Analogue Interfacing
What is a signal?
• Signal: Function of one or more independent
variable(s) such as space or time
• Examples include images and speech
Continuous vs. Discrete Time
• Continuous time signals
– Defined at all instances in time (or other
I.V.s)
– e.g. f(t) = sin(t)
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• Discrete time signals
– Defined only at a set of discrete (possibly
infinite in number) times
– Time sequence {x[n], n = 0,±1,±2, ….}
– e.g. x[n] = sin(2πn/N), n integer
– Not the same as digital which is discrete in
the dependent variable as well
• e.g. a sampled continuous time signal with
analog digital converter
• Signal level (voltage) represented by a binary
number with limited precision (8, 10, 12, or 16bit fixed point number)
– Often x[n] is a sampled version of x(t) at
rate 1/TS (uniform spacing)
x[n] = x(nTS), n = 0,±1,±2, …
The world is analogue
• One of the key functions of many
embedded systems is to control and
react to events in the real world
• In digital systems we deal entirely with
discrete signals
• The real world is temporally continuous
and analogue
• Signals are not electronic: heat,
pressure, light, ….
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• Need to
– Convert signals of interest into electrical
form suitable for electronic processing
(sensing and transduction)
– Perform ‘signal conditioning’ to amplify,
filter and otherwise transform analogue
signals
– Convert continuous-time, analogue signals
to discrete-time sequence of binary
numbers (or other digital form)
– Process the discrete signals, need to retain
the relationship with physical properties
– Convert and digital outputs to analogue
signals. May need to filter and condition.
– Convert electrical signals to heat, light,
motion, pressure … as appropriate
(transduction, actuation)
Physical
Signal
Sensing/
Transduction
Signal
Conditioning
ADC
Processing
DAC
Physical
Signal
Actuation/
Display
Filtering/
Conditioning
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Sensors and transduction
Sensors
• Many sensors exist to convert a wide
range of analogue signals to electronic
form
– Temperature
– Pressure
– Speed or Displacement
– Acceleration
– Acidity
– Many others
Example: Optical Encoder
From www.usdigital.com
4
Ex: Analog Devices ADXRS300
Gyroscopic Sensor
From www.analogdevices.com
Ex: Linear Variable Differential
Transformer
From www.analogdevices.com
5
Example: Thermocouple
• Seebeck Effect: junction between two
dissimilar metals creates temperature
dependent voltage
• Basis for thermocouple, a common
temperature sensor widely used in process
control
http://www.picotech.com/applications/thermocouple.html
• Typically convert signal of interest to
analogue electrical signal
– Voltage or current varies monotonically
with physical signal of interest
– Need to calibrate, amplify and filter …
Signal Conditioning
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Signal Conditioning
• Amplification and level shifting
– Convert the range and mean value (offset)
of a signal to fit the range of the analogue
to digital converter
– Amplify
– Attenuate
– Level shift
• Filtering
– Remove unwanted frequency components
in a signal (noise, interference …)
– Shape signal to account for effects of
signal transduction and transmission
(equalisation)
– Many filtering operations can be performed
after conversion to digital form; some
cannot (antialias filtering)
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• Linearisation, calibration
– Many sensors have nonlinear relationships
between the physical signal and its
electrical analogue
– Can be calibrated before (analogue) or
after (digital) analogue to digital conversion
– Calibration before conversion allows faster
processing; After is more precise, flexible
and reconfigurable
Inverting
Non-Inverting
Figures from Sedra and Smith
Filter
Differential Amplifier
Buffer
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Analogue to Digital
Conversion
Analogue-Digital Conversion
• Convert voltage (analogue signal) to
time series of digital numbers
• Key considerations include resolution,
dynamic range, sampling frequency and
accuracy
• 8, 10, 12, 16-bit ADCs are common,
higher resolutions available
• Acronyms ADC, A/D, ATD
• Typically, analogue signal is sampled by
analogue sample and hold circuit
– Maintains a stable signal to convert
• HCS12 has two built-in 8/10-bit
analogue-digital converters
– 8 channels can share each converter in
time-multiplexed manner
– Interrupt-based interface possible
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Quantization Error
• Representation as digital number
– Digital signal can only change as fast as
least significant bit
– Changes are quantized to increments of
the digital number. 12-bit ADC with linear
mapping, each increment is 1/4096 of fullscale
– Causes numerical error between the true
value and the digital representation (error
range 0-1 LSB or +/-0.5 LSB)
Sampling Error
• Sampling interval is a key consideration
– Limits temporal resolution
– Mean latency of 1/2 sample period from
sampling alone
• Irregular sampling can cause distortion
of the sampled signal
• Sampling rate should be controlled
through timer circuitry
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Effects of Irregular Sampling
12
10
8
6
4
2
0
0
2
4
6
8
10
12
12
10
8
6
True Analogue
Delayed Analogue
Irregular Digital
4
2
0
0
2
4
6
8
10
12
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• Temporal resolution
limited by sampling rate
• Can up-sample to
interpolate missing
samples
– Makes assumptions about
signal
From Catsoulis
Aliasing
• Periodicity
– Periodic signals repeat regularly
x(t ) = x(t + T )
for some T and all t, fundamental period is
the smallest such T ,
– e.g.
