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What is ADC ?

Analog to Digital Converter

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What is ADC ?

• Definition

• Examples of use• Conversion process

•  Accuracy

What is ADC ?

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• Most signals we want to process are analog

• i.e.: they are continuous and can take an

inifinity of values

x(t)

t

What is ADC ?

Definition

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• Digital systems require discrete digital data

•  ADC converts an analog information into a

digital information

Digital System? Analog Digital

What is ADC ?

Definition

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• Voltmeter

What is ADC ?

Examples of use

• Cell phone (microphone) 

ΔV 7.77 V 

Wave

Voice

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3 steps:

• Sampling

• Quantification

• Coding

These operations are all performed in a sameelement: the A to D Converter 

What is ADC ?

Conversion process

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xs(t=k*Ts)

• Digital system works with discrete states

• The signal is only defined at determinedtimes

• The sampling times are proportional to thesampling period (Ts)

x(t)

Ts

What is ADC ?

Conversion process: Sampling

x(t)

tTs 

xs(t)

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• sampling process is performed by measuring the

continuous signal's value every T units of time (or

space), which is called the sampling interval .

Sampling results in a sequence of numbers,

called samples, to represent the original signal.Each sample value is associated with the instant in

time when it was measured. The reciprocal of the

sampling interval (1/T ) is the sampling

frequency denoted f s

, which is measured in

samples per unit of time. If T is expressed

in seconds, then  f s is expressed in hertz.

What is ADC ?

Nyquist-Shannon theorem: 

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The signal can only take determined valuesBelonging to a range of conversion (ΔVr)

• Based on number of bit combinations thatthe converter can output

• Number of possible states:N=2n where n is number of bits

• Resolution: Q= ΔVr/N

What is ADC ?

Conversion process: Quantification

tTs 

xs(t)

 ΔVr Q

xq(t)

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•  Assigning a unique digital word to eachsample

• Matching the digital word to the input signalWhat is ADC ?

Conversion process: Coding

tT

s

 

 ΔVr Q

xq(t)

012

N-1N-2

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The accuracy of an ADC can be improved by

increasing:

• The sampling rate (Ts)• The resolution (Q)

What is ADC ?

Accuracy

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t

Ts 

Q

xq(t)

What is ADC ?

Accuracy

tTs 

xq(t)

Higher Sampling rate

t

Q

xq(t)

Higher Resolution

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What is ADC ?

Sampling rate

Nyquist-Shannon theorem: Minimum

sampling rate should be at least twice the

highest data frequency of the analog signal

fs>2*fmax

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What is ADC ?

Sampling rate

• Analog signals are composed of an infinity of 

harmonics

•Need to limit the frequency band to its useful part

•Use of an analog filter 

ADC Analog Digital AnalogAnalogFilter

In practice: f s ≈ (3…5)*f filter 

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What is ADC ?

Example

• 8 bits converter: n=8

• Range of conversion: ΔVr=5V

• Sampling time: Ts=1ms

 Analog

0

5

0

255

Digital

• Number of possible states: N=28=256

• Resolution: Q= ΔVr/N=19.5 mV

• Analog Filter: f filter ≈ fs/5 = 200 Hz 

f Gain

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x(t) = Acos(t), A = 5V) 

What is ADC ?