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Together Towards A Green Environment 1
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Lecture Outcome
Describe methods of interfacing digital circuits to analogue circuits,
Demonstrate an application of such an interface.
Syllabus
The concepts of representing analogue signals in a digital format.
Discussion of typical circuits which can implement D/A conversion,
Interface methods, typical examples of application.
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Main Objectives
Upon completion of this chapter, you will be able to:
Understand the theory of operation of several types of digital-to-analogconverters (DACs).
Read and understand the various DAC manufacturer specifications.
Analyze the process by which a computer, reconstructs the analog signal from
the digital data.
REVIEW OF DIGITAL VERSUS ANALOG
A digital quantity has a value that is specified as one of two possibilities,
such as 0 or 1, LOW or HIGH, true or false, and so on.
By contrast, an analog quantity can take on any value over a continuous
range of values
Analog-to-digital converter (ADC): converts analog input to a digital output
Digital-to-analog converter (DAC): converts digital input to a analog output
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Information Domains Currency
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DIGITAL-TO-ANALOG CONVERSION
D/A conversion is the process of taking a value represented in digital code and
converting it to a voltage or current that is proportional to the digital value.
analog output = K X digital input
- K is the proportionality constant value.- The analog output can be a voltage or a current.
- When it is a voltage, K will be in voltage units,
and when the output is a current, K will be in current units.
For the DAC of above figure, K = 1 V VOUT = (1 V) X digital input
For example, with a digital input of 11002=1210, we obtain VOUT= 1 V X 12 = 12 V
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Example 1
A five-bit DAC has a current output. For a digital input of 01010, an output
current of 5 mA is produced. What will IOUTbe for a digital input of 11101?
Solution
The digital input 010102is equal to decimal 10.
Because IOUT= 5 mA for this case, the proportionality factor must be 0.5 mA.
Thus, we can find IOUTfor any digital input such as 111012= 2910as follows:
IOUT= (0.5 mA) X29
= 14.5 mA
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Example 2
What is the largest value of output voltage from an eight-bit DAC that
produces 2.0 V for a digital input of 00110010 ?
Solution
001100102= 5010.
2.0 V = K X 50.
Therefore, K = 40 mV
The largest output will occur for an input of 111111112= 25510 .
VOUT
(max) = 40 mV X255
= 10.2 V
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Input Weights
For the 4 bits DAC, note that each digital input contributes a
different amount to the analog output.This is easily seen if we examine the cases where only one input is
HIGH (see Table).
Thus, A, which is the LSB, has a weight of 1 V;
B has a weight of 2 V;
C has a weight of 4 V;
and D, the MSB, has the largest weight, 8 V.
The weights are successively doubled for each bit, beginning with
the LSB.
Thus, we can consider VOUTto be the weighted sum of the digital
inputs.
For instance, to find VOUTfor the digital input 0111, we can add the
weights of the C, B, and A bits to obtain 4 V + 2 V + 1 V = 7 V.
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Resolution (Step Size)
Resolution of a D/A converter is defined as the
smallest change that can occur in the analog output
as a result of a change in the digital input.
The resolution is always equal to the weight of the
LSB and is also referred to as the step size because
it is the amount that VOUTwill change as the digital
input value is changed from one step to the next
For the given table, we can see that the resolution
is 1 V because VOUTcan change by no less than 1 V
when the digital input value is changed.
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Resolution (Step Size)
The resolution (or step size) is the size of the jumps in the staircase waveform; in this case,
each step is 1 V.
Note that the staircase has 16 levels corresponding to the 16 input states, but there are
only 15 steps or jumps between the 0-V level and full-scale.
Figure: Output waveforms of a DAC as inputs are provided by a binary counter.
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Resolution (Step Size)
In general, for an N-bit DAC, the number of different levels will be 2N
,and the number of steps will be 2N-1.
Figure: Output waveforms of a DAC as inputs are provided by a binary counter.
analog output = K X digital input
Resolution (step size) =K constant in the DAC input/output relationship
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Resolution (Step Size)
If we define:Afsas the analog full-scale output,
nis the number of bits, then
Figure: Output waveforms of a DAC as inputs are provided by a binary counter.
fs
n
AResolution K
(2 1)
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Example 4 (Resolution)
A five-bit D/A converter produces VOUT= 0.2 V for a digital input of 00001.