x(t ) = sin(t ) = sin(t + 2π ) = sin(t + 4π )
is periodic with period 2π
• Fourier theory states that we can
compose arbitrary signals by combining
sinusoids
– Periodic signals with Fourier Series
– Aperiodic signals with Fourier Transform
• But cannot represent all frequencies in
an analogue signal in a sampled digital
signal
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if f 0 = 1 2 , period N = 2, ω 0 = 2πf 0
then if x[n] = cos(nω 0 )
x[0] = 1
x[1] = -1
x[2] = 1
Alternates sign every discrete interval, obviously fastest
alternation possible
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e.g. ω 0 = π , period N = 0.8
2
then if x[n] = cos(nω 0 )
x[0] = 1
x[1] = 0
x[2] = −1
x[3] = 0
x[4] = 1
• looks like ω0 = 2π/5 or N =5
• when one frequency is indistinguishable
from another it is known as aliasing
Nyquist Rate
• To be able to reconstruct a signal from
a sampled digital signal unambiguously
– Need to sample at least twice the highest
frequency in the signal
– Or need to limit the highest frequency in
the signal to less than one half the
sampling rate (anti-aliasing filter)
• Theoretical limitations, practically need
to sample faster than Nyquist rate
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• Anti-aliasing filtering needs to be done
before sampling
Flash Converters
• In parallel, compare
with voltage levels
corresponding to all
possible digital
numbers
• Priority encoder
chooses largest
digital number less
than input
• Very fast but
expensive in
circuitry (e.g. 1024
comparators for 10bit ADC)
• Can implement
nonlinear converters
easily
www.allaboutcircuits.com
14
Successive Approximation
• Based on
comparison with
input
– Successively count
up or down ADC
digital number
– When digital number
equals input,
conversion is done
from www.allaboutcircuits.com
Successive Approximation
• Special counter: count first by mostsignificant bit and work to leastsignificant bit. Faster than standard
count
Example 10-bit Successive
Approximation Converter
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• Successive approximation converters
are typically slower than flash since they
convert over multiple cycles
• Can compromise and estimate several
bits at each cycle (pipelined converter)
http://www.analog.com/library/analogDialogue/archives/33-08/adc/index.html
Sigma-Delta
• A ‘1-bit’ DAC suitable for high
resolution, low measurement rate
applications
http://www.analog.com/library/analogDialogue/archives/33-08/adc/index.html
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Image acquisition
• Analogue signals are not only 1-D, for
example images acquired by a CCD
array are analogue
Representation of analogue
signals
Engineering Units and Fixed
Point Representations
• Physical signal expressed in standard
unit: Watts, cd/m2, N, …
• Converted to voltage which is
represented by a digital number (e.g. 0255 for 8-bit converter)
• Often more useful to work in
‘engineering units’ that represent
physical units
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• Could represent as a floating point
number with floating point support
– Slow in software
– Additional circuitry for hardware support in
custom processor
– Hardware support may not be available or
economical on chosen processor
• One can consider the digital number as
a fixed point representation
– Can define the decimal point at any
convenient bit position
– After bit zero gives standard integer
representation
– Setting before most significant bit gives
range 0 to 1 (actually one step less than
one)
Codecs
• Stands for coder/decoder
– Where paired coding and decoding of
signals (eg ADC and DAC) occurs the
device is called a codec
– Many different ways of mapping the signal
to the code
• Linear
• Logarithmic
• Differential pulse coded
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Digital to Analogue
Conversion
Digital to analogue conversion
• One approach: Sum up contribution of
each bit set in digital number
• Weight each bit according to its place 1, 2, 4, 8
http://www.allaboutcircuits.com
• This converts to analogue voltages but
still need to handle time discretisation
• Zero-order hold: output is staircase like,
switching at each sample
• Can filter to remove components above
Nyquist rate and recover signal
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PWM
• Pulse width modulation (PWM) can
support a form of analogue output
interfacing
• Control the duty cycle of a periodic
binary signal
• If signal has high frequency, filtering
with external filter or by a ‘slow’ output
device (e.g. an electric motor) can
remove the high frequency switching
• Leaves lower frequency signal
– voltage is average over the cycle
– Variations in filtered signal reflect
variations in duty cycle
From Heath, 2003
Actuators, Motors and
Displays
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Interfacing with Actuators and
Switching Power
• Switching large loads requires special
interacing and protection circuitry
• Many options exist for switching/
controlling devices requiring large
amounts of power; choice depends on
– Level and type of control desired
– Type of load
– Requirements for protection, isolation, EMC
…
H Bridge circuits
From Heath, 2003
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