analog to digital & digital to analog converters
TRANSCRIPT
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ByK. SAI KRISHNAAssistant Professor
Introduction:
Most of information carrying signals such as voltage, current, temperature, pressure and time are available in the analog form.
For processing, transmission and storage purposes, it is often more convenient to express such signals in the digital form. When expressed in the digital form, they provide better accuracy and reduce noise.
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Basic DAC Techniques:
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we shall discuss the following resistive techniques only:
1.Binary-Weighted resistor DAC2.R-2R ladder3.Inverted R-2R ladder
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1.Binary-Weighted resistor DAC
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Basic Ideas:
• Use a summing op-amp circuit
• Use transistors to switch between high and ground
Assumptions:
• Ideal Op-Amp
• No Current into Op-Amp
• Virtual Ground at Inverting Input
•Vout = -IRf
Binary-Weighted resistor DAC
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For ON-Switch ( i/p is 1), I=
For OFF Switch ( i/p is 0), I=0
R
VR
Binary-Weighted resistor DAC
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Advantages◦Simple◦Fast
DisadvantagesoNeeds large range of resistor values (2000:1 for 12-bit) with high precision in low resistor values.oNeeds very small switch resistances.
Summary◦Use in fast, low-precision converter
2. R/2R Ladder Digital-to-Analog ConvertersOnly two resistor values
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Each bit corresponds to a switch:
If the bit is high, the corresponding switch is connected to the inverting input of the op-amp.
If the bit is low, the corresponding switch is connected to ground.
R/2R Ladder Digital-to-Analog ConvertersCurrent division and analog output
versus digital input
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Output for R-2R network, Here,
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R
VD
R
VD
R
VD
R
VDRV f
16842ref
0ref
1ref
2ref
3out
Where b3 corresponds to bit 3,b2 to bit 2, etc….If bit n is set, bn=1, If bit n is clear, bn=0
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1
8
1
4
1
2
10123refout bbbbVV
For general n-Bit R-2R Ladder or Binary Weighted Resister DAC
i
n
iinbVV
2
1
1refout
For a 4-Bit R-2R Ladder
RRR SF 2
R/2R Ladder Digital-to-Analog Converters
Current division and analog output versus digital input
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3. Inverted R-2R Ladder Digital-to-Analog Converters
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R/2R Ladder Digital-to-Analog Converters
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AdvantagesAdvantages Only two resistor valuesOnly two resistor values Does not need the kind of precision as Binary Does not need the kind of precision as Binary
weighted DACsweighted DACs Easy to manufactureEasy to manufacture Faster response timeFaster response time
DisadvantagesDisadvantages More confusing analysisMore confusing analysis
Monolithic/Hybrid Integrated-Circuit Digital-to-Analog Converters
IC 1408 DAC block diagram and pin configuration
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Monolithic / Hybrid Integrated-Circuit Digital-to-Analog Converters
IC 1408 DAC Application
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Important Electrical Characteristics for IC 1408:
1. Reference Current: 2mA
2. Supply Voltage: +5v (Vcc) & -15v (-VEE)3. Setting Time: 300ns4. Full Scale Output Current: 1.992mA
5. Accuracy: 0.19%
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Hybrid Integrated-Circuit Digital-to-Analog Converters
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Analog to Digital Converters:
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ADC Basic Principle:The basic principle of operation is to use the comparator principle to determine whether or not to turn on a particular bit of the binary number output.Where d1 is the most significant bit and dn is the least significant bit. An ADC usually has two additional control lines: the START input to tell the ADC when to start the conversion and the EOC (end of conversion) output to announce when the conversion is complete. Depending upon the type of application, ADCs are designed for microprocessor interfacing or to directly drive LCD or LED displays.
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Different Types Of A/D Converter:
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Direct Type
Integrating Type
Counter type converter
Tracking or servo converter
Successive approximation type converter
Parallel comparator(Flash) type converter
Charge balancing ADC
Dual slope ADC
A/D Converter
Direct types ADCs compare a given analog signal with the internally generated equivalent, signal.
Integrating type ADCs perform conversion in an indirect manner by first changing the analog input signal to a linear function of time or frequency and then to a digital code.
The most commonly used ADCS are successive approximation and the integrator type. The successive approximation ADCs are used in applications such as instrumentation where conversion speed is important.
The flash (comparator) type is expensive for high degree of accuracy.
The integrating type converter is used in applications such as digital meter and monitoring systems. 23
1. Parallel Comparator (Flash) Analog-to-Digital Converters
Also called simultaneous, multiple comparator, or flash converting
Several comparators with different reference voltages drive a priority encoder.
