lec05 ad da conversion

7/29/2019 Lec05 Ad Da Conversion

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James A. Mynderse ME588 A/D and D/A Conversion 1

ANALOG DIGITAL CONVERSION

Physical world is analog (to a certain extend)

Analog/digital conversion can be a part of the instrument or theactuator, e.g.

Incremental encoder analog position get encoded into digital pulse

Stepper motor digital step pulse get transformed to analog position

To be processed by computers, all information must be converted:

Quantization Level (Q)

For an N-bit converter

Quantization error can be up to one full quantization level (usually

referred to as the least significant bit, LSB)

Analog World

Digital World

2 1


INTEGER CODES

Digital word is finite precision

Coding is arbitrary

Once in a computer (digital form), codes are relative easy to

convert from one type code to another

Unipolar Voltages

Can be coded to unsigned integers

Example 0-5 volts coded to 3 bit unsigned integer


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INTEGER CODES

Bipolar Coding

Twos Complement

Offset Binary

Voltage(1) Voltage(2) Digital Value Decimal Equivalent

+3.75 +5 011 3

+2.50 +3.33 010 2

+1.25 +1.67 001 1

0 0 000 0

-1.25 -1.67 111 -1

-2.50 -3.33 110 -2

-3.75 -5 101 -3

-5 -- 100 -4

Voltage Digital Value Decimal Equivalent

-5 000 0

-3.57 001 1-2.14 010 2

-0.71 011 3+0.71 100 4+2.14 101 5

+3.57 110 6

+5 111 7


INTEGER CODES

Sign Extension

Precision of ADC or DAC is independent of the precision being

used in the computer.

A/D and D/A converter precision rarely match the computers word

size.

To convert from one to the other, filling of extra (additional) bits to

the right depends on the coding scheme.

Offset binary and unsigned integer codes have no ambiguity.

Twos complement coding requires a bit more consideration.

Negative numbers must be filled with 1s and positive numbers

with 0s.

Example:

3 bit Code 6 bit Code

101 111 101011 000 011


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DIGITAL-TO-ANALOG (D/A) CONVERSION

Ideal DA Conversion:

DA Conversion Errors:

000 001 010 011 100 101 110 111



Digital value is stored in a register (latch), then converted.

Output of the DAC remains the same until the next value is sent to the

register (latch) a zero-order hold.

Basic concept:

Weighted (Scaled) Resistor DAC

Fast!

Not practical for large number of bits.

Requires

Accurate reference voltage.

Higher precision resistor.VREF

VOUT

D/A

Converte

r

LatchDigital

Input

Analog

Output

2 2

2 2

2


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R/2R Ladder DAC

Requires only two resistance values (2R and R) closely matched.

Input forms a resistor divider network, different digital values

configure the switches to form a different series-parallel voltage

divider configuration.

Bipolar output can be achieved by substituting the ground with a

negative voltage source.

If only MSB (100) is

asserted:

If all bits are asserted (111):

4

8

1

2

7

8

2 2

2 2

2



Multiplying DAC

Conventional DAC has internal reference voltage VREF that is

derived from the fixed power supply.

Multiplying DAC has an externally supplied reference voltage.

Advantages:

Use a constant frequency sinusoidal reference signal to achieve

amplitude modulation, i.e. let VREF = VR sin(t).

External reference voltage can be precisely controlled to adjust as

well as compensated for drift.

Internally

ReferencedMultiplying DAC

(Externally Referenced)

2 2

2 2

2


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Interfacing with a DAC

Non-multiplying DAC use AD558 as example



Pulse Width Modulation (PWM)

Poor mans DAC

Low pass filter the PWM signal can obtain an analog signal whose

magnitude is proportional to the pulse width of the PWM signal

For motor/motion control, the motor/motion

system will act as the low pass filter

Unipolar output

Best suited when an analog output is needed

but does not require a high resolution DACarea

under

the curveIntegrate

20 dB/decade

1/T

T

Cut-off

frequency

Mag

log

1/(RC) =


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ANALOG-TO-DIGITAL (A/D) CONVERSION

Ideal AD Conversion:

AD Conversion Error:

0 1/8 1/4 3/8 1/2 5/8 3/4 7/8

0 FS



Flash ADC

Uses comparators to determine the input voltage range.

Uses logic to convert comparator outputs to digital value.

Fast! Typical conversion time: 10 100 nsec.

Typically, 4 to 8 bit precision (8 bits requires 254 comparators).

Example: 2 bit Flash ADC

Code:

Needs: 3 comparators Use truth table to get output values:

C1: V > 1.25

C2: V > 2.5

C3: V > 3.75

0 1.25 2.5 3.75 5

00 01 10 11

C3 C2 C1 MSB LSB

0 0 0 0 00 0 1 0 1

0 1 0 X X0 1 1 1 0

1 0 0 X X

1 0 1 X X1 1 0 X X1 1 1 1 1


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Flash ADC

If input is changing during conversion, erroneous value will be

produced Need to provide sample-and-hold at the input side.

Output is only valid a specific time after input is held.

Continuous sampling can be done by using Gray code as input

changes, the outputs are guaranteed to be continuous. Requires lots of comparators:

Adjacent comparators must have monotonic range change.

2No.ofBits 1


SUCCESSIVE APPROXIMATION ADC

Workhorse method.

Used for wide variety of applications

Slower than flash ADC. Typical conversion time: 1 100 sec.Easily extensible to higher precision.

Precision is limited by the quality of the components.

Basic idea: Check bits starting from the high order bit (MSB).

Algorithm:

This is a form ofinterval halving.

START CONVERSION

SET Result to 0

FOR i = N-1 TO 0

SET i-th bit of Result to 1

IF INPUT VOLTAGE < DtoA(Result)SET i-th bit of Result to 0

END FOR-loop

OUTPUT Result

END CONVERSION


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SUCCESSIVE APPROXIMATION ADC

General structure:

Successive-approximation converters are quite expensive.

Usually used with a multiplexer -- many channels feed to a single

converter.

Effective conversion speed for multiplexed ADC depends on

number of channel used.

Sample-and-hold normally precedes the converter.


INTEGRATING CONVERTERS

Slowest of the commonly used converters. Typical conversion

time is many milliseconds.

Can be made very accurate and precise used in DVMs (several

conversion per second).

Uses timing to determine digital value of unknown (input) voltage.


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Interfacing with an ADC

Successive approximation ADC use AD673 as exampleConvert timing

Reading timing



ADC with Serial Output

Reduce pinouts and package size

Can be easily interfaced with a microcontroller or a microprocessor

with built in serial interface (SCLK, SDATA, T/R)

Sample rate limited by the maximum SCLK rate.

Use AD7476 as example 1 MSPS 6 pin ADC


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lec05 ad da conversion

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