DAC Slides

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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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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



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.




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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In general, for an N-bit DAC, the number of different levels will be 2N

,and the number of steps will be 2N-1.


analog output = K X digital input

Resolution (step size) =K constant in the DAC input/output relationship


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If we define:Afsas the analog full-scale output,

nis the number of bits, then


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


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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T h T d A G E i 31

Applications
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