ec2351 measurements and instrumentation

ec2351 measurements and instrumentation
FATIMA MICHAEL COLLEGE OF ENGINEERING & TECHNOLOGY
Senkottai Village, Madurai – Sivagangai Main Road,
Madurai -625 020
An ISO 9001:2008 Certified Institution
EC2351
MEASUREMENTS
AND
INSTRUMENTATION
Branch: ECE
Year & Semester: III & 6th
Name of the Staff: G.Sasi, ASP/ECE
1
Syllabus
EC2351 MEASUREMENTS AND INSTRUMENTATION
LTPC
3 0 0 3
UNIT I BASIC MEASUREMENT CONCEPTS
9
Measurement systems – Static and dynamic characteristics – units and standards of
measurements – error :- accuracy and precision, types, statistical analysis – moving coil,
moving iron meters – multimeters – Bridge measurements : – Maxwell, Hay, Schering,
Anderson and Wien bridge.
UNIT II BASIC ELECTRONIC MEASUREMENTS
9
Electronic multimeters – Cathode ray oscilloscopes – block schematic – applications –
special oscilloscopes :– delayed time base oscilloscopes, analog and digital storage
oscilloscope, sampling oscilloscope – Q meters – Vector meters – RF voltage and
power measurements – True RMS meters.
UNIT III SIGNAL GENERATORS AND ANALYZERS
9
Function generators – pulse and square wave generators, RF signal generators –
Sweep generators – Frequency synthesizer – wave analyzer – Harmonic distortion
analyzer – spectrum analyzer :- digital spectrum analyzer, Vector Network Analyzer –
Digital L,C,R measurements, Digital RLC meters.
UNIT IV DIGITAL INSTRUMENTS
9
Comparison of analog and digital techniques – digital voltmeter – multimeters –
frequency counters – measurement of frequency and time interval – extension of
frequency range – Automation in digital instruments, Automatic polarity indication,
automatic ranging, automatic zeroing, fully automatic digital instruments, Computer
controlled test systems, Virtual instruments.
UNIT V DATA ACQUISITION SYSTEMS AND FIBER OPTIC MEASUREMENT 9
Elements of a digital data acquisition system – interfacing of transducers – multiplexing –
data loggers –computer controlled instrumentation – IEEE 488 bus – fiber optic
measurements for power and system loss – optical time domains reflectometer.
TOTAL: 45 PERIODS
TEXT BOOKS
1. Albert D.Helfrick and William D.Cooper – Modern Electronic Instrumentation and
Measurement Techniques, Pearson / Prentice Hall of India, 2007.
2. Ernest O. Doebelin, Measurement Systems- Application and Design, TMH, 2007.
REFERENCES
1. Joseph J.Carr, Elements of Electronics Instrumentation and Measurement, Pearson
Education, 2003.
2. Alan. S. Morris, Principles of Measurements and Instrumentation, 2nd Edition,
Prentice Hall of India, 2003.
3. David A. Bell, Electronic Instrumentation and measurements, Prentice Hall of India
Pvt Ltd, 2003.
4. B.C. Nakra and K.K. Choudhry, Instrumentation, Meaurement and Analysis, 2nd
Edition, TMH, 2004.
5. James W. Dally, William F. Riley, Kenneth G. McConnell, Instrumentation for
Engineering Measurements, 2nd Edition, John Wiley, 2003.
2
UNIT I - BASIC MEASUREMENT CONCEPTS:
Functional elements of Instruments
 Primary sensing element
 Variable conversion element
 Data presentation element
Primary sensing element
The quantity under measurement makes its first contact with primary
sensing element of a measurement system
here, the primary sensing element
transducer. This transducer converts measured into an analogous electrical signal.
Variable conversion element
The output of the primary sensing element is the electrical signal. It may be a
voltage a frequency or some other electrical parameter. But this output is not suitable for
this system.
For the instrument to perform the desired function, it may be necessary to
convert this output to some other suitable form while retaining the original signal.
Consider an example, suppose output is an analog signal form and the next of system
accepts input signal only in digital form . Therefore we have to use and to digital
converter in this system.
Variable manipulation element
The main function of variable manipulation element is to manipulation element
is to manipulate the signal presented to it preserving the original nature of the signal.
Here, manipulation means a change in numerical value of the signal.
3
Consider a small example, an electric amplifier circuit accepts a small voltage
signal as input and produces an output signal which is also voltage but of greater
amplifier. Thus voltage amplifier acts as a variable manipulation element.
Data presentation element
The information about the quantity under measurement has to be conveyed to
the personal handling the instrument or system for control or analysis purposes. The
information conveyed must be in the form of intelligible to the personnel. The above
function is done by data presentation element.
The output or data of the system can be monitored by using visual display
devices may be analog or digital device like ammeter, digital meter etc. In case the
data to be record, we can use analog or digital recording equipment. In industries , for
control and analysis purpose we can use computers.
The final stage in a measurement system is known as terminating stage . when
a control device is used for the final measurement stage it is necessary to apply some
feedback to the input signal to accomplish the control 0bjective.
The term signal conditioning includes many other functions in addition to
variable conversion and variable manipulation. In fact the element that follows the
primary sensing element in any instrument or instrumentation system should be called
signal conditioning element.
When the element of an instrument is physically separated, it becomes necessary
to transmit data from one to another. This element is called transmitting element. The
signal conditioning and transmitting stage is generally known as intermediate stage.
4
Measurement system:
Measurement system any of the systems used in the process of associating numbers with
physical quantities and phenomena. Although the concept of weights and measures today
includes such factors as temperature, luminosity, pressure, and electric current, it once
consisted of only four basic measurements: mass (weight), distance or length, area, and
volume (liquid or grain measure). The last three are, of course, closely related. Basic to
the whole idea of weights and measures are the concepts of uniformity, units, and
standards.Uniformity, the essence of any system of weights and measures, requires
accurate, reliable standards of mass and length .
Static Characteristics of Instrument Systems:
Output/Input Relationship
Instrument systems are usually built up from a serial linkage of distinguishable building
blocks. The actual physical assembly may not appear to be so but it can be broken down into
a representative diagram of connected blocks. In the Humidity sensor it is activated by an
input physical parameter and provides an output signal to the next block that processes the
signal into a more appropriate state.
A key generic entity is, therefore, the relationship between the input and output of the
block. As was pointed out earlier, all signals have a time characteristic, so we must consider
the behavior of a block in terms of both the static and dynamic states.
The behavior of the static regime alone and the combined static and dynamic regime can
be found through use of an appropriate mathematical model of each block. The
mathematical description of system responses is easy to set up and use if the elements all act
as linear systems and where addition of signals can be carried out in a linear additive
manner. If nonlinearity exists in elements, then it becomes considerably more difficult —
perhaps even quite impractical — to provide an easy to follow mathemat- ical explanation.
Fortunately, general description of instrument systems responses can be usually be
adequately covered using the linear treatment.
The output/input ratio of the whole cascaded chain of blocks 1, 2, 3, etc. is given as:
[output/input]total = [output/input]1× [output/input]2× [output/input]3 …
5
The output/input ratio of a block that includes both the static and dynamic characteristics is
called the transfer function and is given the symbol G.
The equation forG can be written as two parts multiplied together. One expresses the
static behavior of the block, that is, the value it has after all transient (time varying) effects
have settled to their final state. The other part tells us how that value responds when the block is in its
dynamic state. The static part is known as the transfer characteristic and is
often all that is needed to be known for block description.
The static and dynamic response of the cascade of blocks is simply the multiplication of
all individual blocks. As each block has its own part for the static and dynamic behavior, the
cascade equations can be rearranged to separate the static from the dynamic parts and then
by multiplying the static set and the dynamic set we get the overall response in the static and
dynamic states. This is shown by the sequence of Equations.
Instruments are formed from a connection of blocks. Each block can be represented by a
conceptual and mathematical model. This example is of one type of humidity sensor.
6
Drift :
It is now necessary to consider a major problem of instrument performance called
instrument drift . This is caused by variations taking place in the parts of the instrumentation
over time. Prime sources occur as chemical structural changes and changing mechanical
stresses. Drift is a complex phenomenon for which the observed effects are that the
sensitivity and offset values vary. It also can alter the accuracy of the instrument differently
at the various amplitudes of the signal present.
Detailed description of drift is not at all easy but it is possible to work satisfactorily with
simplified values that give the average of a set of observations, this usually being quoted in a
conservative manner. The first graph (a) in Figure shows typical steady drift of a measuring
spring component of a weighing balance. Figure (b) shows how an electronic amplifier might
settle down after being turned on.
Drift is also caused by variations in environmental parameters such as temperature,
pressure, and humidity that operate on the components. These are known as influence
parameters. An example is the change of the resistance of an electrical resistor, this resistor
forming the critical part of an electronic amplifier that sets its gain as its operating
7
temperature changes.
Unfortunately, the observed effects of influence parameter induced drift often are the same as for
time varying drift. Appropriate testing of blocks such as electronic amplifiers does allow the two
to be separated to some extent. For example, altering only the temperature of the
amplifier over a short period will quickly show its temperature dependence.
Drift due to influence parameters is graphed in much the same way as for time drift. Figure
shows the drift of an amplifier as temperature varies. Note that it depends significantly on the
temperature
Drift in the performance of an instrument takes many forms:
(a ) drift over time for a spring balance;
( b ) how an electronic amplifier might settle over time to a final value after power is
supplied;
(c ) drift, due to temperature, of an electronic amplifier varies with the actual temperature of
operation.
Dynamic Characteristics of Instrument Systems:
Dealing with Dynamic States:
Measurement outcomes are rarely static over time. They will possess a dynamic component
that must be understood for correct interpretation of the results. For example, a trace made
on an ink pen chart recorder will be subject to the speed at which the pen can follow the
input signal changes.Drift in the performance of an instrument takes many forms: (a ) drift
over time for a spring
8
Error of nonlinearity can be expressed in four different ways: (a) best fit line (based on
selected method used to decide this); (b) best fit line through zero; (c) line joining 0% and 100%
points; and (d) theoretical line
To properly appreciate instrumentation design and its use, it is now necessary to develop
insight into the most commonly encountered types of dynamic response and to develop the
9
mathematical modeling basis that allows us to make concise statements about responses.
If the transfer relationship for a block follows linear laws of performance, then a generic
mathematical method of dynamic description can be used. Unfortunately, simple
mathematical methods have not been found that can describe all types of instrument
responses in a simplistic and uniform manner. If the behavior is nonlinear, then description
with mathematical models becomes very difficult and might be impracticable. The behavior of nonlinear
systems can, however, be studied as segments of linear behavior joined end to end. Here,
digital computers are effectively used to model systems of any kind provided the user is
prepared to spend time setting up an adequate model.
Now the mathematics used to describe linear dynamic systems can be introduced. This
gives valuable insight into the expected behavior of instrumentation, and it is usually found
that the response can be approximated as linear.
The modeled response at the output of a blockGresult is obtained by multiplying the
mathematical expression for the input signalGinput by the transfer function of the block
under investigationGresponse, as shown in below equation
Gresult = Ginput × Gresponse
To proceed, one needs to understand commonly encountered input functions and the various
types of block characteristics. We begin with the former set: the so-called forcing functions.
Forcing Functions
Let us first develop an understanding of the various types of input signal used to perform
tests. The most commonly used signals are shown in Figure 3.12. These each possess
different valuable test features. For example, the sine-wave is the basis of analysis of all
complex wave-shapes because they can be formed as a combination of various sinewaves, each having individual responses that add to give all other wave- shapes. The step
function has intuitively obvious uses because input transients of this kind are commonly
encountered. The ramp test function is used to present a more realistic input for those
systems where it is not possible to obtain instantaneous step input changes, such as
attempting to move a large mass by a limited size of force. Forcing functions are also chosen
because they can be easily described by a simple mathematical expression, thus making
mathematical analysis relatively straightforward.
10
Characteristic Equation Development
The behavior of a block that exhibits linear behavior is mathematically represented in the
general form of expression given as Equation
Here, the coefficientsa2,a1, anda0 are constants dependent on the particular block of interest. The lefthand side of the equation is known as the characteristic equation. It is specific to the internal
properties of the block and is not altered by the way the block is used.
The specific combination of forcing function input and block characteristic equation collectively
decides the combined output response. Connections around the block, such as feedback
from the output to the input, can alter the overall behavior significantly: such systems, however, are
not dealt with in this section being in the domain of feedback control systems.
11
Unit of measurement:
A unit of measurement is a definite magnitude of a physical quantity, defined and
adopted by convention and/or by law, that is used as a standard for measurement of the
same physical quantity.[1] Any other value of the physical quantity can be expressed as a
simple multiple of the unit of measurement.For example, length is a physical quantity. The
metre is a unit of length that represents a definite predetermined length. When we say 10
metres (or 10 m), we actually mean 10 times the definite predetermined length called
"metre".The definition, agreement, and practical use of units of measurement have played a
12
crucial role in human endeavour from early ages up to this day. Disparate systems of units
used to be very common. Now there is a global standard, the International System of Units
(SI), the modern form of the metric system.In trade, weights and measures is often a subject
of governmental regulation, to ensure fairness and transparency. The Bureau international
des poids et mesures (BIPM) is tasked with ensuring worldwide uniformity of
measurements and their traceability to the International System of Units (SI). Metrology is
the science for developing nationally and internationally accepted units of weights and
measures.In physics and metrology, units are standards for measurement of physical
quantities that need clear definitions to be useful. Reproducibility of experimental results is
central to the scientific method. A standard system of units facilitates this. Scientific
systems of units are a refinement of the concept of weights and measures developed long
ago for commercial purposes.Science, medicine, and engineering often use larger and
smaller units of measurement than those used in everyday life and indicate them more
precisely. The judicious selection of the units of measurement can aid researchers in
problem solving (see, for example, dimensional analysis).In the social sciences, there are no
standard units of measurement and the theory and practice of measurement is studied in
psychometrics and the theory of conjoint measurement.
Error Analysis :
Introduction
The knowledge we have of the physical world is obtained by doing experiments and
making measurements. It is important to understand how to express such data and how to
analyze and draw meaningful conclusions from it.In doing this it is crucial to understand
that all measurements of physical quantities are subject to uncertainties. It is never possible
to measure anything exactly. It is good, of course, to make the error as small as possible but
it is always there. And in order to draw valid conclusions the error must be indicated and
dealt with properly.Take the measurement of a person's height as an example. Assuming
that her height has been determined to be 5' 8", how accurate is our result?Well, the height
of a person depends on how straight she stands, whether she just got up (most people are
slightly taller when getting up from a long rest in horizontal position), whether she has her
shoes on, and how long her hair is and how it is made up. These inaccuracies could all be
called errors of definition. A quantity such as height is not exactly defined without
specifying many other circumstances.Even if you could precisely specify the
13
"circumstances," your result would still have an error associated with it. The scale you are
using is of limited accuracy; when you read the scale, you may have to estimate a fraction
between the marks on the scale, etc.
If the result of a measurement is to have meaning it cannot consist of the measured value
alone. An indication of how accurate the result is must be included also. Indeed, typically
more effort is required to determine the error or uncertainty in a measurement than to
perform the measurement itself. Thus, the result of any physical measurement has two
essential components: (1) A numerical value (in a specified system of units) giving the best
estimate possible of the quantity measured, and (2) the degree of uncertainty associated
with this estimated value. For example, a measurement of the width of a table would yield a
result such as 95.3 +/- 0.1 cm.
Significant Figures :
The significant figures of a (measured or calculated) quantity are the meaningful digits in
it. There are conventions which you should learn and follow for how to express numbers so
as to properly indicate their significant figures.
Any digit that is not zero is significant. Thus 549 has three significant figures and
1.892 has four significant figures.
Zeros between non zero digits are significant. Thus 4023 has four significant figures.
Zeros to the left of the first non zero digit are not significant. Thus 0.000034 has
only two significant figures. This is more easily seen if it is written as 3.4x10-5.
For numbers with decimal points, zeros to the right of a non zero digit are
significant. Thus 2.00 has three significant figures and 0.050 has two significant
figures. For this reason it is important to keep the trailing zeros to indicate the
actual number of significant figures.
For numbers without decimal points, trailing zeros may or may not be significant.
Thus, 400 indicates only one significant figure. To indicate that the trailing zeros
are significant a decimal point must be added. For example, 400. has three
significant figures, and
has one significant figure.
Exact numbers have an infinite number of significant digits. For example, if there
are two oranges on a table, then the number of oranges is 2.000... . Defined numbers
14
are also like this. For example, the number of centimeters per inch (2.54) has an
infinite number of significant digits, as does the speed of light (299792458 m/s).
There are also specific rules for how to consistently express the uncertainty associated
with a number. In general, the last significant figure in any result should be of the same
order of magnitude (i.e.. in the same decimal position) as the uncertainty. Also, the
uncertainty should be rounded to one or two significant figures. Always work out the
uncertainty after finding the number of significant figures for the actual measurement.
For example,
9.82 +/- 0.02
10.0 +/- 1.5
4 +/- 1
The following numbers are all incorrect.
9.82 +/- 0.02385 is wrong but 9.82 +/- 0.02 is fine
10.0 +/- 2 is wrong but 10.0 +/- 2.0 is fine
4 +/- 0.5 is wrong but 4.0 +/- 0.5 is fine
In practice, when doing mathematical calculations, it is a good idea to keep one more digit
than is significant to reduce rounding errors. But in the end, the answer must be expressed
with only the proper number of significant figures. After addition or subtraction, the result
is significant only to the place determined by the largest last significant place in the original
numbers. For example,
89.332 + 1.1 = 90.432
should be rounded to get 90.4 (the tenths place is the last significant place in 1.1). After
multiplication or division, the number of significant figures in the result is determined by
the original number with the smallest number of significant figures. For example,
(2.80) (4.5039) = 12.61092
should be rounded off to 12.6 (three significant figures like 2.80).
Refer to any good introductory chemistry textbook for an explanation of the
methodology for working out significant figures.
15
The Idea of Error :
The concept of error needs to be well understood. What is and what is not meant by
"error"? A measurement may be made of a quantity which has an accepted value which can
be looked up in a handbook (e.g.. the density of brass). The difference between the
measurement and the accepted value is not what is meant by error. Such accepted values
are not "right" answers. They are just measurements made by other people which have
errors associated with them as well. Nor does error mean "blunder." Reading a scale
backwards, misunderstanding what you are doing or elbowing your lab partner's measuring
apparatus are blunders which can be caught and should simply be disregarded. Obviously, it
cannot be determined exactly how far off a measurement is; if this could be done, it would
be possible to just give a more accurate, corrected value. Error, then, has to do with
uncertainty in measurements that nothing can be done about. If a measurement is repeated,
the values obtained will differ and none of the results can be preferred over the others.
Although it is not possible to do anything about such error, it can be characterized. For
instance, the repeated measurements may cluster tightly together or they may spread
widely. This pattern can be analyzed systematically.
Classification of Error :
Generally, errors can be divided into two broad and rough but useful classes: systematic
and random.Systematic errors are errors which tend to shift all measurements in a
systematic way so their mean value is displaced. This may be due to such things as
incorrect calibration of equipment, consistently improper use of equipment or failure to
properly account for some effect. In a sense, a systematic error is rather like a blunder and
large systematic errors can and must be eliminated in a good experiment. But small
systematic errors will always be present. For instance, no instrument can ever be calibrated
perfectly.Other sources of systematic errors are external effects which can change the
results of the experiment, but for which the corrections are not well known. In science, the
reasons why several independent confirmations of experimental results are often required
(especially using different techniques) is because different apparatus at different places may
be affected by different systematic effects. Aside from making mistakes (such as thinking
one is using the x10 scale, and actually using the x100 scale), the reason why experiments
sometimes yield results which may be far outside the quoted errors is because of systematic
effects which were not accounted for.
16
Random errors are errors which fluctuate from one measurement to the next. They yield
results distributed about some mean value. They can occur for a variety of reasons.
They may occur due to lack of sensitivity. For a sufficiently a small change an
instrument may not be able to respond to it or to indicate it or the observer may not
be able to discern it.
They may occur due to noise. There may be extraneous disturbances which
cannot be taken into account.
They may be due to imprecise definition.
They may also occur due to statistical processes such as the roll of dice.
Random errors displace measurements in an arbitrary direction whereas systematic errors
displace measurements in a single direction. Some systematic error can be substantially
eliminated (or properly taken into account). Random errors are unavoidable and must be
lived with. Many times you will find results quoted with two errors. The first error
quoted is usually the random error, and the second is called the systematic error. If only
one error is quoted, then the errors from all sources are added together. (In quadrature as
described in the section on propagation of errors.)A good example of "random error" is
the statistical error associated with sampling or counting. For example, consider
radioactive decay which occurs randomly at a some (average) rate. If a sample has, on
average, 1000 radioactive decays per second then the expected number of decays in 5
seconds would be 5000. A particular measurement in a 5 second interval will, of course,
vary from this average but it will generally yield a value within 5000 +/- . Behavior like
this, where the error,
, (1)
is called a Poisson statistical process. Typically if one does not know
that,, in order to estimate this error.
A. Mean Value
Suppose an experiment were repeated many, say N, times to get,
,
17
it is assumed
N measurements of the same quantity, x. If the errors were random then the errors in these
results would differ in sign and magnitude. So if the average or mean value of our
measurements were calculated,
, (2)
some of the random variations could be expected to cancel out with others in the sum. This
is the best that can be done to deal with random errors: repeat the measurement many times,
varying as many "irrelevant" parameters as possible and use the average as the best
estimate of the true value of x. (It should be pointed out that this estimate for a given N will
differ from the limit as the true mean value; though, of course, for larger N it will be closer
to the limit.) In the case of the previous example: measure the height at different times of
day, using different scales, different helpers to read the scale, etc.Doing this should give a
result with less error than any of the individual measurements. But it is obviously
expensive, time consuming and tedious. So, eventually one must compromise and decide
that the job is done. Nevertheless, repeating the experiment is the only way to gain
confidence in and knowledge of its accuracy. In the process an estimate of the deviation of
the measurements from the mean value can be obtained.
B. Measuring Error
There are several different ways the distribution of the measured values of a
repeated experiment such as discussed above can be specified.
Maximum Error
The maximum and minimum values of the data set,
and
, could be
specified. In these terms, the quantity,
, (3)
is the maximum error. And virtually no measurements should ever fall outside
.
18
Probable Error
The probable error,
the measured values.
, specifies the range
which contains 50% of
Average Deviation
The average deviation is the average of the deviations from the mean,
. (4)
For a Gaussian distribution of the data, about 58% will lie within
.
Standard Deviation
For the data to have a Gaussian distribution means that the probability of
obtaining the result x is,
, (5)
where
is most probable value and
, which is called the standard deviation,
determines the width of the distribution. Because of the law of large numbers this
assumption will tend to be valid for random errors. And so it is common practice to
quote error in terms of the standard deviation of a Gaussian distribution fit to the
observed data distribution. This is the way you should quote error in your reports.
It is just as wrong to indicate an error which is too large as one which is too small. In the
measurement of the height of a person, we would reasonably expect the error to be +/-1/4" if
a careful job was done, and maybe +/-3/4" if we did a hurried sample measurement.
Certainly saying that a person's height is 5' 8.250"+/-0.002" is ridiculous (a single jump will
compress your spine more than this) but saying that a person's height is 5' 8"+/- 6" implies
that we have, at best, made a very rough estimate!
C. Standard Deviation
The mean is the most probable value of a Gaussian distribution. In terms of the mean, the
standard deviation of any distribution is,
. (6)
19
The quantity , the square of the standard deviation, is called the variance. The best
estimate of the true standard deviation is,
. (7)
The reason why we divide by N to get the best estimate of the mean and only by N-1 for the
best estimate of the standard deviation needs to be explained. The true mean value of x is
not being used to calculate the variance, but only the average of the measurements as the
best estimate of it. Thus,
as calculated is always a little bit smaller than
,
the quantity really wanted. In the theory of probability (that is, using the assumption that the
data has a Gaussian distribution), it can be shown that this underestimate is corrected by
using N-1 instead of N.If one made one more measurement of x then (this is also a
property of a Gaussian distribution) it would have some 68% probability of lying within
. Note that this means that about 30% of all experiments will disagree with the
accepted value by more than one standard deviation.However, we are also interested in
the error of the mean, which is smaller than sx if there were several measurements. An
exact calculation yields,
, (8)
for the standard error of the mean. This means that, for example, if there were 20
measurements, the error on the mean itself would be = 4.47 times smaller then the error of
each measurement. The number to report for this series of N measurements of x is
where
. The meaning of this is that if the N measurements of x were repeated there
would be a 68% probability the new mean value of would lie within
and
(that is between
). Note that this also means that there is a 32% probability that it will fall
outside of this range. This means that out of 100 experiments of this type, on the average,
32 experiments will obtain a value which is outside the standard errors.
20
Examples :
Suppose the number of cosmic ray particles passing through some detecting device
every hour is measured nine times and the results are those in the following table. Thus
we have = 900/9 = 100 and
= 1500/8 = 188 or
= 14. Then the probability that one
more measurement of x will lie within 100 +/- 14 is 68%.The value to be reported for
this series of measurements is 100+/-(14/3) or 100 +/- 5. If one were to make another
series of nine measurements of x there would be a 68% probability the new mean would
lie within the range 100 +/- 5.Random counting processes like this example obey a
Poisson distribution for which
. So one would expect the value of
to be 10.
This is somewhat less than the value of 14 obtained above; indicating either the process
is not quite random or, what is more likely, more measurements are needed.
i
-----------------------------------------1
80
400
2
95
25
3
100
0
4
110
100
5
90
100
6
115
225
7
85
225
8
120
400
9
105
25
S
900
1500
------------------------------------------
The same error analysis can be used for any set of repeated measurements whether they
arise from random processes or not. For example in the Atwood's machine experiment to
measure g you are asked to measure time five times for a given distance of fall s. The
mean value of the time is,
, (9)
and the standard error of the mean is,
21
, (10)
where n = 5.
For the distance measurement you will have to estimate [[Delta]]s, the precision with
which you can measure the drop distance (probably of the order of 2-3 mm).
Propagation of Errors :
Frequently, the result of an experiment will not be measured directly. Rather, it will be
calculated from several measured physical quantities (each of which has a mean value
and an error). What is the resulting error in the final result of such an experiment?
For instance, what is the error in Z = A + B where A and B are two measured quantities
with errors
and respectively?
A first thought might be that the error in Z would be just the sum of the errors in A and
B. After all,
(11)
and
. (12)
But this assumes that, when combined, the errors in A and B have the same sign and
maximum magnitude; that is that they always combine in the worst possible way. This
could only happen if the errors in the two variables were perfectly correlated, (i.e.. if the
two variables were not really independent).If the variables are independent then sometimes
the error in one variable will happen to cancel out some of the error in the other and so, on
the average, the error in Z will be less than the sum of the errors in its parts. A reasonable
way to try to take this into account is to treat the perturbations in Z produced by
perturbations in its parts as if they were "perpendicular" and added according to the
Pythagorean theorem,
. (13)
That is, if A = (100 +/- 3) and B = (6 +/- 4) then Z = (106 +/- 5) since
.
This idea can be used to derive a general rule. Suppose there are two measurements, A and
B, and the final result is Z = F(A, B) for some function F. If A is perturbed by
then Z
22
will be perturbed by
where (the partial derivative) [[partialdiff]]F/[[partialdiff]]A is the derivative of F with
respect to A with B held constant. Similarly the perturbation in Z due to a perturbation in
B is,
.
Combining these by the Pythagorean theorem yields
, (14)
In the example of Z = A + B considered above,
,
so this gives the same result as before. Similarly if Z = A - B then,
,
which also gives the same result. Errors combine in the same way for both addition and
subtraction. However, if Z = AB then,
,
so
, (15)
Thus
, (16)
or the fractional error in Z is the square root of the sum of the squares of the fractional errors
in its parts. (You should be able to verify that the result is the same for division as it is for
multiplication.) For example,
.