This is the simplest possible A/D converter. It is at the same time, the fastest and most expensive technique.
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I. DIRECT TYPE ADCs:
Parallel Comparator Analog-to-Digital Converters
Three-bit parallel encoded ADC.
priority encoder.Analog range of
0-7 V.3 bit (8 level)
resolution (3-bit priority encoder
(8 to 3)).25
Parallel Comparator A/D Converters
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Parallel Comparator A/D Converters
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The number of comparators required for n bit resolution is ,
no.of comparators= The maximum frequency for a sine wave Vin
to be digitised within accuracy if is,
Where Maximum input frequency.
= Conversion Time.n= no.of bits.
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12 n
LSB
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1max nf
T c
f max
Tc
Parallel Comparator A/D Converters
Parallel Comparator A/D Converters
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AdvantagesAdvantages• Very fast
DisadvantagesDisadvantages• Needs many parts
(255 comparators for 8-bit ADC)
• Lower resolution • Expensive• Large power
consumption
2.Counter Type-Ramp Analog-to-Digital Converters
Counter used in conjunction with a D/A converter
To change for continuous conversions end-of-conversion line is tied back to clear input
Disadvantage is slow conversion time
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The Counter Type A/D converter
The Counter Type A/D converterOperation of the Counter:Initially, counter is reset then o/p is set to zero.By applying reset pulse the digital i/p to DAC. DAC is also zero then Vd is also zero.When analog i/p voltage Va is applied to ADC then Va>Vd. Then the comparator goes high value.When the comparator o/p is high then it allows the clock pulse through AND gate.Then the counter starts the counting clock pulse.The steps are continued till Vd is less than Va. Then comparator o/p goes low then Vd> Va.For a new value of analog input Va, a second reset pulse is applied to clear the counter.
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Counter Type Analog-to-Digital Converters
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Disadvantage is slow conversion time.Conversion time is not constant.
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The Counter Type A/D converter
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3.Tracking or servo A/D converter
Tracking or servo A/D converter
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AdvantagesAdvantages• Simple
DisadvantagesDisadvantages• Time needed to
stabilize as a new conversion value.
4. Successive-Approximation Analog-to-Digital Conversion
Most used in modern ADC ICsConverter circuit is similar to counter-
rampUses successive approximation register to
quickly narrow in on the analog valueResult is a much faster conversion when
compared to the counter method.
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Successive-Approximation Analog-to-Digital Conversion
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Successive-Approximation Analog-to-Digital Conversion
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Successive-Approximation Analog-to-Digital Conversion
Simplified SAR A/D converter
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comparator
Table 1 Voltage-level contributions by each successive approximation register bit.
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Figure : Timing waveforms for a successive approximation A/D conversion.
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Successive-Approximation Analog-to- Digital Conversion
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AdvantagesAdvantages
• Capable of high speed
• Medium accuracy compared to other ADC types
• Good tradeoff between speed and cost
DisadvantagesDisadvantages
• Higher resolution successive approximation ADCs will be slower
• Speed limited ~5Msps
II. Integrating Type of ADCs1. Charge Balancing ADC:The principle of charge balancing ADC is to first convert the input signal to a frequency using a voltage to frequency (V/F) converter. This frequency is then measured by a counter and converted to an output code proportional to the analog input. The main advantage of these converters is that it is possible to transmit frequency even in noisy environment or in isolated form.The limitation of the circuit is that the output of V/F converter depends upon an RC product whose value cannot be easily maintained with temperature and time. The drawback of the charge balancing ADC is eliminated by the dual slope conversion. 44
2. Dual Slope ADC (Ramp Generator):
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The voltage v0 will be equal to v1 at the instant t2 and can be written as
Dual Slope ADC
Dual Slope ADC
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AdvantagesAdvantages
• Input signal is averaged
• Greater noise immunity than other ADC types
• High accuracy
DisadvantagesDisadvantages
• Slow• High precision
external components required to achieve accuracy
Dual Slope ADC
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Dual Slope ADC
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DAC/ADC SPECIFICATIONS
Both D/A and A/D converters are available with wide range of specifications:
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Resolution Output Voltage Range Accuracy Setting Time or Conversion
Time Linearity Stability Quantization Error
For D/A Converters:1.Resolution:
(a) A DAC that can provide number of different analog output values is called resolution.
