10144ec602 measurements and instrumentation

10144ec602 measurements and instrumentation
PREPARED BY: Ms. G.GEETHA/ Assistant Professor/ECE
Measurement systems – Static and dynamic characteristics – Units and standards of
measurements – Error analysis – Moving coil, moving iron meters – Multimeters – True
meters – Bridge measurements – Maxwell ,Hay ,Schering ,Anderson and Wien bridge.
Electronic multimeters – Cathode ray oscilloscopes – Block schematic – Applications –
Special oscilloscopes – Q meters – Vector meters – RF voltage and power measurements. –
True RMS meters.
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.
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
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
1. Helfrick, A.D. and William Cooper, D., ―Modern Electronic Instrumentation and
Measurement Techniques‖, PHI, 2007.
2. Ernest O. Doebelin, ― Measurement Systems- Application and Design‖, TMH, 2007.
1. Carr, J.J., ―Elements of Electronics Instrumentation and Measurement‖, Pearson
2. David A. Bell,‖Electronic Instrumentation and measurements‖, Prentice Hall of India
Pvt Ltd, 2003.
3. B.C. Nakra and K.K. Choudhry, Instrumentation, ―Measurement and Analysis,
Edition‖, TMH, 2004.
4. James W. Dally, William F. Riley, Kenneth G. McConnell, Instrumentation for
Engineering Measurements, 2nd Edition, John Wiley, 2003.
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 …
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.
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
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
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
( b ) how an electronic amplifier might settle over time to a final value after power is
(c ) drift, due to temperature, of an electronic amplifier varies with the actual temperature of
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
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
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 www.annauniversityplus.com
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 Equation 3.5.
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.
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 left- hand 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
Solution of the combined behavior is obtained using Laplace transform methods to obtain
the output responses in the time or the complex frequency domain. These mathematical
methods might not be familiar to the reader, but this is not a serious difficulty for the cases
most encountered in practice are
. . . . . . . . a d y dt
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 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
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
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
Error Analysis :
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 "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 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.
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
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.www.annauniversityplus.com
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
it is assumed
in order to estimate this error.
A. Mean Value
Suppose an experiment were repeated many, say N, times to get,
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,
In these terms, the quantity,
, could be specified.
, (3)
is the maximum error. And virtually no measurements should ever fall outside
Probable Error
The probable error,
measured values.
, specifies the range
which contains 50% of the
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)
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
. 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
(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.
For a Gaussian distribution there is a 5% probability that the true value is outside of the
, i.e. twice the standard error, and only a 0.3% chance that it is outside the range
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.
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,
, (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
A first thought might be that the error in Z would be just the sum of the errors in A and B.
After all,
. (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 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
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,
, (15)
, (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,
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,
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
Relation between Z Relation between errors
and ( ,
2 Z=A-B
Z = AB
Z = A/B
Z = An
Z = ln A
Z = eA
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
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.
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 meters based on galvanometer sensors.
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
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 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 multi-meter indicates RMS values for sinewaves 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 sinewave, 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.
Wheatstone bridge
Wheatstone's bridge circuit diagram
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
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
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
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:
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
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.
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
L1 = R3R1C1 / [1 + (2πfR2C1)2]; and
R4 = (2πfC1)2R2R3R1 / [1 + (2πfR2C1)2]
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
The modern circuit is derived from William Hewlett's 1939 Stanford University master's
degree thesis. Hewlett, along with David Packard co-founded Hewlett-Packard. 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 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 the oscillator 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.[citation needed]
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
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:
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
Substituting this value yields:
Similarly, the input resistance at the frequency above is:
For Av = 3:
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.
