8 signal processing

7/27/2019 8 Signal Processing ...

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Electronic InstrumentationLecturer Touseef Yaqoob 1

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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Electronic Instrumentation

Lecturer Touseef Yaqoob

14

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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15

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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23

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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Electronic Instrumentation 51

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.

8 signal processing

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