Ele2mdd Lect 13 - Adc

8/2/2019 Ele2mdd Lect 13 - Adc

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Analog to Digital Converters

Lecturer:

Robert Ross


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Overview

Introduction to ADCs

Types of ADCs

Further Reading:

R.J. Tocci, Digital Systems, Principles and

Applications, Prentice Hall (Chapter 10) Demystifying Sigma-Delta ADCs, Maxim

Semiconductors (http://www.maxim-ic.com/app-notes/index.mvp/id/1870)
http://www.maxim-ic.com/app-notes/index.mvp/id/1870http://www.maxim-ic.com/app-notes/index.mvp/id/1870http://www.maxim-ic.com/app-notes/index.mvp/id/1870http://www.maxim-ic.com/app-notes/index.mvp/id/1870http://www.maxim-ic.com/app-notes/index.mvp/id/1870http://www.maxim-ic.com/app-notes/index.mvp/id/1870


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Introduction ADCs

The real world is full of analog, continuoussignals

Microprocessors use digital electronics(encoded with discrete binary values) for

processing Analog to Digital Converters (ADC or A/D)

convert continuous analog signals to discretedigital numbers allowing digital electronics to

sample real world signals ADCs are Mixed Signal Devices as theycombine analog circuits with DSP

Reverse of the operation of the DAC (Digital toAnalog Converter)


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Important Terms

Resolution: Smallest analog incrementcorresponding to a 1 LSB change in conversion

Voltage Reference: the voltage against which

the input is compared, taken as the full scalevoltage

Conversion Time: Time required for a completemeasurement

Number of Bits: Number of bits used to digitallyencode the measured signal


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Calculations

Analog Input = K X Digital Output

12

n

fsAKResolution =

Afs: Analog full scalevoltage

n: Number of bits

Digital Output = Analog Input / K

Number of voltage levels = 2n

Number of voltage steps = 2n -1


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Example

A 10 bit ADC is used to sample over therange 0 to 5 Volts (VREF+ = 5V, VREF-=0V)

What is the step size?

5/ (210-1)= 4.89mV/step

How would 2.1V be encoded?(2.1/4.89mV) = 429 (Binary: 0110101101)

What voltage would correspond to 321being returned by the ADC?(321) x 4.89mV = 1.57V


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Example

A 8 bit ADC is used to sample over the range 0 to 2Volts (VREF+ = 2V, VREF-=0V)

What is the step size?2/ (28 - 1)= 7.84mV/step

How would 0.5V be encoded?0.5/7.84mV = 64 (Binary: 01000000) How would 0.75V be encoded?

0.75/7.84mV = 96 (Binary: 01100000)

How would 2V be encoded?

2/7.84mV = 255 (Binary: 11111111) What voltage would a code of 5 belong to?

5 x 7.84mV = 39mV

What voltage would a code of 190 belong to?190 x 7.84mV = 1.49V


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Nyquist Frequency

Goal of ADC: Get the digital representation asclose to analog as possible

In order to avoid loss of information, data needs

to be sampled at least twice its highestfrequency component

Eg. If you are sampling a 5kHz signal, yoursampling frequency (FS) should be at least

10kHz This minimum sampling frequency is called the

Nyquist Frequency (after Harry Nyquist)


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Different Sampling Frequencies

Period = 200msFin = 5kHz

Undersampled:(5kHz)

Digitised frequency

is 0Hz (flat line)

Undersampled:(7.5kHz)

Digitised frequencyis 2.5kHz (Alias =10kHz 7.5kHz)


Period = 400ms

Fdig = 2.5kHz


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Different Sampling Frequencies

Nyquist Sampled(10kHz)

Digitised frequency

is 5kHz (the correctinput frequency)

Oversampled:(20kHz)

Digitised frequencyis 5kHz (Correctinput frequency)


Period = 200msFdig = 5kHz


Period = 200msFdig = 5kHz


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Nyquist Summary

To digitise signals accurately, the samplingfrequency (FS) must be at least twice themaximum frequency in the input (FIN(MAX))

)(2 MAXINS FF


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Types of ADCs

Flash

Ramp-Compare (Integrating)

Successive Approximation Sigma-Delta


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Flash ADC

Flash ADC (AKA Direct orParallel ADC) uses alinear ladder ofcomparators to compare

many different voltagereferences at the sametime

Very fast -> HighBandwidth

Requires manycomparators

Therefore typically lowresolution

v

v

v

v

v

v

v

k

k

v 10

7

10


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Ramp-Compare (Integrating) ADC

A comparison voltageVAX is ramped up

When the comparison

voltage matches thesampled voltage (VA)the comparator istriggered the

sampled voltage hasbeen determined


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Two differentimplementations:

Timing of a charging

capacitor Driving a DAC with a

counter


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Variable Conversion Time(depends when rampsignal matches actualsignal)

Best case = 1 cycle Worst case = 2n cycles Average conversion time:

2n/2 Cycles, where n isthe number of bits

Slower than Flash, butmuch less comparatorsallows for higheraccuracy


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Successive Approximation ADC

SuccessiveApproximation ADCs usea binary search toconverge on the closestquantisation level

Binary search uses adivide and conqueralgorithm

Binary search: Select middle element

If too high select middleelement of lower group

If too low select middleelement of upper group

Repeat until 1 elementremains


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Successive Approximation ADC

Slower than Flash,but far fewercomparators allows

for higher accuracy Constant conversion

time: n cycles

Each cycle allows thenext MSB to bedetermined

4 Bit SAC

Bit3

=

1

Bit2

=

0

Bit1

=

1

Bit0

=

0


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Sigma-Delta ADC

Sigma-Delta ADCs use a 1-Bit ADC with some complex digitalprocessing to increase the resolution

By oversampling a signal we can increase the resolution

Oversampling a signal by a factor of 4 (4 x Fs) increases the SNR by6dB = 1 extra bit of resolution.

By performing noise shaping, (shifting the noise away from the signalbefore filtering it out),

First order: Doubling of sampling rate = 9dB increase for SNR

Second order: Doubling of sampling rate = 15dB increase for SNR


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Sigma-Delta ADC

Difference amp used to compare signal input withfeedback from 1-bit DAC (which is simply high or low)

Integrator performs noise shaping to improve SNR

Comparator gives 0 or 1where the density of 1srepresents the analog voltage (lots of 1s over aspecified time interval corresponds to a higher voltage)

Adding 1s up over time interval gives conversion value


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Summary

Analog to Digital converters allow digitalelectronics to sample real world analogsignals

Nyquist rate specifies that sampling ratemust be at least twice the maximumfrequency of signal being sampled

Depending on the resolution andbandwidth requirements different methodsof performing ADC can be used

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Ele2mdd Lect 13 - Adc