Download Lecture 8

Introduction to D/A
and A/D conversion
Professor: Dr. Miguel Alonso Jr.
Outline
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Analog to Digital Conversion Process
Sampling – lowpass and bandpass signals
Uniform and non-uniform quantization and
encoding
Oversampling in A/D
D/A conversion: signal recovery
The DAC
Oversampling in D/A conversion
Analog to digital conversion
process
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Most signals in nature are in analog form
In order for transmission through a digital
communication system, they must be
sampled
Untill now we have seen, PAM, PWM, PPM,
and DM
DM was the first step towards representing
the amplitude of the analog signal ( the
intelligence or message we are trying to
send) into a binary number for transmission
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Steps for A/D conversion are
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Bandlimit the signal: anti-aliasing low-pass filter
Sample the analog signal into a discrete-time and
continuous amplitude signal
Convert the amplitude of each signal sample into
one of 2B levels, where B is the number of bits used
to represent a sample in the ADC
The discrete amplitude levels are represented or
encoded into distinct binary words each of length B
bits
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Analog input signal – continuous in time and amplitude
Sampled Signal – continuos in amplitude, but only defined at
discrete points in time. Thus, the signal is zero except at time t=nT (
where T is the sampling period and n is the sample number
Digital signal – signal exists only at discrete points in time and at
each time point, can only have one of 2B values. Discrete time and
discrete amplitude
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The discrete-time signal and the digital signal
can each be represented as a sequence of
numbers, x(nT), or simply x(n) where
n=0,1,2,3,4…
Sampling- lowpass and
bandpass
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The sampling theorem: if the highest
frequency component in a signal is fmax,
then the signal should be sampled at a rate of
at least 2*fmax for the samples to describe
the signal completely
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Fs ≥ 2*fmax
Aliasing and spectra of
sampled signals
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Suppose a signal is sampled at a frequency
of 1/T hertz
There exists another frequency component
with the same set of samples as the original.
Thus, the frequency component can be
mistaken for the lower frequency component
This is aliasing
1
Message
Aliased Sample
0.5
Aliased Signal
0
-0.5
-1
0
0.5
1
1.5
2
2.5
3
3.5
4
0
0.5
1
1.5
2
2.5
3
3.5
4
1
0.8
0.6
0.4
0.2
0
Anti-aliasing filtering
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To reduce the effects of aliasing, sharp cutoff
anti-aliasing filters are used to bandlimit the
signal
Or, the sampling frequency is increased
Ideally, the AA filter should remove all
frequency components above the fold over
frequency
Practical filters: stop band attenuation is
given by Amin = 20 log (sqrt(1.5) * 2B)
Where B is the number of bits in the A/D
Key Equations for A/D
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Amplitude response of a butterworth filter:
H( f ) 
1

 f 
1  
 f 


c 


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



1
2
where N is the filter order
RMS of the input: A/sqrt(2)
Quantization Step Size: q = 2*A / 2B - 1≈ 2*A / 2B
RMS quantization noise: q/(2*sqrt(3))
fs ≥ 2*fmax from computed from the minimum
attenuation level
Example Problem:
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2N
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A to D system with
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3rd Order butterworth AA filter
12-bit ADC with sample and hold
Find:
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the minimum stop band attenuation, Amin, for the AA
filter
Minimum sampling frequency Fs
Types of A/D chips