8 signal processing
TRANSCRIPT
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Signal Processing Manipulationand Transmission
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Signal Conditioning Circuits
Why do we need to do signal conditioning?
Well consider a sensor called a
thermocouple. A thermocouple is simply twodissimilar wires joined together at a point
called a junction. At the junction, a voltage
potential will form that is a function of the
temperature of the junction. As a result, thesesensors are frequently used in making digital
thermometers.
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The typical voltage level for the junction is onthe order of less than 10 millivolts. Clearly, thatsnot much! But think back to the lab where you
hooked a wire to an oscilloscope and observednoise from the florescent fixtures in lab. Youmay not have noticed the amplitude of thisnoise, but it can easily be on the order of 100 ormore millivolts. That means that signal noise, in
this example, is actually ten times greater thanthe signal itself!
How could we possibly measure the signal wewant (from the thermocouple) when we have ten-times more signal noise??
ANSWER: WE CANT!
So the key is to perform signal conditioning
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Signal amplifications
Signal amplification is carried out when thetypical signal level of a measurement transduceris considered to be too low.
Amplification by analog means is carried out by
an operational amplifier. Normally requires to have a high input
impedance so that loading effect on thetransducer output signal is minimized.
When amplifying the output signal fromaccelerometers and some optical detectors, theamplifier must have a high frequency response,to avoid distortion of the output reading.
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Instrumentation Amplifier
Some applications requiring the amplification
of very low-level signals, a special type of
amplifier known as an instrumentation
amplifier is used.
The first advantage is differential input
impedance is much higher.
Common mode rejection capability is muchbetter.
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Instrumentation Amplifier
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Signal attenuation
The progressive reduction in {amplitude} of a
signal as it travels farther from the point of
origin.
One method of attenuating signals by analog
means is to use a potentiometer connected in
a voltage-dividing circuit.
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Voltage divider circuit
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Signal linearization
The transfer function for many electronicdevices, which relates the input to output,contains a nonlinear factor. In most cases
this factor is small enough to be ignored.However, in some applications it must becompensated either in hardware or software.Thermocouples, for example, have a
nonlinear relationship from input temperatureto output voltage, severe enough to requirecompensation.
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Example
Light intensity transducers typically have anexponential relationship between the output andthe input light intensity.
V = K exp (-alpha Q)
If the diode is placed between the input andoutput terminals of the amplifier the relationshipis
V = C log (V1)
Now if the output of the light transducer isconditioned by an amplifier, the voltage level ofthe processed signal is given by
V = C log (K) alpha CQ
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Bias removal
Sometimes either because of the nature ofthe measurement transducer itself, or as aresult of the other signal conditioning
operations, a bias exists in the output signal. This can be expressed mathematically
Y = Kx + C
Analog processing consists of using anoperational amplifier connected in adifferential amplification mode.
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Filters - Introduction
Filters are circuits that are capable of passingsignals within a band of frequencies whilerejecting or blocking signals of frequenciesoutside this band. This property of filters is alsocalled frequency selectivity.
Filter circuits built using components such asresistors, capacitors and inductors only areknown as passive filters.
Active filters on the other hand often employtransistors or op-amps in addition to resistorsand capacitors
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Advantages of Active Filters over
Passive Filters
Active filters can be designed to provide
required gain, and hence no attenuation as
in the case of passive filters
No loading problem, because of high input
resistance and low output resistance of op-
amp.
Active Filters are cost effective as a widevariety of economical op-amps are
available.
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Basic Filter Responses
Low Pass Fi lter Character ist ics
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High Pass Fil ter Characterist ic s
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Band Pass Fil ter Characterist ics
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Band Reject Fil ter Characterist ic s
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Active filters
Active filters are mainly used incommunication and signal processing circuits.They are also employed in a wide range ofapplications such as entertainment, medicalelectronics, etc.
Most commonly used active filters:
Low pass filters
High pass filters
Band pass filters
Band reject filters
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Each of these filters can be built using op-ampas the active element and resistors andcapacitors as the passive elements (frequencyselective part). Better filter performance isobtained by employing op-amps with higherslew rates and higher gain-bandwidths.
The filtering behaviour of the circuit is bestrepresented by the frequency response
characteristics of the circuit, which shows thevariation of the filter circuit gain with respect tooperating frequency.
