Lecture-10: ADC and DAC

50 Pages·2013·0.74 MB·English

by  Sudhamsh Reddy

The University of Texas at Arlington
Lecture 10
ADC and DAC
CSE 3442/5442
Measuring Physical Quantities
•  (Digital) computers use discrete values, and use
these to emulate continuous values if needed.
•  In the physical world most everything is
continuous (analog), e.g., temperature,
pressure, acceleration, location, etc.
•  We can measure many physical quantities but to
use them in circuits we need transducers (some
physical quantity is converted into a electric
quantity).
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Sensors and Transducers
•  “Transducer” – often used
interchangeably with “sensor”
•  Many sensors are actually a type of
transducer.
•  Transducers are devices that convert one
form of energy into another. They include
both actuators and a subset of the various
types of sensors.
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Sensors with Analog Outputs
•  Many sensors output analog (only) signals
where output is proportional to some kind of
measured physical quantity (temperature,
acceleration, etc.)
•  Accuracy or precision of a sensor determines
how close the measured (and output) value is to
the real value. (What is the smallest unit that
makes a difference in the measurement).
•  Dynamic range: what is the relation of the full-
scale value to the minimally detectable signal
variation.
•  In order to use the outputs of analog sensors in
calculations, their outputs have to be digitized.
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A/D Conversion
•  The process of A/D conversion involves:
–  Band-limiting the analog signal
–  Setting periodic sampling points (setting a
sampling period) at which the continuous time
analog signal is going to be digitized.
–  Freezing the analog signal at the sampling
points so that the signal does not change for
the duration of conversion (sample and hold)
–  Determining what digital value best represents
the analog signal level (quantizing).
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Limiting Bandwidth of Signal
•  Real life physical quantities can change extremely rapidly (i.e.,
continuously), i.e., being capable of an immediate change and thus
having an infinite frequency band.
•  Sensors measuring these quantities (as they have to deal with
mechanical and electrical inertia of their measuring ways) usually
reduce that bandwidth significantly (i.e., if they reduce it to a
100kHz, that means that they could not pick up a sudden 1ns flip-
flop of the real value).
•  In most cases sensor’s bandwidths are orders of magnitudes above
what we are interested in (e.g., temperature changes, we do not
really care about sub second changes).
•  In order to ignore sudden changes (and so that they do not
negatively influence our ADC) we need to limit the bandwidth of the
signal (smooth it out) based on our frequency resolution needs.
•  Usually, analog low-pass filters (many cases with simple sensors –
simple R/C circuitry) is used.
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Periodic Sampling
•  Now that we have limited the bandwidth of the
signal, we need to sample it.
•  The Nyquist/Shannon theorems say that you
need to sample the signal at least at twice the
maximum frequency contained in the signal.
(E.g., if you limited your signal to a max
frequency of 10Hz, You should sample it at least
at 20Hz, i.e., 20 times a second).
•  In many cases though we start from the
sampling frequency and having a good
understanding of that we limit the signal to at
most half of that.
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Example: Output of a Sensor
Continuous-Time Signal; x(t) = cos(10t) + cos(25t)
2
1.5
1
0.5
e
d
u
plit 0
m
A
-0.5
-1
-1.5
-2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time (s)
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This is the superposition of two sine signals (two frequencies present)
Example: Output of a Sensor (cont’d)
•  Y(t) = cos(10t+0)+cos(25t+0)
•  Thus, two frequencies one with
Continuous-Time Signal; x(t) = cos(10t) + cos(25t)
ω =10 and the other with 2
1
ω =25 1.5
2
•  This means f =10/(2π), f =25/ 1
1 2
(2π)
0.5
•  f2 is higher (~4Hz) plitude 0
m
A
•  Thus, to be able to reconstruct
-0.5
the signal (without loosing any
-1
of its features) we need to
sample at least 8 times a -1.5
second (8Hz).
-2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time (s)
•  So, what happens if we over-
or under-sample?
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Example: Oversampling
•  If original signal was
indeed nicely limited, Sampled Version of x(t) with T = 0.05 s
s
2
oversampling will result
in more samples than
1.5
we need for processing
and reconstruction (i.e.,
1
burden on our
calculations/ processor 0.5
time)
e
d
u
•  Shown here is 20 mplit 0
A
samples per second (a
-0.5
sampling clock of 20Hz)
-1
-1.5
-2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time (s) 10