23
It should be noted that since the above applies only when the two measured quantities are
independent of each other it does not apply when, for example, one physical quantity is
measured and what is required is its square. If Z = A2 then the perturbation in Z due to a
perturbation in A is,
. (17)
Thus, in this case,
(18)
and not A2 (1 +//A) as would be obtained by misapplying the rule for independent
variables. For example,
(10 +/- 1)2 = 100 +/- 20 and not 100 +/- 14.
If a variable Z depends on (one or) two variables (A and B) which have independent errors (
and
) then the rule for calculating the error in Z is tabulated in following table for a
variety of simple relationships. These rules may be compounded for more complicated
situations.
Relation between Z Relation between errors
and(A,B)
and ( , )
---------------------------------------------------------------1
Z=A+B
2
Z=A-B
3
Z = AB
4
Z = A/B
5
Z = An
6
Z = ln A
7
Z = eA
Voltmeter:
The design of a voltmeter, ammeter or ohmmeter begins with a current-sensitive element.
Though most modern meters have solid state digital readouts, the physics is more readily
24
demonstrated with a moving coil current detector called a galvanometer. Since the
modifications of the current sensor are compact, it is practical to have all three functions in a
single instrument with multiple ranges of sensitivity. Schematically, a single range
"multimeter" might be designed as illustrated.
A voltmeter measures the change in voltage between two points in an electric circuit and
therefore must be connected in parallel with the portion of the circuit on which the
measurement is made. By contrast, an ammeter must be connected in series. In analogy with
a water circuit, a voltmeter is like a meter designed to measure pressure difference. It is
necessary for the voltmeter to have a very high resistance so that it does not have an
appreciable affect on the current or voltage associated with the measured circuit. Modern
solid-state meters have digital readouts, but the principles of operation can be better
appreciated by examining the older moving coil meters based on galvanometer sensors.
25
Ammeter:
An ammeter is an instrument for measuring the electric current in amperes in a branch of an
electric circuit. It must be placed in series with the measured branch, and must have very
low resistance to avoid significant alteration of the current it is to measure. By contrast, an
voltmeter must be connected in parallel. The analogy with an in-line flowmeter in a water
circuit can help visualize why an ammeter must have a low resistance, and why connecting
an ammeter in parallel can damage the meter. Modern solid-state meters have digital
readouts, but the principles of operation can be better appreciated by examining the older
moving coil metersbased on galvanometer sensors.
26
Ohmmeter :
The standard way to measure resistance in ohms is to supply a constant voltage to the
resistance and measure the current through it. That current is of course inversely
proportional to the resistance according to Ohm's law,so that you have a non-linear scale.
The current registered by the current sensing element is proportional to 1/R, so that a large
current implies a small resistance. Modern solid-state meters have digital readouts, but the
principles of operation can be better appreciated by examining the older moving coil meters
based on galvanometer sensors.
RMS stands for Root Mean Square:
RMS, or Root Mean Square, is the measurement used for any time varying signal's
effective value: It is not an "Average" voltage and its mathematical relationship to peak
voltage varies depending on the type of waveform. By definition, RMS Value, also called
the effective or heating value of AC, is equivalent to a DC voltage that would provide the
same amount of heat generation in a resistor as the AC voltage would if applied to that
same resistor. Since an AC signal's voltage rises and falls with time, it takes more AC
voltage to produce a given RMS voltage. In other words the grid must produce about 169
volts peak AC which turns out to be 120 volts RMS (.707 x 169). The heating value of the
voltage available is equivalent to a 120 volt DC source (this is for example only and does
not mean DC and AC are interchangeable). The typical multi-meter is not a True RMS
reading meter. As a result it will only produce misleading voltage readings when trying to
27
measure anything other than a DC signal or sine wave. Several types of multi-meters
exist, and the owner's manual or the manufacturer should tell you which type you have.
Each handles AC signals differently, here are the three basic types. A rectifier type multimeter indicates RMS values for sine waves only. It does this by measuring average
voltage and multiplying by 1.11 to find RMS. Trying to use this type of meter with any
waveform other than a sine wave will result in erroneous RMS readings. Average reading
digital volt meters are just that, they measure average voltage for an AC signal. Using the
equations in the next column for a sine wave, average voltage (Vavg) can be converted to
Volts RMS (Vrms), and doing this allows the meter to display an RMS reading for a
sinewave.A True RMS meter uses a complex RMS converter to read RMS for any type of
AC waveform.
Bridge Measurements:
A Maxwell bridge (in long form, a Maxwell-Wien bridge) is a type of Wheatstone
bridge used to measure an unknown inductance (usually of low Q value) in terms of
calibrated resistance and capacitance. It is a real product bridge. With reference to the
picture, in a typical application R1 and R4 are known fixed entities, and R2 and C2 are
known variable entities. R2 and C2 are adjusted until the bridge is balanced.R3 and L3
can then be calculated based on the values of the other components:
To avoid the difficulties associated with determining the precise value of a variable
capacitance, sometimes a fixed-value capacitor will be installed and more than one resistor
will be made variable. The additional complexity of using a Maxwell bridge over simpler
bridge types is warranted in circumstances where either the mutual inductance between
the load and the known bridge entities, or stray electromagnetic interference, distorts the
measurement results. The capacitive reactance in the bridge will exactly oppose the
inductive reactance of the load when the bridge is balanced, allowing the load's resistance
and reactance to be reliably determined.
28
Wheatstone bridge
It is used to measure an unknown electrical resistance by balancing two legs of a bridge
circuit, one leg of which includes the unknown component. Its operation is similar to
the original potentiometer.
Operation :
Rx is the unknown resistance to be measured; R1, R2 and R3 are resistors of known
resistance and the resistance of R2 is adjustable. If the ratio of the two resistances in the
known leg (R2 / R1) is equal to the ratio of the two in the unknown leg (Rx / R3), then the
voltage between the two midpoints (B and D) will be zero and no current will flow
through the galvanometer Vg. R2 is varied until this condition is reached. The direction of
the current indicates whether R2 is too high or too low.
Detecting zero current can be done to extremely high accuracy (see galvanometer).
Therefore, if R1, R2 and R3 are known to high precision, then Rx can be measured to high
29
precision. Very small changes in Rx disrupt the balance and are readily detected.At the
point of balance, the ratio of R2 / R1 = Rx / R3
Therefore,
Alternatively, if R1, R2, and R3 are known, but R2 is not adjustable, the voltage
difference across or current flow through the meter can be used to calculate the value of
Rx, using Kirchhoff's circuit laws (also known as Kirchhoff's rules). This setup is
frequently used in strain gauge and resistance thermometer measurements, as it is usually
faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.
Then, Kirchhoff's second rule is used for finding the voltage in the loops ABD and BCD:
The bridge is balanced and Ig = 0, so the second set of equations can be rewritten as:
Then, the equations are divided and rearranged, giving:
From the first rule, I3 = Ix and I1 = I2. The desired value of Rx is now known to be given
as:
If all four resistor values and the supply voltage (VS) are known, the voltage across
the bridge (VG) can be found by working out the voltage from each potential divider and
subtracting one from the other. The equation for this is:
30
This can be simplified to:
With node B being (VG) positive, and node D being (VG) negative.
Significance :
The Wheatstone bridge illustrates the concept of a difference measurement, which
can be extremely accurate. Variations on the Wheatstone bridge can be used to measure
capacitance, inductance, impedance and other quantities, such as the amount of combustible
gases in a sample, with an explosimeter. The Kelvin bridge was specially adapted from the
Wheatstone bridge for measuring very low resistances. In many cases, the significance of
measuring the unknown resistance is related to measuring the impact of some physical
phenomenon - such as force, temperature, pressure, etc. - which thereby allows the use of
Wheatstone bridge in measuring those elements indirectly.
Schering Bridge:
A Schering Bridge is a bridge circuit used for measuring an unknown electrical
capacitance and its dissipation factor. The dissipation factor of a capacitor is the the ratio
of its resistance to its capacitive reactance. The Schering Bridge is basically a four-arm
alternating-current (AC) bridge circuit whose measurement depends on balancing the
loads on its arms. Figure 1 below shows a diagram of the Schering Bridge.
The Schering Bridge
31
In the Schering Bridge above, the resistance values of resistors R1 and R2 are known,
while the resistance value of resistor R3 is unknown. The capacitance values of C1 and
C2 are also known, while the capacitance of C3 is the value being measured. To measure
R3 and C3, the values of C2 and R2 are fixed, while the values of R1 and C1 are adjusted
until the current through the ammeter between points A and B becomes zero. This
happens when the voltages at points A and B are equal, in which case the bridge is said to
be 'balanced'. When the bridge is balanced, Z1/C2 = R2/Z3, where Z1 is the impedance of
R1 in parallel with C1 and Z3 is the impedance of R3 in series with C3. In an AC circuit
that has a capacitor, the capacitor contributes a capacitive reactance to the impedance. The
capacitive reactance of a capacitor C is 1/2πfC.
As such, Z1 = R1/[2πfC1((1/2πfC1) + R1)] = R1/(1 + 2πfC1R1) while Z3 =
1/2πfC3 + R3. Thus, when the bridge is balanced:
2πfC2R1/(1+2πfC1R1) = R2/(1/2πfC3 + R3); or
2πfC2(1/2πfC3 + R3) = (R2/R1)(1+2πfC1R1); or
C2/C3 + 2πfC2R3 = R2/R1 + 2πfC1R2.
When the bridge is balanced, the negative and positive reactive components are equal and
cancel out, so
2πfC2R3 = 2πfC1R2 or
R3 = C1R2 / C2.
Similarly, when the bridge is balanced, the purely resistive components are equal, so
C2/C3 = R2/R1 or
C3 = R1C2 / R2.
A Hay Bridge is an AC bridge circuit used for measuring an unknown inductance by
balancing the loads of its four arms, one of which contains the unknown inductance. One of
the arms of a Hay Bridge has a capacitor of known characteristics, which is the principal
component used for determining the unknown inductance value. Figure 1 below shows a
diagram of the Hay Bridge.
32
The Hay Bridge :
As shown in Figure 1, one arm of the Hay bridge consists of a capacitor in series
with a resistor (C1 and R2) and another arm consists of an inductor L1 in series with
a resistor (L1 and R4). The other two arms simply contain a resistor each (R1 and
R3). The values of R1and R3 are known, and R2 and C1 are both adjustable. The
unknown values are those of L1 and R4.Like other bridge circuits, the measuring
ability of a Hay Bridge depends on 'balancing' the circuit. Balancing the circuit in
Figure 1 means adjusting R2 and C1 until the current through the ammeter between
points A and B becomes zero. This happens when the voltages at points A and B are
equal. When the Hay Bridge is balanced, it follows that Z1/R1 = R3/Z2 wherein Z1
is the impedance of the arm containing C1 and R2 while Z2 is the impedance of the
arm containing L1 and R4.
Thus, Z1 = R2 + 1/(2πfC) while Z2 = R4 + 2πfL1.
Mathematically, when the bridge is balanced,
[R2 + 1/(2πfC1)] / R1 = R3 / [R4 + 2πfL1]; or [R4 +
2πfL1] = R3R1 / [R2 + 1/(2πfC1)]; or R3R1 = R2R4 +
2πfL1R2 + R4/2πfC1 + L1/C1.
When the bridge is balanced, the reactive components are equal, so
2πfL1R2 = R4/2πfC1, or R4 = (2πf)2L1R2C1.
Substituting R4, one comes up with the following equation:
R3R1 = (R2+1/2πfC1)((2πf)2L1R2C1) + 2πfL1R2 + L1/C1; or L1 =
R3R1C1 / (2πf)2R22C12 + 4πfC1R2 + 1); or
L1 = R3R1C1 / [1 + (2πfR2C1)2] after dropping the reactive components of the
equation since the bridge is balanced.
Thus, the equations for L1 and R4 for the Hay Bridge in Figure 1 when it is
balanced are:
L1 = R3R1C1 / [1 + (2πfR2C1)2]; and
R4 = (2πfC1)2R2R3R1 / [1 + (2πfR2C1)2]
33
Wien bridge :
A Wien bridge oscillator is a type of electronic oscillator that generates sine waves. It
can generate a large range of frequencies. The circuit is based on an electrical network
originally developed by Max Wien in 1891. The bridge comprises four resistors and two
capacitors. It can also be viewed as a positive feedback system combined with a bandpass
filter. Wien did not have a means of developing electronic gain so a workable oscillator
could not be realized.The modern circuit is derived from William Hewlett's 1939 Stanford
University master's degree thesis. Hewlett, along with David Packard co-founded HewlettPackard. Their first product was the HP 200A, a precision sine wave oscillator based on the
Wien bridge. The 200A was one of the first instruments to produce such low distortion.
The frequency of oscillation is given by:
Amplitude stabilization :
The key to Hewlett's low distortion oscillator is effective amplitude
stabilization. The amplitude of electronic oscillators tends to increase until clipping or
other gain limitation is reached. This leads to high harmonic distortion, which is often
undesirable.Hewlett used an incandescent bulb as a positive temperature coefficient
(PTC) thermistor in the oscillator feedback path to limit the gain. The resistance of light
bulbs and similar heating elements increases as their temperature increases. If the
oscillation frequency is significantly higher than the thermal time constant of the
heating element, the radiated power is proportional to the oscillator power. Since
34
heating elements are close to black body radiators, they follow the Stefan-Boltzmann
law. The radiated power is proportional to T4,so resistance increases at a greater rate
than amplitude. If the gain is inversely proportional to the oscillation amplitude, the
oscillator gain stage reaches a steady state and operates as a near ideal class A
amplifier,achieving very low distortion at the frequency of interest. At lower
frequencies the time period of the oscillator approaches the thermal time constant of the
thermistor element and the output distortion starts to rise significantly.
Light bulbs have their disadvantages when used as gain control elements in Wien
bridge oscillators, most notably a very high sensitivity to vibration due to the bulb's
microphonic nature amplitude modulating theoscillator output, and a limitation in high
frequency response due to the inductive nature of the coiled filament. Modern Wien bridge
oscillators have used other nonlinear elements, such as diodes, thermistors, field effect
transistors, or photocells for amplitude stabilization in place of light bulbs. Distortion as
low as 0.0008% (-100 dB) can be achieved with only modest improvements to Hewlett's
original circuit.Wien bridge oscillators that use thermistors also exhibit "amplitude bounce"
when the oscillator frequency is changed. This is due to the low damping factor and long
time constant of the crude control loop, and disturbances cause the output amplitude to
exhibit a decaying sinusoidal response. This can be used as a rough figure of merit, as the
greater the amplitude bounce after a disturbance, the lower the output distortion under
steady state conditions.
Analysis :
Input admittance analysis
If a voltage source is applied directly to the input of an ideal amplifier with feedback, the
input current will be:
35
Where vin is the input voltage, vout is the output voltage, and Zf is the feedback impedance.
If the voltage gain of the amplifier is defined as:
And the input admittance is defined as:
Input admittance can be rewritten as:
For the Wien bridge, Zf is given by:
If Av is greater than 1, the input admittance is a negative resistance in parallel with an
inductance. The inductance is:
If a capacitor with the same value of C is placed in parallel with the input, the circuit has a
natural resonance at:
Substituting and solving for inductance yields:
If Av is chosen to be 3:
Lin = R2C
36
Substituting this value yields:
Or:
Similarly, the input resistance at the frequency above is:
For Av=3 and Rin=-R
If a resistor is placed in parallel with the amplifier input, it will cancel some of the
negative resistance. If the net resistance is negative, amplitude will grow until clipping
occurs. Similarly, if the net resistance is positive, oscillation amplitude will decay. If a
resistance is added in parallel with exactly the value of R, the net resistance will be infinite
and the circuit can sustain stable oscillation at any amplitude allowed by the
amplifier.Notice that increasing the gain makes the net resistance more negative, which
increases amplitude. If gain is reduced to exactly 3 when a suitable amplitude is reached,
stable, low distortion oscillations will result. Amplitude stabilization circuits typically
increase gain until a suitable output amplitude is reached. As long as R, C, and the
amplifier are linear, distortion will be minimal.
37
QUESTION BANK
UNIT I
BASIC MEASUREMENT CONCEPTS
PART – A (2 Marks)
1. What are the basic elements of a generalized measurement system?
The basic elements are,
Primary sensing element which is generally a transducer.
Data conditioning element which further consists of variable conversion
element and variable manipulation element.
Data transmission and presentation elements which include data
transmission system and data display system.
2. List any four static characteristics of a measuring system.
The various static characteristics of a measuring system are accuracy, precision,
error, resolution, sensitivity, reproducibility, stability, linearity etc.
3. Define the term accuracy.
The accuracy is defined as the degree of clones with which the instrument reading
approaches the true value of the quantity to be measured. It indicates the ability of
an instrument to indicate the true of the quantity.
4. Define the term precision.
It is the measure of the consistency or repeatability of measurements. It denotes the
amount by which the individual readings are departed about the average of number
of readings.
5. What is an error?
The algebraic difference between the indicated value and the true value of the
quantity to be measured is called an error.
6. What is calibration?
Calibration is the process of making an adjustment or marking a scale so that the
readings of an instrument agree with the accepted value and the certified standard.
7. Classify the errors that may occur in an instrument ?
i.
ii.
iii.
iv.
Gross errors
Systematic errors
Instrumental errors
Environmental errors
38
v.
Observational errors
vi.
Random Errors
8. What are the sources of errors in DC voltage measurement?
In DC voltage measurement, the various possible errors are,
The friction in moving system
The heat generated changes the resistance of working coil, causing errors.
The aging of permanent magnet and control spring.
9. What is a transfer instrument?
A transfer instrument is one which is calibrated with DC source and used without
any modifications for AC measurements. It has same accuracy for AC and DC
measurements.
10. Write the two conditions to be satisfied to make an AC bridge balance
11. Define Standard deviation?
The standard deviation or root mean square deviation of a sample is
both mathematically more convenient and statistically more meaningful for
analyzing grouped data than is the average deviation by definition, the
standard deviation of a sample is given by
S=
=
12. What are all the different types of standard?
International standards
Primary standards
Secondary standards
Working standards
13. Define arithmetic mean?
The average value or arithmetic mean value is the most probable
value obtained from a series of readings of a given quantity. As a general
rule the more readings the more closely the computed average represents the
most probable value. The average value
is calculated by taking the sum
of all the readings and divided by the number of readings, so that
=
Where
=
= the average value or arithmetic mean
39
= the value of the i th reading
n = the number of readings
14. What is meant by average deviation?
The mean or average is a measure how much the data is varied from
the average value. The mean
is calculated by adding all the absolute
values of deviations of a set of measured values and dividing this sum by
the number of observations ‘n’ so that
=
=
15. What is a standard?
A standard is a physical representation of a unit of measurement. A
known accurate measure of physical quantity is termed as standard.
16. Define systematic error?
The errors that occur due to instrument errors, environmental errors and
observational errors are classified into instrumental errors.
17. What are all the types of systematic errors?
- Instrumental errors
- Environmental errors
- Observational errors
PART-B (16 Marks)
1.
Explain and detail about functional elements of an instruments? (AU
APRIL 2007,2009)
(16)
Figures shows the functional elements of a generalized measurement system
most of the measurement systems. Contain three main functional elements.
1. Primary sensing element
2. Variable conversion element
3. Data presentation element
40
Primary sensing element:
The quantity under measurement makes its first contact with primary sensing
element of a measurement system here, the primary sensing element transducer.
This transducer converts measured into an analogous electrical signal.
Variable conversion element:
The output of the primary sensing element is the electrical signal. It may be
a voltage a frequency or some other electrical parameter. But this output is not
suitable for this system.
For the instrument to perform the desired function, it may be necessary to
convert this output to some other suitable form while retaining the original signal.
Consider an example, suppose output is an analog signal form and the next of
system accepts input signal only in digital form . Therefore we have to use and to
digital converter in this system.
Variable manipulation element:
The main function of variable manipulation element is to manipulation
element is to manipulate the signal presented to it preserving the original nature of
the signal. Here, manipulation means a change in numerical value of the signal.
Consider a small example, an electric amplifier circuit accepts a small voltage
signal as input and produces an output signal which is also voltage but of greater
amplifier. Thus voltage amplifier acts as a variable manipulation element.
Data presentation element:
41
The information about the quantity under measurement has to be conveyed
to the personal handling the instrument or system for control or analysis purposes.
The information conveyed must be in the form of intelligible to the personnel. The
above function is done by data presentation element.
The output or data of the system can be monitored by using visual display
devices may be analog or digital device like ammeter, digital meter etc. In case the
data to be record, we can use analog or digital recording equipment. In industries ,
for control and analysis purpose we can use computers.
The final stage in a measurement system is known as terminating stage .
when a control device is used for the final measurement stage it is necessary to
apply some feedback to the input signal to accomplish the control 0bjective.
The term signal conditioning includes many other functions in addition to
variable conversion and variable manipulation. In fact the element that follows the
primary sensing element in any instrument or instrumentation system should be
called signal conditioning element.
When the element of an instrument is physically separated, it becomes
necessary to transmit data from one to another. This element is called transmitting
element. The signal conditioning and transmitting stage is generally known as
intermediate stage.
2.
Explain the static and dynamic character of an instrument ? (AU APRIL
2005,2006)
(16)
Static characteristics:
The static characteristics of a instrument are consider for instrument which
are used to measure an unvarying process condition. All the static perform ate
characteristics are obtained by one form another of a process called calibration. The
main static characteristics are accrued sensitivity, resolution, precision, drift static
error, dead zone etc.
Accuracy:
It is a measure of the closeness with which an instrument measure
true value of a quantity.
42
the
Precision:
It is a measure of the consistency or repeatability of a series of
measurements. Although accuracy implies precision, precision does not necessarily imply
accuracy.
A precise instrument can be very inaccurate. The precision of a
given
measurement can be very inaccurate. The precision of a given measurement can be
given by
Precision = 1Sensitivity:
It is a measure of the change in reading of an instrument for a given
change in the measured quantity.
Resolution:
It is the smallest change in the measured quantity that will produce a
deductible change in the instrument reading.
Error:
Error is the deviation from the true value of the measured quantity . Error
can be expressed as absolute quantity or as a percentage.
% error =
Range:
The range of an instrument describes the limits of magnitude over which a
quantity may be measured. It is normally specified by stating its lower and upper
limits. For example an ammeter whose scale reads from 0 to 1 MB is said to have
a range from 0 to 1 MA
Span:
The span of an instrument is the algebraic difference between the upper and
lower limits of the instrument range for a- 10 MA to + 10 MA galvanometer, the
span is than 20 MA
Drift:
It is the variation of the measured value with time. Perfect reproducibility means
that the instrument has no drift. There are 3 types of drifts. They are zero drift and zonal
drift. Drift is an undesirable quality in industrial instruments because it is rarely
apparent and cannot be easily compensated for thus it must be carefully guarded
by continuous prevention, inspection and maintenance.
Dead zone:
43
It is defined as the largest change of input quantity for which there is no
output of the instrument. The factors which produce dead zone are hysterias and
back lash in the instrument.
Threshold:
It is clear that if the input into the instrument is increased very gradually
from 0, there will be some minimum value below which no output change can be
detected. This minimum value defines the threshold of the instrument.
Dynamic characteristics:
The dynamic behavior of an instrument can be determined by applying some
form of known and predetermined input to its primary element and then study the
output , movement of the pointer generally the behavior is judged for three types of
inputs.
Step change:
In this case the input is changed suddenly to a finite value and then
remains constant.
Linear change:
In this case the input changes linearly with time.
Sinusoidal change:
In this case the magnitude of the input changes in accordance with a
sinusoidal function of constant amplitude.
The dynamic characteristics of any instrument is defined and evaluated by
the following terms.
Speed of response:
It is the rapidly with which an instrument responds to changes in the
measured quantity.
Lag:
It Is the retardation or delay in the response of an instrument to changes in
the measured quantity. The measuring lag can be either of retardation type in
44
which case the response of the instrument beings immediately on a changes in
measured variable.
Generally the dead time lag is very small. Instrument having appreciable dead time
are not satisfactory for measuring a variable than fluctuates rapidly. The dead time
can also be caused by a finite dead zone in the instrument as a result of friction.
In such cases, the instrument does not respond for a certain time delay and acts
only sufficiently to overcome the starting friction. The dead time due to this cause
depends on how fast the measured variable is changing and on the extent of the
instrument dead zone. It is shown in figure.
3.
Explain in detail about error? (AU APRIL 2003,2004,2006.DEC 2005)
(16)
A major skill in taking measurements is the ability to interpret results in
terms of possible errors. No matter how carefully the measurements are taken and
no matter how accurate the instruments that are used, some error will always be
present. The tree systematic errors and random errors.
45
Grass error:
This class of errors mainly covers human mistakes in reading or using
instruments and in recording and calculating measured values. As long a human
beings are involved. Some gross errors will definitely be committed. Although complete
elimination of gross errors is probably impossible, are should try to anticipate and
correct them. Some gross errors are easily detected while others may be very
difficult to detect. The experiment may grossly misread the scale.
 Great care should be taken in reading and recording the data.
 Two , three or even more readings should be taken for the quantity under
measurement.
These
readings
should
be
taken preferably
by
different
experimenters and the readings should be taken at a different reading point to
avoid re-reading with the same error. Never place complete dependence on
one reading but take at least three
separate readings. Preferably under
conditions in which instruments are switched off- on.
Systematic error:
These types of errors are divided into three categories such as instrumental
errors. Environmental errors and observational errors.
Instrumental errors:
These errors arise due to inherent short comings in the instruments misuse
of the instruments and loading effects.
Environmental errors:
These errors are due to conditions external to the measuring device including
conditions in the area surrounding the instrument. These may be effects of
temperature,
pressure,
humidity,
dust, vibrations
or
of
external
magnetic
or
electrostatic fields.
The connective measures employed to eliminate to reduce these undesirable effects.
Random errors:
This occurs
are due to unknown causes and are observed when the
magnitude and polarity of a measurement future in an unpredictable manner. Some
of the more common random errors are:
(i) Rounding error:
This occurs when readings are between scale graduations and the reading is
rounded up or down to the nearest graduation.
(ii) Periodic error:
46
This occurs when an analog meter reading swings or fluctuates about the
correct reading. In addition, the meter reading quickly changes in the
immediate vicinity of the corrected value, but changes slowly at the extremes of
the swing. Since it could be easier to read the meter when it is slowly
changing, the correct value would be less likely read than an incorrect value.
The other random errors are due to noise backlash and ambient influence.
Random errors cannot normally be predicted or corrected but they can be
minimized by skilled observes using a well maintained quality instrument.
4.
Define calibration and explain difference methods of calibration? (AU APRIL
2007, Dec 2008)
(16)
All measuring instruments are to prove themselves their ability to
measure reliably and accurately . For this the results of measurement are to be
compared with higher standards which are traceable to national or international
standards. The procedure involved is termed as calibration.
Calibration is thus a set of operations that establish the relationship
between the values that are indicated by the measuring instrument and corresponding
known values of measured.
Primary calibration:
If the instrument is calibrated against primary standards, then the
calibration is called primary calibration. After the primary calibration, the instrument
can be used as a secondary calibration instrument.
Secondary calibration:
The secondary calibration instrument is used as secondary for further
calibration of other devices of lesser accuracy. This type of instruments are used in
general laboratory practice as well as in the industry because they are practical
calibration sources.
47
Secondary calibration can further be classified into two types.
 Direct calibration
 Indirect calibration
Direct calibration:
Direct calibration with a known input source is in general
of the same
order of accuracy as primary calibration. So, the instrument which are calibrated
directly are also used as secondary calibration instruments.
Indirect calibration:
This procedure is based on the equivalence of two different devices
adopting same similarity concept.