1. What is the resolution (step size) of the DAC ?
2. Describe the staircase signal out of this DAC.
3. Determine VOUTfor a digital input of 10001.
Solution
1. The LSB for this converter has a weight of 0.2 V. This is the resolution or step size.
2. A staircase waveform can be generated by connecting a five-bit counter to the DAC
inputs. The staircase will have 32 levels, from 0 V up to a full-scale output of 6.2 V,
and 31 steps of 0.2 V each
3. The step size is 0.2 V, which is the proportionality factor K. The digital input is
10001 = 1710. Thus, we have
VOUT= (0.2 V) X17
= 3.4 V
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Percentage Resolution
Figure: Output waveforms of a DAC as inputs are provided by a binary counter.
To illustrate, the DAC of Figure below has a maximum full-scale output of 15 V
(when the digital input is 1111).
The step size is 1 V. This gives a percentage resolution of
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Example 5 (Percentage Resolution)
A 10-bit DAC has a step size of 10 mV. Determine the full-scale output voltage
and the percentage resolution.
Solution
With 10 bits, there will be 210- 1 = 1023 steps of 10 mV each.
The full-scale output will therefore be 10 mV X1023 = 10.23 V, and
The percentage resolution can also be calculated from
For an N-bit binary input code, the total number of steps is 2N1.
Thus, for the previous example,
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DAC CIRCUITRY
Simple DAC using an op-amp summing amplifier with binary weighted resistors.
For example, if the digital input is 1010, then
VD=VB=5V and VC=VA=0 V. Thus
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Example 5 (DAC CIRCUITRY)
Determine:1. The resolution of this D/A converter.
2. The weight of each input bit
3. The full-scale output if RF= 250
Solution
1. The weighting of the LSB, which is
(1/8) X 5 V = 0.625 V.
As shown in the table, the analog output increases by
0.625 Vas the binary input number advances one step.
2. The MSB passes with gain 1, so its weight in the output is 5 V. Thus
3. If RFis reduced by a factor of 4, to 250 , each input weight
will be four times smaller than the values above.
Thus, the full-scale output will be reduced by this same
factor and becomes -9.375/4 = -2.344 V.
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Formula
Resolution = Step Size = Input bit for LSB
Vout (analog output)= K x Digital Input
K = Total Voltage/Current Or Analog Output
Number Of Step Digital Input* K = the factor of proportionality and is a fixed value for a DAC
Digital Input = Number of Step
Number of Step = 2n1
Where;
n = Number of input bits
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Errors
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Offset Errors
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Full Scale Error
Combination of gain error and offset error
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Non Linearity Error
Combination of gain error and offset error
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Accuracy
The two most common ways of specifying accuracy are:full-scale error and linearity error which are normally expressed as a percentage of the
converters full-scale output (% F.S.).
Full-scale error is the maximum deviation of the DACs output from its expected (ideal) value,
expressed as a percentage of full scale.
For example,
4-bit DAC has +0.01%FS accuracy and DAC full- scale is15V.
So 0.01% X15 = 1.5mV.
This means that the DAC output will be different from the ideal value 1.5mV
Linearity error is the maximum deviation in step size from the ideal step size.
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Example
An 8-bit DAC has 2mA full-scale value and +0.5% FS accuracy. What is theoutput range for input 10000000?
Solution
100000002 12810
Step Size = 2mA = 7.84A255
Ideal output for input 12810 = 12810 X7.84A= 1004A
Error = 0.5% FSX
2mA= 10A
Actual output will deviate as much as 1004
The actual range is 994A-1014A after with error.
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Settling Time
the time required for the DAC output to go from zero to full scale as the binary input is
changed from all 0s to all 1s.
Actually, it is the time for the DAC output to settle within step size (resolution) of
its final value.
For example, if a DAC has a resolution of 10 mV, settling time is measured as the time
it takes the output to settle within 5 mV of its full-scale value.
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Monotonicity
A DAC is monotonic if its output increases as the binary input is incremented
from one value to the next.
Bin Bin
Vout
a and b is Monotonic but c is not Monotonic
Bin
Vout
Vout
b ca
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Monotonicity
Another way to describe this is that the staircase output will have no downward stepsas the binary input is incremented from zero to full scale.
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Advantages of using a computer to control devices rather than people
Cheaper - If a computer is monitoring and controlling applications, you donot need to employ people.
Higher Work
Rate -Computers can control applications all day, every daywithoutgetting tired or bored.
Safer - Computers can work inconditionsthat would be too dangerousfor people. Examples include chemical plants, radioactive sitesand extremely cold areas (antarctic).
Accuracy - Computers will respond to inputs from sensors accurately everytime. E.g. a heater will be switched on as soon as the temperaturefalls below 10C.
Speed - Computers will respond to data received from sensors veryquickly. E.g. as soon as an infrared sensor detects an intruder thealarm will sound.
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Applications
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Applications
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