Measurement Noise & Signal Processing
5.3 Introduction to signal processing
This Signal processing aims at improving the quality of the reading
or signal at the output of a measurement system.
It also aims to attenuate any noise in the measurement signal that
has not been eliminated (due to design limitation) of the
measurement system. However, signal processing performs many
other functions apart from dealing with noise.
The exact procedures that are applied depend on the nature of
the raw output signal from a measurement transducer.
Procedures of signal filtering, signal amplification, signal
attenuation, signal linearization and bias removal are applied
according to the form of correction required in the raw signal.
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5.3 Introduction to signal processing. …
Traditionally, signal processing has been carried out by analogue
techniques in the past, using various types of electronic circuit. Recent
trend is to go for digital signal processing, using software modules to
condition the input measurement data.
Digital signal processing is inherently more accurate than analogue
techniques, but this advantage is greatly reduced in the case of
measurements coming from analogue sensors and transducers.
Because an analogue-to-digital conversion stage is necessary before
the digital processing can be applied, thereby introducing conversion
errors.
Analogue processing remains the faster of the two, in spite of recent
advances in the speed of digital signal processing. Some preliminary
analogue processing is often carried out even when the major part of the
processing is carried out digitally.
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Early operational amplifiers were used primarily to perform
mathematical operations such as addition, subtraction, integration and
differentiation- hence the term operational.
Early operational amplifiers were constructed with vacuum tubes and
worked with high voltages. Today’s op-amps are linear integrated circuits
(IC’s) that use relatively low dc voltages and are reliable and inexpensive.
Symbol and terminals
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The Ideal Op-Amp
-It has infinite voltage gain.
-It has infinite input impedance (open), so that it does not load the
driving source.
-It has zero output impedance.
-The input voltage Vin appears between the two input terminals and the
output voltage is Av Vin.
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The Practical Op-Amp
Although modern integrated circuit op-amps approach parameter
values that can be treated as ideal in many cases, the ideal device can
never be made.
Op amps have both voltage and current limitations
-It has very high voltage gain.
-It has very high input impedance.
-It has very low output impedance.
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The Differential Amplifier
The op-amp in its basic form typically consists of two or more
differential amplifiers stages. Because the differential amplifier (diff-amp) is
fundamental to the op-amp’s internal operation, it is useful to have a basic
understanding of this type of circuit.
A basic differential amplifier circuit and its symbol are shown in the
figure below
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The Differential Amplifier
The diff amp stages that make up part of the op-amp provide high
voltage gain and common mode rejection.
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Basic Operation
An op-amp typically has more than one differential amplifier stage, we
will use a single diff-amp stage to illustrate the basic operation.
First, when both inpts are grounded (0 V), the emitters are at -0.7 V
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Basic Operation
It is assumed that the transistors
are identically matched by careful
process control during manufacturing
so that their dc emitter currents are
at the same level, when there is no
input signal.
IE1 = IE2
Since both the emitter currents
combine through RE,
IE1 = IE2 = IRe/2
Where
IRe = VE- VEE/RE
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Basic Operation
Based on the approximation that
IC~= IE , it can be stated that
IC1= IC2 ~= IRe/2
Since both the collector currents
and both collector resistors are equal
(when the input voltage is zero).
VC1 = VC2 = VCC - ICRC
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Basic Operation
Next, input 2 is left grounded and
a positive bias voltage is applied to
input 1 as shown in the fig.
The positive voltage on the base
Q1 increases IC1 and raises the emitter
voltage to
VE = VB – 0.7
This action reduces the forward
bias (VBE) of Q2 because its base is
held at 0 V (ground), thus causing IC2
to decrease as indicated in part(b) of
the diagram.
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Basic Operation
The net result is that IC1 causes a
decrease in VC1 and decrease in IC2
causes an increase in VC2.
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Basic Operation
Finally, input 1 is grounded and a
positive bias voltage is applied to
input 2.
The positive bias voltage causes
Q2 to conduct more, thus increasing
IC2.
Coincidently, the rise in emitter
voltage causes forward bias of Q1 to
decrease and causes IC1 to decrease.
VC1
And conversely, decrease VC2 and
to increase.
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Modes of Signal Operation
Single-Ended Input
When a diff-amp is operated in
this mode. one input is grounded and
the signal voltage is applied only to
the other input as shown in Figure.
In the case where the
voltage is applied to input 1
part, an inverted, amplified
voltage appears at output
shown.
signal
as in
signal
1 as
Also, a signal voltage appears in
phase at the emitter of Q1 Since the
emitters of Q1 and Q2 are common.
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Modes of Signal Operation
The emitter signal becomes an
input to Q2 which functions as a
common-base amplifier. The signal is
amplified by Q2
and appears, non-inverted, at
output 2.
.
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Modes of Signal Operation
Differential Input
In this mode, two oppositepolarity (out-of-phase) signals are
applied to the inputs, as shown in
Figure. This type of operation is also
referred to as double-ended.
Figure (b) shows the output
signals due to the signal on input I
acting alone as a single-ended input.
