adc lecture csitus
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7/30/2019 ADC Lecture Csitus
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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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