Important Questions: Unit –I
1. What are the functional elements of an instrument? (2)
2. What is meant by accuracy of an instrument? (2)
3. Define international standard for ohm? (2)
4. What is primary sensing element? (2)
5. What is calibration? (2)
6. Define the terms precision & sensitivity. (2)
7. What are primary standards? Where are they used? (2)
8. When are static characteristics important? (2)
9. What is standard? What are the different types of standards? (2)
10. Define static error. Distinguish reproducibility and repeatability. (2)
11. Distinguish between direct and indirect methods of measurements. (2)
12. With one example explain ―Instrumental Errors‖. (2)
13. Name some static and dynamic characteristics. (2)
14. State the difference between accuracy and precision of a measurement. (2)
15. What are primary and secondary measurements? (2)
16. What are the functions of instruments and measurement systems? (2)
17. What is an error? How it is classified? (2)
18. Classify the standards of measurement? (2)
19. Define standard deviation and average deviation. (2)
20. What are the sources of error? (2)
21. Define resolution. (2)
22. What is threshold? (2)
23. Define zero drift. (2)
24. Write short notes on systematic errors. (2)
25. What are random errors? (2)
1. Describe the functional elements of an instrument with its block diagram.
And illustrate them with pressure gauge, pressure thermometer and
D’Arsonval galvanometer. (16)
2. (i) What are the three categories of systematic errors in the instrument and
explain in detail. (8)
(ii) Explain the Normal or Gaussian curve of errors in the study of random
effects. (8)
3. (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)
4. (i) Discuss in detail various types of errors associated in measurement
and how these errors can be minimized? (10)
(ii) Define the following terms in the context of normal frequency
distribution of data (6)
a) Mean value, b) Deviation, c) Average deviation, d) Variance
e) Standard deviation.
5. (i) Define and explain the following static characteristics of an instrument. (8)
a) Accuracy, b) Resolution, c) Sensitivity and d) Linearity
(ii) Define and explain the types of static errors possible in an instrument. (8)
6. Discuss in detail the various static and dynamic characteristics of a measuring
system. (16)
Electronic Multimeters :
Cathode-Ray Oscilloscope :
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.
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 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
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 verical 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 appliying 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.
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.
Power and Scale Illumination: Turns instrument on and controls illumination of the
Focus: Focus the spot or trace on the screen.
Intensity: Regulates the brightness of the spot or trace.
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.
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.
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).
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
(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.
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 verticle 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.
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).
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 can not
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
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 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
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 frequence 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).
Q meter :
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.
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
(See Footnote on how this is done.)
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
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.
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 1
MHz, 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 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.
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
Important Questions : Unit-II
1. State the principle of digital voltmeter. (2)
2. Give the importance of iron loss measurement. (2)
3. List two instruments for measurement of frequency. (2)
4. Write the function of instrument transformer. (2)
5. Brief the principle of digital phase meter. (2)
6. Write any two advantages and disadvantages of digital voltmeter. (2)
7. Explain the purpose of Schmitt trigger in digital frequency meter. (2)
8. Which torque is absent in energy meter? Why? (2)
9. What are the errors that take place in moving iron instrument? (2)
10. Explain the principle of analog type electrical instruments. (2)
11. How a PMMC meter can be used as voltmeter and ammeter? (2)
12. What is loading effect? (2)
13. State the basic principle of moving iron instrument. (2)
14. Why an ammeter should have a low resistance? (2)
15. Define the sensitivity of a moving coil meter. (2)
16. What are the precautions taken while using a DC voltmeter and DC Ammeter? (2)
17. What is the use of Multimeter? Write its advantages and disadvantages. (2)
18. Voltmeter has high resistance, why it is connected in series? (2)
19. What is an energy meter? Mention some advantages and disadvantages
of energy meter. (2)
20. What is meant by creep adjustment in three phase energy meter? (2)
21. List some advantages and disadvantages of electrodynamic instrument. (2)
22. List the advantages of electronic voltmeter. (2)
23. What is a magnetic measurements and what are the tests performed for
magnetic measurements? (2)
24. Mention the advantages and disadvantages of flux meter. (2)
25. What are the methods used to determine B-H Curve? (2)
26. What are the errors in instrument transformers? (2)
27. What is frequency meter and classify it? (2)
28. What is phase meter and what
are its type? (2)
29. Differentiate ammeter an voltmeter. (2)
30. Define leakage factor. (2)
1. (i) Describe the construction and working of a permanent magnetic moving
coil instruments. (10)
(ii) Explain the design of three phase wattmeters and give the reactive power
measurement in 3 phase circuits. (6)
2. (i) How B-H curve is determined for a ring specimen. (8)
(ii) Explain the frequency measurement in Wien’s bridge (8)
3. Discuss why it is 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)
4. Explain the function of three phase wattmeter and energy meter. (16)
5. (i) Discuss in detail the working of the successive approximation DVM.(8)
(ii) With a neat diagram, explain the various methods of magnetic measurements. (8)
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.
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 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
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 voltagewww.annauniversityplus.com
controlled oscillator) between two operator-determined 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
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
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
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
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 towww.annauniversityplus.com
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
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.
Construction :
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
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.
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)
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.
Is a filter of resolution. The spectrum analyzer captures the measure on having displaced a
filter of small bandwidth along the window of frequencies.