48
5. What is the standard and write and detail about different types of standards?
(AU APRIL DEC 2003)
(16)
A standard is a physical representation of a unit of measurement. A known
accurate measure of physical quantity is termed as standard. These standards are
used to determine the values of other physical quantities by the comparison
methods.
In fact , a unit is realized by reference to a material standard or to natural
phenomena, including physical and atomic constants. For example, the fundamental
unit of length in the international system (SI) is the meter defined as the distance
between two fine lines engraved on gold plugs near the ends of a platinum-iridium
alloy at
c and mechanically supported in a prescribed manner.
Based on the functions an application. Standards are classified into four categories as
(i)
International standards
(ii)
Primary standards
(iii)
Secondary standards
(iv)
Working standards
International standards:
International standards are defined by international agreement. They
are periodically evaluated and checked by absolute measurement in terms of
fundamental units of physics . They represent certain units of measurement to the
closest possible accuracy attainable by the science and technology of measurement .
These international standards are not available to ordinary users for measurements
and calibrations.
International ohms:
It is defined as the resistance offered by a column of mercury
having a mass of 14.4521gms, uniform cross sectional area and length of 106.300
cm, to the flow at constant current at the melting point of ice.
International Amperes:
It is an unvarying current , which when passed through a solution of silver
nitrate in water deposits silver at the rate of 0.00111gm/5.
49
Primary standards:
The Principle function of primary standards is the calibration and verification
of secondary standards. Primary standards are maintained at the National standards
Laboratories in different countries. They are not available for use outside the
National Laboratory. These Primary standards are absolute standards of high
accuracy that can be used as ultimate reference standard .
Secondary standards:
Secondary standards are basic reference standards used by measurement and
calibration laboratories in industries. These secondary standards are maintained by
the particular industry to which they belong. Each industry has its own secondary
standard to the National Standards Laboratory for calibration, the National Standards
Laboratory returns the secondary standards to the particular industrial laboratory
with a certification of measuring accuracy in terms of a primary standards.
Working standards:
Working standards are the principal tools of a measurement laboratory. These
standards are used to check and calibrate laboratory instruments for accuracy and
performance for example, manufactures of electronic components Such as capacitors
resistors etc. Use a standard called a working standard for checking the component
values being manufactured
a standard resistor for checking of resistance value
manufactured.
6. Maxwell inductance Bridge. (AU DEC 2004, APRIL 2005)
(16)
The maxwell bridge is used to measure unknown inductance in terms of calibrated
resistance and capacitance. Calibration-grade inductors are more difficult to manufacture
than capacitors of similar precision, and so the use of a simple "symmetrical" inductance
bridge is not always practical.
Because the phase shifts of inductors and capacitors are exactly opposite each
other, capacitive impedance can balance out an inductive impedance if they are located in
opposite legs of a bridge, as they are here.
Another advantage of using a Maxwell bridge to measure inductance rather than a
symmetrical inductance bridge is the elimination of measurement error due to mutual
inductance between two inductors.
Magnetic fields can be difficult to shield, and even a small amount of coupling
between coils in a bridge can introduce substantial errors in certain conditions. With no
second inductor to react with in the Maxwell bridge, this problem is eliminated.
50
As shown in Figure, one arm of the Maxwell bridge consists of a capacitor in
parallel with a resistor (C1 and R2) and another arm consists of an inductor L1 in
series with a resistor (L1 and R4). The other two arms just consist of a resistor each
(R1 and R3). The values of R1 and R3 are known, and R2 and C1 are both
adjustable. The unknown values are those of L1 and R4.
Like other bridge circuits, the measuring ability of a Maxwell Bridge depends on
'balancing' the circuit. Balancing the circuit in Figure 1 means adjusting C1 and R2
until the current through the bridge between points A and B becomes zero. This
happens when the voltages at points A and B are equal.
When the Maxwell Bridge is balanced, it follows that Z1/R1 = R3/Z2 wherein
Z1 is the impedance of C2 in parallel with R2, and Z2 is the impedance of L1 in
series with R4. Mathematically, Z1 = R2 + 1/(2πfC1); while Z2 = R4 + 2πfL1.
Thus, when the bridge is balanced,
(R2 + 1/(2πfC1)) / R1 = R3 / [R4 + 2πfL1]; or
R1R3 = [R2 + 1/(2πfC1)] [R4 + 2πfL1];
When the bridge is balanced, the negative and positive reactive components cancel
out, so R1R3 = R2R4, or R4 = R1R3/R2
51
7.Schering bridge (AU APRIL DEC 2006)
(16).
A Schering Bridge is a bridge circuit used for measuring an unknown electrical
capacitance and its dissipation factor. The dissipation factor of a capacitor is the the ratio of
its resistance to its capacitive reactance. The Schering Bridge is basically a four-arm
alternating-current (AC) bridge circuit whose measurement depends on balancing the loads
on its arms. Figure 1 below shows a diagram of the Schering Bridge.
In the Schering Bridge above, the resistance values of resistors R1 and R2 are
known, while the resistance value of resistor R3 is unknown. The capacitance values of C1
and C2 are also known, while the capacitance of C3 is the value being measured. To
measure R3 and C3, the values of C2 and R2 are fixed, while the values of R1 and C1 are
adjusted until the current through the ammeter between points A and B becomes zero. This
happens when the voltages at points A and B are equal, in which case the bridge is said to
be 'balanced'.
When the bridge is balanced, Z1/C2 = R2/Z3, where Z1 is the impedance of R1 in
parallel with C1 and Z3 is the impedance of R3 in series with C3. In an AC circuit that has
a capacitor, the capacitor contributes a capacitive reactance to the impedance. The
capacitive reactance of a capacitor C is 1/2πfC.
As such, Z1 = R1/[2πfC1((1/2πfC1) + R1)] = R1/(1 + 2πfC1R1) while Z3 = 1/2πfC3 + R3.
Thus, when the bridge is balanced:
2πfC2R1/(1+2πfC1R1) = R2/(1/2πfC3 + R3); or
2πfC2(1/2πfC3 + R3) = (R2/R1)(1+2πfC1R1); or
C2/C3 + 2πfC2R3 = R2/R1 + 2πfC1R2.
When the bridge is balanced, the negative and positive reactive components are equal and
cancel out, so
2πfC2R3 = 2πfC1R2 or
52
R3 = C1R2 / C2.
Similarly, when the bridge is balanced, the purely resistive components are equal, so
C2/C3 = R2/R1 or
C3 = R1C2 / R2.
Note that the balancing of a Schering Bridge is independent of frequency.
7. Kelvin double Bridge (AU APRIL 2007)
(8).
A Kelvin bridge (also called a Kelvin double bridge and some countries
Thomson bridge) is a measuring instrument invented by William Thomson, 1st Baron
Kelvin. It is used to measure an unknown electrical resistance below 1 Ω. Its operation is
similar to the Wheatstone bridge except for the presence of additional resistors. These
additional low value resistors and the internal configuration of the bridge are arranged to
substantially reduce measurement errors introduced by voltage drops in the high current
(low resistance) arm of the bridge
ACCURACY
There are some commercial devices reaching accuracies of 2% for resistance ranges from
0.000001 to 25 Ω. Often, ohmmeters include Kelvin bridges, amongst other measuring
instruments, in order to obtain large measure ranges, for example, the Valhalla 4100 ATC
Low-Range Ohmmeter.
The instruments for measuring sub-ohm values are often referred to as low-resistance
ohmmeters, milli-ohmmeters, micro-ohmmeters, etc
PRINCIPLE OF OPERATION
The measurement is made by adjusting some resistors in the bridge, and the balance is
achieved
53
when:
Resistance R should be as low as possible (much lower than the measured value) and for
that reason is usually made as a short thick rod of solid copper. If the condition R3·R`4 =
R`3·R4 is met (and value of R is low), then the last component in the equation can be
neglected and it can be assumed that:
Which is equivalent to the Wheatstone bridge
9.
PMMC Instruments (DEC 2010)
(16)
The permanent magnet moving coil instruments are most accurate type for direct
current measurements. The action of these instruments is based on the motoring principle.
When a current carrying coil is placed in the magnetic field produced by permanent
magnet, the coil experiences a force and moves.
As the coil is moving and the magnet is permanent, the instrument is called
permanent magnet moving coil instrument. This basic principle is called D’Arsonval
principle. The amount of force experienced by the coil is proportional to the current
passing through the coil.
The moving coil is either rectangular or circular in shape. It has number of turns of
fine wire. The coil is suspended so that it is free to turn about its vertical axis.
The coil is placed in uniform, horizontal and radial magnetic field of a permanent
magnet in the shape of a horse-shoe. The iron core is spherical if coil is circular and is
cylindrical if the coil is rectangular. Due to iron core, the deflecting torque increase,
increasing the sensitivity of the instrument
The controlling torque is provided by two phosphor bronze hair springs.
The damping torque is provided by eddy current damping. It is obtained by movement of
aluminum former, moving in the magnetic field of the permanent
54
The pointer is carried by the spindle and it moves over a graduated scale. The
pointer has light weight so that it deflects rapidly. The mirror is placed below the pointer to
get the accurate reading by removing the parallax.
The weight of the instrument is normally counter balanced by the weights situated
diametrically opposite and rapidly connected to it. The scale markings of the basic d.c
PMMC instruments are usually linearly spaced as the deflecting torque and hence the
pointer deflections are directly proportional to the current passing through the coil.
The top view of PMMC instrument is shown in the below image.
The various advantages of PMMC instruments are, It has uniform scale.
With a powerful magnet, its torque to weight ratio is very high. So operating current of
PMMC is small. The sensitivity is high. The eddy currents induced in the metallic former
over which coil is wound, provide effective damping. It consumes low power, of the order
of 25 W to 200 mW. It has high accuracy. Instrument is free from hysteresis error.
Extension of instrument range is possible. Not affected by external magnetic fields called
stray magnetic fields
55
Unit-II BASIC ELECTRONIC MEASUREMENTS
Electronic Multimeters :
Introduction: The cathode-ray oscilloscope (CRO) is a common laboratory instrument that
provides accurate time and aplitude measurements of voltage signals over a wide range of
frequencies. Its reliability, stability, and ease of operation make it suitable as a general
purpose laboratory instrument. The heart of the CRO is a cathode-ray tube shown
schematically in Fig. 1.
56
The cathode ray is a beam of electrons which are emitted by the heated cathode
(negative electrode) and accelerated toward the fluorescent screen. The assembly of the
cathode, intensity grid, focus grid, and accelerating anode (positive electrode) is called
an electron gun. Its purpose is to generate the electron beam and control its intensity and
focus. Between the electron gun and the fluorescent screen are two pair of metal plates one oriented to provide horizontal deflection of the beam and one pair oriented ot give
vertical deflection to the beam. These plates are thus referred to as the horizontal and
vertical deflection plates. The combination of these two deflections allows the beam to
reach any portion of the fluorescent screen. Wherever the electron beam hits the screen,
the phosphor is excited and light is emitted from that point. This coversion of electron
energy into light allows us to write with points or lines of light on an otherwise darkened
screen.In the most common use of the oscilloscope the signal to be studied is first
amplified and then applied to the vertical (deflection) plates to deflect the beam
vertically and at the same time a voltage that increases linearly with time is applied to
the horizontal (deflection) plates thus causing the beam to be deflected horizontally at a
uniform (constant> rate. The signal applied to the verical plates is thus displayed on the
screen as a function of time. The horizontal axis serves as a uniform time scale.The
linear deflection or sweep of the beam horizontally is accomplished by use of a sweep
generator that is incorporated in the oscilloscope circuitry. The voltage output of such a
57
generator is that of a sawtooth wave as shown in Fig. 2. Application of one cycle of this
voltage difference, which increases linearly with time, to the horizontal plates causes the
beam to be deflected linearly with time across the tube face. When the voltage suddenly
falls to zero, as at points (a) (b) (c), etc...., the end of each sweep - the beam flies back to
its initial position. The horizontal deflection of the beam is repeated periodically, the
frequency of this periodicity is adjustable by external controls.
To obtain steady traces on the tube face, an internal number of cycles of the unknown
signal that is applied to the vertical plates must be associated with each cycle of the sweep
generator. Thus, with such a matching of synchronization of the two deflections, the pattern
on the tube face repeats itself and hence appears to remain stationary. The persistance of
vision in the human eye and of the glow of the fluorescent screen aids in producing a
stationary pattern. In addition, the electron beam is cut off (blanked) during flyback so that
the retrace sweep is not observed.
CRO Operation: A simplified block diagram of a typical oscilloscope is shown in Fig. 3.
In general, the instrument is operated in the following manner. The signal to be displayed is
amplified by the vertical amplifier and applied to the vertical deflection plates of the CRT.
A portion of the signal in the vertical amplifier is applied to the sweep trigger as a triggering
signal. The sweep trigger then generates a pulse coincident with a selected point in the cycle
of the triggering signal. This pulse turns on the sweep generator, initiating the sawtooth
wave form. The sawtooth wave is amplified by the horizontal amplifier and applied to the
horizontal deflection plates. Usually, additional provisions signal are made for applying an
external triggering signal or utilizing the 60 Hz line for triggering. Also the sweep generator
may be bypassed and an external signal applied directly to the horizontal amplifier.
58
CRO Controls :
The controls available on most oscilloscopes provide a wide range of operating
conditions and thus make the instrument especially versatile. Since many of these controls
are common to most oscilloscopes a brief description of them follows.
59
CATHODE-RAY TUBE
Power and Scale Illumination: Turns instrument on and controls illumination of the
graticule.
Focus: Focus the spot or trace on the screen.
Intensity: Regulates the brightness of the spot or trace.
VERTICAL AMPLIFIER SECTION
Position: Controls vertical positioning of oscilloscope display.
Sensitivity: Selects the sensitivity of the vertical amplifier in calibrated steps.
Variable Sensitivity: Provides a continuous range of sensitivities between the calibrated
steps. Normally the sensitivity is calibrated only when the variable knob is in the fully
clockwise position.
AC-DC-GND: Selects desired coupling (ac or dc) for incoming signal applied to vertical
amplifier, or grounds the amplifier input. Selecting dc couples the input directly to the
amplifier; selecting ac send the signal through a capacitor before going to the amplifier thus
blocking any constant component.
60
HORIZONTAL-SWEEP SECTION
Sweep time/cm: Selects desired sweep rate from calibrated steps or admits external signal
to horizontal amplifier.Sweep time/cm Variable: Provides continuously variable sweep
rates. Calibrated position is fully clockwise.Position: Controls horizontal position of trace
on screen.Horizontal Variable: Controls the attenuation (reduction) of signal applied to
horizontal aplifier through Ext. Horiz. connector.
TRIGGER
The trigger selects the timing of the beginning of the horizontal sweep.
Slope: Selects whether triggering occurs on an increasing (+) or decreasing (-) portion of
trigger signal.
Coupling: Selects whether triggering occurs at a specific dc or ac level.
Source: Selects the source of the triggering signal.
INT - (internal) - from signal on vertical amplifier
EXT - (external) - from an external signal inserted at the EXT. TRIG. INPUT.
LINE - 60 cycle triger
Level: Selects the voltage point on the triggering signal at which sweep is triggered. It also
allows automatic (auto) triggering of allows sweep to run free (free run).
CONNECTIONS FOR THE OSCILLOSCOPE
Vertical Input: A pair of jacks for connecting the signal under study to the Y (or vertical)
amplifier. The lower jack is grounded to the case.
Horizontal Input: A pair of jacks for connecting an external signal to the horizontal
amplifier. The lower terminal is graounted to the case of the oscilloscope.
External Tigger Input: Input connector for external trigger signal.
Cal. Out: Provides amplitude calibrated square waves of 25 and 500 millivolts for use in
calibrating the gain of the amplifiers.
Accuracy of the vertical deflection is + 3%. Sensitivity is variable.
Horizontal sweep should be accurate to within 3%. Range of sweep is variable.
Operating Instructions: Before plugging the oscilloscope into a wall receptacle, set the
controls as follows:
(a) Power switch at off
(b) Intensity fully counter clockwise
(c) Vertical centering in the center of range
61
(d) Horizontal centering in the center of range
(e) Vertical at 0.2
(f) Sweep times 1
Plug line cord into a standard ac wall recepticle (nominally 118 V). Turn power on. Do not
advance the Intensity Control.Allow the scope to warm up for approximately two minutes,
then turn the Intensity Control until the beam is visible on the screen.
PROCEDURE:
I. Set the signal generator to a frequency of 1000 cycles per second. Connect the output from
the gererator to the vertical input of the oscilloscope. Establish a steady trace of this input
signal on the scope. Adjust (play with)all of the scope and signal generator controls until
you become familiar with the functionof each. The purpose fo such "playing" is to allow the
student to become so familiar with the oscilloscope that it becomes an aid (tool) in making
measurements in other experiments and not as a formidable obstacle. Note: If the vertical
gain is set too low, it may not be possible to obtain a steady trace.
II. Measurements of Voltage: Consider the circuit in Fig. 4(a). The signal generator is used
to produce a 1000 hertz sine wave. The AC voltmeter and the leads to the vertical input of
the oscilloscope are connected across the generator's output. By adjusting the Horizontal
Sweep time/cm and trigger, a steady trace of the sine wave may be displayed on the screen.
The trace represents a plot of voltage vs. time, where the vertical deflection of the trace
about the line of symmetry CD is proportional to the magnitude of the voltage at any instant
of time.
62
To determine the size of the voltage signal appearing at the output of terminals of the
signal generator, an AC (Alternating Current) voltmeter is connected in parallel across these
terminals (Fig. 4a). The AC voltmeter is designed to read the dc "effective value" of the
voltage. This effective value is also known as the "Root Mean Square value" (RMS) value
of the voltage.The peak or maximum voltage seen on the scope face (Fig. 4b) is Vm volts
and is represented by the distance from the symmetry line CD to the maximum deflection.
The relationship between the magnitude of the peak voltage displayed on the scope and the
effective or RMS voltage (VRMS) read on the AC voltmeter is
VRMS = 0.707 Vm (for a sine or cosine wave).
Thus
Agreement is expected between the voltage reading of the multimeter and that of the
oscilloscope. For a symmetric wave (sine or cosine) the value of Vm may be taken as 1/2 the
peak to peak signal Vpp.The variable sensitivity control a signal may be used to adjust the
display to fill a concenient range of the scope face. In this position, the trace is no longer
calibrated so that you cannot just read the size of the signal by counting the number of
divisions and multiplying by the scale factor. However, you can figure out what the new
calibration is an use it as long as the variable control remains unchanged.Caution: The
mathematical prescription given for RMS signals is valid only for sinusoidal signals. The
meter will not indicate the correct voltage when used to measure non-sinusoidal signals.
III. Frequency Measurements: When the horizontal sweep voltage is applied, voltage
measurements can still be taken from the vertical deflection. Moreover, the signal is
displayed as a function of time. If the time base (i.e. sweep) is calibrated, such
measurements as pulse duration or signal period can be made. Frequencies can then be
determined as reciprocal of the periods.Set the oscillator to 1000 Hz. Display the
signal on the CRO and measure the period of the oscillations. Use the horizontal
distance between two points such as C to D in Fig. 4b.Set the horizontal gain so that
only one complete wave form is displayed.Then reset the horizontal until 5 waves are
seen. Keep the time base control in a calibrated position. Measure the distance (and
63
hence time) for 5 complete cycles and calculate the frequency from this measurement.
Compare you result with the value determined above.Repeat your measurements for
other frequencies of 150 Hz, 5 kHz, 50 kHz as set on the signal generator.
IV. Lissajous Figures: When sine-wave signals of different frequencies are input to the
horizontal and vertical amplifiers a stationary pattern is formed on the CRT when the ratio
of the two frequencies is an intergral fraction such as 1/2, 2/3, 4/3, 1/5, etc. These stationary
patterns are known as Lissajous figures and can be used for comparison measurement of
frequencies.Use two oscillators to generate some simple Lissajous figures like those shown
in Fig.5. You will find it difficult to maintain the Lissajous figures in a fixed configuration
because the two oscillators are not phase and frequency locked. Their frequencies and
phase drift slowly causing the two different signals to change slightly with respect to each
other.
V. Testing what you have learned: Your instructor will provide you with a small oscillator
circuit. Examine the input to the circuit and output of the circuit using your oscilloscope.
Measure such quantities as the voltage and frequency of the signals. Specify if they are
sinusoidal or of some other wave character. If square wave, measure the frequency of the
wave. Also, for square waves, measure the on time (when the voltage is high) and off time
(when it is low).
64
Q meter :
Introduction:
For many years, the Q meter has been an essential piece of equipment for laboratories
engaged in the testing of radio frequency circuits. In modem laboratories, the Q meter has
been largely replaced by more exotic (and more expensive) impedance measuring devices
and today, it is difficult to find a manufacturer who still makes a Q meter. For the radio
amateur, the Q meter is still a very useful piece of test equipment and the writer has given
some thought to how a simple Q meter could be made for the radio shack. For those who are
unfamiliar with this type of instrument, a few introductory notes on the definition of Q and
the measurement of Q, are included.
WHAT IS Q AND HOW IS IT MEASURED?
The Q factor or quality factor of an inductance is commonly expressed as the ratio of its
series reactance to its series resistance. We can also express the Q factor of a capacitance as
the ratio of its series reactance to its series resistance although capacitors are generally
specified by the D or dissipation factor which is the reciprocal of Q.A tuned circuit, at
resonance, is considered to have a Q factor. In this case, Q is equal to the ratio of either the
inductive reactance, or the capacitive reactance, to the total series loss resistance in the
tuned circuit. The greater the loss resistance and the lower the Q, the greater the power lost
on each cycle of oscillation in the tuned circuit and hence the greater the power needed to
maintain oscillation.
Another way to derive Q is as follows:
Q = fo/Δf where fo is the resonant frequency and Δf is the 3 dB bandwidth.Sometimes we
talk of loaded Q (such as in transmitter tank circuits) and, in this case, resistance for
calculation of Q is the unloaded tuned circuit series resistance plus the additional loss
resistance reflected in series into the circuit from its coupled load. There are other
ways of expressing Q factor. It can be expressed approximately as the ratio of
equivalent shunt resistance to either the inductive or the capacitive reactance. Series
loss resistance can be converted to an equivalent shunt resistance using the following
formula:
65
R(shunt) = R (series). (Q² + 1)
Finally, Q factor of a resonant circuit is equal to its voltage magnification factor and
Q can also be expressed as the ratio of voltage developed across its reactive elements to the
voltage injected in series with the circuit to produce the developed voltage. To measure Q
factor, Q meters make use of this principle.A basic Q meter is shown in Figure 1.
Terminals are provided to connect the inductance (Lx) to be measured and this is resonated
by a variable tuning capacitor (C). Terminals are also provided to add capacitance (Cx), if
required. The tuned circuit is excited from a tunable signal source which develops voltage
across a resistor in series with the tuned circuit. The resistor must have a resistance small
compared to the loss resistance of the components to be measured so that its value can be
ignored. A resistance of a mere fraction of an ohm is necessary. Metering is provided to
measure the AC injection voltage across the series resistor and the AC output voltage
across the terminals of the tuning capacitor. The output measurement must be a high input
impedance circuit to prevent loading of the tuned circuit by the metering circuit.
Basic Q Meter
At resonance of Lx and Cx, Q = V2/V1
*Meter V2 is Calibrated to read voltage referred to that across C.
Q is measured by adjusting the source frequency and/or the tuning capacitor for a
peak in output voltage corresponding to resonance. Q factor is calculated as the ratio of
output voltage measured across the tuned circuit to that injected into it. In practice, the
signal source level is generally set for a calibrate point on the meter which measures injected
voltage and Q is directly read from calibration on the meter which measures output voltage.
66
Some of the uses of Q Meter:
The Q meter can be used for many purposes. As the name implies, it can measure Q and is
generally used to check the Q factor of inductors. As the internal tuning capacitor has an air
dielectric its loss resistance is negligible compared to that of any inductor and hence the Q
measured is that of the inductor. The value of Q varies considerable with different types of
inductors used over different ranges of frequency. Miniature commercial inductors, such as
the Siemens B78108 types or the Lenox-Fugal Nanored types, made on ferrite cores and
operated at frequencies up to 1MHz, have typical Q factors in the region of 50 to 100. Air
wound inductors with spaced turns, such as found in transmitter tank circuits and operating
at frequencies above 10 MHz, can be expected to have Q factors of around 200 to 500.
Some inductors have Q factors as low as five or 10 at some frequencies and such inductors
are generally unsuitable for use in selective circuits or in sharp filters. The Q meter is very
useful to check these out.The tuning capacitor (C) of the Q meter has a calibrated dial
marked in pico-farads so that, in conjunction with the calibration of the oscillator source,
the value of inductance (Lx) can be derived. The tuned circuit is simply set to resonance by
adjusting the frequency and/or the tuning capacitor for a peak in the output voltage meter
and then calculating the inductance (Lx) from the usual formula:
Lx = 1/4π²f²C
For L in μH, C in pF and f in MHz this reduces to: 25330/f²C
Another use of the Q meter is to measure the value of small capacitors. Providing the
capacitor to be tested is smaller than the tuning range of the internal tuning capacitor, the
test sample can be easily measured. Firstly, the capacitor sample is resonated with a selected
inductor by adjusting the source frequency and using the tuning capacitor set to a low value
on its calibrated scale. The sample is then disconnected and using the same frequency as
before, the tuning capacitor is reset to again obtain resonance. The difference in tuning
capacitor calibration read for the two tests is equal to the capacitance of the sample. Larger
values of capacitance can be read by changing frequency to obtain resonance on the second
test and manipulating the resonance formula. A poorly chosen inductor is not the only cause
of low Q in a tuned circuit as some types of capacitor also have high loss resistance which
lowers the Q. Small ceramic capacitors are often used in tuned circuits and many of these
have high loss resistance, varying considerably in samples often taken from the same batch.
If ceramic capacitors must be used where high Q is required, it is wise to select them for
low loss resistance and the Q meter can be used for this purpose. To do this, an inductor
67
having a high Q, of at least 200, is used to resonate the circuit, first with the tuning
capacitor (C) on its own and then with individual test sample capacitors in parallel. A
drastic loss in the value of Q, when the sample is added, soon shows up which capacitor
should not be used.
DISTRIBUTED COIL CAPACITANCE :
Direct measurement of Q in an inductor, as discussed in previous paragraphs. is based on the
circuit having two components, inductance and capacitance. Inductors also have distributed
capacitance (Cd) and if this represents a significant portion of the total tuning capacitance,
the Q value read will be lower than its actual value. High distributed capacitance is common
in large value inductors having closely wound turns or having multiple layers.
Actual Q can be calculated from Qe, as read, from the following:
Q = Qe (1 + Cd/C)
where Cd = Distributed capacitance
and C = Tuning Capacitance
Q value error is reduced by resonating with a large value of tuning capacitance, otherwise
distributed capacitance can be measured and applied to the previous formula. Two methods
of measuring distributed capacitance are described in the "Boonton Q Meter Handbook".
The simplest of these is said to be accurate for distributed capacitance above 10 pF and this
method is described as follows:
1. With the tuning capacitor (C) set to value C1 (say 50 pF), resonate with the sample
inductor by adjusting the signal source frequency.
2. Set the signal source to half the original frequency and re-resonate by adjusting C to a
new value of capacitance C2.
3. Calculate distributed capacitance as follows: Cd = (C2 -4C1) /3
Another effect of distributed capacitance in the inductor is to make its inductance value (as
calculated from the calibration of the tuning capacitance and the calibration of the signal
source) appear higher than its actual value. Again, this error can be reduced by tuning with a
large value of capacitance C and/or adding Cd to C in the calculation
68
Question Bank
UNIT-II
BASIC ELECTRONIC MEASUREMENTS
PART-A (2 Marks)
1. What is vector voltmeter?
The voltmeter which is defined as the ratio of power stored in the element to the power
dissipated in the element. It is also defined as the ratio of reactance to resistance of the
reactive element. It is also defined as the ratio of reactance to resistance of the reactive
element.