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Modes of Signal Operation
Figure (c) shows the output
signals due to the signal on input 2
acting alone as a single-ended input.
Notice in parts (b) and (c) that
the signals on output I are of the
same polarity. The same is also true
for output 2. By superimposing both
output 1 signals and both output 2
signals.
we get the total differential
operation. as pictured in (d)
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Modes of Signal Operation
Figure (c) shows the output
signals due to the signal on input 2
acting alone as a single-ended input.
Notice in parts (b) and (c) that
the signals on output I are of the
same polarity. The same is also true
for output 2. By superimposing both
output 1 signals and both output 2
signals.
we get the total differential
operation. as pictured in (d)
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Modes of Signal Operation
Common mode input
One of the most important
aspects of the operation of a diff-amp
can be seen by considering the
common-mode condition where two
signal voltages of the same phase,
frequency, and amplitude are applied
to the two inputs, as shown in Figure
(a).
Again, by considering each input
signal as acting alone, the basic
operation can be understood.
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Modes of Signal Operation
Figure(b) shows the output
signals due to the signal on only input
1,
Figure(c) shows the output
signals due to the signal on only input
2.
Notice that the corresponding
signals on output I are of the
opposite polarity and so are the ones
on output 2.
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Modes of Signal Operation
When the input signals are
applied to both inputs. the outputs
are superimposed and they cancel,
resulting in a zero output voltage, as
shown in Figure (d).
This action is called commonmode rejection. Its importance lies in
the situation where an unwanted
signal appears commonly on both
diff-amp inputs.
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Modes of Signal Operation
Common-mode rejection means
that this unwanted signal will not
appear on the outputs and distort the
desired signal.
Common-mode signals (noise)
generally are the result of the pick-up
of radiated energy on the input lines
from adjacent lines, the 60 Hz power
line, or other sources.
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Common Mode Rejection Ratio
Un-wanted signals (noise) appearing with the same polarity on both
input lines are essentially cancelled by the diff-amp and do not appear on
the outputs. The measure of an amplifier's ability to reject commonmode signals is a parameter called
the common-mode rejection ratio (CMRR).
Ideally, a diff-amp provides a very high gain for desired signals
(single-ended or differential) and zero gain for common-mode signals.
Practical diff-amps has a very small common-mode gain (usually
much less than 1), while providing a high differential voltage gain
(usually several thousand).
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Common Mode Rejection Ratio
The higher the differential gain with respect to the common-mode
gain, the better the performance of the diff-amp in terms of rejection of
common-mode signals.
This suggests that a good measure of the diff-amp's performance in
rejecting unwanted common-mode signals is the ratio of the differential
voltage gain Av(d) to the common-mode gain, Acm. This ratio is the
common-mode rejection ratio, CMRR.
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Common Mode Rejection Ratio
A very high value of CMRR means that the differential gain Av(d) is
high and the common-mode gain Acm is low.
The CMRR is often expressed in decibels (dB) as
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A Simple Op-Amp Arrangement
The figure shows two differential
amplifier stages and an emitter follower
connected to form a simple op-amp.
The first stage can be used with a
single ended or a differential input.
The differential outputs of the first
stage are directly coupled into the
differential inputs of the second stage.
The output of the second stage is
single ended to drive an emitter follower
to achieve a low output impedance.
Both diff. stages provide a high
voltage gain and a high CMRR.
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Emitter Follower
In order to fully appreciate an omamp. We have to have a clear
understanding of an emitter follower.
When the output is taken from the
emitter terminal of the transistor. The
configuration is known as emitter follower
configuration as shown in the figure.
The output voltage is always slightly
less than 1 due to the drop from base to
emitter.
The gain Av ~=1
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Emitter Follower
Unlike the collector voltage, the
emitter voltage is in phase with the signal
V i.
The fact that Vo “follows” the
magnitude of Vi with an in-phase
relationship accounts for the terminology
emitter-follower.
The figure shows the most common
emitter-follower configuration. This is also
known as common collector configuration.
Substituting the re equivalent circuit
into the network will result in the network.
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Emitter Follower
Substituting the re equivalent circuit
into the network will result in the network.
Zi, the input impedance will result in
With
or
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Emitter Follower
And
Zo: The output impedance is best
described by first writing the equation for
the current Ib:
And then multiplying with (β+1) o
establish Ie. That is,
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Emitter Follower
Substituting for Zb gives
Constructing the network for the equation,
will result in
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Emitter Follower
Since RE is typically much greater than
re, the following approx. is often applied
Av, voltage gain can be determined
using the voltage divider rule
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Emitter Follower
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Op-Amp parameters
Input offset voltage
Ideal op-amp produces zero volts out for zero volts in.
Practical op-amp has a small dc voltage, VOUT(error) when no
differential input voltage is applied.
Its primary cause is a slight mismatch of the base-emitter voltages
of the differential input stage of an op-amp.
the output voltage of the differential input stage is expressed as
VOUT = IC2RC – IC1RC
In data sheet, the input offset voltage, VOS, is the differential dc
voltage required between the inputs to force the differential output to
zero. Typical values are in the range of 2 mV or less.