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Filter Design Criterion
Pass Band Gain
With active filters, it is possible to achieve a
pass band gain higher than 1. Most active filtersemploy an amplifier which determines the passband gain of the filter.
Filters with a flat pass-band gain are commonlyused, and such a response is provided byButterworth filters. An another class of filterscalled chebyshev filters, provide a ripple (orovershoots in) pass-band gain.
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Cut-of f Frequencies
The cut-off frequencies fH and fL are determined
by the component values of the capacitors andresistors in the filter circuit.
Roll-off Rate
Roll-off rate of a filter is the rate at which the
gain of the filter changes in the stop-band.
Higher the roll-off rate, better the frequency
selection! The roll-off rate is determined by the
order of the filter. For instance, a first order filter
gives 20 dB/decade roll off, whereas a second
order filter gives 40 dB/decade roll off.
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First Order Low Pass Filter
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Derivat ion o f Trans fer
Funct ion
The RC network behaves as a voltage divider supplied by vi, and
hence the voltage at the non-inverting terminal of the op-amp is
given as:
iC
C vjXR
jXv
Where
fC2j
1jXand1j C
fRC2j1
vv i
The eqn for v + then reduces to:
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Where,
We know that the output of an op-amp non-
inverting amplifier is given by:
vR
R1v
1
Fo
Substituting for v + from the previous equation,
i
1
Fo v
fRC2j1
1
R
R1v
HF
i
o
ffj1
A
v
v
RC2
1fH
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filtertheofgainband-passR
R1A
1
FF
signalinputtheoffrequencytheisf
fH = high cut-off frequency of the filter
The gain magnitude and phase angle eqns forthe filter can be obtained as
2H
F
i
o
ff1
A
v
v
H
1
f
ftanand
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The operation of the low-pass filter can be
verified from the gain magnitude equation:
F
i
o Av
v
1. At very low frequencies, that is f < fH,
FF
i
o A70702
A
v
v.
2. At cut-off frequency, that is f = fH,
F
i
o Av
v
3. At higher frequencies, that is f > fH,
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Roll-off Rate
From the gain magnitude equation, we seethat, if the frequency is increased 10 fold (1
decade), the voltage gain is divided by 10. Inother words the gain decreases 20 dB (= 20log 10) each time the frequency is increasedby 10. Hence the roll-off rate of the first order
filter in the stop band is 20 dB/decade. At cut-off frequency, fH, the gain falls by 3 dB
(= 20 log 0.707).
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Example: Design a first order low-pass filter with a cut-off
frequency at 1 KHz and pass-band gain of 2. Draw the frequency
response of the circuit.
.
Assume, C = 0.01 mF
KHz1RC21fH
K9215R .
To design for:1. fH = 1 KHz2. AF = 23. First order low-pass filter
1. From the specified cut-off frequency
F)10xHz)(0.01(102
1
Cf2
1R 63
H
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2. From the specified pass-band gain
2R
R1A
1
F
F
This implies, RF/R1= 1, or RF = R1
Assume, RF = R1 = 10K
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The designed low pass filter circuit is shown
in figure
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Second Order Filters
Second order filters provide 40 dB/decaderoll-off in the stop-band, and hence perform
better frequency selection than the first order
type.
With second order, and higher-order filters,
we can obtain interesting frequency
responses. Consider the two frequency
responses shown in figure
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Butterworth filters gives us a reasonably flat
gain in the pass-band, whereas the
chebyshev filters show a ripple or overshoot
in the frequency response. The trade-off isthat at the cut-off frequency, chebyshev filter
shows a higher roll-off rate.
These frequency response types aredetermined the damping factor of the filter
circuits.
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Damping Facto r
The damping factor (DF) of
an active filter circuit
determines which response
characteristics the filter
exhibits whether,
butterworth or chebyshev or
others.
The damping factor is
determined by the negative
feedback circuit and is
defined by the following
equation:
1
F
R
R2DF
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To achieve a second-order
butterworth response, for
example, the damping factor
must be 1.414. Therefore, to
implement this dampingfactor, the feedback resistor
ratio must be
41412DF2R
R
1
F.
Hence, for a second-order butterworthresponse, RF = 0.586R1
5860R
R
1
F.
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Signal manipulation
To complete the discussion on analog signal
processing techniques, mention must also be
made of certain other special purpose
devices and circuits used to manipulatesignals.