2. What are the main parts of CRT?
The main parts of CRT are 1) Electron gun, 2) Deflection system, 3) Fluorescent
screen,
4) Glass tube and 5) Base.
3. Define deflection sensitivity of CRO.
The horizontal deflection x is proportional to the horizontal deflection voltage V x
applied to x input.
4. What is fluorescence?
The material like phosphor converts electrical energy to light energy. Thus phosphor
emits light when bombarded by the electrons. This emission of light due to excitation of
phosphor is called fluorescence.
5. What is the principle of sampling oscilloscope?
Using sampling procedure, high frequency signal is converted to the low frequency
signal. Thus instead of monitoring the input signal continuously it is sampled at the regular
intervals. These samples are presented on the screen in the form of dots. Such samples are
merged to reconstruct the input signal. The very high frequency more than 300 MHz
performance can be achieved using sampling technique used in the sampling oscilloscope.
6. What is an electronic voltmeter?
The voltmeter which uses rectifiers, diodes and other supporting electronic circuits to
produce a current proportional to the quantity to be measured is called electronic
voltmeter.
7. Define Q factor of coil.
The Q factor is defined as the ratio of power stored in the element to the power
dissipated in the element. It also defined as the ratio of reactance to the resistance of the
reactive element. Thus for a coil it is defined as Q = X L / R.
69
8. State the advantages of chopper amplifier.
Chopper eliminates the need for a high gain DC amplifier which has drift and stability
problems.
The input impedance is very high for direct current.
A very high gain of the order of 105 to 106 can be achieved.
9. What is the function of focusing anodes?
The electron beam consists of many electrons and all are similarly charged. Hence
the electrons repel each other. Due to such repulsive forces, the beam tends to diverge. To
compensate for such repulsive forces and produce sharp beam spot, an adjustable
electrostatic field is created between the two cylindrical anodes which are called focusing
anodes.
10. What is the function of trigger circuit?
It is necessary that the horizontal deflection starts at the same point of the input vertical
signal, each time it sweeps. Hence to synchronize horizontal deflection with vertical
deflection, the trigger circuit is used.
PART-B (16 Marks)
1. Vector voltmeter. (AU APRIL 2003,2005)
(16).
The vector voltmeter gives on line both, phase and amplitude of the ERG
(electroretinogram) response to a flickering stimulus. This makes the apparatus useful in
determining spectral sensitivity functions and dark adaptation curves of man and animals,
in particular since it enables automatic measurement of these functions. The limitations
and applications are briefly discussed.
In electroretinography (ERG) the use of the averaging computer has become standard
practice for extracting the often low responses from the background electrical noise. If,
besides the response magnitude the waveform of the response is of interest to the
experimenter, the averaging technique indeed is a powerful tool.
There are situations however, in which the waveform of the ERG is not of primary
interest, for instance for the determination of spectral sensitivity functions, or the recovery
of sensitivity after exposure to a very bright light (dark adaptation curve).
The usual way to measure, e.g., spectral sensitivity, is to obtain a set of response vs.
intensity curves and then, for each wavelength, to determine the intensity necessary to
evoke a certain criterion response. In this particular application the averaging technique is
an inefficient and time consuming way of data reduction:
70
One measures by hand the amplitude of the waveform from the obtained records while
the waveform itself is disregarded in the final sensitivity curves. Besides being time
consuming the averaging technique constitutes more problems.
Because of uncontrollable non stationarities (e.g., eye movements, blinks) the accuracy
is considerably limited, as the averaged response is only available off-line after, e.g.,
plotting on a recorder. These drawbacks cumulate if one wants to measure dark adaptation
curves, as they represent a change of sensitivity in time. Recently a so called "vector
voltmeter" has become commercially available, which operates essentially with a flickering
stimulus. The apparatus selectively amplifies the stimulus-locked part of the ERG, canceling at the
same time the non stimulus locked background noise. In this respect its action is comparable to an
averaging computer, but with the enormous advantage that it gives on line, the response magnitude
as a DC (direct current) voltage.
This opens the possibility of adjusting the light intensity such that a criterion response is
obtained, which is analogous to what is done in psychophysical sensitivity measurements.
With an extension of the basic system even automatic measurement of the spectral sensitivity
functions and the dark adaptation curve becomes possible. In this paper, a short description of the
operation of the vector voltmeter in ERGs will be given, together with examples of its performance
in the measurement of spectral sensitivity and dark adaptation.
2. Solid state electronic multimeter (AU APRIL2003,2005)
(16).
A multimeter or a multitester, also known as a volt/ohm meter or VOM, is an
electronic measuring instrument that combines several measurement functions in one unit.
A typical multimeter may include features such as the ability to measure voltage, current
and resistance. Multimeters may use analogor digital circuits—analog multimeters and
digital multimeters (often abbreviated DMM or DVOM.) Analog instruments are usually
based on amicroammeter whose pointer moves over a scale calibration for all the different
measurements that can be made; digital instruments usually display digits, but may display
a bar of a length proportional to the quantity measured.
71
A multimeter can be a hand-held device useful for basic fault finding and field service
work or a bench instrument which can measure to a very high degree of accuracy. They
can be used to troubleshoot electrical problems in a wide array of industrial and household
devices such as electronic equipment, motor controls, domestic appliances, power
supplies, and wiring systems.
The first moving-pointer current-detecting device was the galvanometer. These
were used to measure resistance and voltage by using a Wheatstone bridge, and
comparing the unknown quantity to a reference voltage or resistance. While useful in
the lab, the devices were very slow and impractical in the field. These galvanometers
were bulky and delicate.
The D'Arsonval/Weston meter movement used a fine metal spring to give
proportional measurement rather than just detection, and built-in permanent field
magnets made deflection independent of the 3D orientation of the meter. These
features enabled dispensing with Wheatstone bridges, and made measurement quick
72
and easy. By adding a series or shunt resistor, more than one range of voltage or
current could be measured with one movement.
Multimeters were invented in the early 1920s as radio receivers and other vacuum tube
electronic devices became more common.
QUANTITIES MEASURED
Contemporary multimeters can measure many quantities. The common ones are:
Voltage, alternating and direct, in volts.
Current, alternating and direct, in amperes. The frequency range for which AC
measurements are accurate must be specified.
Resistance in ohms.
ADDITIONALLY, SOME MULTIMETERS MEASURE:
Capacitance in farads.
Conductance in siemens.
Decibels.
Duty cycle as a percentage.
Frequency in hertz.
Inductance in henrys.
Temperature in degrees Celsius or Fahrenheit, with an appropriate temperature
test probe, often a thermocouple.
DIGITAL MULTIMETERS MAY ALSO INCLUDE CIRCUITS FOR:
Continuity; beeps when a circuit conducts.
Diodes (measuring forward drop of diode junctions, i.e., diodes and transistor
junctions) and transistors (measuring current gain and other parameters).
Battery checking for simple 1.5 volt and 9 volt batteries. This is a current
loaded voltage scale. Battery checking (ignoring internal resistance, which
increases as the battery is depleted), is less accurate when using a DC voltage
scale.
VARIOUS SENSORS CAN BE ATTACHED TO MULTIMETERS TO TAKE
MEASUREMENTS SUCH AS:
Light level
Acidity/Alkalinity(pH)
Wind speed
Relative humidity
73
DIGITAL
While a digital display can easily be extended in precision, the extra digits are of
no value if not accompanied by care in the design and calibration of the analog
portions of the multimeter. Meaningful high-resolution measurements require a good
understanding of the instrument specifications, good control of the measurement
conditions, and traceability of the calibration of the instrument.
ANALOG
Resolution of analog multimeters is limited by the width of the scale pointer,
vibration of the pointer, the accuracy of printing of scales, zero calibration, number of
ranges, and errors due to non-horizontal use of the mechanical display. Accuracy of
readings obtained is also often compromised by miscounting division markings, errors
in mental arithmetic, parallax observation errors, and less than perfect eyesight.
Mirrored scales and larger meter movements are used to improve resolution; two and a
half to three digits equivalent resolution is usual (and is usually adequate for the
limited precision needed for most measurements).
3. Explain the working principle of Q meter. (AU APRIL, DEC 2006)
(8)
The Q Meter has frequently been described as one of the most flexible instruments
available with applications limited largely by the ingenuity of the person using it. It is
our desire here to delineate some of those techniques, not normally encountered in
everyday work, in the hope that wider dissemination of information gathered through
many channels, will prove of some value. In order to approach our specific problems in
a general way, it might be well to review some basic facts relative to the operation of
the Q Meter. The Q Meter is always operated with a coil connected to its coil
terminals.
If we are interested in measuring the Q of a coil, this coil will be connected to
these terminals and it will be measured in one operation. If we are interested in making
other measurements; (i.e., the Q of a capacitor, the impedance of a circuit, the
parameters of a tuned circuit; etc.), we still need a coil, even though we are interested
in that particular coil only as .a reference. This so-called “work coil“ would probably
be a shielded unit to prevent stray coupling, hand-capacitance effects, etc.; and might
be selected for its inductance, Q; etc., as needed for the particular application
involved.
In making measurements (other than the Q of a coil} of circuit parameters there
will be two steps involved. The first will be with the work coil mounted on the Q
meter, where the resonating capacitance (Cl), circuit Q (Ql), and frequency will be
recorded. The second will be with the unknown connected in addition to the work coil
and once again the above reading will be noted, this time as C2 and Qz.
74
From this data the desired parameters can be determined using the appropriate
formula selected from those shown in figure 2. High impedance circuits are measured
by connecting them in parallel with the Q Cupacibor; i.e., across the “Capacitor”
terminals, and using the formulas shown under the heading “Parallel Connection to Q
Circuit”. If the unknown consists of more than one parameter, it should be noted that
the equivalent parallel parameters are obtained in this manner.
Low impedance circuits are measured by connecting them in series with the
“Low” side of the coil. In like manner the “Series Connection to Q Circuit” formulas
are used to yield the equivalent series $urdmeters of the circuit involved. With the
above in mind, it might be well to resolve some specific problems.
4. CRO ( Cathode ray oscilloscope)
(AU APRIL 2003, 2004 DEC 2005)
The device consists mainly of a vacuum tube which contains a cathode, anode,
grid, X&Y-plates, and a fluorescent screen (see Figure below). When the cathode is
heated (by applying a small potential difference across its terminals), it emits electrons.
Having a potential difference between the cathode and the anode (electrodes),
accelerate the emitted electrons towards the anode, forming an electron beam, which
passes to fall on the screen.
When the fast electron beam strikes the fluorescent screen, a bright visible spot is
produced. The grid, which is situated between the electrodes, controls the amount of
electrons passing through it thereby controlling the intensity of the electron beam. The
X&Y-plates, are responsible for deflecting the electron beam horizontally and
75
vertically. A sweep generator is connected to the X-plates, which moves the bright spot
horizontally across the screen and repeats that at a certain frequency as the source of
the signal. The voltage to be studied is applied to the Y-plates. The combined sweep
and Y voltages produce a graph showing the variation of voltage with time.
BLOCK DIAGRAM
TECHNICAL INFORMATION
Some technical parameters:
Bandwidth: 0 –20 MHz to 0 –few GHz
High input impedance
Sensitivity: From μVcm-1to few 100 Vcm-1
Basic Classification:
Manual
Programmable
Automatic
Averaging
CLASSIFICATION
Storage Oscilloscope
Sampling Oscilloscope
Digital Oscilloscope
Storage Oscilloscope:
Special CRT which can store a waveform
Used to capture and examine non-repetitive signals
Used to store signals with low frequencies (10Hz)
Highest frequency that can be recorded : 0.1MHz
76
Sampling Oscilloscope:
Used in the case of repetitive waveforms
Equivalent Sampling:
One sample is taken from every period
Shape of signal is acquired when displayed sequentially
Frequency limit: 10-50GHz
Sensitive to noise
Random Sampling:
Samples of signal and time base are taken randomly
Samples are displayed randomly rather in sequence
No frequency limitation (theoretically)
Digital Oscilloscope:
Contain memory facility for storage or precision measurement
Uses input signal sampling, A to D conversion or DSP
Plotters can be attached to oscilloscopes to obtain hard copies of recorded signal
Instrumentation interfaces can be used for interconnected measurements
5.
CRT (AU APRIL 2003)
(8).
A Video Display Controller or VDC is an integrated circuit which is the main
component in a video signal generator, a device responsible for the production of a TV
video signal in a computing or game system. Some VDCs also generate a sound signal, but
in that case it's not their main function. VDCs were most often used in the old homecomputers of the 80s, but also in some early video game systems.
The VDC is always the main component of the video signal generator logic, but
sometimes there are also other supporting chips used, such as RAM to hold the pixel data,
ROM to hold character fonts, or perhaps some discrete logic such as shift registers were
necessary to build a complete system. In any case, it's the VDC's responsibility to generate
the timing of the necessary video signals, such as the horizontal and vertical
synchronisation signals, and the blanking interval signal.
Most often the VDC chip is completely integrated in the logic of the main
computer system, (its video RAM appears in the memory map of the main CPU), but
sometimes it functions as a coprocessorthat can manipulate the video RAM contents
independently
Video Display Controllers vs. Video Display Processors and Graphics processing
units The difference between a VDC and the more modern Video Display Processor
(VDP) is not that the VDCs could not generate graphics, but they did not have the special
77
hardware accelerators to create2D and 3D images, while a typical 1990s VDP does have at
least some form of hardware graphics acceleration. Also VDCs often had special hardware
for the creation of "sprites", a function that in more modern VDP chips is done with the
"Bit Blitter" using the "Bit blit" function.
One example of a typical Video Display Processor is the "VDP2 32-bit background
and scroll plane video display processor" of the Sega Saturn. Another example is the
Advanced Graphics Architecture (AGA) chip that was used for the improved graphics
of the later generation Amiga computers.
This said, it is not completely clear when a "Video chip" is a "Video Display
Controller" and when it is a "Video Display Processor". For example, the TMS9918 is
sometimes called a "Video Display Controller" and sometimes a "Video Display
Processor". In general however a "Video Display Processor" has some power to "Process"
the contents of the Video RAM (filling an area of RAM for example), while a "Video
Display Controller" only controls the timing of the Video synchronisation signals and the
access to the Video RAM.
The Graphics processing unit (GPU) goes one step further than the VDP and
normally also supports 3D functionality. It is the chip that is now used in modern personal
computers.
Types of Video Display Controllers
Video Display controllers can be (arbitrarily) divided in several different types (here
listed from simple to complex);
Video shifters, or "Video shift register based systems" (there is no generally agreed
upon name for these type of devices) are the most simple type of video controllers; they
are, (directly or indirectly) responsible for the video timing signals, but they normally do
not access the Video RAM directly. They get the video data from the main CPU, a byte at
a time, and convert it to a serial bitstream (hence the technical name "Video shifter"). This
serial data stream is then used, together with the synchronisation signals, to output a
(colour) video signal. The main CPU needs to do the bulk of the work. Normally these
chips only support a very low resolution Raster graphics mode.
A CRTC, or Cathode Ray Tube Controller, generates the video timings and reads
video data from a RAM attached to the CRTC, to output it via an external character
generator ROM, (for text modes) or directly, (for high resolution graphics modes) to the
video output shift register. Because the actual capabilities of the video generator depend to
a large degree on the external logic, video generator based on a CRTC chip can have a
wide range of capabilities. From very simple (text mode only) systems to very high
78
resolution systems supporting a wide range of colours. Sprites however are normally not
supported by these systems.
Video interface controllers are much more complex than CRT controllers, and the
external circuitry that is needed with a CRTC is embedded in the video controller chip.
Sprites are often supported, as are (RAM based) character generators and video RAM
dedicated to colour attributes and pallette registers (Color lookup tables) for the highresolution and/or text-modes.
Video coprocessors have their own internal CPU dedicated to reading (and writing)
their own video RAM, and converting the contents of this video RAM to a video signal.
The main CPU can give commands to the coprocessor, for example to change the video
modes or to manipulate the video ram contents. The video coprocessor also controls the
(most often RAM based) character generator, the colour attribute RAM, Palette registers
and the Spite logic (as long as these exist of course).
79
UNIT III - SIGNAL GENERATORS AND ANALYZERS
FUNCTION GENERATOR:
A function generator is a device which produces simple repetitive waveforms. Such
devices contain an electronic oscillator, a circuit that is capable of creating a repetitive
waveform. (Modern devices may use digital signal processing to synthesize waveforms,
followed by a digital to analog converter, or DAC, to produce an analog output). The most
common waveform is a sine wave, but sawtooth, step (pulse), square,and triangular
waveform oscillators are commonly available as are arbitrary waveform generators
(AWGs). If the oscillator operates above the audio frequency range (>20 kHz), the generator
will often include some sort of modulation function such as amplitude modulation (AM),
frequency modulation (FM), or phase modulation (PM) as well as a second oscillator that
provides an audio frequency modulation waveform.
Function generators are typically used in simple electronics repair and design; where
they are used to stimulate a circuit under test. A device such as an oscilloscope is then used
to measure the circuit's output. Function generators vary in the number of outputs they
feature, frequency range, frequency accuracy and stability, and several other parameters.A
function generator is a piece of electronic test equipment or software used to generate
electrical waveforms. These waveforms can be either repetitive or single-shot, in which case
some kind of triggering source is required (internal or external).Function Generators are
used in development, testing and repair of electronic equipment, e.g. as a signal source to
test amplifiers, or to introduce an error signal into a control loop.
Explanation
Analog function generators usually generate a triangle waveform as the basis for all of its
other outputs. The triangle is generated by repeatedly charging and discharging a capacitor
from a constant current source. This produces a linearly ascending or descending voltage
ramp. As the output voltage reaches upper and lower limits, the charging and discharging is
reversed using a comparator, producing the linear triangle wave. By varying the current and
the size of the capacitor, different frequencies may be obtained. Sawtooth waves can be
produced by charging the capacitor slowly, using a current, but using a diode over the
current source to discharge quickly - the polarity of the diode changes the polarity of the
resulting sawtooth, i.e. slow rise and fast fall, or fast rise and slow fall. A 50% duty cycle
square wave is easily obtained by noting whether the capacitor is being charged or
80
discharged, which is reflected in the current switching comparator's output. Other duty
cycles (theoretically from 0% to 100%) can be obtained by using a comparator and the
sawtooth or triangle signal. Most function generators also contain a non-linear diode
shaping circuit that can convert the triangle wave into a reasonably accurate sine wave. It
does so by rounding off the hard corners of the triangle wave in a process similar to
clipping in audio systems. A typical function generator can provide frequencies up to 20
MHz. RF generators for higher frequencies are not function generators in the strict sense
since typically produce pure or modulated sine signals only. Function generators, like most
signal generators, may also contain an attenuator, various means of modulating the output
waveform, and often the ability to automatically and repetitively "sweep" the frequency of
the output waveform (by means of a voltage- controlled oscillator) between two operatordetermined limits. This capability makes it very easy to evaluate the frequency response of
a given electronic circuit.Some function generators can also generate white or pink
noise.More advanced function generators use Direct Digital Synthesis (DDS) to generate
waveforms. Arbitrary waveform generators use DDS to generate any waveform that can be
described by a table of amplitudes.
Signal generator :
A signal generator, also known variously as function generator, pitch generator,
arbitrary waveform generator, digital pattern generator or frequency generator is an
electronic device that generates repeating or non-repeating electronic signals (in either the
analog or digital domains). They are generally used in designing, testing, troubleshooting,
and repairing electronic or electroacoustic devices; though they often have artistic uses as
well. There are many different types of signal generators, with different purposes and
applications (and at varying levels of expense); in general, no device is suitable for all
possible applications. Traditionally, signal generators have been embedded hardware units,
but since the age of multimedia-PCs, flexible, programmable software tone generators have
also been available.
Basic Sweep Generator
A basic system for the sweep generator is shown in figure 1. A low-frequency
sawtooth wave is generated from some form of oscillator or waveform generator. The
instantaneous voltage of the sawtooth wave controls the frequency of an RF oscillator with
its centre frequency set at the centre frequency of the device under test (filter or IF channel
81
etc). Over a single sweep of frequency, RF output voltage from the device, as a function of
time, is a plot of the filter response. By rectifying and RF filtering in a simple AM detector,
the output is converted to a DC voltage varying as a function of time and this voltage is
applied to the vertical input of the CRO. By synchronising the sweep of the CRO with the
sawtooth output, the device response is plotted on the CRO screen.
Figure 1 - Basic Sweep Generator arrangement
To achieve this for a range of frequencies, it is easiest to sweep a single frequency (say
1MHz) and heterodyne this to the test frequency required. The system developed is shown
in the block diagram, figure 2. A 1MHz oscillator is frequency modulated by the output of a
sawtooth generator operating at 33 Hz. The modulated output is beat with an external signal
generator set to provide the difference frequency centered at the center frequency of the
filter or IF circuit under test. The output of circuit under test is fed to a simple AM detector
which provides varying DC output level to fed the CRO vertical input. By synchronising the
CRO sweep circuit to the 33 Hz sweep generator, a plot of test circuit response is displayed
in terms of amplitude verses frequency
82
Total Harmonic Distortion (THD) Analyzers:
It calculates the total distortion introduced by all the harmonics of the fundamental
frequency wave. In most cases THD is the amount required to be calculated, rather than
distortion caused by individual harmonics. This type of analysis is very important in systems
(e.g. Audio) in which filters with extremely small passband/ stopband are desired, such as a
notch filter in a parametric equalizer.
Block Diagram of a THD Analyzer
This is a specific type of THD analyzer, in which basically the fundamental frequency of the
input wave is suppressed so as to remove it from the spectra of the meters used for distortion
measurement, and the total gain of all the harmonics, is calculated, thus obtaining the total
distortion caused by the harmonics.
83
Fig.The frequency response of a Fundamental Suppression Analyzer
A block diagram of a Fundamental Suppression Analyzer is shown in Fig.1. This basic
construction consists of three main sections: Input section with impedance matcher, a
rejection amplifier section and an output metering circuit. Notice the feedback from the
bridge amplifier to the pre-amp section, that enables the rejection circuit to work more
accurately.
Working :
The applied input wave is impedance matched with the rejection circuit with the help of an
attenuator and an impedance matcher. This signal is then applied to a pre-amplifier which
raises the signal level to a desired value. The following section consists of a Wien bridge.
The bridge is tuned to the fundamental frequency by frequency control and it is balanced for
zero output by adjusting the bridge controls, thus giving a notch in the frequency response of
the rejection section. After the Wien Bridge, a bridge amplifier follows that simply amplifies
low harmonic voltage levels to measurable higher levels. A feedback loop is formed from
Bridge Amp o/p to the Pre-Amp i/p thus eliminating even the slightest effect of fundamental
frequency. This filtered output is then applied to a meter amplifier which can be an
instrumentation amplifier. This amp raises the voltage levels to the compatibility of the
meter scale/digital meter which follows. Thus the total voltage obtained at the meter output
shows the amount of distortion present in the wave due to harmonics of fundamental.A
spectrum analyzer or spectral analyzer is a device used to examine the spectral composition
of some electrical, acoustic, or optical waveform. It may also measure the power spectrum.
84
Types :
There are analog and digital spectrum analyzers:
An analog spectrum analyzer uses either a variable band-pass filter whose midfrequency is automatically tuned (shifted, swept) through the range of frequencies of
which the spectrum is to be measured or a superheterodyne receiver where the local
oscillator is swept through a range of frequencies.
A digital spectrum analyzer computes the discrete Fourier transform
(DFT), a mathematical process that transforms a waveform into the
components of its frequency spectrum.
Some spectrum analyzers (such as "real-time spectrum analyzers") use a hybrid
technique where the incoming signal is first down-converted to a lower frequency using
superheterodyne techniques and then analyzed using fast fourier transformation (FFT)
techniques. Typical functionality: Allows one to fix the window of frequencies to
visualize and center the display on a chosen frequency. Controls the position and
function of markers and indicates the value of power. Several spectrum analyzers have
a "Marker Delta" function that can be used to measure Signal to Noise Ratio or
Bandwidth.
Bandwidth/average
Is a filter of resolution. The spectrum analyzer captures the measure on having displaced
a filter of small bandwidth along the window of frequencies.
Amplitude
The maximum value of a signal at a point is called amplitude. A spectrum analyzer
that implements amplitude analysis is called a Pulse height analyzer.Manages
parameters of measurement. It stores the maximum values in each frequency and a
solved measurement to compare it.
85
Superheterodyne spectrum
analyzer: Operation
Usually, a spectrum analyzer displays a power spectrum over a given frequency
range, changing the display as the properties of the signal change. There is a trade-off
between how quickly the display can be updated and the frequency resolution, which is
for example relevant for distinguishing frequency components that are close together.
With a digital spectrum analyzer, the frequency resolution is Δν = 1 / T, the inverse of the
time T over which the waveform is measured and Fourier transformed (according to
Uncertainty principle). With an analog spectrum analyzer, it is dependent on the
bandwidth setting of the bandpass filter. However, an analog spectrum analyzer will not
produce meaningful results if the filter bandwidth (in Hz) is smaller than the square root
of the sweep speed (in Hz/s)[citation needed], which means that an analog spectrum
analyzer can never beat a digital one in terms of frequency resolution for a given
acquisition time. Choosing a wider bandpass filter will improve the signal-to-noise ratio
at the expense of a decreased frequency resolution.
With Fourier transform analysis in a digital spectrum analyzer, it is necessary to
sample the input signal with a sampling frequency νs that is at least twice the highest
frequency that is present in the signal, due to the Nyquist limit. A Fourier transform will
then produce a spectrum containing all frequencies from zero to νs / 2. This can place
considerable demands on the required analog-to-digital converter and processing power for
the Fourier transform. Often, one is only interested in a narrow frequency range, for
example between 88 and 108 MHz, which would require at least a sampling frequency of
216 MHz, not counting the low-pass anti-aliasing filter. In such cases, it can be more
economic to first use a superheterodyne receiver to transform the signal to a lower range,
86
such as 8 to 28 MHz, and then sample the signal at 56 MHz. This is how an analog-digitalhybrid spectrum analyzer works. For use with very weak signals, a pre-amplifier can be
used, although harmonic and intermodulationdistortion may lead to the creation of new
frequency components that were not present in the original signal. A new method, without
using a high local oscillator (LO) (that usually produces a high-frequency signal close to
the signal) is used on the latest analyzer generation like Aaronia´s Spectran series. The
advantage of this new method is a very low noise floor near the physical thermal noise
limit of -174 dBm/Hz.A digital voltmeter typically consists of an analog to digital
converter (A/D) with a digital display. The analog signal is converted into a digital code
proportionate to the magnitude of the signal. Voltages from picovolts to megavolts are
measurable, though the scale usually graduates in millivolts, volts, or kilovolts.
Frequencies between zero and several megahertz may also be measured.
DVMs measure both alternating current (AC) and direct current (DC) in electronics.
Common laboratory and commercial applications involve electromechanical machinery with
a current flowing through wires and circuits. Often, a digital voltmeter is used to monitor a
unit, such as a generator. Portable or handheld devices, such as the digital multimeter
(DMM), for example, may combine several functions into one instrument measuring
voltage, current, and resistance. This is the preferred tool of an electrician. Many DVMs
integrate outputs for monitoring, controlling, transmitting, and printing of data. Advanced
systems are often connected to computers, allowing for automation, optimization of
processes, and prevention of malfunctions and critical failure safeties. Chemical plants can
convert measurements to voltage, and control and monitor temperature, pressure, level, or
flow. Medical equipment, such as x-ray machines, may use a digital voltmeter to make sure
the voltage of the equipment is in the proper range.