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.
Superheterodyne spectrum analyzer:
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
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,
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
intermodulation distortion 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.
Important Questions : Unit - III
1. Draw Maxwell’s AC bridge and give the balance equation interms of resistance. (2)
2. Explain any two technical parameters to be consider in grounding. (2)
3. Give some applications of Wheatstone’s bridge. (2)
4. What is a potentiometer? (2)
5. List the applications of dc and ac potentiometer. (2)
6. Differentiate the principle of dc potentiometer and ac potentiometer. (2)
7. What is meant by transformer ratio bridge (2)
8. What are the features of ratio transformer? List its applications. (2)
9. What is meant by electromagnetic interference? (2)
10. List the sources of electromagnetic interference. (2)
11. What are the ways of minimizing the electromagnetic interference? (2)
12. Define electromagnetic compatibility.(EMC) (2)
13. What are the main causes of group loop currents? (2)
14. What are the limitations of single point grounding method? (2)
15. What is the necessity of grounding and state is advantages. (2)
16. What is meant by ground loop? How it is created? (2)
17. What are the sources of errors in bridge measurement? (2)
18. Define standardization. (2)
19. Give the relationship between the bridge balance equation of DC bridge and AC
bridge (2)
20. What does a bridge circuit consists of ? (2)
1. (i) Explain in detail about the laboratory type DC potentiometer. (10)
(ii) Give the applications of AC potentiometers. (6)
2. (i) Describe about the multiple earth and earth loops. (10)
(ii) Explain the different techniques of grounding. (6)
3. Explain voltage sensitive self balancing bridge, and derive the bridge
sensitivity of voltage sensitive bridge with fundamentals. (16)
4. (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)
5. (i) Explain Kelvin’s double bridge method for the measurement of low resistance. (8)
(ii) Explain how inductance in measured by using Maxwell’s bridge. (8)
6. (i) Explain the working principle of Anderson’s bridge and also derive its
balance equations. (8)
(ii) Explain the working principle of Schering bridge and also derive its balance
equations. (8)
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.
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
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,
M is the ADC's resolution in bits.
That is, one voltage interval is assigned per code level. However, figure 3 shows a situation
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 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"
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)
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 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.
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.
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 non-linearity (INL) and differential nonlinearity (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.
, where q
input frequency
1 Hz 44.1 kHz 192 kHz 1 MHz 10 MHz 100 MHz 1 GHz
in bit
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 405 ps 77.7 ps 7.77 ps
0.78 ps 0.08 ps
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.[4]
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.[5]
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 bandlimited 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 the Shannon-Nyquist sampling 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.
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
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 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.
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 realised and then the signal can be
downsampled 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.
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.[6][7]
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 a 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
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.[8][9]
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
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.
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.
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
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
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.
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.
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 24-bit/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
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 number
(0 to 65535). We only need to add two resistors for each additional binary
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 half-current 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).
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.
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. any time
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.
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.
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.
Table 5-1.—Front Panel Controls and Neets Module 16-Introduction to
Test Equipment
Digital voltmeter
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 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.
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 highspeed 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 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 proportional to the quantity measured.
(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.
Additionally, some multimeters
Capacitance in farads.
Conductance in siemens.
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
Wind speed
Relative humidity
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
By convention, a half digit can display either a zero or a one, while a three-quarters
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 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 digit
multimeter 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.
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.[5]
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
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
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 high-resistance 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 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[citation needed].
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 anwww.annauniversityplus.com
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
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.
Important Questions : Unit - IV
1. What is meant by deflection sensitivity of a CRT? (2)
2. Write two advantages of LED in electronic displays. (2)
3. State the features of ink-jet printers. (2)
4. Differentiate between LED and LCD. (2)
5. What are the different types of magnetic recording? (2)
6. What are the different materials used in LED? Also name the colours
emitted. (2)
7. Give a short note on LED. (2)
8. What is delayed sweep? (2)
9. Explain the characteristics of Time domain output device using in measurements. (2)
10. Explain the following term as applied to digital displays. (2)
3 ½ digit and 4 ½ digit displays.
