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Analog to Digital (A/D) Conversion

An overview of A/D techniques

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A/D fundamentals

• A / D conversion is a process where an analog signal is converted into a numeric representation.– Analog input is normally classified into one of two types and

a voltage range• Types and typical ranges

– Uni-polar (0 -1 V, 0 - 5V, 0 - 10V)– Bi-polar (-1 to 1V, -5 to 5V, -10 to 10V)

– Digital output is normally binary at the hardware level and typically decimal at the software interface level. Hardware generally controls observed voltage resolution.

• Primary critical specifications for A/D conversions– Resolution (voltage resolution)– Conversion rate (time resolution)– Elements contributing to inaccuracy (non-linearity,

offset/bias, missing codes, non-monotonicity)

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A/D fundamentals• Resolution

– Normally specified in terms of the number of binary digits that the analog value is converted to:

• eg. 8 bit conversion, 12 bit conversion, 16 bit conversion

– Analog resolution can be computed from the specified resolution:

• analog resolution = analog range / [2^(binary digits in result)]• example: a bi-polar A/D converter set to input a range of -10 to

+10 V with a 12 bit conversion• analog resolution = 20V / [2^12] = 20/4096 V / bit = 4.9 mV/bit

• Conversion Rate– The rate at which an A/D converter can make sequential a

conversions. In general higher resolutions require greater time or greater cost or both.

– Typically specified in samples per second (sometimes MSPS)

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Transfer Function

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tpu

t C

od

e

Input Voltage

0000

0001

0010

0011

0100

0101

0110

0111

1000

1001

1010

1011

1100

1101

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tpu

t C

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eMissing Code

0

1 LSB

Nominal Quantized

value + 1/2 LSB

• The ideal output from an A/D converter is a stair-step function (see right)– Ideal worst case error in

conversion is 1/2 bit.

– Missing codes or the imperfections where increasing voltage does not result in the next step being output are described as non-monotonicity.

– Errors in A/D conversion may be significant particularly if the full range of the analog signal is significantly less than the range of the analog input of the A/D.

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A/D Converter Types

• Dual Slope Integrating

Control Logic

Counter

Start of ConversionStatus

Clock

Analog Input (Va)

Digital Output 12

+

-

Comparator output

+

--Vreference

Comparator

Integrator

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A/D Converter Types

• Operation• Reference signal is

integrated for a fixed time• Input is switched to the

analog input and is integrated until the integrator output is zero

• The time required to integrate the signal back to zero is used to compute the value of the signal

• Accuracy dependent on Vref and timing

• Characteristics• Noise tolerant (Integrates

variations in the input signal during the T1 phase)

• Typically slow conversion rates (Hz to few kHz)

21

00

21 11

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dtVC

areference

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utpu

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Time

Sta

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f Con

vers

ion

.......T1......T2

.......T1......T2

ConstantSlope

Integrator output

with small Va

InputIntegrator output with

Vreference InputIntegrator output

with large Va

Input

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• Successive Approximation (Digital to Analog Conversion + null balancing)

– 4 bit D/A using a summing amplifier and switch

– 4 bit D/A using R-2R ladder

• Digital value (D1, D2, D3 etc.) is converted to an analog value

A/D Converter Types – D to A conversion

+

-

2R

4R

8R

R

1V

R

D0

D1

D2

D3

+

-

R

2R

R

2R2R2R

R R1V

2R

D0D1D2D3

i=1/2R i=1/4R i=1/8R i=1/16R

å +8

1

4

1outV

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A/D Converter Types

• Successive Approximation

– The input signal must be “held at a single level during conversion. (A sample and hold circuit is required on the input.

– Note that conversion time depends on the input level and the convergence method.

D/A Converter

SuccessiveApproximation

RegisterStart of ConversionStatus

Clock

Analog Input

Digital Output 12

+

-

Comparator output

Converter Schematic

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• Conversion– At start of conversion, the

clock is used to cycle a counter that drives the D/A converter.

– When the D/A output is larger than the input then the count is reduced otherwise it is increased using an algorithm to home in on the matching value.

– When the counter step size is within the tolerance desired (usually 1 count) then conversion is stopped and the digital value being output to the D/A is output

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Time

Sta

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T1

T2

T3

T4 T5

T6

T7 Analog Input

D/A Converteroutput

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Sample and hold devices

• Some A/D converters require the input analog signal to be held constant during conversion, (eg. successive approximation devices)

• In other cases, peak capture or sampling at a specific point in time necessitates a sampling device.

• This function is accomplished by a sample and hold device as shown to the right:

• These devices are incorporated into some A/D converters

Analog InputSignal

Samplingswitch

HoldCapacitor

OutputSignal

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A/D Converter Types

• Flash Conversion– A multi-level voltage divider

is used to set voltage levels over the complete range of conversion.

– A comparator is used at each level to determine whether the voltage is lower or higher than the level.

– The series of comparator outputs are encoded to a binary number in digital logic (an encoder)

+

-

Encoder

+

-

+

-

+

-

+

-

+

-

+

-

1V

Vin

Comparators3R

2R

2R

2R

2R

2R

2R

R

3

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A/D Converter Types

• Sigma / Delta

DigitalFilter

Start of ConversionStatus

Analog Input (Va)

Digital Output

+

-

Comparator output

+

-Comparator

Integrator

Decimation

ControlLogic

-

+

Bit stream

VF

An

alo

g V

olta

ge

leve

l

Time

Analog Input

Comparatoroutput

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A/D Converter Types

• Operation– Comparator feedback signal

is subtracted from analog input and the difference is integrated.

– The average value of VF is forced to equal Va.

– VF is a digital pulse stream whose duty cycle is proportional to Va This is known as Delta modulation

– This pulse stream is sampled digitally and averaged numerically (decimation) Giving a numerical representation of the voltage in.

– The error in the average or mean is:

– The greater the number of samples averaged, the greater the accuracy

– The greater the number of samples averaged, the greater the time between the start of gathering samples and the output of the mean (group delay)

– This A/D does not work well if switched from channel to channel because of the delay till valid result

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