87
Question Bank
UNIT-III
SIGNAL GENERATORS AND ANALYZERS
PART-A (2 Marks)
1. What are the general requirements of signal generator? (AU APRIL 2007)
 The output frequency of signal generator should be very stable.
 The amplitude of output signal of signal generator should be controllable from
low values to relatively large values.
 The amplitude of output signal must be stable.
 The harmonic contents in the output should be as low as possible.
 The output signal should be distortion free.
2. What is an Oscillator?
The oscillator uses an active device such as an operational amplifier. The output of an
operational amplifier is fed back in phase with input. This positive feedback causes
regenerative action resulting an oscillation.
3. What is a function generator? (AU APRIL 2007)
The function generator is an instrument which generates different types of waveforms.
The frequency of these waveforms can be varied over wide range. The most required
common waveforms like sine, square, saw tooth, triangular and DC pulses.
4. What is sweep frequency generator? (AU NOV 2004)
Sweep frequency generator provides a sinusoidal output voltage whose frequency
varies smoothly and continuously over an entire frequency band. The process of frequency
modulation may be accomplished electronically or mechanically.
5. Give short notes on wave Analyzer. (AU APRIL 2010)
A wave analyzer is an instrument designed to measure relative amplitudes of single
frequency components in a complex waveform. It can analysis of waveforms includes the
determination of amplitude, frequency and phase angle of the harmonic components.
6. What are the two types of wave analyzer?
 Frequency selective wave analyzer.
 Heterodyne wave analyzer.
7. List few applications of wave analyzer
 To measure the harmonic distortion of an amplifier
 To carry out complete harmonic analysis
 To measure the signal energy with the well defined bandwidth.
8. What is meant by harmonic distortion? (AU APRIL 2005,2006)
88
The distortion caused due to the nonlinear behavior of the circuit elements is called
harmonic distortion.
9. Give few useful applications of spectrum analyzer (AU APRIL 2006)
 Modulation measurement.
 Continuous wave signal frequency stability.
 Harmonic distortion measurement.
 Noise measurement.
 Examining pulse modulation.
PART-B (16 Marks)
1. Describe the working of function generator with the block diagram. (AU APRIL,
NOV 2004,2005)
(16)
The function generator is an instrument which generates different types of waveforms.
The frequency of these waveforms can be varied over wide range. The most required
common waveforms like sine, square, saw tooth, triangular and DC pulses.
The function generator can be phase locked to a standard frequency of the source.
Then all the output waveforms of the generator will have same accuracy and stability as
that of standard source.
Block diagram
89
Frequency controlled voltage
It is used to regulate two current sources namely upper current source and lower
current source.
Upper and lower current source
The upper current source supplies constant current to an integrator. The lower
current source supplies opposite current to the integrator.
Integrator
The output voltage of integrator then increases linearly with time. Hence this controls
frequency. The output of the integrator has triangular waveform. The frequency of this
triangular waveform is determined by the magnitudes of the currents supplied by upper
current source and lower current source.
Voltage comparator or multivibartor
This circuit changes the state of the network when the output voltage integrator
equals the maximum predetermined upper level. To get square wave the output of the
integrator is passed through comparator. The voltage comparator delivers square wave
output voltage of same frequency as that of input triangular.
Diode resistance network
The sine wave is derived from triangular wave. The triangular wave is synthesized
into sine wave using diode resistance network. In this shaper circuit the slope of triangular
wave is changed as its amplitude changes. This results in a sine wave with less than 1 %
distortion.
The two output amplifiers provide two simultaneous, individually selected outputs
of any of the waveform functions.
The function of the signal generator is to supply signals of known amplitude and
known frequency.
Features of function generators
 The frequency range is 0.01Hz to 100 KHz.
 Accuracy + 1 %
 Can be phase locked to another external signal source
 Can produce various waveforms.
90
2. Describe the working of spectrum analyzer with a block diagram. Explain the
various applications of the spectrum analyzer. (AU APRIL 2007, NOV 2005,
2008)
(16)
Based on the technique used, the spectrum analyzers can be classified as scanning
type and non-scanning type. The scanning type analyzers use swept technique, while
the non-scanning type is called real time spectrum analyzers.
Let us discuss the basic spectrum analyzer using swept technique. This analyzer
uses a swept receiver of superhetrodyne type hence this analyzer is also called swept
superhetrodyne spectrum analyzer.
Block diagram
The basic blocks of the swept superhetrodyne spectrum analyzer are
I.
II.
Wideband input mixer
Swept local oscillator driving wideband mixer
III.
Resolution bandwidth filter, deciding intermediate frequency
IV.
Detector and video filter.
V.
Display
Input attenuator
The attenuator decides the level of the input signals so as to keep it within the
operating range of other blocks of the instrument. Generally spectrum analyzer can handle
0 to 10 dBm.
91
Input filter
The input filter is used to reject unwanted signals. It suppresses the spurious
signals. This is necessary because mixer responds to both sums and differences of
frequencies. Mostly the filter is low pass filter.
Wideband input mixer
It multiplies the input signal from filter and the local oscillator signal. It provides
two signals at the output which are proportional in amplitude to the input signal but having
frequencies which are sum difference of frequencies of the input signal and the local
oscillator signal.
Intermediate frequency (I.F) section
This is most important stage in analyzer where real analysis takes place. The stage
function is to provide a wide selection of resolution bandwidth filters. These filters are
described by their 3-dB bandwidth. These filters decide the resolving power of the
analyzers.
Log amplifier
It processes incoming signal in a logarithmic fashion. The logarithmic processing
allows a large range of incoming signals to be measured and compared
Detector
The detector used in the analyzer is called linear envelope detector. This is exactly
similar to the detectors used in A.M. radios. The detector receives a signal from log
amplifier which is compressed one. This is somewhat releases the large linear range
requirement of a detector.
Video filter
These filters are used for post filtering or averaging the detector output. The
bandwidth setting of video filter is same or larger than resolution bandwidth filter. If the
signal is along with noise, averaging is necessary. Averaging removes the random noise
and pure signal remains.
Display
The output of the video filter is given to CRO for display purpose.
Swept local oscillator
The swept local oscillator puts a limit on the stability and spectral purity in many
performance areas.
Applications
 Modulation measurement.
92
 Continuous wave signal frequency stability.
 Harmonic distortion measurement.
 Noise measurement.
 Examining pulse modulation.
3. Describe the working of a sweep frequency generator. (AU APRIL 2004, 2010,
NOV 2003,2006)
(16)
The sine wave generator discussed in earlier sections generates output voltage at a
known and stable frequency. But in some applications such as measuring frequency
response of amplifiers, filters and other networks, a variable frequency source is used. In
such cases sweep frequency generators are used.
In the early days, the method for varying frequency electronically was not invented.
Some other methods were used to get variable frequency source. Reactance tube
modulator used was providing very little frequency variation, so most of the times, electromechanical systems such as motor driven capacitors were used.
The sweep generator is very much simple signal generator. In the simple signal
generator, an oscillator is tuned to fixed single frequency. In the sweep generator, an
oscillator is electronically tuned and by using voltage controlled oscillator variable
frequency is obtained. As name indicates, a sweep voltage generator provides voltage,
known as control voltage, to the voltage controlled oscillator (VCO).
The function of voltage controlled oscillator is to provide various frequency
sweeps according to voltage provide by sweep voltage generator. But the relationship
between sweep voltage and frequency is nonlinear. To obtain linearity, a compensation
93
circuit is provided between sweep frequency voltage and oscillator tuning voltage. The
compensation circuit is called linearizing circuit.
4. Give the principle of wave analyzer with the help of suitable diagrams. (AU
APRIL, NOV 2009)
(16)
A wave analyzer is an instrument designed to measure relative amplitudes of single
frequency components in a complex waveform. It can analysis of waveforms includes the
determination of amplitude, frequency and phase angle of the harmonic components.
Types of wave analyzer
 Frequency selective wave analyzer.
 Heterodyne wave analyzer.
Frequency selective wave analyzer
The waveform to be analyzed is passed through an adjustable attenuator. This acts
as a range multiplier.
The driver amplifier feeds the waveform to a high Q filter.
This filter consists of cascade arrangement of RC resonant sections and filter
amplifiers.
The capacitors are used for range changing.
The potentiometer is used to change frequency within the selected pass band.
94
The entire AF range is covered in decade steps by the switching capacitors in the
RC section
The final amplifier stage supplies the selected signal to the meter circuit and to an
untuned buffer amplifier.
The function of buffer amplifier is to drive the output devices, such as the
recorders, electronic counters etc.
The analyzer input must have low input distortion.
The meter has several voltage ranges as well as decibel scale marked on it. It is
driven by an average reading rectifier type detector.
Heterodyne wave analyzer
This is RF range analyzer works on the principle of mixing i.e. heterodyning.
In this type of wave analyzer the input signal is heterodyned to a higher
intermediate frequency (IF) by an internal local oscillator.
Tuning the local oscillator shifts the various signal frequency components into the
pass band of the IF amplifier.
The output of the IF amplifier is then rectified and applied to the metering circuit.
The input is applied first to the attenuator section. This gives the output frequency
in the range of 0 to 18 MHz
The untuned amplifier amplifies this signal and gives it to the first mixer.
95
The first mixer heterodynes the input with the frequency from local oscillator. This
oscillator has frequency range 30-48 MHz
The output of the first mixer difference frequency of 30 MHz
The IF amplifier amplifies this signal and gives it to the second mixer.
The second mixer heterodynes the signal with 30 MHz frequency crystal oscillator.
Thus at the output of second mixer the zero difference frequency is obtained.
The active filter having controlled bandwidth and symmetrical slopes of 72 dB per
octave, then passes the selected component to the meter amplifier and detector.
The output from the meter detector is then used to obtain final indication on the
output meter which is having a decibel calibrated scale.
The output from detector may be applied to a recording device.
Applications of wave analyzer
 To measure the harmonic distortion of an amplifier
 To carry out complete harmonic analysis
 To measure the signal energy with the well defined bandwidth.
5. Explain the distortion analyzer with the help of suitable diagrams. (AU APRIL
2006, NOV 2007)
(16)
The application of purely sinusoidal input signal to an amplifier should result in
purely sinusoidal signal at the output. But practically output waveform is not exact replica
of the input. This because of presence of various types of distortions. Such distortions due
to the inherent nature of amplifier or nonlinear characteristics of various components used.
The distortion caused due to the nonlinear behavior of the circuit elements is called
harmonic distortion.
Suppression Distortion Analyzer
This is used to measure the distortion factor (T.H.D) rather than the contribution by
each component. In this analyzer, the input is applied to such a network that suppresses or
rejects the fundamental component but passes all the harmonic frequency components for
the measurement.
96
The analyzer consists of four major sections
I.
II.
III.
IV.
Impedance converter
Rejection amplifier
Metering circuit
Power supply.
The impedance converter provides a low noise, high impedance input circuit.
The rejection amplifier rejects the fundamental frequency,
The metering circuit measures the harmonic distortion present which provides
visual indication of the T.H.D in terms of a percentage of the total input voltage.
The power supply provides the supply for proper circuit operation.
There are two modes of operation:
Voltmeter mode
In this, it acts as a normal AC voltmeter. The input is applied through 1: 1 and 100:
1 attenuator which selects proper meter range. The impedance converter bypasses the
rejection amplifier as shown dotted. The meter measures the RMS value of the AC input
voltage.
Distortion mode
In this, output of the impedance converter is applied to the rejection amplifier. But
before applying to the impedance converter, now the input signal is applied to 1 MΩ input
97
attenuator which provides the 50 dB attenuation in 10 dB steps. This is controlled by a
front panel control named sensitivity. Due to low noise high impedance provided by
impedance converter, accurate measurement is possible.
The rejection amplifier circuit consists of a pre-amplifier, a wien bridge and a
bridge amplifier.
The pre-amplifier provides further amplification at extremely low distortion levels.
The bridge is connected as an interstate coupling between the pre-amplifier and the
bridge amplifier.
By the front panel, the bridge is tuned and balanced, no output results due to
balancing. Hence fundamental frequency component is rejected.
For other frequencies, wien bridge provides varying output which is amplified by
bridge amplifier.
The output is then given to meter circuit through post attenuator.
Heterodyne Harmonic Distortion Analyzer
The variable frequency oscillator output is mixed with each harmonic of the input
signal, with the help of balanced mixer, either the sum or difference frequency is
made equal to the frequency of the filter.
The quartz crystal type highly selective filters can be used as each harmonic
frequency is converted to a constant frequency.
This allows selecting constant frequency signal related to a particular harmonic and
passing it to the metering circuit.
The balanced mixer consists of a balanced modulator and it eliminates original
frequency of the harmonic. Generation of low harmonic distortion is the advantage
of the balanced modulator.
98
In some cases, the meter reading is calibrated directly in terms of voltage while in
some cases the harmonics are compared with a reference voltage, which is
representation of the fundamental component.
As the calibration in terms of voltage is the feature of direct reading heterodyne
harmonic distortion analyzer, they are also called frequency voltmeters.
These instruments are also called carrier frequency voltmeters and selective level
voltmeters.
99
UNIT IV- DIGITAL INSTRUMENTS
Comparison of analog and digital techniques :
An analog-to-digital converter (abbreviated ADC, A/D or A to D) is a device that
converts a continuous quantity to a discrete digital number. The reverse operation is
performed by a digital-to-analog converter (DAC).
Typically, an ADC is an electronic device that converts an input analog voltage (or
current) to a digital number proportional to the magnitude of the voltage or current.
However, some non-electronic or only partially electronic devices, such as rotary encoders,
can also be considered ADCs.
The digital output may use different coding schemes. Typically the digital output
will be a two's complement binary number that is proportional to the input, but there are
other possibilities. An encoder, for example, might output a Gray code.
An ADC might be used to make an isolated measurement. ADCs are also used to
quantize time-varying signals by turning them into a sequence of digital samples. The result
is quantized in both time and value.
Resolution :
An 8-level ADC coding scheme.
100
An 8-level ADC coding scheme. As in figure 1 but with mid-tread coding.
An 8-level ADC mid-tread coding scheme. As in figure 2 but with equal half-LSB
intervals at the highest and lowest codes. Note that LSB is now slightly larger than in figures
1 and 2.The resolution of the converter indicates the number of discrete values it can produce
over the range of analog values. The values are usually stored electronically in binary form,
so the resolution is usually expressed in bits. In consequence, the number of discrete values
available, or "levels", is usually a power of two. For example, an ADC with a resolution of 8
bits can encode an analog input to one in 256 different levels, since 28 = 256. The values
can represent the ranges from 0 to 255 (i.e. unsigned integer) or from -128 to 127 (i.e. signed
integer), depending on the application.Resolution can also be defined electrically, and
expressed in volts. The minimum change in voltage required to guarantee a change in the
output code level is called the LSB (least significant bit, since this is the voltage represented
by a change in the LSB). The resolution Q of the ADC is equal to the LSB voltage. The
voltage resolution of an ADC is equal to its overall voltage measurement range divided by
the number of discrete voltage intervals:
101
where:
N is the number of voltage intervals,
EFSR is the full scale voltage range, given by,
the upper and lower extremes respectively of the voltages that can be coded.
Normally, the number of voltage intervals is given by,
where
M is the ADC's resolution in bits.
That is, one voltage interval is assigned per code level. However, figure 3 shows a situation
where
Some examples:
Example 1
o Coding scheme as in figure 1
o Full scale measurement range = 0 to 10 volts
o ADC resolution is 12 bits: 212 = 4096 quantization levels (codes)
o ADC voltage resolution, Q = (10V - 0V) / 4096 = 10V / 4096 0.00244 V
2.44 mV.
Example 2
o Coding scheme as in figure 2
o Full scale measurement range = -10 to +10 volts
o ADC resolution is 14 bits: 214 = 16384 quantization levels (codes)
o ADC voltage resolution is, Q = (10V - (-10V)) / 16384 = 20V / 16384
0.00122 V 1.22 mV.
Example 3
o Coding scheme as in figure 3
o Full scale measurement range = 0 to 7 volts
o ADC resolution is 3 bits: 23 = 8 quantization levels (codes)
o ADC voltage resolution is, Q = (7 V − 0 V)/7 = 7 V/7 = 1 V = 1000 mV
In most ADCs, the smallest output code ("0" in an unsigned system) represents a voltage
range which is 0.5Q, that is, half the ADC voltage resolution (Q). The largest code
represents a range of 1.5Q as in figure 2 (if this were 0.5Q also, the result would be as figure
3). The other N − 2 codes are all equal in width and represent the ADC voltage resolution
(Q) calculated above. Doing this centers the code on an input voltage that represents the M 102
th division of the input voltage range. This practice is called "mid-tread" operation. This
type of ADC can be modeled mathematically as:
The exception to this convention seems to be the Microchip PIC processor, where all M
steps are equal width, as shown in figure 1. This practice is called "Mid-Rise with Offset"
operation.
In practice, the useful resolution of a converter is limited by the best signal-to-noise ratio
(SNR) that can be achieved for a digitized signal. An ADC can resolve a signal to only a
certain number of bits of resolution, called the effective number of bits (ENOB). One
effective bit of resolution changes the signal-to-noise ratio of the digitized signal by 6 dB, if
the resolution is limited by the ADC. If a preamplifier has been used prior to A/D
conversion, the noise introduced by the amplifier can be an important contributing factor
towards the overall SNR.
Linear ADCs
Most ADCs are of a type known as linear[1] The term linear as used here means that the
range of the input values that map to each output value has a linear relationship with the
output value, i.e., that the output value k is used for the range of input values from
m(k + b) to m(k + 1 + b)
where m and b are constants. Here b is typically 0 or −0.5. When b = 0, the ADC is referred to
as mid-rise, and when b = −0.5 it is referred to as mid-tread.
Non-linear ADCs
If the probability density function of a signal being digitized is uniform, then the signal-tonoise ratio relative to the quantization noise is the best possible. Because this is often not the
case, it is usual to pass the signal through its cumulative distribution function (CDF) before
the quantization. This is good because the regions that are more important get quantized
with a better resolution. In the dequantization process, the inverse CDF is needed.This is the
same principle behind the companders used in some tape-recorders and other communication
systems, and is related to entropy maximization.For example, a voice signal has a Laplacian
103
distribution. This means that the region around the lowest levels, near 0, carries more
information than the regions with higher amplitudes. Because of this, logarithmic ADCs are
very common in voice communication systems to increase the dynamic range of the
representable values while retaining fine-granular fidelity in the low-amplitude region.
An eight-bit A-law or the μ-law logarithmic ADC covers the wide dynamic range and has a
high resolution in the critical low-amplitude region, that would otherwise require a 12-bit
linear ADC.
Accuracy
An ADC has several sources of errors. Quantization error and (assuming the ADC is
intended to be linear) non-linearity is intrinsic to any analog-to-digital conversion. There is
also a so-called aperture error which is due to a clock jitter and is revealed when digitizing a
time-variant signal (not a constant value). These errors are measured in a unit called the
LSB, which is an abbreviation for least significant bit. In the above example of an eight-bit
ADC, an error of one LSB is 1/256 of the full signal range, or about 0.4%.
Quantization error
Quantization error is due to the finite resolution of the ADC, and is an unavoidable
imperfection in all types of ADC. The magnitude of the quantization error at the sampling
instant is between zero and half of one LSB.In the general case, the original signal is much
larger than one LSB. When this happens, the quantization error is not correlated with the
signal, and has a uniform distribution. Its RMS value is the standard deviation of this
distribution, given by
.
In the eight-bit ADC example, this represents 0.113% of the full signal range.
At lower levels the quantizing error becomes dependent of the input signal, resulting
in distortion. This distortion is created after the anti-aliasing filter, and if these distortions
are above 1/2 the sample rate they will alias back into the audio band. In order to make the
quantizing error independent of the input signal, noise with an amplitude of 2 least
significant bits is added to the signal. This slightly reduces signal to noise ratio, but, ideally,
completely eliminates the distortion. It is known as dither.
104
Non-linearity :
All ADCs suffer from non-linearity errors caused by their physical imperfections, causing
their output to deviate from a linear function (or some other function, in the case of a
deliberately non-linear ADC) of their input. These errors can sometimes be mitigated by
calibration, or prevented by testing.Important parameters for linearity are integral nonlinearity (INL) and differential non- linearity (DNL). These non-linearities reduce the
dynamic range of the signals that can be digitized by the ADC, also reducing the effective
resolution of the ADC.
Aperture error :
Imagine that we are digitizing a sine wave x(t) = Asin(2πf0t). Provided that the actual
sampling time uncertainty due to the clock jitter is Δt, the error caused by this phenomenon
can be estimated as
.
The error is zero for DC, small at low frequencies, but significant when high frequencies
have high amplitudes. This effect can be ignored if it is drowned out by the quantizing error.
Jitter requirements can be calculated using the following formula:
is a number of ADC bits.
105
, where q
ADC
resolution
in bit
Input frequency
1 Hz 44.1 kHz 192 kHz 1 MHz 10 MHz 100 MHz 1 GHz
8 1243 µs
28.2 ns 6.48 ns 1.24 ns 124 ps
12.4 ps 1.24 ps
10 311 µs
7.05 ns 1.62 ns 311 ps 31.1 ps
3.11 ps 0.31 ps
12 77.7 µs
1.76 ns
0.78 ps 0.08 ps
405 ps 77.7 ps 7.77 ps
106
14 19.4 µs
441 ps
16 4.86 µs
110 ps 25.3 ps 4.86 ps 0.49 ps
18 1.21 µs
27.5 ps 6.32 ps 1.21 ps 0.12 ps
20 304 ns
6.88 ps 1.58 ps 0.16 ps
24 19.0 ns
0.43 ps 0.10 ps
32 74.1 ps
–
101 ps 19.4 ps 1.94 ps
–
0.19 ps 0.02 ps
0.05 ps
–
–
–
–
–
–
–
–
–
–
–
–
–
–
This table shows, for example, that it is not worth using a precise 24-bit ADC for sound
recording if there is not an ultra low jitter clock. One should consider taking this
phenomenon into account before choosing an ADC.Clock jitter is caused by phase
noise.[2][3] The resolution of ADCs with a digitization bandwidth between 1 MHz and
1 GHz is limited by jitter.When sampling audio signals at 44.1 kHz, the anti-aliasing
filter should have eliminated all frequencies above 22 kHz. The input frequency (in this
case, 22 kHz), not the ADC clock frequency, is the determining factor with respect to
jitter performance.
Sampling rate :
The analog signal is continuous in time and it is necessary to convert this to a flow of digital
values. It is therefore required to define the rate at which new digital values are sampled
from the analog signal. The rate of new values is called the sampling rate or sampling
frequency of the converter. A continuously varying band limited signal can be sampled (that
is, the signal values at intervals of time T, the sampling time, are measured and stored) and
then the original signal can be exactly reproduced from the discrete-time values by an
interpolation formula. The accuracy is limited by quantization error. However, this faithful
reproduction is only possible if the sampling rate is higher than twice the highest frequency
of the signal. This is essentially what is embodied in theorem. Since a practical ADC cannot
make an instantaneous conversion, the input value must necessarily be held constant during
the time that the converter performs a conversion (called the conversion time). An input
circuit called a sample and hold performs this task—in most cases by using a capacitor to
store the analog voltage at the input, and using an electronic switch or gate to disconnect the
capacitor from the input. Many ADC integrated circuits include the sample and hold
subsystem internally.
107
Aliasing :
All ADCs work by sampling their input at discrete intervals of time. Their output is
therefore an incomplete picture of the behaviour of the input. There is no way of knowing,
by looking at the output, what the input was doing between one sampling instant and the
next. If the input is known to be changing slowly compared to the sampling rate, then it can
be assumed that the value of the signal between two sample instants was somewhere
between the two sampled values. If, however, the input signal is changing rapidly compared
to the sample rate, then this assumption is not valid.If the digital values produced by the
ADC are, at some later stage in the system, converted back to analog values by a digital to
analog converter or DAC, it is desirable that the output of the DAC be a faithful
representation of the original signal. If the input signal is changing much faster than the
sample rate, then this will not be the case, and spurious signals called aliases will be
produced at the output of the DAC. The frequency of the aliased signal is the difference
between the signal frequency and the sampling rate. For example, a 2 kHz sine wave being
sampled at 1.5 kHz would be reconstructed as a 500 Hz sine wave. This problem is called
aliasing.To avoid aliasing, the input to an ADC must be low-pass filtered to remove
frequencies above half the sampling rate. This filter is called an anti-aliasing filter, and is
essential for a practical ADC system that is applied to analog signals with higher frequency
content.Although aliasing in most systems is unwanted, it should also be noted that it can
be exploited to provide simultaneous down-mixing of a band-limited high frequency signal
(see undersampling and frequency mixer).
In A-to-D converters, performance can usually be improved using dither. This is a
very small amount of random noise (white noise) which is added to the input before
conversion. Its amplitude is set to be twice the value of the least significant bit. Its effect is
to cause the state of the LSB to randomly oscillate between 0 and 1 in the presence of very
low levels of input, rather than sticking at a fixed value. Rather than the signal simply
getting cut off altogether at this low level (which is only being quantized to a resolution of 1
bit), it extends the effective range of signals that the A-to-D converter can convert, at the
expense of a slight increase in noise - effectively the quantization error is diffused across a
series of noise values which is far less objectionable than a hard cutoff. The result is an
accurate representation of the signal over time. A suitable filter at the output of the system
can thus recover this small signal variation.An audio signal of very low level (with respect
to the bit depth of the ADC) sampled without dither sounds extremely distorted and
108
unpleasant. Without dither the low level may cause the least significant bit to "stick" at 0 or
1. With dithering, the true level of the audio may be calculated by averaging the actual
quantized sample with a series of other samples [the dither] that are recorded over time.
A virtually identical process, also called dither or dithering, is often used when
quantizing photographic images to a fewer number of bits per pixel—the image becomes
noisier but to the eye looks far more realistic than the quantized image, which otherwise
becomes banded. This analogous process may help to visualize the effect of dither on an
analogue audio signal that is converted to digital.Dithering is also used in integrating
systems such as electricity meters. Since the values are added together, the dithering
produces results that are more exact than the LSB of the analog-to-digital converter.
Note that dither can only increase the resolution of a sampler, it cannot improve the
linearity, and thus accuracy does not necessarily improve.
Oversampling
Usually, signals are sampled at the minimum rate required, for economy, with the result that
the quantization noise introduced is white noise spread over the whole pass band of the
converter. If a signal is sampled at a rate much higher than the Nyquist frequency and then
digitally filtered to limit it to the signal bandwidth then there are three main advantages:
digital filters can have better properties (sharper rolloff, phase) than analogue
filters, so a sharper anti-aliasing filter can be realized and then the signal can be
down sampled giving a better result
a 20-bit ADC can be made to act as a 24-bit ADC with 256× oversampling
the signal-to-noise ratio due to quantization noise will be higher than if the whole
available band had been used. With this technique, it is possible to obtain an
effective resolution larger than that provided by the converter alone
The improvement in SNR is 3 dB (equivalent to 0.5 bits) per octave of oversampling
which is not sufficient for many applications. Therefore, oversampling is usually
coupled with noise shaping (see sigma-delta modulators). With noise shaping, the
improvement is 6L+3 dB per octave where L is the order of loop filter used for noise
shaping. e.g. - a 2nd order loop filter will provide an improvement of 15 dB/octave.
109
Relative speed and precision
The speed of an ADC varies by type. The Wilkinson ADC is limited by the clock rate which
is processable by current digital circuits. Currently, frequencies up to 300 MHz are possible.
