B
Vref Rf
Rf
I1 B Rf
AI I4 IO
2R 2R B I I7
3VREF/4 -
2
2 I3 2R
I(1 R -
Vth1 I 2R
2
-
- Vref/2 +
R (1 R + 2 - +2)
2R +2)I2 I5 R
-
I(1RRVth + 2
VOU
T
VOU
2 T +2) 2
VOUT R
R 2
I4 = VrefR/2R. I7 = 3Vref/4R = -Io
I1 = Vref/2R, I2 = 0 I5 = Vref/4R, VOUT (11) = Io X Rf
I3 = I 1 + I 2 = I6 = I 4 + I 5 = = 3Vref/(4R) x Rf
3Vref/4R R
Vref/2R Rth = 2R//2R = = (3Vref/4) f
Rth = 2R//2R = R, R
R,
Vth1 = Vref/2 Vth2 = 3V ref/4
DAC circuit for R/2R for 102 bit input

General equation for output is;

Vref R f V R 3Vref R f
V0ut = V00 + V01 + V10 + V11 = 0 + + ref f +
4 R 2 R 4 R

 V0ut =
Vref R f
0 + 1 + 2 + 3
4 R

6.1.5 Specification for DAC

Most of the digital to analog converters are available in the form of Integrated
circuit (IC). It is important that you know some features or specifications of the
manufacturer to apply on any circuit. There are five specifications for the DAC,
which we discuss.

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Figure 6.1.3 shows the DAC receives digital input from mode counter 16. 4-bit DAC has a
resolution of 1 V and maximum output voltage or full-scale voltage of 15 V. Now let us
examine the specifications for digital to analog converter.

Resolution

Defined as the smallest change achieved in the analog output as a result of changes in
digital input.
Manufacturers often refer to the resolution of the DAC is in the number of bits. For
example, 10-bit DAC has a resolution of 10 bits. 10-bit DAC has a resolution smaller than
8-bit DAC.

Resolution can be expressed in two cases, either the Voltage or Ampere and percent.
Resolution in the voltage or Ampere is also known as the step size. You can see in Figure
6.1.3 above, the output waveform versus the digital input is shaped into a staircase has
15 stairs and 16 step. 15 stairs is known as the number of steps. So the step size or
resolution for digital to analog converter in this figure is 1 V. To your knowledge is often
the resolution is equal to the value of the product when the first digital input of 00012.
Percentage Resolution can be expressed as the amount of it is also useful to express it as
a percentage of the full-scale output.

Resolution = Step Size = LSB for input bit

1 stepsize
% Resolution = n
 100 =  100 , where;
2 −1 fullscalevoltage
n=number of input bit, (2n – 1) = total step

Example
Digital to analog converter 10-bit with step size 10 mV. Search for full-scale voltage and
the percent resolution.

Solution
Number of bits = 10
The total step size = 210-1 = 1023 steps
Thus, the full-scale output voltage = 10mV x 1023 = 10.23 V

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stepsize 10mV
% Resolution =  100 =  100 = 0.1%
fullscalevoltage 10 .23 V
1 1
or % resolution =  100 =  100 = 0.1%
totalstep 1023

What is Advantages and Disadvantages of Resistive Divider and R /2R ladder

diagram

Advantages

Resistive Divider R/2R

• Fewer Components • Greater Stability

• Easy to build for IC’s • Needs only two values of

resistors

• Less reference voltage loading

Disadvantages
Resistive Divider R/2R
• Hard to match resistors • More parts

• Stability with temperature • Harder to construct

change

• Large R more susceptible to

noise

• Wide range of reference

voltage loading

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6.2 Converting analog-to-digital signals (ADC)

An analog-to-digital converter, or simply ADC, is a semiconductor device

that is used to convert an analog signal into a digital code. In the real world, most of
the signals sensed and processed by humans are analog signals. Analog-to-digital
conversion is the primary means by which analog signals are converted into digital
data that can be processed by computers for various purposes.

An analog signal is a signal that may assume any value within a continuous
range. Examples of analog signals commonly encountered every day are sound, light,
temperature, and pressure, all of which may be represented electrically by an analog
voltage or current. A device that is used to convert an analog signal into an analog
voltage or current is known as a transducer. An analog-to-digital converter is used
to further translate this analog voltage or current into digital codes that consist of 1's
and 0's.

MSB
D
Clock
ADC C
Input
0– B
Voltage LSB
Aanalog 3V A

Figure 7.5: ADC block diagram

A typical ADC, therefore, has an analog input and a digital output, which may
either be 'serial' (consisting of just one output pin that delivers the output code one
bit at a time) or 'parallel' (consisting of several output pins that deliver all the bits of
the output code at the same time).

Analog-to-digital converters come in many forms; there are digital ramp

converter, successive approximation converter, flash converter and etc.

a) Digital ramp converter

Conversion from analog to digital form inherently involves comparator action

where the value of the analog voltage at some point in time is compared with
some standard. A common way to do that is to apply the analog voltage to one
terminal of a comparator and trigger a binary counter which drives a DAC. The

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output of the DAC is applied to the other terminal of the comparator. Since the
output of the DAC is increasing with the counter, it will trigger the comparator at
some point when its voltage exceeds the analog input. The transition of the
comparator stops the binary counter, which at that point holds the digital value
corresponding to the analog voltage.