Voltage to current conversion
Current to voltage conversion Signal integration
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Signal manipulation (Continued)
Voltage follower (Pre-amplifier)
Voltage comparator
Signal addition Signal multiplication
Sample and hold circuits
Analog to digital conversion Digital to analog conversion
A l & di it l i l
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-0.2
-0.1
0
0.1
0.2
0.3
0 2 4 6 8 10sampling time, tk [ms]
Voltage
[V]
ts
-0.2
-0.1
0
0.1
0.2
0.3
0 2 4 6 8 10sampling time, tk [ms]
Voltage
[V]
ts
Analog & digital signals
Continuous function V ofcontinuous variable t (time,
space etc) : V(t).
Analog
Discrete function Vk ofdiscrete sampling variable tk,
with k = integer: Vk = V(tk).
Digital
-0.2
-0.1
0
0.1
0.2
0.3
0 2 4 6 8 10
time [ms]
Voltage
[V]
Uniform (periodic) sampling.Sampling frequency fS = 1/ tS
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Digital vs analog processingDigital Signal Processing (DSPing)
More flexible.
Often easier system upgrade.
Data easily stored.
Better control over accuracy
requirements.
Reproducibility.
Advantages
A/D & signal processors speed:
wide-band signals still difficult to
treat (real-time systems).
Finite word-length effect.
Obsolescence (analog
electronics has it, too!).
Limitations
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DSPing: aim & tools
Software Programming languages: Pascal, C / C++ ...
High level languages: Matlab, Mathcad, Mathematica
Dedicated tools (ex: filter design s/w packages).
Applications Predicting a systems output.
Implementing a certain processing task.
Studying a certain signal.
General purpose processors (GPP), m-controllers.
Digital Signal Processors (DSP).
Programmable logic ( PLD, FPGA ).
Hardware real-timeDSPing
Fast
Faster
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Digital system example
ms
V AN
ALOG
DO
MAIN
ms
VFilterAntialiasing
k
A DIGITAL
DOMAIN
A/D
k
A
DigitalProcessing
ms
V
ANALOG
DOMAIN
D/A
ms
V FilterReconstruction
Sometimes steps missing
- Filter + A/D
(ex: economics);
- D/A + filter
(ex: digital output wanted).
General scheme
Important
DigitalProcessing
FilterAntialiasing
A/D
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Digital system implementation
Sampling rate.
Pass / stop bands.
KEY DECISION POINTS:
Analysis bandwidth, Dynamic range
No. of bits. Parameters.
1
2
3
Digital
Processing
A/D
AntialiasingFilter
ANALOG INPUT
DIGITAL OUTPUT
Digital format.What to use for processing?
See slide DSPing aim & tools
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SamplingHow fast must we sample a continuous
signal to preserve its info content?
Ex: train wheels in a movie.
25 frames (=samples) per second.
Frequency misidentification due to low sampling frequency.
Train starts wheels go clockwise.
Train accelerates wheels go counter-clockwise.
Why?
*Sampling: independent variable (ex: time) continuous discrete.Quantisation: dependent variable (ex: voltage) continuous discrete.Here well talk about uniform sampling.
*
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Signal Transmission
There is a necessity in many measurement system totransmit measurement signals over quite large distancesfrom the point of measurement to the place where thesignals are recorded and/or used in a process controlsystem.
This creates Several problems for which a solution must befound
Difficulties associated with long distance signaltransmission include serious contamination of themeasurement signal by Noise
Radiated electromagnetic fields from electrical machineryand power cables, induced fields through wiring loops andspikes on the ac power supply
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Performance parameters
Signal amplification
Amplification of the signal prior to transmission is essentialif a reasonable signal-to-noise ratio is to be obtained aftertransmission.
ShieldingShielding provides a high degree of noise protection,especially against capacitive-induced noise due to proximityof signal wires to high current power conductors.
Current loop transmission
The signal attenuation effect of conductor resistance can beminimized if varying voltage signals are transmitted asvarying current signals.
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Voltage to frequency conversion
Better immunity to noise can be obtained in
signal transmission if the signal is transmitted in
a digital format. Fiber optic transmission
Noise corruption of signals is almost eliminated
by the use of fiber optic transmission cables, but
there is a cost penalty associated with thisbecause of the higher cost of the fiber optic
system.