11. What is a recorder and what are the types of it? (2)
12. What is magnetic tape recorder? (2)
13. What are the basic components of a tape recorder? (2)
14. List the advantages and disadvantages of direct recording? (2)
15. What are display devices? (2)
16. What are the advantages and disadvantages of digital data recording? (2)
17. Compare line printer and dot matrix printer. (2)
18. What is CRO? What are the sections of a CRO? (2)
19. List the advantages of digital storage oscilloscope. (2)
20. Differentiate between dual trace and dual beam CRO. (2)
21. List out the advantages of X-Y records over strip chart recorder. (2)
22. List the advantages of laser printer. (2)
23. List the two advantages of digital X-Y recorder. (2)
24. What is power requirement of LCD? (2)
25. What are Lissajous patterns? (2)
1. 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)
2. (i) Explain the basic elements of a magnetic tape recorder. (8)
(ii) Explain the block diagram of oscilloscope with a neat sketch (8)
3. (i) Describe the basic components of a CRT. (10)
(ii) Write short notes on liquid crystal displays. (6)
4. (i) With a neat block diagram, explain the working of digital storage oscilloscope. (8)
(ii) Discuss briefly about the applications of LED. (8)
5. (i) What are the various types of oscilloscopes? (4)
(ii) Discuss in detail the construction of a storage type oscilloscope. What are the
accessories for a CRO? (12)
6. (i) Explain in detail, how the data is stored in a magnetic disk and tape? (10)
(ii) Describe the performance of digital plotter. (6)
7. (i) Explain the block diagram of a general purpose oscilloscope and also
describe about the observation of waveform on CRO. (10)
(ii) Write short notes on Printers. (6)
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.
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
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
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).
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
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, AppleBus, 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.
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.
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 higher-level 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 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 multi-antenna 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
diversity (improved robustness to fading) or beamforming (improved selectivity) rather than
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.[2]
A variant technology, called wavelength-division multiplexing (WDM) is used in optical
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.
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.
Application areas
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
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.
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
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
Signal multiplexing of satellite TV and radio channels is typically carried out in a central signal
playout and uplink centre, 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 onchannel 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.
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.
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 as
the 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
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 8bit 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 programming
interface and terminology, however.
Advantages and disadvantages
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
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.
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.
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
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%).
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.
Important Questions : Unit – V
1. Give the factors to be considered for selecting a transducer. (2)
2. Why is an A/D converter usually considered as an encoder? (2)
3. Define inverse transducer with example. (2)
4. Explain the principle of piezoelectric transducers and name any two
piezoelectric materials. (2)
5. Name the transducers used for sensing acceleration. (2)
6. Mention the use of capacitive transducers. (2)
7. Classify the transducers and what is the other name of it. (2)
8. What are active and passive transducers? Give examples. (2)
9. What are the characteristics of transducers? (2)
10. What is meant by data acquisition system? List its types. (2)
11. Give the operating principle of a resistive transducer. Also give some examples (2)
12. What is piezoelectric effect? (2)
13. What is LVDT? (2)
14. List the advantages and disadvantages of LVDT. (2)
15. What is thermocouple? (2)
16. What are the advantages and disadvantages of LVDT? (2)
17. What is seeback voltage? (2)
18. What is strain gauge? List its types. (2)
19. What is gauge factor? Give its expression. (2)
20. What is resistance thermometer? (2)
21. What are the salient features of thermistor? (2)
22. What are capacitive transducers? Give the expression for a capacitance of
a capacity transducer. (2)
23. What are optical detectors? List its types. (2)
24. What are photoelectric transducers? (2)
25. List the types of A/D and D/A converters. (2)
26. Draw the transfer characteristics of ADC and DAC. (2)
27. What are the advantages and disadvantages of dual slope ADC? (2)
28. Give a short note on data acquisition system. (2)
29. What is the composition of materials used in thermistor? (2)
30. State the laws of thermoelectric. (2)
1. (i) Explain the principle of inductive and capacitive transducer. (8)
(ii) Explain the construction and working of LVDT with a neat sketch (8)
2. (i) Explain different strain gauges with their principle of operation. (8)
(ii) Discuss in detail about resistive transducers. (8)
3. (i) Explain the various types of temperature transducers. (8)
(ii) Explain the function of piezoelectric transducer. (8)
4. (i) Explain the binary weighted resistor technique of D/A conversion.(8)
(ii) Define the following terms for D/A converters:
a) Resolution b) Accuracy c)Monotonicity and d) conversion time(8)
5. (i) Explain the resistive transducer with respective to potentiometer. (4)
(ii) Explain the capacitive transducer. (6)
(iii) Describe the piezoelectric transducer and give the formula for coupling
coefficient. (6)
6. (i) Explain schematic block diagram of a general data acquisition system
(DAS) and give its objectives (8)
(ii) Discuss R-2R ladder type D/A converter. (8)
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