Q0
Clock = Q1 Output
A CK digital
Q2
START
B Counter Q3
Mod 16
Input reset
VA
analog
VA’ + Voltage
- Comparator DAC
VA > VA’ = 1
VA < VA’ = 0

VOUT
Figure : 4-Bit Digital Ramp Circuit

If the VA is positive, the operations of the circuit are as follows above;

1. A positive pulse 'Start' is supplied, a count restored to zero. AND gate output is low,
so there is no receive any triggered counter bell-shaped.
2. When the zero count, VA '= 0, so the comparator output is high voltage. When the
pulse returns low and triggered at the output of the AND gate will be high (because
all entries are in a logic high) and allows the counter count.
3. Output DAC, VA 'increase in the voltage step (step voltage) corresponding to the
step size or resolution.
4. This process will continue until the VA ' VA. Comparator output will be low; the
counter will stop on the count represented by the VA. The conversion process is
complete; the conversion at the output of the comparator from high to low the
conversion process is complete (EOC - End Of Conversion).

Example
Now let's see an example of the conversion of analog inputs, VA = 0.75 V using a
converter 4-bit digital ramp with a step size 0.2V.

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Table 4: Example for ADC with Input Analog 0.75V and 0.33 V digital Ramp 4-bit
Cycle Row Device Input Condition Output
1 Comparator VA = 0.75V, VA’ = 0V, VA > VA’ ‘1’
2 Get DAN active A = clock, B = ‘1’ 1st Pulse
1
3 Counter 1 clock 0001
4 Display Q0=’1’, Q1= Q2= Q3=’0’ 0001
5 DAC 0001 VOUT = 0.2V
6 Comparator VA = 0.75V, VA’ = 0.2V,VA > VA’ ‘1’
7 Get DAN active A = clock, B = ‘1’ Pulse 2 to counter
2
8 Comparator 1 clock 0
9 Display Q1 = ’1’, Q0= Q2= Q3=’0’ 0010
10 DAC 0010 VOUT = 0.4V
11 Comparator VA = 0.75V, VA’ = 0.4V,VA > VA’ ‘1’
12 Get DAN active A = clock, B = ‘1’ Pulse 3 to counter
3
13 Counter 1 clock 0011
14 Display Q1= Q0 = ’1’, Q2= Q3=’0’ 0011
15 DAC 0011 VOUT = 0.6V
16 Comparator VA = 0.75V, VA’ = 0.6V,VA > VA’ Tinggi
17 Get DAN active A = clock, B = ‘1’ Pulse 4 to counter
4
18 Counter 1 clock 0100
19 Display Q0= Q1= Q3=’0’ , Q2=’1’ 0100
20 DAC 0100 VOUT = 0.8V
21 Comparator VA = 0.75V, VA’ = 0.8V,VA < VA’ ‘0’
22 Get DAN not active A = clock, B = ‘0’ No Pulse
5
23 Counter Q0= Q1= Q3=’0’ , Q2=’1’ 0100
24 Display Output counter 0100

Analog Input VA = 0.33 V

1 Comparator VA = 0.33V, VA’ = 0V, VA > VA’ ‘1’

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2 Get DAN active A = clock, B = ‘1’ Pulse 1 to counter

3 Counter 1 clock 0001
4 Display Q0=’1’, Q1= Q2= Q3=’0’ 0001
5 DAC 0001 VOUT = 0.2V
6 Comparator VA = 0.33V, VA’ = 0.2V,VA > VA’ ‘1’
7 Get DAN active A = clock, B = ‘1’ Pulse 2 to counter
2
8 Counter 1 clock Counter 0010
9 Display Q0=’0’, Q1=1’’ ,Q2= Q3 = ’0’ 0010
10 DAC 0010 VOUT = 0.4V
11 Comparator VA = 0.33V, VA’ = 0.4V,VA < VA’ ‘0’
12 DAN = ‘’0 A = clock, B = ‘0’ No Pulse
3
13 Counter Counter 0010
14 Display Q0=’0’, Q1=1’’ ,Q2= Q3 = ’0’ 0010

Digital Ramp Converter Specification

i. Resolution and accuracy

Resolution and accuracy of the analog to digital converter is the same as the resolution
and accuracy for the digital to analog converter

ii. Conversion time, TC (Conversion Time)

Conversion time is the time taken to convert the analog input digital exit. For the
digital ramp converters, counters count from 0 to VA ' VA. Time to complete the
conversion process, depending on the value of analog input, VA. The greater the value
of the VA, then more steps and longer time of conversion. We will now see the
expression for the exchange of digital ramp converter.

Tc(max) = (2n – 1) clock/cycle = Total Step X Tinput

TC (max), max time to convert happed when VA  VFS .

