dac converter

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Reference books :- PC-Based instrumentation concepts and practice by N.mathivanan, Prentic hall of

india, 2007

Introduction

1. Signals in digital form are more convenient than analog form for processing and control

operation.

2. Real world signals originated from temperature, pressure , flow rate, force or any other sensors

are however in analog form and for processing or control by digital systems like computer.

3. Conversion between analog form and digital form is needed.

4. Data acquisition systems (DAS) in general have the following basic components:-

a. Digital to analog convertor

b. Analog to digital convertor

c. Digital I/O devices

d. Timer

e. Sample and hold amplifier

f. multiplexer

5. the DAC and ADC are the important basic components that determine the capabilities and

performance of the DAS.

Sampling & reconstruction

1. sampling

a. Computer process information represented by digital data.

b. Real world signals in measurement and control instrumentation application are however

analog and continuous in time

c. For processing the continuous analog signals by a computer, the analog signal is

converted to digital data at regular time intervals and the digitized data are presented

to the computer.

d. There are 2 process involved in this conversion:-

i. Amplitude quantization

ii. Discrete time sampling

2. Reconstruction

a. Series of digital data obtained by periodic sampling of a continuous analog signal are

the sample of the analog signal.

b. The samples represent the analog signal at specific instants.

c. The original signal can be reconstructed by applying back the digital data in sequence at

the same time intervals to a digital to analog convertor (DAC).

d. The DAC generates quantized analog outputs for the digital inputs.

e. Since the digital input data to DAC represent the analog signal in discrete time and

amplitude, it cannot faithfully represent and reconstruct the original signal without

error.

f. The accuracy of reconstruction can be improved if the number of samples taken in unit

time is increased.

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g. The number of samples collected in unit time is called as the sampling rate.

h. Increasing the sampling rate gets samples of analog signal at close intervals.

Examples

A 1 kHz sine wave is sampled at three different rates, i.e at 4,8,16 samples. Show the reconstructed

waveforms schematically.

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Digital to analog converters (DAC)

1. A DAC converts digital quantities represented by binary codes to proportional analog voltage or

currents.

2. Several techniques are used for digital to analog conversion.

Basic inputs and outputs

1. A basic n-bit DAC has n digital inputs, an analog voltage output and a reference voltage input

2. The DAC receives the digital representation (in binary format) of information to be converted to

analog value through the digital input pins.

3. The width of digital word (the number of bits in the digital world) defines the accuracy of the

analog representation of the information to be produced by the DAC and a term resolution is

used to indicate this.

4. Typically – resolutions ranging from 8 to 20 bits.

5. The DAC produces analog voltages representing the input digital quantity on the analog output

pin.

1. Internally an n-bit DAC consists of an n latches, n switches and a resistor network block.

2. The n latches hold the n bits of the digital input word.

3. Output of each latch, controls a transistor switch in the resistor network.

4. The resistor network block in the converter performs the actual digital to analog conversion.

5. Each switched “ON” resistor in the network passes definite amount of current.

6. The Opamp performs the sum of current and output the analog quantity.

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Digital to analog Conversion techniques.

1. Weight resistor network

2. R-2R ladder network

3. Current output DAC

4. Multiplying DAC

5. Pulse width modulation

Weight resistor network

1. Resistors in the network are binary weighted.

2. Each of the digital inputs controls a transistor switch in the network.

3. When a switch is closed, current flows from the reference source through the binary-weighted

resistor to the summing point (virtual ground).

4. The opamp performs the sum of currents through the resistors and outputs a proportional

voltage.

5. Functionality, the binary weighted resistors produce binary-weighted currents that are summed

and converted to voltage by an op amp.

6. For a 4 bit DAC, the output Vo is given by,

7. Where, S3,S2,S1 and S0 represent the status of switches and take value 1 or 0 if the respective

switch is closed or opened.

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8. If resistor are in binary weights, i.e , R3 = 2RF ,R2 = 4RF , R1 = 8RF and R0 = 16RF the previous

equation reduce to;

9. The 4 bits of the digital input control the 4 switches to provide 16 different switch settings and

produce 16 different discrete voltage at the output.

10. In general, an n bit digital quantity produce 2n different discrete analog voltages.

Example:-

A 4-bit DAC has -5V internal reference. Find output for all possible inputs

Solution:-

The binary pattern of 4 bit digital word is 0000,0001,0010,….,1111. The output voltage for each word is

obtained using the equation

1. Construction of a DAC based on the binary –weighted resistor network is practically difficult

2. The construction of an n-bit DAC needs n+1 resistors with values 20R, 2

1R, 2

2R,…., 2

nR.

3. The value of LSB resistor is 2n times the feedback resistor, RF.

4. The nominal value of feedback resistor is 5kohm, for 8 bit = 1.28M @ 28 X 5k and for 12 bit =

20.48 Mohm. Such high values are not easily achievable in the ICs.

5. Solution:-

a. Is to separate the inputs into groups of four bits and converting each group with

difference voltages that are in multiples of 16

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b. Another solution is illustrated in figure below, where 3 op amps are used to cpnvert 8

bit digital data. 2 groups of 4 bits are independently converted and their output are

added in 1:16 ration using another op amp.

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R-2R ladder network

1. The R-2R ladder resistor network solves the above problem in a simple way.

2. The figure shown in figure below uses resistors with only 2 values, R and 2R, in the ladder

arrangement.

3. The current entering a branch in the network splits into two equal halves at a node and further

divides equally again at each node as it proceeds through the ladders.

4. Each digital input controls a switch to steer current through the resistor either to the summing

point or to the ground.

5. The op amp performs the sum of currents reaching the summing point (Is) and outputs

proportional voltage.

6. Analog output voltage for a digital input quantity is given as,

Where S3,S2,S1 and S0 represent the status of the switches and take value of respective digital

input (1 or 0)

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Example

Find the current output of R-2R ladder network for a digital input of 1011. The ladder network has

resistor values of R = 10K ohm, 2R = 20K ohm. Vref = 10V

Solution:-

The current reaching the summing point, IS ,for a digital input is

For digital input is 1011,

Disadvantages of a weight resistor network over an R-2R ladder network

1. Each resistance in the network has a difference value. Since the dividers are usually constructed

using precision resistor, their cost factor increases.

2. The value of LSB resistor is 2n times the feedback resistor Rf, in high bit input design, LSB resistor

value is too high and the value are not easily available in the ICs.

3. The resistance used in the MSB is required to handle a much large current than the LSB resistor (

for example the current through the MSB may be 500 times larger than that through the LSB )

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Current output DAC

1. In previous techniques, the op amp performs the sum of currents and converts them to voltage.

2. The performance of such devices depends in the speed of output op amp.

3. Even though devices producing voltage outputs are more convenient to use, better performance

could be obtained with current output devices.

4. The current output could then be easily converted to voltage.

5. In current DAC, binary-weighted current are generated by an array of transistor current sources

and switched either to output terminal or ground depending on the binary input.

6. Figure below shows the circuit of a 4 bit current output DAC.

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Characteristics of DAC

The DACs operating on different principles are commercially available in the market.in order to

distinguish their performance, several characteristic parameter are defined. Manufacturers provide

typical values for the parameters in the datasheets.

1. Resolution

2. Full-scale output

3. Output-input equation

4. Range of operation

5. Settling time

6. Accuracy

7. Errors

8. Differential non linear error

9. Integral non linearity error

10. Offset error

11. Gain error.