The conversion time is directly proportional to the number of channels. For a successive
approximation ADC, the conversion time scales with the logarithm of the number of
channels. Thus for a large number of channels, it is possible that the successive
approximation ADC is faster than the Wilkinson. However, the time consuming steps in the
Wilkinson are digital, while those in the successive approximation are analog. Since analog
is inherently slower than digital, as the number of channels increases, the time required also
increases. Thus there are competing processes at work. Flash ADCs are certainly the fastest
type of the three. The conversion is basically performed in a single parallel step. For an 8-bit
unit, conversion takes place in a few tens of nanoseconds.There is, as expected, somewhat of
a trade off between speed and precision. Flash ADCs have drifts and uncertainties associated
with the comparator levels, which lead to poor uniformity in channel width. Flash ADCs
have a resulting poor linearity. For successive approximation ADCs, poor linearity is also
apparent, but less so than for flash ADCs. Here, non-linearity arises from accumulating
errors from the subtraction processes. Wilkinson ADCs are the best of the three. These have
the best differential non-linearity. The other types require channel smoothing in order to
achieve the level of the Wilkinson.
The sliding scale principle
The sliding scale or randomizing method can be employed to greatly improve the channel
width uniformity and differential linearity of any type of ADC, but especially flash and
successive approximation ADCs. Under normal conditions, a pulse of particular amplitude
is always converted to a certain channel number. The problem lies in that channels are not
always of uniform width, and the differential linearity decreases proportionally with the
divergence from the average width. The sliding scale principle uses an averaging effect to
110
overcome this phenomenon. A random, but known analog voltage is added to the input
pulse. It is then converted to digital form, and the equivalent digital version is subtracted,
thus restoring it to its original value. The advantage is that the conversion has taken place at
a random point. The statistical distribution of the final channel numbers is decided by a
weighted average over a region of the range of the ADC. This in turn desensitizes it to the
width of any given channel.
ADC structures
These are the most common ways of implementing an electronic ADC:
A direct conversion ADC or flash ADC has a bank of comparators sampling the
input signal in parallel, each firing for their decoded voltage range. The comparator
bank feeds a logic circuit that generates a code for each voltage range. Direct
conversion is very fast, capable of gigahertz sampling rates, but usually has only 8
bits of resolution or fewer, since the number of comparators needed, 2N - 1, doubles
with each additional bit, requiring a large expensive circuit. ADCs of this type have a
large die size, a high input capacitance, high power dissipation, and are prone to
produce glitches on the output (by outputting an out-of-sequence code). Scaling to
newer submicrometre technologies does not help as the device mismatch is the
dominant design limitation. They are often used for video, wideband
communications or other fast signals in optical storage.
A successive-approximation ADC uses a comparator to reject ranges of voltages,
eventually settling on a final voltage range. Successive approximation works by
constantly comparing the input voltage to the output of an internal digital to analog
converter (DAC, fed by the current value of the approximation) until the best
approximation is achieved. At each step in this process, a binary value of the
approximation is stored in a successive approximation register (SAR). The SAR uses
a reference voltage (which is the largest signal the ADC is to convert) for
comparisons. For example if the input voltage is 60 V and the reference voltage is
100 V, in the 1st clock cycle, 60 V is compared to 50 V (the reference, divided by
two. This is the voltage at the output of the internal DAC when the input is a '1'
followed by zeros), and the voltage from the comparator is positive (or '1') (because
60 V is greater than 50 V). At this point the first binary digit (MSB) is set to a '1'. In
the 2nd clock cycle the input voltage is compared to 75 V (being halfway between
111
100 and 50 V: This is the output of the internal DAC when its input is '11' followed
by zeros) because 60 V is less than 75 V, the comparator output is now negative (or
'0'). The second binary digit is therefore set to a '0'. In the 3rd clock cycle, the input
voltage is compared with 62.5 V (halfway between 50 V and 75 V: This is the output
of the internal DAC when its input is '101' followed by zeros). The output of the
comparator is negative or '0' (because 60 V is less than 62.5 V) so the third binary
digit is set to a 0. The fourth clock cycle similarly results in the fourth digit being a
'1' (60 V is greater than 56.25 V, the DAC output for '1001' followed by zeros). The
result of this would be in the binary form 1001. This is also called bit-weighting
conversion, and is similar to a binary search. The analogue value is rounded to the
nearest binary value below, meaning this converter type is mid-rise (see above).
Because the approximations are successive (not simultaneous), the conversion takes
one clock-cycle for each bit of resolution desired. The clock frequency must be equal
to the sampling frequency multiplied by the number of bits of resolution desired. For
example, to sample audio at 44.1 kHz with 32 bit resolution, a clock frequency of
over 1.4 MHz would be required. ADCs of this type have good resolutions and quite
wide ranges. They are more complex than some other designs.
A ramp-compare
ADC produces a saw-tooth signal that ramps up or down then quickly returns to
zero. When the ramp starts, a timer starts counting. When the ramp voltage matches
the input, a comparator fires, and the timer's value is recorded. Timed ramp
converters require the least number of transistors.The ramp time is sensitive to
temperature because the circuit generating the ramp is often just some simple
oscillator. There are two solutions: use a clocked counter driving a DAC and then
use the comparator to preserve the counter's value, or calibrate the timed ramp.
A special advantage of the ramp-compare system is that comparing a second signal
just requires another comparator, and another register to store the voltage value. A
very simple (non-linear) ramp-converter can be implemented with a microcontroller
and one resistor and capacitor [10]. Vice versa, a filled capacitor can be taken from an
integrator, time-to-amplitude converter, phase detector, sample and hold circuit, or
peak and hold circuit and discharged. This has the advantage that a slow comparator
cannot be disturbed by fast input changes.
112
An integrating ADC (also dual-slope or multi-slope ADC) applies the unknown
input voltage to the input of an integrator and allows the voltage to ramp for a fixed
time period (the run-up period). Then a known reference voltage of opposite polarity
is applied to the integrator and is allowed to ramp until the integrator output returns to
zero (the run-down period). The input voltage is computed as a function of the
reference voltage, the constant run-up time period, and the measured run-down time
period. The run-down time measurement is usually made in units of the converter's
clock, so longer integration times allow for higher resolutions. Likewise, the speed
of the converter can be improved by sacrificing resolution. Converters of this type
(or variations on the concept) are used in most digital voltmeters for their linearity
and flexibility.
A delta-encoded ADC or Counter-ramp has an up-down counter that feeds a digital to
analog converter(DAC). The input signal and the DAC both go to a comparator. The
comparator controls the counter. The circuit uses negative feedback from the
comparator to adjust the counter until the DAC's output is close enough to the input
signal. The number is read from the counter. Delta converters have very wide ranges,
and high resolution, but the conversion time is dependent on the input signal level,
though it will always have a guaranteed worst-case. Delta converters are often very
good choices to read real-world signals. Most signals from physical systems do not
change abruptly. Some converters combine the delta and successive approximation
approaches; this works especially well when high frequencies are known to be small in
magnitude.
A pipeline ADC (also called subranging quantizer) uses two or more steps of
subranging. First, a coarse conversion is done. In a second step, the difference to the
input signal is determined with a digital to analog converter (DAC). This difference
is then converted finer, and the results are combined in a last step. This can be
considered a refinement of the successive approximation ADC wherein the feedback
reference signal consists of the interim conversion of a whole range of bits (for
example, four bits) rather than just the next-most-significant bit. By combining the
merits of the successive approximation and flash ADCs this type is fast, has a high
resolution, and only requires a small die size.
113
A Sigma-Delta ADC (also known as a Delta-Sigma ADC) oversamples the desired
signal by a large factor and filters the desired signal band. Generally, a smaller
number of bits than required are converted using a Flash ADC after the filter. The
resulting signal, along with the error generated by the discrete levels of the Flash, is
fed back and subtracted from the input to the filter. This negative feedback has the
effect of noise shaping the error due to the Flash so that it does not appear in the
desired signal frequencies. A digital filter (decimation filter) follows the ADC which
reduces the sampling rate, filters off unwanted noise signal and increases the
resolution of the output (sigma-delta modulation,also called delta-sigma modulation).
A Time-interleaved ADC uses M parallel ADCs where each ADC sample data
every M:th cycle of the effective sample clock. The result is that the sample rate is
increased M times compared to what each individual ADC can manage. In practice,
the individual differences between the M ADCs degrade the overall performance
reducing the SFDR. However, technologies exist to correct for these timeinterleaving mismatch errors.
An ADC with intermediate FM stage first uses a voltage-to-frequency converter to
converts the desired signal into an oscillating signal with a frequency proportional to
the voltage of the desired signal, and then uses a frequency counter to convert that
frequency into a digital count proportional to the desired signal voltage. Longer
integration times allow for higher resolutions. Likewise, the speed of the converter
can be improved by sacrificing resolution. The two parts of the ADC may be widely
separated, with the frequency signal passed through a opto-isolator or transmitted
wirelessly. Some such ADCs use sine wave or square wave frequency modulation;
others use pulse-frequency modulation. Such ADCs were once the most popular way
to show a digital display of the status of a remote analog sensor.
There can be other ADCs that use a combination of electronics and other technologies:
A Time-stretch analog-to-digital converter (TS-ADC) digitizes a very wide
bandwidth analog signal, that cannot be digitized by a conventional electronic ADC,
by time-stretching the signal prior to digitization. It commonly uses a photonic
preprocessor frontend to time-stretch the signal, which effectively slows the signal
down in time and compresses its bandwidth. As a result, an electronic backend ADC,
that would have been too slow to capture the original signal, can now capture this
slowed down signal. For continuous capture of the signal, the frontend also divides
114
the signal into multiple segments in addition to time-stretching. Each segment is
individually digitized by a separate electronic ADC. Finally, a digital signal
processor rearranges the samples and removes any distortions added by the frontend
to yield the binary data that is the digital representation of the original analog signal.
Commercial analog-to-digital converters
These are usually integrated circuits.Most converters sample with 6 to 24 bits of resolution,
and produce fewer than 1 megasample per second. Thermal noise generated by passive
components such as resistors masks the measurement when higher resolution is desired. For
audio applications and in room temperatures, such noise is usually a little less than 1 μV
(microvolt) of white noise. If the Most Significant Bit corresponds to a standard 2 volts of
output signal, this translates to a noise-limited performance that is less than 20~21 bits, and
obviates the need for any dithering. Mega- and gigasample per second converters are
available, though (Feb 2002). Megasample converters are required in digital video cameras,
video capture cards, and TV tuner cards to convert full-speed analog video to digital video
files. Commercial converters usually have ±0.5 to ±1.5 LSB error in their output.In many
cases the most expensive part of an integrated circuit is the pins, because they make the
package larger, and each pin has to be connected to the integrated circuit's silicon. To save
pins, it is common for slow ADCs to send their data one bit at a time over a serial interface
to the computer, with the next bit coming out when a clock signal changes state,
say from zero to 5V. This saves quite a few pins on the ADC package, and in many cases,
does not make the overall design any more complex (even microprocessors which use
memory-mapped I/O only need a few bits of a port to implement a serial bus to an ADC).
Commercial ADCs often have several inputs that feed the same converter, usually through
an analog multiplexer. Different models of ADC may include sample and hold circuits,
instrumentation amplifiers or differential inputs, where the quantity measured is the
difference between two voltages.
Applications
Application to music recording
ADCs are integral to current music reproduction technology. Since much music
production is done on computers, when an analog recording is used, an ADC is needed to
create the PCM data stream that goes onto a compact disc or digital music file.The
current crop of AD converters utilized in music can sample at rates up to 192 kilohertz.
115
High bandwidth headroom allows the use of cheaper or faster anti-aliasing filters of less
severe filtering slopes. The proponents of oversampling assert that such shallower antialiasing filters produce less deleterious effects on sound quality, exactly because of their
gentler slopes. Others prefer entirely filterless AD conversion, arguing that aliasing is
less detrimental to sound perception than pre-conversion brickwall filtering.
Considerable literature exists on these matters, but commercial considerations often play
a significant role. Most[citation needed] high-profile recording studios record in 24bit/192-176.4 kHz PCM or in DSD formats, and then downsample or decimate the signal
for Red-Book CD production (44.1 kHz or at 48 kHz for
Digital to Analog Conversion :
One common requirement in electronics is to convert signals back and forth between
analog and digital forms. Most such conversions are ultimately based on a digital-to-analog
converter circuit. Therefore, it is worth exploring just how we can convert a digital number
that represents a voltage value into an actual analog voltage.
The circuit to the right is a basic digital-to-analog (D to A) converter. It assumes a 4-bit
binary number in Binary-Coded Decimal (BCD) format, using +5 volts as a logic 1 and 0
volts as a logic 0. It will convert the applied BCD number to a matching (inverted) output
voltage. The digits 1, 2, 4, and 8 refer to the relative weights assigned to each input. Thus, 1
is the Least Significant Bit (LSB) of the input binary number, and 8 is the Most Significant
Bit (MSB).
If the input voltages are accurately 0 and +5 volts, then the "1" input will cause an output
voltage of -5 × (4k/20k) = -5 × (1/5) = -1 volt whenever it is a logic 1. Similarly, the "2,"
"4," and "8" inputs will control output voltages of -2, -4, and -8 volts, respectively. As a
116
result, the output voltage will take on one of 10 specific voltages, in accordance with the
input BCD code.Unfortunately, there are several practical problems with this circuit.
First, most digital logic gates do not accurately produce 0 and +5 volts at their outputs.
Therefore, the resulting analog voltages will be close, but not really accurate. In addition,
the different input resistors will load the digital circuit outputs differently, which will
almost certainly result in different voltages being applied to the summer inputs.
The circuit above performs D to A conversion a little differently. Typically the
inputs are driven by CMOS gates, which have low but equal resistance for both logic 0 and
logic 1. Also, if we use the same logic levels, CMOS gates really do provide +5 and 0 volts
for their logic levels.The input circuit is a remarkable design, known as an R-2R ladder
network. It has several advantages over the basic summer circuit we saw first:
1.
Only two resistance values are used anywhere in the entire circuit. This
means that only two values of precision resistance are needed, in a resistance
ratio of 2:1. This requirement is easy to meet, and not especially expensive.
2. The input resistance seen by each digital input is the same as for every other
input. The actual impedance seen by each digital source gate is 3R. With a
CMOS gate resistance of 200 ohms, we can use the very standard values of
10k and 20k for our resistors.
3. The circuit is indefinitely extensible for binary numbers. Thus, if we use
binary inputs instead of BCD, we can simply double the length of the ladder
network for an 8-bit number (0 to 255) or double it again for a 16-bit
117
number(0 to 65535). We only need to add two resistors for each additional
binary input.
4. The circuit lends itself to a non-inverting circuit configuration. Therefore we
need not be concerned about intermediate inverters along the way. However,
an inverting version can easily be configured if that is appropriate.
One detail about this circuit: Even if the input ladder is extended, the output will
remain within the same output voltage limits. Additional input bits will simply allow the
output to be subdivided into smaller increments for finer resolution. This is equivalent to
adding inputs with ever-larger resistance values (doubling the resistance value for each bit),
but still using the same two resistance values in the extended ladder.The basic theory of the
R-2R ladder network is actually quite simple. Current flowing through any input resistor
(2R) encounters two possible paths at the far end. The effective resistances of both paths
are the same (also 2R), so the incoming current splits equally along both paths. The halfcurrent that flows back towards lower orders of magnitude does not reach the op amp, and
therefore has no effect on the output voltage. The half that takes the path towards the op
amp along the ladder can affect the output.
The most significant bit (marked "8" in the figure) sends half of its current toward
the op amp, so that half of the input current flows through that final 2R resistance and
generates a voltage drop across it. This voltage drop (from bit "8" only) will be one-third of
the logic 1 voltage level, or 5/3 = 1.667 volts. This is amplified by the op amp, as controlled
by the feedback and input resistors connected to the "-" input. For the components shown,
this gain will be 3 (see the page on non-inverting amplifiers). With a gain of 3, the amplifier
output voltage for the "8" input will be 5/3 × 3 = 5 volts.The current from the "4" input will
split in half in the same way. Then, the half going towards the op amp will encounter the
junction from the "8" input. Again, this current "sees" two equal-resistance paths of 2R
each, so it will split in half again. Thus, only a quarter of the current from the "4" will reach
the op amp. Similarly, only 1/8 of the current from the "2" input will reach the op amp and
be counted. This continues backwards for as many inputs as there are on the R-2R ladder
structure.The maximum output voltage from this circuit will be one step of the least
significant bit below 10 volts. Thus, an 8-bit ladder can produce output voltages up to
9.961 volts (255/256 × 10 volts). This is fine for many applications. If you have an
application that requires a 0-9 volt output from a BCD input, you can easily scale the output
upwards using an amplifier with a gain of 1.6 (8/5).
118
If you want an inverting D to A converter, the circuit shown above will work well.
You may need to scale the output voltage, depending on your requirements. Also, it is
possible to have a bipolar D to A converter. If you apply the most significant bit to an
analog inverter and use that output for the MSB position of the R-2R ladder, the binary
number applied to the ladder will be handled as a two's-complement number, going both
positive and negative. A frequency counter is an electronic instrument, or component of
one, that is used for measuring frequency. Frequency is defined as the number of events
of a particular sort occurring in a set period of time. Frequency counters usually measure
the number of oscillations or pulses per second in a repetitive electronic signal.
Operating principle :
Most frequency counters work by using a counter which accumulates the number of events
occurring within a specific period of time. After a preset period (1 second, for example), the
value in the counter is transferred to a display and the counter is reset to zero. If the event
being measured repeats itself with sufficient stability and the frequency is considerably
lower than that of the clock oscillator being used, the resolution of the measurement can be
greatly improved by measuring the time required for an entire number of cycles, rather than
counting the number of entire cycles observed for a pre-set duration (often referred to as the
reciprocal technique). The internal oscillator which provides the time signals is called the
timebase, and must be calibrated very accurately.If the thing to be counted is already in
electronic form, simple interfacing to the instrument is all that is required. More complex
signals may need some conditioning to make them suitable for counting. Most general
purpose frequency counters will include some form of amplifier, filtering and shaping
circuitry at the input. DSP technology, sensitivity control and hysteresis are other
techniques to improve performance. Other types of periodic events that are not inherently
electronic in nature will need to be converted using some form of transducer. For example,
a mechanical event could be arranged to interrupt a light beam, and the counter made to
count the resulting pulses.
119
Frequency counters designed for radio frequencies (RF) are also common and operate on the
same principles as lower frequency counters. Often, they have more range before they
overflow. For very high (microwave)frequencies, many designs use a high-speed prescaler
to bring the signal frequency down to a point where normal digital circuitry can operate. The
displays on such instruments take this into account so they still display the correct value.
Microwave frequency counters can currently measure frequencies up to almost 100 GHz.
Above these frequencies the signal to be measured is combined in a mixer with the signal
from a local oscillator, producing a signal at the difference frequency, which is low enough
to be measured directly.
Accuracy :
The accuracy of a frequency counter is strongly dependent on the stability of its timebase.
Highly accurate circuits are used to generate this for instrumentation purposes, usually using
a quartz crystal oscillator within a sealed temperature-controlled chamber known as a crystal
oven or OCXO (oven controlled crystal oscillator). For higher accuracy measurements, an
external frequency reference tied to a very high stability oscillator such as a GPS disciplined
rubidium oscillator may be used. Where the frequency does not need to be known to such a
high degree of accuracy, simpler oscillators can be used. It is also possible to measure
frequency using the same techniques in software in an embedded system. A CPU for
example, can be arranged to measure its own frequency of operation provided it has some
reference timebase to compare with.
I/O Interfaces
I/O interfaces allow the user to send information to the frequency counter and receive
information from the frequency counter. Commonly-used interfaces include RS232, USB,
GPIB and Ethernet. Besides sending measurement results, a counter can notify the user
when user-defined measurement limits are exceeded. Common to many counters are the
SCPI commands used to control them. A new development is built-in LAN-based control
via Ethernet complete with GUI's. This allows one computer to control one or several
instruments and eliminates the need to write SCPI commands.
120
Measurement Error :
The true score theory is a good simple model for measurement, but it may not always be an
accurate reflection of reality. In particular, it assumes that any observation is composed of
the true value plus some random error value. But is that reasonable? What if all error is not
random? Isn't it possible that some errors are systematic, that they hold across most or all of
the members of a group? One way to deal with this notion is to revise the simple true score
model by dividing the error component into two subcomponents, random error and
systematic error. here, we'll look at the differences between these two types of errors and try
to diagnose their effects on our research.
What is Random Error?
Random error is caused by any factors that randomly affect measurement of the
variable across the sample. For instance, each person's mood can inflate or deflate their
performance on any occasion. In a particular testing, some children may be feeling in a good
mood and others may be depressed. If mood affects their performance on the measure, it
may artificially inflate the observed scores for some children and artificially deflate them for
others. The important thing about random error is that it does not have any consistent effects
across the entire sample. Instead, it pushes observed scores up or down randomly. This
means that if we could see all of the random errors in a distribution they would have to sum
to 0 -- there would be as many negative errors as positive ones. The important property of
random error is that it adds variability to the data but does not affect average performance
for the group. Because of this, random error is sometimes considered noise.
121
What is Systematic Error?
Systematic error is caused by any factors that systematically affect measurement of the
variable across the sample. For instance, if there is loud traffic going by just outside of a
classroom where students are taking a test, this noise is liable to affect all of the children's
scores -- in this case, systematically lowering them. Unlike random error, systematic errors
tend to be consistently either positive or negative -- because of this, systematic error is
sometimes considered to be bias in measurement.
122
Reducing Measurement Error :
So, how can we reduce measurement errors, random or systematic? One thing you can do is
to pilot test your instruments, getting feedback from your respondents regarding how easy or
hard the measure was and information about how the testing environment affected their
performance. Second, if you are gathering measures using people to collect the data (as
interviewers or observers) you should make sure you train them thoroughly so that they
aren't inadvertently introducing error. Third, when you collect the data for your study you
should double-check the data thoroughly. All data entry for computer analysis should be
"double-punched" and verified. This means that you enter the data twice, the second time
having your data entry machine check that you are typing the exact same data you did the
first time. Fourth, you can use statistical procedures to adjust for measurement error. These
range from rather simple formulas you can apply directly to your data to very complex
modeling procedures for modeling the error and its effects. Finally, one of the best things
you can do to deal with measurement errors, especially systematic errors, is to use multiple
measures of the same construct. Especially if the different measures don't share the same
systematic errors, you will be able to triangulate across the multiple measures and get a
more accurate sense of what's going on.
123
A digital voltmeter, or DVM, is used to take highly accurate voltage
measurements. These instruments measure the electrical potential difference between two
conductors in a circuit. DVMs are electric voltmeters, and the preferred standard, as they
offer several benefits over their analog counterparts. Voltmeters are used to measure the
gain or loss of voltage between two points in a circuit. The leads are connected in parallel
on each side of the circuit being tested. The positive terminal of the meter should be
connected closest to the power supply. In turn, the negative terminal would be connected
after the circuit being tested. The analog dial or digital display will exhibit the voltage
measurement.
A digital voltmeter typically consists of an analog to digital converter (A/D)
with a digital display. The analog signal is converted into a digital code
proportionate to the magnitude of the signal. Voltages from picovolts to megavolts
are measurable, though the scale usually graduates in millivolts, volts, or kilovolts.
Frequencies between zero and several megahertz may also be measured.DVMs
measure both alternating current (AC) and direct current (DC) in electronics.
Common laboratory and commercial applications involve electromechanical
machinery with a current flowing through wires and circuits. Often, a digital
124
voltmeter is used to monitor a unit, such as a generator. Portable or handheld
devices, such as the digital multimeter (DMM), for example, may combine several
functions into one instrument measuring voltage, current, and resistance. This is the
preferred tool of an electrician.Many DVMs integrate outputs for monitoring,
controlling, transmitting, and printing of data. Advanced systems are often
connected to computers, allowing for automation, optimization of processes, and
prevention of malfunctions and critical failure safeties. Chemical plants can convert
measurements to voltage, and control and monitor temperature, pressure, level, or
flow. Medical equipment, such as x-ray machines, may use a digital voltmeter to
make sure the voltage of the equipment is in the proper range.
Frequency counter :
A frequency counter is an electronic instrument, or component of one, that is
used for measuring frequency. Frequency is defined as the number of events of a
particular sort occurring in a set period of time. Frequency counters usually measure
the number of oscillations or pulses per second in a repetitive electronic signal.
125
Operating principle :
Most frequency counters work by using a counter which accumulates the
number of events occurring within a specific period of time. After a preset period (1
second, for example), the value in the counter is transferred to a display and the
counter is reset to zero. If the event being measured repeats itself with sufficient
stability and the frequency is considerably lower than that of the clock oscillator
being used, the resolution of the measurement can be greatly improved by measuring
the time required for an entire number of cycles, rather than counting the number of
entire cycles observed for a pre-set duration (often referred to as the reciprocal
technique). The internal oscillator which provides the time signals is called the
timebase, and must be calibrated very accurately.If the thing to be counted is already
in electronic form, simple interfacing to the instrument is all that is required. More
complex signals may need some conditioning to make them suitable for counting.
Most general purpose frequency counters will include some form of amplifier,
filtering and shaping circuitry at the input. DSP technology, sensitivity control and
hysteresis are other techniques to improve performance. Other types of periodic
events that are not inherently electronic in nature will need to be converted using
some form of transducer. For example, a mechanical event could be arranged to
interrupt a light beam, and the counter made to count the resulting pulses.
Frequency counters designed for radio frequencies (RF) are also common and
operate on the same principles as lower frequency counters. Often, they have more
range before they overflow. For very high (microwave) frequencies, many designs
use a high- speed prescaler to bring the signal frequency down to a point where
normal digital circuitry can operate. The displays on such instruments take this into
account so they still display the correct value. Microwave frequency counters can
currently measure frequencies up to almost 100 GHz. Above these frequencies the
signal to be measured is combined in a mixer with the signal from a local oscillator,
producing a signal at the difference frequency, which is low enough to be measured
directly.
126
Accuracy :
The accuracy of a frequency counter is strongly dependent on the stability of its
timebase. Highly accurate circuits are used to generate this for instrumentation purposes,
usually using a quartz crystal oscillatorwithin a sealed temperature-controlled chamber
known as a crystal oven or OCXO (oven controlled crystal oscillator). For higher accuracy
measurements, an external frequency reference tied to a very high stability oscillator such as
a GPS disciplined rubidium oscillator may be used. Where the frequency does not need to
be known to such a high degree of accuracy, simpler oscillators can be used. It is also
possible to measure frequency using the same techniques in software in an embedded
system. A CPU for example, can be arranged to measure its own frequency of operation
provided it has
some reference timebase to compare with.
I/O Interfaces :
I/O interfaces allow the user to send information to the frequency counter and
receive information from the frequency counter. Commonly-used interfaces include
RS232, USB, GPIB and Ethernet. Besides sending measurement results, a counter can
notify the user when user-defined measurement limits are exceeded. Common to many
counters are
the SCPI commands used to control them. A new development is built-in LANbased control via Ethernet complete with GUI's. This allows one computer to control
one or several instruments and eliminates the need to write SCPI commands any
time
Multimeter :
Multimeter or a multitester, also known as a volt/ohm meter or VOM, is an
electronic measuring instrument that combines several measurement functions in one unit.
A typical multimeter may include features such as the ability to measure voltage, current
and resistance. Multimeters may use analog or digital circuits—analog multimeters and
digital multimeters (often abbreviated DMM or DVOM.) Analog instruments are usually
based on a microammeter whose pointer moves over a scale calibration for all the different
measurements that can be made; digital instruments usually display digits, but may display
a bar of a length
127
BASIC
CIRCUIT: (i)
Block Diagram:
(ii) Circuit:
A multimeter can be a hand-held device useful for basic fault finding and field
service work or a bench instrument which can measure to a very high degree of accuracy.
They can be used to troubleshoot electrical problems in a wide array of industrial and
household devices such as electronic equipment, motor controls, domestic appliances,
power supplies, and wiring systems.