Tc(ave) = TC (max)/ 2  (2n – 1) clock/cycle

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Example
Digital ramp ADC has the following values:

Bell-shaped frequency = 1 MHz, the VT (voltage 'threshold sensitivity' = (VA '- VA) =
0.1 mV, filled with Scale voltage 10-bit DAC = 10.23V. Find the following values;
a) If VA = 3568 V, what is the equivalent output.
b) conversion time.
c) The resolution of the converter in volts and percent.

Solution:-

a) Number of steps = 210-1 = 1023 steps

V FS 10 .23
 size step = resolution = = = 10 mV
totalstep 1023

This means VA 'increased by 10 mV / step when we use the count upward.

VA = 3568 V, VT = 0.1mV; The VA "must reach more V or 3.5681 before the
comparator output changes to low.

Then this will result in: -

3.5681
= 356 .81 = 357 step  [Remember! These formulas are similar to the DAC
10 mV

output divided by the number of steps, before we know the number of steps =
full-scale voltage / step size]

When completed the process of conversion, the output of the counter is 35 710 =
01,011,001,012, a digital output when VA = 3.568V.

b) From a) above we know that the 357 steps required to get products
01011001012. Then 357 clock cycles occur at a rate of 1  s. So this will give time
for the conversion of 357  s.

1
c) Resolution = DAC step size = 10 mv,% resolution = x 100 = 0.1%
1023

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b) Successive approximation converter

The conversion technique based on a successive-approximation register

(SAR), also known as bit-weighing conversion, employs a comparator to weigh the
applied input voltage against the output of an N-bit digital-to-analog converter
(DAC). Using the DAC output as a reference, this process approaches the final
result as a sum of N weighting steps, in which each step is a single-bit conversion.

General block diagram of Successive approximation converter

Initially all bits of SAR are set to 0. Then, beginning with the most
significant bit, each bit is set to 1 sequentially. If the DAC output does not exceed
the input signal voltage, the bit is left as a 1. Otherwise it is set back to 0. It is kind
of a binary search. For an n-bit ADC, n steps are required.

Masukan
VA
analog
VA’
+
-
jam Successive-approximation
DR (Data ready end-of-
register (SAR) conversion)
MSB LSB
START
Q7
Cp
Q6
Output Q5 Keluaran
register Q digital
4
Q3
Vref = Q2
10Vto digital process
Explanation of analog
8-Bit D/A
for SAC :- Q1
Vout Converter (DAC)
Q0
Block diagram of 8-Bit SAR

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1. SAC has a shorter conversion time and fixed (not dependent on the analog input
value).

2. SAC circuit using the register circuit to provide input to the DAC block where logic
controllers ("control logic") to change the contents of the register-to-bit bit up in the
registry data with an analog input, VA (within the resolution of the converter). Figure
7.5 is a block diagram of the successive approximation converter.

Analog to digital conversion process for the SAC are as follows:

1. Control logic (in block list of tools SAC) Recharge the registrar to the logic high MSB
and other bits to logic low. This produces a value VA 'on the weight of the DAC
output with the MSB last. If the VA '> VA, the comparator output will be' low 'and this
will cause the control logic will be reset to low MSB. If the VA '<VA MSB still' high '.

2. Recharge control logic of the next bit to '1 '. This results in the VA 'a new one. If this
value is greater than the VA, the comparator output will be 'low' and the control logic
will be reset that bit to 0. Otherwise, the left bit ' 1 '.

3. This process continues for each bit in the registry. This process requires a bell-
shaped per bit. After all bits have been tested registrar will store the digital
equivalent of the VA.

Example
SAC 4-bit converter with 1V step size was used to change the input values, VA
= 9.9 V. Show each step of the conversion.

Step Register VA’ (V) VA (V) Comparato

r

Starting Condition 0000 0 9.9 ‘1’

Set MSB to ‘1’, VA’ < VA 1000 8 9.9 ‘1’

Let ‘1’ set bit next to ‘1’, VA’ > VA 1100 12 9.9 ‘0’

Reset bit to 2 and set next to. ’,VA’ > 1010 10 9.9 ‘0’
VA
Reset bit to 3 and set LSB ,VA’ < VA 1001 9 9.9 ‘1’

Output display 1001

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 ELECTRICAL ENGINEERING DEPARTMENT
POLITEKNIK SULTAN ABDUL HALIM MU’ADZAM
SHAH
06000 JITRA, KEDAH DARUL AMAN

DEE30043–Electronic Circuits

6.2.7 Difference Between Digital Ramp and Successive Approximation Circuit

While all analog-to-digital converters are classified by their resolution or number

of bits, how the A/D circuitry achieves this resolution varies from device to device.
There are four primary types of A/D converters used for industrial and laboratory
applications-successive approximation, flash/parallel, integrating, and
ramp/counting. Some are optimized for speed, others for economy, and others for
a compromise among competing priorities (Figure 7.8). Industrial and lab data
acquisition tasks typically require 12 to 16 bits-12 is the most common. As a rule,
increasing resolution results in higher costs and slower conversion speed.

Figure 6.2.7 : Alternative A/D Converters Design

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