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Op-Amp parameters
Input offset voltage drift with temperature
The input offset voltage drift is a parameter related to VOS that
specifies how much change occurs in the input offset voltage for each
degree change in temperature.
Typical values range from 5μV per ⁰C to about 50μV per ⁰C.
Usually an op-amp with a higher nominal value of input offset voltage
exhibits a higher drift.
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Op-Amp parameters
Input Bias Current
The input terminals of a bipolar differential amplifier are the
transistor bases, therefore, the input currents are the base currents.
The input bias current is the dc current required by the inputs of
the amplifier to properly operate the first stage.
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Op-Amp parameters
Input Impedance
There are two basic ways of specifying the input impedance of an
op-amp. They are the differential and the common mode.
The differential input impedance is the total resistance between the
inverting and non-inverting inputs.
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Op-Amp parameters
Input Impedance
There are two basic ways of specifying the input impedance of an
op-amp. They are the differential and the common mode.
The common mode input impedance is the resistance between each
input and ground.
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Op-Amp parameters
Input Offset current
Ideally the two input bias currents are equal, and thus their
difference is zero. In a practical op-amp, however, the bias currents are
not exactly equal.
The input offset current is the difference of the input bias currents,
expressed as an absolute value.
IOS = |I1-I2|
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Op-Amp parameters
Input Offset current
Actual magnitudes of offset are usually atleast ten times less than
the bias current.
High-gain, high input impedance amplifiers should as little IOS as
possible, the difference in currents through large input resistances
develops a substantial offset voltage.
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Op-Amp parameters
Input Offset current
The offset voltage developed by the input offset Current is
Vos = I1Rin - I2Rin = (I1 – I2)Rin
Vos = IosRin
The error created by los is amplified by the gain Av of the op-amp
and appears in the output as
VOUT(error) = AvIos Rin
A change in offset current with temperature affects the error
voltage. Values of temperature coefficient for the offset current in the
range of 0.5 nA per degree centigrade are common.
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Op-Amp
Negative Feedback
Negative feedback is one of the most useful concepts in electronics,
particularly in op-amp applications. Negative feedback is the process
whereby a portion of the output voltage of an amplifier is returned to
the input with a phase angle that opposes (or subtracts from) the input
signal.
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Op-Amp
Why use Negative Feedback?
◼
The open loop gain of a typical op-amp is very high (greater than
100,000), therefore, an extremely small input voltage drives the opamp into its saturated output states.
Even the input offset voltage of the op-amp can drive it into
saturation.
For example, assume VIN = 1 mV and Aol = 100,000. Then,
VinAol = (l mV)(100,000) = lOO V
Since the output level of an op-amp can never reach 100V, it is driven
into saturation and the output is limited to its max output levels.
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Op-Amp
Why use Negative Feedback?
◼
The usefulness of an op-amp is
severely restricted if it is without
negative feedback.
◼
With negative feedback, the closed
loop voltage gain (Acl) can be
reduced and controlled so that
op-amp can function as a linear amplifier.
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Op-Amp
Closed loop gain, Acl
The closed-loop voltage gain is the voltage gain of an op-amp with
external feedback. The amplifier configuration consists of the op-amp
and an external negative feedback circuit that connects the output to
the inverting input. The closed-loop voltage gain is determined by the
external component values and can be precisely controlled by them.
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Op-Amp
Non-inverting amplifier
An op-amp connected in a closed loop configuration is a noninverting amplifier with a controlled amount of voltage gain
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Op-Amp
Non-inverting amplifier
Ri and Rf form a voltage divider circuit which reduces Vout and
connects the reduced voltage Vf to the inverting input
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Op-Amp
Non-inverting amplifier
Therefore,
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Op-Amp
Non-inverting amplifier
Therefore,
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Op-Amp
Non-inverting amplifier
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Op-Amp
Voltage Follower
The voltage-follower configuration is a special case of the noninverting amplifier where all of the output voltage is fed back to the
inverting (-) input by a straight connection, as shown in Figure
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Op-Amp
Voltage Follower
As you can see, the straight feedback connection has a voltage
gain of 1 (which means there is no gain). The closed-loop voltage gain
of a noninverting amplifier is 1/B as previously derived. Since B = 1 for
a voltage-follower, the closed-loop voltage gain of the voltage-follower
is
Acl(VF) = I
It has very high input impedance and very low output impedance
making it an ideal buffer for interfacing high impedance sources and
low impedance loads.
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Op-Amp
Comparator
A comparator is a type of op-amp circuit that compares two input
voltages and produces an output in either of two states indicating the
greater than or less than relationship of the inputs.
One application of an op-amp used as a comparator is to determine
when an input voltage exceeds a certain level.
The Figure shows a zero-level detector.
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Op-Amp
Comparator
Notice that the inverting ( - ) input is grounded to produce a zero
level and that the input signal voltage is applied to the non-inverting
(+) input.
Because of the high open-loop voltage gain, a very small difference
voltage between the two inputs drives the amplifier into saturation,
causing the output voltage to go to its limit.
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