Quantities measured :
Contemporary multimeters can measure many quantities. The common ones are:
Voltage, alternating and direct, in volts.
Current,alternating and direct, in amperes.
The frequency range for which AC measurements are accurate must be
specified.
Resistance in ohms.
128
Additionally, some multimeters measure:
Capacitance in farads.
Conductance in siemens.
Decibels.
Duty cycle as a percentage.
Frequency in hertz.
Inductance in henrys.
Temperature in degrees Celsius or Fahrenheit, with an appropriate temperature test
probe, often a thermocouple.
Digital multimeters may also include circuits for:
Continuity; beeps when a circuit conducts.
Diodes (measuring forward drop of diode junctions, i.e., diodes and transistor
junctions) and transistors (measuring current gain and other parameters).
Battery checking for simple 1.5 volt and 9 volt batteries. This is a current loaded
voltage scale. Battery checking (ignoring internal resistance, which increases as the
battery is depleted), is less accurate when using a DC voltage scale.
Various sensors can be attached to multimeters to take measurements such as:
Light level
Acidity/Alkalinity(pH)
Wind speed
Relative humidity
Resolution
Digital
The resolution of a multimeter is often specified in "digits" of resolution. For
example, the term 5½ digits refers to the number of digits displayed on the display of a
multimeter.By convention, a half digit can display either a zero or a one, while a threequarters digit can display a numeral higher than a one but not nine. Commonly, a
three-quarters digit refers to a maximum value of 3 or 5. The fractional digit is always
the most significant digit in the displayed value. A 5½ digit multimeter would have
five full digits that display values from 0 to 9 and one half digit that could only display
0 or 1.[3] Such a meter could show positive or negative values from 0 to 199,999. A
3¾ digit meter can display a quantity from 0 to 3,999 or 5,999, depending on the
manufacturer.While a digital display can easily be extended in precision, the extra
digits are of no value if not accompanied by care in the design and calibration of the
analog portions of the multimeter. Meaningful high-resolution measurements require a
129
good understanding of the instrument specifications, good control of the measurement
conditions, and traceability of the calibration of the instrument.
Specifying "display counts" is another way to specify the resolution. Display counts
give the largest number, or the largest number plus one (so the count number looks nicer)
the multimeter's display can show, ignoring a decimal separator. For example, a 5½
digitmultimeter can also be specified as a 199999 display count or 200000 display count
multimeter. Often the display count is just called the count in multimeter specifications.
Analog :
Resolution of analog multimeters is limited by the width of the scale pointer,
vibration of the pointer, the accuracy of printing of scales, zero calibration, number
of
ranges, and errors due to non-horizontal use of the mechanical display. Accuracy of
readings obtained is also often compromised by miscounting division markings, errors in
mental arithmetic, parallax observation errors, and less than perfect eyesight. Mirrored
scales and larger meter movements are used to improve resolution; two and a half to three
digits equivalent resolution is usual (and is usually adequate for the limited precision
needed for most measurements).Resistance measurements, in particular, are of low
precision due to the typical resistance measurement circuit which compresses the scale
heavily at the higher resistance values. Inexpensive analog meters may have only a single
resistance scale, seriously restricting the range of precise measurements. Typically an
analog meter will have a panel adjustment to set the zero-ohms calibration of the meter, to
compensate for the varying voltage of the meter battery.
Accuracy
Digital multimeters generally take measurements with accuracy superior to their
analog counterparts. Standard analog multimeters measure with typically three percent
accuracy,[4] though instruments of higher accuracy are made. Standard portable digital
multimeters are specified to have an accuracy of typically 0.5% on the DC voltage
ranges. Mainstream bench-top multimeters are available with specified accuracy of better
than
±0.01%. Laboratory grade instruments can have accuracies of a few parts per
million.Accuracy figures need to be interpreted with care. The accuracy of an analog
instrument usually refers to full-scale deflection; a measurement of 10V on the 100V scale
of a 3% meter is subject to an error of 3V, 30% of the reading. Digital meters usually
130
specify accuracy as a percentage of reading plus a percentage of full-scale value,
sometimes expressed in counts rather than percentage terms.Quoted accuracy is specified
as being that of the lower millivolt (mV) DC range, and is known as the "basic DC volts
accuracy" figure. Higher DC voltage ranges, current, resistance, AC and other ranges will
usually have a lower accuracy than the basic DC volts figure. AC measurements only meet
specified accuracy within a specified range of frequencies.
Test equipment tends to drift out of calibration over time, and the specified
accuracy cannot be relied upon indefinitely. For more expensive equipment, manufacturers
and third parties provide calibration services so that older equipment may be recalibrated
and recertified. The cost of such services is disproportionate for inexpensive equipment;
however extreme accuracy is not required for most routine testing. Multimeters used for
critical measurements may be part of a metrology program to assure calibration.
Sensitivity and input impedance
When used for measuring voltage, the input impedance of the multimeter must
be very high compared to the impedance of the circuit being measured; otherwise circuit
operation may be changed, and the reading will also be inaccurate.Meters with
electronic amplifiers (all digital multimeters and some analog meters) have a fixed input
impedance that is high enough not to disturb most circuits. This is often either one or ten
megohms;the standardization of the input resistance allows the use of external highresistance probes which form a voltage divider with the input resistance to extend
voltage range up to tens of thousands of volts.
Most analog multimeters of the moving-pointer type are unbuffered, and draw
current from the circuit under test to deflect the meter pointer. The impedance of the meter
varies depending on the basic sensitivity of the meter movement and the range which is
selected. For example, a meter with a typical 20,000 ohms/volt sensitivity will have an
input resistance of two million ohms on the 100 volt range (100 V * 20,000 ohms/volt =
2,000,000 ohms). On every range, at full scale voltage of the range, the full current required
to deflect the meter movement is taken from the circuit under test. Lower sensitivity meter
movements are acceptable for testing in circuits where source impedances are low
compared to the meter impedance, for example, power circuits; these meters are more
rugged mechanically. Some measurements in signal circuits require higher sensitivity
movements so as not to load the circuit under test with the meter impedance. Sometimes
131
sensitivity is confused with resolution of a meter, which is defined as the lowest voltage,
current or resistance change that can change the observed reading.For general-purpose
digital multimeters, the lowest voltage range is typically several hundred millivolts AC or
DC, but the lowest current range may be several hundred milliamperes, although
instruments with greater current sensitivity are available. Measurement of low resistance
requires lead resistance (measured by touching the test probes together) to be subtracted for
best accuracy.The upper end of multimeter measurement ranges varies considerably;
measurements over perhaps 600 volts, 10 amperes, or 100 megohms may require a
specialized test instrument.
Burden voltage
Any ammeter, including a multimeter in a current range, has a certain resistance.
Most multimeters inherently measure voltage, and pass a current to be measured through
a shunt resistance, measuring the voltage developed across it. The voltage drop is known
as the burden voltage, specified in volts per ampere. The value can change depending on
the range the meter selects, since different ranges usually use different shunt resistors.The
burden voltage can be significant in low-voltage circuits. To check for its effect on
accuracy and on external circuit operation the meter can be switched to different ranges;
the current reading should be the same and circuit operation should not be affected if
burden voltage is not a problem. If this voltage is significant it can be reduced (also
reducing the inherent accuracy and precision of the measurement) by using a higher
current range.
Alternating current sensing
Since the basic indicator system in either an analog or digital meter responds to DC
only, a multimeter includes an AC to DC conversion circuit for making alternating current
measurements. Basic meters utilize a rectifier circuit to measure the average or peak
absolute value of the voltage, but are calibrated to show the calculated root mean square
(RMS) value for a sinusoidal waveform;this will give correct readings for alternating
current as used in power distribution. User guides for some such meters give correction
factors for some simple non-sinusoidal waveforms, to allow the correct root mean square
(RMS) equivalent value to be calculated. More expensive multimeters include an AC to DC
converter that measures the true RMS value of the waveform within certain limits; the user
manual for the meter may indicate the limits of the crest factor and frequency for which the
132
meter calibration is valid. RMS sensing is necessary for measurements on non-sinusoidal
periodic waveforms, such as found in audio signals and variable-frequency drives.
133
Question Bank
UNIT-IV
DIGITAL INSTRUMENTS
PART-A (2 Marks)
1. What is digital voltmeter?
The digital voltmeters generally referred as DVM, convert the analog signals into
digital and display the voltages to be measured as discrete numerical instead of pointer
deflection, on the digital displays.
2. Give classification of digital voltmeters? (AU APRIL 2004)
DVM mainly classified into two types.
I.
Non integrating type.
II.
Integrating type.
Non-integrating type DVM.
i.
Potentiometric type
a) Servo potentiometric type
b) Successive approximation type
c) Null balance type
ii.
Ramp type
a) Linear type
b) Staircase type
Integrating type DVM
i.
Voltage to frequency converter type
ii.
Potentiometric type
iii.
Dual slope integrating type
3. What is the principle of ramp type digital voltmeter? (AU APRIL 2005)
The basic principle of such measurement is based on the measurement of the time
taken by a linear ramp to rise 0 v to the level of the input voltage or to decrease the
electronic time interval counter and the count is displayed in the numeric form with the
help of a digital display.
4. What are the essential parts of the ramp type DVM? (AU NOV 2004)
 Comparator
 Oscillator
 Attenuator
 Gate
 Counter
134
5. What are the advantages of digital instruments? (AU APRIL 2006)
 Very high accuracy
 No loading effect.
 No moving parts
 Auto range and polarity
 Very high input impedance
 Reading speed is high
 Computerized control
6. Why period mode is preferred for measurement of very low frequency in a
frequency counter? (AU NOV 2006)
The time period T = 1/f. So if the frequency to be measured low, then the accuracy of
the frequency counter decreases as less number of pulses are connected to the gating
circuit. Thus in low frequency region it is better to measure period rather than the
frequency
7. What is the importance of gate time in frequency counter? (AU APRIL 2007)
The gate time and gating circuit is used to adjust the train pulses in the frequency
counter. This will done by using the selector switch S in the time base generator.
8. How trigger time error reduced? (AU APRIL 2007)
To limit the trigger level error, we can use the large signal amplitudes and fast rise
times in the signal.
135
9. What is the difference between analog and digital instruments? (AU APRIL 2008)
SL.NO
Parameter
Analog
Digital
1.
Accuracy
Less upto + 0..1 %
Very high upto + 0.005
2.
Resolution
Limited
High
3.
Power
Power required is High
Power required is Low
4.
Cost
Low
High
5.
Frictional errors
Errors due to movimg parts
No movong parts so no errors
6.
Range and polarity
No facility of auto ranging and Has the facility of auto ranging and
7.
Speed
polarity
polarity
Reading speed is low
Reading speed is very high.
PART-B (16 Marks)
1. Draw and explain the circuit of a digital frequency meter. (AU APRIL 2007,2010,
NOV 2006,2008)
(16)
The frequency is the measure of repeatation of any signal. The frequency is nothing
but the number of cycles of the signal per unit time.
Working principle
The signal waveform whose frequency is to be measured is converted into trigger
pulses and applied continuously to one terminal of an AND gate. To the other terminal of
the gate, a pulse of 1 sec is applied. The number of pulses counted at the output terminal
during period of 1 sec indicates the frequency.
136
Digital Frequency Counter
For the unknown frequency measurements the digital frequency counter is the most
accurate and reliable instrument available.
The major components of the digital frequency counter are as given below
1)
2)
3)
4)
Input signal conditioning circuit
Time base generator
Gating circuit
Decimal counter and display unit.
Input signal conditioning circuit.
In this circuit, an amplifier and Schmitt trigger are included. The threshold voltage
of the Schmitt trigger can be controlled by sensitivity control on the control panel. First of
all the input signal of unknown frequency is fed into the input signal conditioning circuit.
There the signal is amplified and then it is converted into square wave by Schmitt trigger
circuit.
137
Time base generator
The crystal oscillator produces a signal of 1 MHz or 100 MHz depending upon the
requirement. In general, the accuracy of the digital frequency counter depends on the
accuracy of the time base signals produced, thus the temperature compensated crystal
oscillator is used. Then the output of the oscillator passed to the other Schmitt trigger
circuit producing square wave output. Then it is fed to frequency dividers connected in
cascade. Thus the train pulses are obtained after each frequency divider section. Using
time base selector switch S the gate time can be adjusted.
Gating circuit
The gating circuit consists of AND gate. When the enable signal is provided to the
AND gate, it allows a train pulses to pass through the gate for the time period selected by
the time base circuit. The pulses are counted and then the second pulse generated from the
time base generator disables AND gate and thus closes it.
Decimal counter and display unit
In this unit, decade counters are connected in the cascade. The output of the AND
gate is connected to the clock input of the first decade counter. Then the output of this
counter to the clock input of next and so on. Using these counters the number of pulses are
counted and are displayed by the display unit. As the number of pulses are counted are
proportional to the input signal frequency, the final display is proportional to the unknown
frequency of the input signal.
2. Explain with a neat block diagram, the operation of ramp type digital voltmeter.
(AU APRIL 2007,2010, NOV 2007,2008,2009)
(16)
Ramp type DVM
It uses a linear ramp technique or staircase ramp technique. The stair case ramp
technique is simpler than the linear ramp technique.
Linear ramp technique
The basic principle of such measurement is based on the measurement of the time
taken by linear ramp to rise from 0 V to the level of the input voltage or to decrease from
the level of the input voltage to zero. The time measured with the help of electronic time
interval counter and the count is displayed in the numeric form with the help of digital
display.
138
Block Diagram
Properly attenuated input signal is applied as one input to the input comparator
The ramp generator generates the proper linear ramp signal which is applied to
both the comparators.
The input comparator is used to send the start pulse while the ground comparator is
used to send the stop pulse.
When the input ramp are applied to the input comparator and at the point when
negative going ramp becomes equal to input voltages the comparator sends the start
pulse due to which gate opens.
The oscillator drives the counter. The counter starts counting the pulses received
from the oscillator.
Now the input ramp is applied to the ground comparator and it is decreasing. Thus
when ramp becomes zero, both the inputs of ground comparator becomes zero and
send it the stop pulse due to which gate closed.
The sample rate multivibartor determines the rate at which the measurement cycles
are initiated.
Staircase Ramp Technique
In this type of DVM, instead of linear ramp, the staircase ramp is used. The
staircase ramp is generated by the digital to analog converter.
The technique of using
staircase ramp is also called null balance technique.
139
Block Diagram
The input voltage is properly attenuated and is applied to a null detector. The input
to null detector is the staircase ramp generated by the digital to analog converter.
The ramp is continuously compared with the input signal.
The logical control circuit sends a rest signal. This signal resets the counter. The
digital to analog converter is also resetted by same signal.
The output counter is given to the digital to analog converter which generates the
ramp signal.
At every count there is an incremental change in the ramp generated. Thus the
staircase ramp is generated at the output of the digital to analog converter.
This is given as the second input of the null detector.
The increase in ramp continues till it achieves the voltage equal to input voltage.
When the two voltages are equal, the null detector generates a signal which inturn
initiates the logic control circuit.
3. Explain with a neat block diagram, the operation of successive approximation
type digital voltmeter. (AU NOV2008)
140
(16)
The potentiometric used in the servo balancing type DVM is a linear divider but in
successive approximation type a digital divider is used.
The digital divider is a Digital to analog (D/A) converter.
The servo motor replaced by an electronic logic.
The basic principle of measurement by this method is similar to the simple
example of determination of weight of the object.
The object is placed on one side of the balance and the approximate weight is
placed on the other side.
If this weight is smaller than the object, another small weight is added weight is
removed and smaller weight is added.
Thus by such successive procedure of adding and removing, the weight of the
object is determined.
The successive approximation type DVM works exactly on the same principle.
In successive approximation type DVM, the comparator compares the output of
digital to analog converter with the unknown voltage.
Accordingly, the comparator provides logic high or low signals.
The digital to analog converter successively generates the set pattern of signals.
The procedure continues till the output of the digital to analog converter becomes
equal to the unknown voltage.
4. Explain with a neat block diagram, the operation of dual slope integrating type
digital voltmeter. (AU APRIL 2008, NOV 2009)
141
(16)
Block Diagram
This is the most popular method of analog to digital conversion.
In the ramp techniques, the noise can cause large errors but in dual slope method
the noise is averaged out by the positive and negative ramps using the process of
integration.
The basic principle of this method is that the input signal is integrated for a fixed
interval of time.
And then the same integrator is used to integrate the reference voltage with reverse
slope.
Hence the name given to the technique is dual slope integration technique.
When the switch S1 is in the position 1, the capacitor C starts charging from zero
level.
The rate of charging is proportional to the input voltage level.
After the interval t 1, the input voltage is disconnected and a negative voltage – V
ref is connected by throwing the switch S1 in position 2.
Thus the input voltage is dependent on the time periods t 1 and t2 and not on the
values of R1 and C.
5. Explain with a neat block diagram, the operation of servo potentiometric type
digital voltmeter. . (AU APRIL 2006)
(16)
142
Block diagram
In this potentiometric type voltmeters internal reference voltage is provided.
A voltage comparison technique is used to measure the input voltage.
The unknown voltage is compared with the reference voltage with the help of the
setting of the calibrated potentiometer i.e. potential divider.
The arm of the potentiometer is varied to obtain the null condition i.e. balance
condition.
The internal reference voltage is present at the two terminals of the potentiometer.
When the null condition is obtained, the value of the unknown voltage is indicated
by the dial setting of the potentiometer.
Practically, the null balancing is not obtained manually but is obtained
automatically.
Such a voltmeter is called self balancing potentiometric type DVM.
The servomotor is used to vary the arm of the potentiometer hence it is also called
servo balancing potentiometer type DVM.
6. Describe a “digital multimeter” with a help of a block diagram explain its
working. (AU NOV 2009)
(16)
Block diagram
143
In the digital multimeter the quantity measured by the meter is displayed by using 7
segment LED displays, alphanumeric displays or liquid crystal displays (LCDs), in
the digital converters and other digital processing circuits.
The digital multimeter is an instrument which is capable of measuring AC voltages
DC voltages, AC and DC currents and resistance over several ranges.
The current is converted to voltage by passing it through low shunt resistance.
The AC quantities are converted to Dc by employing various rectifier and filtering
circuits.
While for the resistance measurements the meter consists of a precision low current
source that is applied across the unknown resistance while gives DC voltages.
All the quantities are digitalized using analog to digital converter and displayed in
the digital form on the display.
The analog multimeters require mo power supply and they suffer less from electric
noise and isolation problems but still the digital multimeters have the following
advantages over analog multimeters.
 Accuracy is very high.
 The input impedance is very high hence there is no loading effect.
 An unambiguous reading at greater viewing distances is obtained.
 The output available is electrical which can be used for interfacing with
external equipment.
 The prices are going down.
 Small in size.
144
UNIT V- DATA ACQUISITION SYSTEMS AND FIBER OPTIC
MEASUREMENTS
Data acquisition systems:
Data acquisition is the process of real world physical conditions and conversion of the
resulting samples into digital numeric values that can be manipulated by a computer. Data
acquisition and data acquisition systems (abbreviated with the acronym DAS) typically involves
the conversion of analog waveforms into digital values for processing. The components of data
acquisition systems include:
Sensors that convert physical parameters to electrical signals.
Signal conditioning circuitry to convert sensor signals into a form that can be converted to
digital values.
Analog-to-digital converters, which convert conditioned sensor signals to digital values.
Data acquisition is the process of extracting, transforming, and transporting data from the source
systems and external data sources to the data processing system to be displayed, analyzed, and
stored. A data acquisition system (DAQ) typically consist of transducers for asserting and
measuring electrical signals, signal conditioning logic to perform amplification, isolation, and
filtering, and other hardware for receiving analog signals and providing them to a processing
system, such as a personal computer. Data acquisition systems are used to perform a variety of
functions, including laboratory research, process monitoring and control, data logging, analytical
chemistry, tests and analysis of physical phenomena, and control of mechanical or electrical
machinery. Data recorders are used in a wide variety of applications for imprinting various types
of forms, and documents. Data collection systems or data loggers generally include memory chips
or strip charts for electronic recording, probes or sensors which measure product environmental
parameters and are connected to the data logger. Hand-held portable data collection systems
permit in field data collection for up-to-date information processing.
Source
Data acquisition begins with the physical phenomenon or physical property to be measured.
Examples of this include temperature, light intensity, gas pressure, fluid flow, and force.
Regardless of the type of physical property to be measured, the physical state that is to be
measured must first be transformed into a unified form that can be sampled by a data acquisition
145
system. The task of performing such transformations falls on devices called sensors.
A sensor, which is a type of transducer, is a device that converts a physical property into a
corresponding electrical signal (e.g., a voltage or current) or, in many cases, into a corresponding
electrical characteristic (e.g., resistance or capacitance) that can easily be converted to electrical
signal.The ability of a data acquisition system to measure differing properties depends on having
sensors that are suited to detect the various properties to be measured. There are specific sensors
for many different applications. DAQ systems also employ various signal conditioning
techniques to adequately modify various different electrical signals into voltage that can then be
digitized using an Analog-to-digital converter (ADC).
146
Signals
Signals may be digital (also called logic signals sometimes) or analog depending on the
transducer used.Signal conditioning may be necessary if the signal from the transducer is not
suitable for the DAQ hardware being used. The signal may need to be amplified, filtered or
demodulated. Various other examples of signal conditioning might be bridge completion,
providing current or voltage excitation to the sensor, isolation, linearization. For transmission
purposes, single ended analog signals, which are more susceptible to noise can be converted to
differential signals. Once digitized, the signal can be encoded to reduce and correct transmission
errors.
DAQ hardware
DAQ hardware is what usually interfaces between the signal and a PC. It could be in the
form of modules that can be connected to the computer's ports (parallel, serial, USB, etc.) or cards
connected to slots (S-100 bus, Apple Bus, ISA, MCA, PCI, PCI-E, etc.) in the mother board.
Usually the space on the back of a PCI card is too small for all the connections needed, so an
external breakout box is required. The cable between this box and the PC can be expensive due to
the many wires, and the required shielding.
147
DAQ cards often contain multiple components (multiplexer, ADC, DAC, TTL-IO, high speed
timers, RAM). These are accessible via a bus by a microcontroller, which can run small programs.
A controller is more flexible than a hard wired logic, yet cheaper than a CPU so that it is alright to
block it with simple polling loops. For example: Waiting for a trigger, starting the ADC, looking
up the time, waiting for the ADC to finish, move value to RAM, switch multiplexer, get TTL
input, let DAC proceed with voltage ramp. Many times reconfigurable logic is used to achieve
high speed for specific tasks and Digital signal processors are used after the data has been
acquired to obtain some results. The fixed connection with the PC allows for comfortable
compilation and debugging. Using an external housing a modular design with slots in a bus can
grow with the needs of the user.Not all DAQ hardware has to run permanently connected to a
PC, for example intelligent stand-alone loggers and oscilloscopes, which can be operated from
a PC, yet they can operate completely independent of the PC.
DAQ software
DAQ software is needed in order for the DAQ hardware to work with a PC. The device
driver performs low-level register writes and reads on the hardware, while exposing a standard
API for developing user applications. A standard API such as COMEDI allows the same user
applications to run on different operating systems, e.g. a user application that runs on Windows
will also run on Linux and BSD.
Multiplexing
In telecommunications and computer networks, multiplexing (also known as muxing) is a
process where multiple analog message signals or digital data streams are combined into one
signal over a shared medium. The aim is to share an expensive resource. For example, in
telecommunications, several phone calls may be transferred using one wire. It originated in
telegraphy, and is now widely applied in communications.The multiplexed signal is transmitted
over a communication channel, which may be a physical transmission medium. The
multiplexing divides the capacity of the low-level communication channel into several higherlevel logical channels, one for each message signal or data stream to be transferred. A reverse
process, known as demultiplexing, can extract the original channels on the receiver side.A
device that performs the multiplexing is called a multiplexer (MUX), and a device that performs
the reverse process is called a demultiplexer (DEMUX).Inverse multiplexing (IMUX) has the
opposite aim as multiplexing, namely to break one data stream into several streams, transfer
148
them simultaneously over several communication channels, and recreate the original data
stream.
Types of multiplexing
Multiplexing technologies may be divided into several types, all of which have significant
variations: space-division multiplexing (SDM), frequency-division multiplexing (FDM), timedivision multiplexing (TDM), and code division multiplexing (CDM). Variable bit rate digital bit
streams may be transferred efficiently over a fixed bandwidth channel by means of statistical
multiplexing, for example packet mode communication. Packet mode communication is an
asynchronous mode time-domain multiplexing which resembles time-division multiplexing.
Digital bit streams can be transferred over an analog channel by means of code-division
multiplexing (CDM) techniques such as frequency-hopping spread spectrum (FHSS) and directsequence spread spectrum (DSSS).In wireless communications, multiplexing can also be
accomplished
through
alternating
polarization
(horizontal/vertical
or
clockwise/counterclockwise) on each adjacent channel and satellite, or through phased multiantenna array combined with a Multiple-input multiple-output communications (MIMO)
scheme.
Space-division multiplexing
In wired communication, space-division multiplexing simply implies different point-topoint wires for different channels. Examples include an analogue stereo audio cable, with one pair
of wires for the left channel and another for the right channel, and a multipair telephone cable.
Another example is a switched star network such as the analog telephone access network
(although inside the telephone exchange or between the exchanges, other multiplexing techniques
are typically employed) or a switched Ethernet network. A third example is a mesh network.
Wired space-division multiplexing is typically not considered as multiplexing.In wireless
communication, space-division multiplexing is achieved by multiple antenna elements forming a
phased array antenna. Examples are multiple-input and multiple-output (MIMO),
single-input and multiple-output (SIMO) and multiple-input and single-output (MISO)
multiplexing. For example, a IEEE 802.11n wireless router with N antennas makes it possible to
communicate with N multiplexed channels, each with a peak bit rate of 54 Mbit/s, thus increasing
the total peak bit rate with a factor N. Different antennas would give different multi-path
propagation (echo) signatures, making it possible for digital signal processing techniques to
separate different signals from each other. These techniques may also be utilized for space
149
diversity (improved robustness to fading) or beamforming (improved selectivity) rather than
multiplexing.
Frequency-division multiplexing
Frequency-division multiplexing (FDM): The spectrums of each input signal are swifted in several
distinct frequency ranges.Frequency-division multiplexing (FDM) is inherently an analog
technology. FDM achieves the combining of several digital signals into one medium by sending
signals in several distinct frequency ranges over that medium.One of FDM's most common
applications is cable television. Only one cable reaches a customer's home but the service provider
can send multiple television channels or signals simultaneously over that cable to all subscribers.
Receivers must tune to the appropriate frequency (channel) to access the desired signal.A variant
technology, called wavelength-division multiplexing (WDM) is used in optical communications.
Time-division multiplexing
Time-division multiplexing (TDM) is a digital technology. TDM involves sequencing groups of a
few bits or bytes from each individual input stream, one after the other, and in such a way that
they can be associated with the appropriate receiver. If done sufficiently and quickly, the receiving
devices will not detect that some of the circuit time was used to serve another logical
communication path.Consider an application requiring four terminals at an airport to reach a
central computer. Each terminal communicated at 2400 bps, so rather than acquire four individual
circuits to carry such a low-speed transmission, the airline has installed a pair of multiplexers.
150
Code-division multiplexing
Code division multiplexing (CDM) is a technique in which each channel transmits its bits
as a coded channel-specific sequence of pulses. This coded transmission typically is accomplished
by transmitting a unique time-dependent series of short pulses, which are placed within chip times
within the larger bit time. All channels, each with a different code, can be transmitted on the same
fiber and asynchronously demultiplexed. Other widely used multiple access techniques are Time
Division Multiple Access (TDMA) and Frequency Division Multiple Access (FDMA).Code
Division Multiplex techniques are used as an access technology, namely Code Division Multiple
Access (CDMA), in Universal Mobile Telecommunications System (UMTS) standard for the third
generation (3G) mobile communication identified by the ITU. Another important application of
the CDMA is the Global Positioning System (GPS).However, the term Code Division Multiple
access (CDMA) is also widely used to refer to a group of specific implementations of CDMA
defined by Qualcomm for use in digital cellular telephony, which include IS-95 and IS-2000. The
two different uses of this term can be confusing. Actually, CDMA (the Qualcomm standard) and
UMTS have been competing for adoption in many markets.