For a DAC having n-bits, Resolution=2n
(or)
(b) A DAC is which the ratio of change in output voltage resulting from a change of LSB (i.e. 1 least significant bit) at the digital inputs is known as resolution.Resolution for n-bit DAC is given by:
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12R eso lutio n FS
nV
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Example: Calculate the resolution of an 8-bit DAC. Solution: Resolution = 8 bits
Percentage resolution = %391.0%100
255
1%100
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12Resolution FS
nV
Digital to Analog Converters-Performance Specifications
-Resolution-Resolution
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Better Resolution(3 bit)Poor Resolution(1 bit)
Vout
Desired Analog signal
Approximate output
2 V
olt.
Lev
els
Digital Input0 0
1
Digital Input
Vout
Desired Analog signal
Approximate output
8 V
olt.
Lev
els
000
001
010
011
100
101
110
111
110
101
100
011
010
001
000
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2. Output Voltage Range: This is the difference between the maximum and minimum output voltages expressed in volts. Example: Calculate the output voltage range of a 4-bit DAC if the output voltage is +4.5V for an input of 0000 and +7.5V for an input of 1111. Solution: Output voltage range = 7.5 – 4.5 = 3.0V
3. Accuracy: It is defined as the difference between the
actual analog output and the expected analog output when a given digital input is applied.
4.Linearity: The linearity of an A/D or D/A
converter is an important measure of its accuracy and tells us how close the converter output is to its ideal transfer characteristics.
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Digital to Analog Converters-Performance Specifications
-Linearity-Linearity
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Linearity(Ideal Case)
Digital Input
Perfect Agreement
Desired/Approximate Output
Ana
log
Out
put V
olta
ge
NON-Linearity(Real World)
Ana
log
Out
put V
olta
ge
Digital Input
Desired Output
Miss-alignment
Approximate output
For A/D Converters:1.Resolution:The resolution of an A/D converter is defined as the smallest change in analog input for a one bit change at the output. As an example, the input range of an 8-bit AID converter is divided into 255 intervals. So the resolution for a 10 V input range is 39.22 mV (= 10 V/255).2. Accuracy:
The accuracy of a given ADC i.e. analog to digital converter determines the number of bits which can be usefully provided.
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3. Quantization error:Quantization error (or quantization noise) is the difference between the original signal and the digitized signal. Hence, the magnitude of the quantization error at the sampling instant is between zero and half of one LSB. Quantization error is due to the finite resolution of the digital representation of the signal, and is an unavoidable imperfection in all types of ADCs.In an ideal analog-to-digital converter, where the quantization error is uniformly distributed between −1/2 LSB and +1/2 LSB.
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212
FS
nEV
Q
Common Specifications For Both A/D and D/A Converters:1.Conversion Time or Setting Time:
It is the time required for conversion of analog signal into its digital equivalent. It is dependent on amplifiers output and switches response time.
2.Monotonicity: If a converter does not miss any step backward
during its entire range stepped by a counter then it is said to have a counter having good monotonicity.
3. Stability: The performance of converter changes with
temperature, age and power supply variations. So all the relevant parameters such as offset, gain, linearity error and monotonicity must be specified over the full temperature and power supply ranges. 59
Summary
Any analog quantity can be represented by a binary number. Longer binary numbers provide higher resolution, which gives a more accurate representation of the analog quantity.
The binary-weighted D/A converter is the simplest to construct, but it has practical limitations in resolution (number of input bits).
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Summary
Operational amplifiers are important building blocks in analog-to-digital (A/D) and digital-to-analog (D/A) converters. They provide a means for summing currents at the input and converting a current to a voltage at the output of converter circuits.
The R/2R ladder D/A converter uses only two different resistor values, no matter how many binary input bits are included. This allows for very high resolution and ease of fabrication in integrated-circuit form.
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Summary
The DAC0808 (or MC1408) IC is an 8-bit D/A converter that uses the R/2R ladder method of conversion. It accepts 8 binary input bits and outputs an equivalent analog current. Having 8 input bits means that it can resolve up to 256 unique binary values into equivalent analog values.
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Summary
Applying an 8-bit counter to the input of an 8-bit D/A converter will produce a 256-step sawtooth waveform at its output.
The simplest way to build an analog-to-digital (A/D) converter is to use the parallel encoding method. The disadvantage is that it is practical only for low-resolution applications.
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Summary
The counter-ramp A/D converter employs a counter, a D/A converter, and a comparator to make its conversion. The counter counts from zero up to a value that causes the D/A output to exceed the analog input value slightly. That binary count is then output as the equivalent to the analog input.
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Summary
The method of A/D conversion used most often is called successive approximation. In this method, successive bits are tested to see if they contribute an equivalent analog value that is greater than the analog input to be converted. If they do, they are returned to zero. After all bits are tested, the ones that are left ON are used as the final digital equivalent to the analog input.
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Thank You
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