Relation to multiple access.A multiplexing technique may be further extended into a multiple
access method or channel access method, for example TDM into Time-division multiple access
(TDMA) and statistical multiplexing into carrier sense multiple access (CSMA). A multiple access
method makes it possible for several transmitters connected to the same physical medium to share
its capacity.Multiplexing is provided by the Physical Layer of the OSI model, while multiple access
also involves a media access control protocol, which is part of the Data Link Layer.The Transport
layer in the OSI model as well as TCP/IP model provides statistical multiplexing of several
application layer data flows to/from the same computer.
151
Application areas
Telegraphy
The earliest communication technology using electrical wires, and therefore sharing an interest in
the economies afforded by multiplexing, was the electric telegraph. Early experiments allowed
two separate messages to travel in opposite directions simultaneously, first using an electric
battery at both ends, then at only one end.
Émile Baudot developed a time-multiplexing system of multiple Hughes machines in the
1870s.
In 1874, the quadruplex telegraph developed by Thomas Edison transmitted two
messages in each direction simultaneously, for a total of four messages transiting the same
wire at the same time.
Several workers were investigating acoustic telegraphy, a frequency-division
multiplexing technique, which led to the invention of the telephone.
Telephony
In telephony, a customer's telephone line now typically ends at the remote concentrator box down
the street, where it is multiplexed along with other telephone lines for that neighborhood or other
similar area. The multiplexed signal is then carried to the central switching office on significantly
fewer wires and for much further distances than a customer's line can practically go. This is
likewise also true for digital subscriber lines (DSL).Fiber in the loop (FITL) is a common method
of multiplexing, which uses optical fiber as the backbone. It not only connects POTS phone lines
with the rest of the PSTN, but also replaces DSL by connecting directly to Ethernet wired into the
home. Asynchronous Transfer Mode is often the communications protocol used.Because all of
the phone (and data) lines have been clumped together, none of them can be accessed except
through a demultiplexer. This provides for more-secure communications, though they are not
typically encrypted.The concept is also now used in cable TV, which is increasingly offering the
same services as telephone companies. IPTV also depends on multiplexing.
Video processing
In video editing and processing systems, multiplexing refers to the process of interleaving audio
and video into one coherent MPEG transport stream (time-division multiplexing).In digital video,
such a transport stream is normally a feature of a container format which may include metadata
and other information, such as subtitles. The audio and video streams may have variable bit rate.
Software that produces such a transport stream and/or container is commonly called a statistical
152
multiplexor or muxer. A demuxer is software that extracts or otherwise makes available for
separate processing the components of such a stream or container.
Digital broadcasting
In digital television and digital radio systems, several variable bit-rate data streams are
multiplexed together to a fixed bitrate transport stream by means of statistical multiplexing. This
makes it possible to transfer several video and audio channels simultaneously over the same
frequency channel, together with various services.In the digital television systems, this may
involve several standard definition television (SDTV) programmes (particularly on DVB-T,
DVB-S2, ISDB and ATSC-C), or one HDTV, possibly with a single SDTV companion channel
over one 6 to 8 MHz-wide TV channel. The device that accomplishes this is called a statistical
multiplexer. In several of these systems, the multiplexing results in an MPEG transport stream.
The newer DVB standards DVB-S2 and DVB-T2 has the capacity to carry several HDTV
channels in one multiplex. Even the original DVB standards can carry more HDTV channels in a
multiplex if the most advanced MPEG-4 compressions hardware is used.On communications
satellites which carry broadcast television networks and radio networks, this is known as
multiple channel per carrier or MCPC. Where multiplexing is not practical (such as where there
are different sources using a single transponder), single channel per carrier mode is used.Signal
multiplexing of satellite TV and radio channels is typically carried out in a central signal playout
and uplinkcentre, such as ASTRA Platform Services in Germany, which provides playout,
digital archiving, encryption, and satellite uplinks, as well as multiplexing, for hundreds of
digital TV and radio channels.In digital radio, both the Eureka 147 system of digital audio
broadcasting and the in-band on- channel HD Radio, FMeXtra, and Digital Radio Mondiale
systems can multiplex channels. This is essentially required with DAB-type transmissions
(where a multiplex is called an ensemble), but is entirely optional with IBOC systems.
Analog broadcasting
In FM broadcasting and other analog radio media, multiplexing is a term commonly given to the
process of adding subcarriers to the audio signal before it enters the transmitter, where modulation
occurs. Multiplexing in this sense is sometimes known as MPX, which in turn is also an old term
for stereophonic FM, seen on stereo systems since the 1960s.
153
IEEE-488 Bus:
IEEE-488 is a short-range digital communications bus specification. It was created for use with
automated test equipment in the late 1960s, and is still in use for that purpose. IEEE-488 was
created as HP-IB (Hewlett-Packard Interface Bus), and is commonly called GPIB (General
Purpose Interface Bus). It has been the subject of several standards.
Characteristics
IEEE-488 is an 8-bit, electrically parallel bus. The bus employs sixteen signal lines — eight used
for bi-directional data transfer, three for handshake, and five for bus management — plus eight
ground return lines.Every device on the bus has a unique 5-bit primary address, in the range from
0 to 30 (31 total possible addresses).The standard allows up to 15 devices to share a single
physical bus of up to 20 meters total cable length. The physical topology can be linear or star
(forked). Active extenders allow longer buses, with up to 31 devices theoretically possible on a
logical bus.Control and data transfer functions are logically separate; a controller can address one
device as a―talker‖ and one or more devices as ―listeners‖ without having to participate in the data transfer. It
is possible for multiple controllers to share the same bus; but only one can be the "Controller In
Charge" at a time In the original protocol, transfers use an interlocked, three-wire ready–valid–
accepted handshake. The maximum data rate is about one Mbyte/s. The later HS-488 extension
relaxes the handshake requirements, allowing up to 8 Mbyte/s. The slowest participating device
determines the speed of the bus.
Use as a computer interface
HP's designers did not specifically plan for IEEE-488 to be a peripheral interface for generalpurpose computers; the focus was on instrumentation. But when HP's early microcomputers
needed an interface for peripherals (disk drives, tape drives, printers, plotters, etc.), HP-IB was
readily available and easily adapted to the purpose.HP computer products which used HP-IB
included the HP series 80, HP 9800 series, the HP 2100 series, and the HP 3000 series. Some
of HP's advanced pocket calculators of the 1980s, such asthe HP-41 and HP-71B series, also
had IEEE-488 capabilities, via an optional HP-IL/HP-IB interface module.Other manufacturers
adopted GPIB for their computers as well, such as with the Tektronix 405x line.The
Commodore PET (introduced 1977) range of personal computers connected their peripherals
using the IEEE-488 bus, but with a non-standard card edge connector. Commodore's following
8- bit machines, including the VIC-20, C-64, and C-128, utilized an unrelated, proprietary
serial interface, using a round DIN connector, for which they retained the IEEE-488
154
programming interface and terminology, however.
Advantages and disadvantages
Advantages
Simple hardware interface
Ease of connecting multiple device to a single host
Allows mixing of slow and fast devices
Well-established and mature, widely supported
Disadvantages
Mechanically bulky connectors and cables
Limited speed and expansion
Lack of command protocol standards (before SCPI)
Implementation options (e.g. end of transmission handling) can complicate interoperability
in pre-IEEE-488.2 devices
No mandatory galvanic isolation between bus and devices
High cost (compared to RS-232/USB/Firewire/Ethernet)
Limited availability (again compared to RS-232/USB/Firewire/Ethernet)
Optical time-domain reflectometer
An optical time-domain reflectometer (OTDR) is an optoelectronic instrument used to
characterize an optical fiber. An OTDR injects a series of optical pulses into the fiber under test. It
also extracts, from the same end of the fiber, light that is scattered (Rayleigh Backscatter) or
reflected back from points along the fiber. (This is equivalent to the way that an electronic timedomain reflectometer measures reflections caused by changes in the impedance of the cable under
test.) The strength of the return pulses is measured and integrated as a function of time, and is
plotted as a function of fiber length.
An OTDR may be used for estimating the fiber's length and overall attenuation, including splice
and mated-connector losses. It may also be used to locate faults, such as breaks, and to measure
optical return loss. To measure the attenuation of multiple fibers, it is advisable to test from each
end and then average the results, however this considerable extra work is contrary to the common
claim that testing can be perfomed from only one end of the fiber.
In addition to required specialized optics and electronics, OTDRs have significant computing
ability and a graphical display, so they may provide significant test automation. However, proper
instrument operation and interpretation of an OTDR trace still requires special technical training
and experience.
155
OTDRs are commonly used to characterize the loss and length of fibers as they go from initial
manufacture, through to cabling, warehousing while wound on a drum, installation and then
splicing. The last application of installation testing, is more challenging, since this can be over
extremely long distances, or multiple splices spaced at short distances, or fibers with different
optical characteristics joined together. OTDR test results are often carefully stored in case of later
fiber failure or warranty claims. Fiber failures can be very expensive, both in terms of the direct
cost of repair, and consequential loss of service.
OTDRs are also commonly used for fault finding on installed systems. In this case, reference to
the installation OTDR trace is very useful, to determine where changes have occurred. Use of an
OTDR for fault finding may require an experienced operator who is able to correctly judge the
appropriate instrument settings to locate a problem accurately. This is particularly so in cases
involving long distance, closely spaced splices or connectors, or PONs.
OTDRs are available with a variety of fiber types and wavelengths, to match common
applications. In general, OTDR testing at longer wavelengths such as 1550 nm or 1625 nm, can be
used to identify fiber attenuation caused by fiber problems, as opposed to the more common splice
or connector losses.
The optical dynamic range of an OTDR is limited by a combination of optical pulse output power,
optical pulse width, input sensitivity, and signal integration time. Higher optical pulse output
power, and better input sensitivity, combine directly to improve measuring range, and are usually
fixed features of a particular instrument. However optical pulse width and signal integration time
are user adjustable, and require trade-offs which make them application specific.
A longer laser pulse improves dynamic range and attenuation measurement resolution at the
expense of distance resolution. For example, using a long pulse length, it may possible to measure
attenuation over a distance of more than 100 km, however in this case an optical event may appear
to be over 1 km long. This scenario is useful for overall characterisation of a link, but would be of
much less use when trying to locate faults. A short pulse length will improve distance resolution
of optical events, but will also reduce measuring range and attenuation measurement resolution
The OTDR "dead zone" is a topic of much interest to users. Dead zone is classified in two ways.
156
Firstly, an "Event Dead Zone" is related to a reflective discrete optical event. In this situation, the
measured dead zone will depend on a combination of the pulse length (see table), and the size of
the reflection. Secondly, an "Attenuation Dead Zone" is related to a non-reflective event. In this
situation, the measured dead zone will depend on a combination of the pulse length (see table).
A long signal integration time effectively increases OTDR sensitivity by averaging the receiver
output. The sensitivity increases with the square root of the integration time. So if the integration
time is increased by 16 times, the sensitivity increases by a factor of 4. This imposes a sensitivity
practical limit, with integration times of seconds to a few minutes.
The dynamic range of an OTDR is usually specified as the attenuation level where the measured
signal gets lost in the detection noise level, for a particular combination of pulse length and signal
integration time. This number is easy to deduce by inspection of the output trace, and is useful for
comparison, but is not very useful in practice, since at this point the measured values are random.
So the practical measuring range is smaller, depending on required attenuation measurement
resolution.
When an OTDR is used to measure the attenuation of multiple joined fiber lengths, the output
trace can incorrectly show a joint as having gain, instead of loss. The reason for this is that
adjacent fibers may have different backscatter coefficients, so the second fiber reflects more light
than the first fiber, with the same amount of light travelling through it. If the OTDR is placed at
the other end of this same fiber pair, it will measure an abnormally high loss at that joint. However
if the two signals are then combined, the correct loss will be obtained. For this reason, it is
common OTDR practice to measure and combine the loss from both ends of a link, so that the loss
of cable joints, and end to end loss, can be more accurately measured.
The theoretical distance measuring accuracy of an OTDR is extremely good, since it is based on
software and a crystal clock with an inherent accuracy of better than 0.01%. This aspect does not
need subsequent calibration since practical cable length measuring accuracy is typically limited to
about 1% due to: The cable length is not the same as the fiber length, the speed of light in the fiber
is known with limited accuracy (the refractive index is only specified to 3 significant figures such
as e.g. 1.45 etc.), and cable length markers have limited accuracy (0.5% - 1%).
157
An OTDR excels at identifying the existence of unacceptable point loss or return loss in cables.
It's ability to accurately measure absolute end-to-end cable loss or return loss can be quite poor, so
cable acceptance ususally includes an end to end test with a light source and power meter, and
optical return loss meter. It's ability to exactly locate a hidden cable fault is also limited, so for
fault finding it may be augmented with other localised tools such as a red laser fault locator, clipon identifier, or "Cold Clamp" optical cable marker.
158
Question Bank
UNIT-V
DATA ACQUISITION SYSTEMS AND FIBER OPTIC MEASUREMENTS
PART-A (2 Marks)
1. What is meant by data acquisition? (AU NOV 2008,2009)
The system used for data processing, data conversion, data transmission, data storage is
called data acquisition system.
2. What are the objectives of Data Acquisition system?
 The data acquisition system must acquire the necessary data at the correct time.
 It must use all the data efficiently to inform the operator about the state of the plant.
 It must monitor the operation of complete plant so that optimum online safe operations
are maintained.
 It must provide effective human communication system.
 It must be able to collect, summarise and store data properly for diagnosis and record
purpose of any operation.
3. What is Multiplexing? (AU APRIL 2006, 2009)
Multiplexing means combining different signals. In data processing and handling it is the
frequently required to combine number of analog signals into a single digital channel. Both
digital signals and analog voltages can be multiplexed.
4. What are the three basic requirements of a computer controlled systems? (AU APRIL
2003)
5. What is an IEE 488 bus system? (AU APRIL 2004)
6. What is meant by IEE 488 standard and GPIB? (AU NOV 2006)
7. What is Optical Time Domain Reflectometer? (AU NOV 2007)
PART-B (16 Marks)
1. Explain the generalized block schematic of a Digital Data Acquisition system.
2. (16 marks) ) (AU NOV 2008)
3. Explain the various techniques of multiplexing? (16 marks) (AU NOV 2006,2009)
4. Explain the block diagram of optical time domain reflectometer. (16 marks)
(AU APRIL 2007, NOV 2009)
5. Write short notes on IEEE 488 bus. (16 marks) (AU APRIL 2010, NOV 2007)
6. Explain microprocessor based measurement. (8 marks) (AU APRIL 2005, NOV 2005)
7. Write short notes on VI (Virtual Instrumentation)
159
Anna University sample Question Paper
B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2011
Sixth Semester
Electronics and Communication Engineering
EC 2351 — MEASUREMENTS AND INSTRUMENTATION
(Regulation 2008)
Time : Three hours Maximum : 100 marks
Answer ALL questions
PART A — (10 × 2 = 20 marks)
1. Mention the significance of measurements.
2. Compare Moving coil with Moving iron instruments.
3. Draw the internal structure of CRT and list its functions.
4. What are the two significant problems with diodes when used for RF
rectification?
5. What is Barkhausen Criteria for sustained oscillation?
6. Draw the block diagram of spectrum analyzer.
7. What are the advantages of digital instruments over analog instruments?
8. What are the different types of Digital Voltmeter?
9. Draw the block diagram of Digital Data Acquisition System.
10. What are the key features of fully automatic digital instruments?
PART B — (5 × 16 = 80 marks)
11. (a) (i) What is the need for standards of measurements? How they are classified?
Explain (8)
(ii) How the unknown frequency is measured using Wein bridge method? (8)
Or
(b) (i) What are the different types of errors in measurement? Explain. (8)
(ii) How do you measure the unknown inductance using Hay Bridge? (8)
12. (a) (i) Draw the block diagram of sampling oscilloscope and explain the principle.
(8)
(ii) Explain the measurement of quality factor of a coil. (8)
Or
(b) (i) Discuss the measurement of DC and AC voltages and currentsusing an
Electronic Multimeter. (8)
(ii) Draw the block diagram of True RMS reading voltmeter and explain its
operation. (8)
13. (a) (i) Explain how function generator generates sine wave, triangular wave and
square wave. (8)
(ii) Draw the block diagram of sweep-frequency generator and explain.(8)
Or
160
(b) (i) What is wave analyzer? How it analyzes the harmonics? Explain. (8)
(ii) Explain the vector network analyzer and list its application. (8)
14. (a) (i) How computer controlled measurement system is used for testing radio
receiver? (8)
(ii) What is virtual instrument? List the advantages of virtual instrument over
conventional instrument (8)
Or
(b) (i) With necessary diagrams explain Ramp type digital voltmeter. (8)
(ii) Draw the block diagram of digital frequency meter and explain. (8)
15. (a) (i) What are the factors to be considered while interfacing transducers to
electronic control and measuring systems? (8)
(ii) Draw the block schematic representation of the IEEE 488 instrumentation bus
and explain. (8)
Or
(b) (i) Explain the optical time domain reflectometer with a neat diagram.(8)
(ii) Write a detailed note on data loggers. (8)
161
B.E/B.Tech DEGREE EXAMINATION NOVEMBER/DECEMBER 2007
Sixth Semester
Electrical and Electronics Engineering
EI 1361 --MEASUREMENTS AND INSTRUMENTATION
(Regulation 2004)
Time:Three hours
marks:100
Maximum
Answer ALL questions
PART A
(10 x 2=20
marks)
1. Distinguish between the direct and indirect methods of measurements.
2. With one example explain "Instrumental Errors"
3. Explain the principle of analog type electrical instruments.
4. How a PMMC meter can be used as voltmeter and ammeter?
5. Draw Maxwell’s AC Bridge and give the balance equation interms of resistance.
6. Explain any two technical parameters to be consider in grounding.
7. Explain the characteristics of Time domain output device using in measurements.
8. Explain the following term as applied to digital displays.
3½ digit and 4½ digit displays.
9. Define inverse transducer with example.
10. Explain the principle of piezoelectric transducers and name any two
piezoelectric materials.
PART B
(5 x 16 =80)
11 (i) What are the basic blocks of a generalized instrumentation system. Draw the
various blocks and explain their functions.
(10)
(ii) Explain in detail calibration technique and draw the calibration curve in
general. (6) (or)
(b) (i) Discuss in detail various types errors associated in measurement and how these
errors can be minimized?
(ii)Define the following terms in the context of normal frequency distribution
of data (6)
(1)Mean value (2)Standard Deviation (3)Average(4) Variance
162
(10)
12. (a) Describe the construction, principle of working and applications of synchro
transformers. (or)
(b) Discuss why is it necessary to carry out frequency domain analysis of
measurement systems? What are the two plots obtained when the frequency
response of a system is carried out? (16)
13 (a) Explain voltage sensitive self balancing bridge, and derive the bridge
sensitivity of voltage sensitive bridge with fundamentals.
(16)
(or)
(b) (i) With fundamentals distinguish between DC and AC potentiometers, and
give any two specific applications for each.(8)
(ii) Discuss the advantages and limitations of electromagnetic interference in
measurements. (8)
14. (a) Describe the construction and working of LCDs, mention the difference
between light scattering and field effect types of LCDs, also explain the
advantages of LCDs. (16)
(or)
(b) (i) What is an XY recorders? How do you distinguish is from X - t and Y - t
recorders? (8)
(ii) Describe the pulse duration modulation (PDM) as used in magnetic tape
recording and explain its merits and demerits. (8)
15. (a) (i) Describe the different criteria for selection transducers for a particular
application. (8) (ii) Explain the different principles of working of
transducers.
capacitive
(8)
O
r
(b) (i) How is a differential output taken from an inductive transducer?Explain the
advantages when inductive transducers are used in push
- pull configuration.
(ii) Describe in detail the successive approximation method of analog to digital
conversion. (8)
163
(8)
B.E./B.Tech. DEGREE EXAMINATION, MAY/JUNE 2010.
Sixth Semester
Electronics and Communication engineering
EC1255-MEASUREMENTS ANDINSTRUMENTAION
(Regulation 2004)
Time:3hrs Maximum:100marks
Answer ALL questions.
PART A - (10X2=20 marks)
1. What are the different types of standard of measurement?
2. What is a transfer instrument?
3. How is the electron beam focused to a fine spot on the face of the cathode ray tube?
4. List the disadvantages of storage cathode ray tube.
5. Give the functions of an attenuator in a signal generator.
6. What are the draw backs of tuned circuit analyzers?
7. What is the importance of gate time in frequency counter?
8. How is trigger time error reduced?
9. Distinguish between analog and digital data acquisition systems.
10. How much elapsed time would occur to a reflection from a break in an optical
fibre of 1.4km if the index of refraction of the core was 1.55?
PART B - (16X5=80 marks)
11.(a)(i)With a neat diagram explain in detail the construction of PMMC
instrument.(8 ) (ii)How do you measure large currents in PMMC
instruments?(4)
(iii)What is
Ayrton shunt?(4)
Or
(b)(i)Discuss in detail about Kelvin double bridge.(8 )
164
(ii)With a neat diagram explain in detail about Hay bridge.(8 )
12.(a)With a neat diagram explain in detail about
(i)Ramp type DVM(8 )
(ii)Successive approximation DVM.(8 )
Or
(b)With a neat block diagram explain in detail about vector impedance meter.(16)
13.(a)With a neat block diagram explain in detail about the frequency divider typer of
signal generator with frequency modulation.(16)
Or
(b)Explain:
(i)General purpose spectrum analyzer.(8 )
(ii)Phase locked circuit for the first local oscillator of spectrum analyzer.(8 )
14.(a)(i)What method can be used to increase the frequency range of frequency
counter.(8 ) (ii)How can this be achieved without degrading the accuracy of the
counter.(8 )
Or
(b)Discuss in detail about
(i)Gating error
(ii)Time-base error and trigger level error.
(iii)Maximum accuracy achieved for frequency measurements.
15.(a)(i)What are the requirements of an automatic test
system? (ii)Explain in detail about IEEE 488 system.
Or
(b)With a neat block diagram explain
(i)Optical power meter (ii) Auto ranging power meter
(iii) Optical time-domain reflectometer.
165
B.E./B.Tech. DEGREE EXAMINATION,
NOVEMBER/DECEMBER 2010
Third emester
Electrical and Electronics Engineering
EE 2201 — MEASUREMENTS AND
INSTRUMENTATION (Regulation 2008)
Time : Three hours
100 Marks
Maximum :
Answer ALL
questions
PART A — (10 × 2 = 20
Marks)
1. Define static characteristics of an instrument.
2. What is meant by absolute error of measurement?
3. Why are the ordinary watt-meters not suitable for low power factor circuits?
4. What is a phase sequence indicator?
5. List the application of D.C. potentiometers.
6. What are parasitic voltages and how are they eliminated?
7. What is the purpose of a Post Deflection Acceleration (PDA) in a CRT?
8. Differentiate between LED and LCD.
9. What are the classifications of encoder?
10. What is the need of sample and hold circuit in A/D converter?
PART B — (5 × 16 = 80 Marks)
11. (a) (i) Draw the block diagram of functional elements of measuring
system and explain the function of each block. (Marks 8)
(ii) Explain the different types of errors in measurements. (8)
Or
(b) (i) The probable values of two resistors and their S.D are specified as
R1 – 18.62 , S.D = 0.025 , R2 = 74.48 , S.D. = 0.05 . Find the probable
value and S.D for the two resistors when they are connected in
(1) Series and
(2) Parallel. (Marks 8)
(ii) Discuss the different types of standards of measurements. (Marks 8)
12. (a) (i) What are the various types of digital voltmeters? With a neat sketch
explain the working principle of any one type of a digital voltmeter. (Marks 8)
(ii) With a neat diagram explain the construction and its working principle of
elector dynamo-meter type watt-meter. Also derive its torque equation. (Marks 8)
166
Or
(b) (i) Explain the method of measurements of B.H curve of
a ring specimen with a neat diagram. (Marks 8)
(ii) Describe the construction and working principle of digital
frequency meter. (Marks 8)
13. (a) (i) Draw a neat sketch of a modern slide-wire D.C
potentiometer and discuss how the potentiometer is standardized.
(Marks 8)
(ii) Describe how co-ordinate type potentiometer can be
used for calibration of a voltmeter and A.C energy meters.
(Marks 8)
Or
(b) (i) Explain the theory and working principle of Kelvin's double
bridge method for measurement of low resistance. Derive the
relation for
finding unknown resistance. (Marks 8)
(ii) Discuss briefly how Hay's Bridge can be used for the
measurement of inductance. (Marks 8)
14. (a) (i) Explain the construction and its working principle of X-Y
Recorder. (6)
(ii) Briefly discuss the features of digital plotters and printers.
(Marks 10) Or
(b) (i) Explain the working principle of electrostatic deflection system in a
CRT. (10)
(ii) Explain the working principle of digital storage oscilloscope. (Marks 6)
15. (a) (i) Explain the construction and working of unbounded and
bonded type strain gauges. ( 8)
(ii) Explain the construction and working of optical encoders
with a neat diagram. (Marks 8)
Or
(b) (i) Draw the generalized block diagram of a digital data
acquisition system and explain. (8)
(ii) Explain the successive approximation method of A/D converter. (8)
167
Reg. No. :
Question Paper Code : 21370
B.E./B.Tech. DEGREE EXAMINATION, MAY/JUNE 2013.
Sixth Semester
Electronics and Communication engineering
EC 2351/EC 61/10144/EC 602 – MEASUREMENTS AND INSTRUMENTATION
(Regulation 2008/2010)
Time : Three hours
Maximum : 100 marks
Answer ALL questions
PART A – (10 X 2 = 20 marks)
1. List out the various standards of measurements.
2. Mention the errors in moving coil meters.
3. Prepare the comparison table between analog and digital storage oscilloscope.
4. Write a short note on true RMS meters.
5. How do you measure the resistance values in digital RLC meters?
6. What is meant by network analyzer?
7. Define automatic ranging.
8. Write a short note on digital voltmeter.
9. List out the drawbacks of reflectometer.
10. Define the term transducer.
PART B – (5 X 16 = 80 marks)
11. (a) With neat circuit diagrams describe in detail about the following bridge
measurement system.
(i) Maxwell bridge (8)
(ii) Wien bridge.
(8)
Or
(b) (i) Explain in detail about the various error measurement systems with
statistical analysis. (8)
(ii) Describe in detail about the moving iron meters with suitable
example.
(8)
12. (a) Discuss in detail about the function of delay time base oscilloscopes with
neat diagram.
(16)
Or
(b) With neat diagram explain in detail about the function of following
168
measurement system.
(i) Vector meter (8)
(ii) Q meter
(8)
13. (a) Explain the operations of RF signal and sweep generators.
Or
(b) Explain with neat diagrams , the working of the following :
(i) Spectrum analyzer (8)
(ii) Frequency synthesizer. (8)
14. (a) Discuss in detail about the computer controlled fully automatic digital
instruments with test systems.
Or
(b) (i) Enumerate the measurement system of frequency and time intervals in
a particular range of signals.
(8)
(ii) Discuss in detail about the digital multimeter. (8)
15. (a) With the neat diagram , explain the working of IEEE 488 bus , operations
and characteristics.
Or
(b) Draw and explain the block diagram of analog and digital data acquisition
system.
--------------------------------------------
169
170
171
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement