APPLIED PHYSICS PROJECT WORK
“DETERMINATION OF PARAMETERS OF
SINUSOIDAL WAVE USING CRO”
DONE BY,
G.V.S ABHISHEK VARMA,
20331A0564,
CSE-A.
PROBLEM STATEMENT: Using a dual channel CRO and function
generator, determine the parameters of the sinusoidal wave i.e. Frequency, RMS
Voltage, form factor and crest factor.
ABSTRACT:
The alternating current (AC) power standard is
usually based on the DC power standard by means of an AC/DC thermoelectric
comparator, or by means of an A/D converter and digital waveform calculation.
In this article, the AC power standard can be based on three parameters - rms
AC voltage, rms AC current, and phase between voltage and current. The error
analysis proves that the AC power standard can be traced to the AC voltage
standard, AC current standard, and phase angle standard. Sine wave distortion
was considered as affecting the measurement error in the error analysis.
AC
Waveform Characteristics
·
The Period, (T) is the length of time in seconds that the waveform takes to repeat
itself from start to finish. This can also be called the Periodic Time of the waveform
for sine waves, or the Pulse
Width for square waves.
·
The Frequency, (ƒ) is the number of times the waveform repeats itself within a one
second time period. Frequency is the reciprocal of the time period, ( ƒ = 1/T ) with the unit of frequency being the Hertz, (Hz).
·
The Amplitude (A) is the magnitude or intensity of the signal waveform measured in
volts or amps.
INTRODUCTION:
● The
parameters of sinusoidal wave include the frequency, RMS Voltage, form factor
and the crest factor.
● Frequency: Frequency is the number of occurrences of a repeating event per unit of time.
It is also referred to as temporal frequency, which emphasizes the contrast to
spatial frequency and angular frequency. The period is the duration of time of
one cycle in a repeating event, so the period is the reciprocal of the
frequency.
●
RMS Voltage: The root
mean square velocity is the square root of the average of the square of
the velocity. As such, it has units of velocity. The reason we use
the rms velocity instead of the average is that for a typical gas
sample the net velocity is zero since the particles are moving in all
directions.
●
Form factor: In electronics or electrical the form factor
of an alternating current waveform is the ratio of the RMS value to the average
value. It identifies the ratio of the direct current of equal power relative to
the given alternating current.
● Crest factor: Crest factor is a parameter of a waveform, such as alternating current or
sound, showing the ratio of peak values to the effective value. In other words,
crest factor indicates how extreme the peaks are in a waveform. Crest factor 1
indicates no peaks, such as direct current or a square wave.
· Dual trace CRO: Dual trace
CRO is used to generate only one electron beam but display
two traces. Thus, the same. electron beam is used for generating
both the traces to display two different input signals.
simultaneously. There are two separate vertical input channels, channel A and
B.
·
Function generator: A function generator will
normally be able to act as a sine wave generator. This is the
standard waveform that oscillates between two levels with a
standard sinusoidal shape. Using the function
generator as a sine wave generator is one of the more
commonly used applications.
AC Wave forms:
When an alternator produces AC voltage,
the voltage switches polarity over time, but does so in a very particular
manner. When graphed over time, the “wave” traced by this voltage of alternating
polarity from an alternator takes on a distinct shape.
Graph
of AC voltage over time (the sine wave).
In the voltage plot from an
electromechanical alternator, the change from one polarity to the other is a
smooth one, the voltage level changing most rapidly at the zero (“crossover”)
point and most slowly at its peak. If we were to graph the trigonometric
function of “sine” over a horizontal range of 0 to 360 degrees, we would find
the exact same pattern as in the Table below. Trigonometric “sine”
function.
|
Angle (°) |
Sin (angle) |
Wave |
Angle (°) |
Sin (angle) |
Wave |
|
0 |
0.0000 |
zero |
180 |
0.0000 |
zero |
|
15 |
0.2588 |
+ |
195 |
-0.2588 |
- |
|
30 |
0.5000 |
+ |
210 |
-0.5000 |
- |
|
45 |
0.7071 |
+ |
225 |
-0.7071 |
- |
|
60 |
0.8660 |
+ |
240 |
-0.8660 |
- |
|
75 |
0.9659 |
+ |
255 |
-0.9659 |
- |
|
90 |
1.0000 |
+peak |
270 |
-1.0000 |
-peak |
|
105 |
0.9659 |
+ |
285 |
-0.9659 |
- |
|
120 |
0.8660 |
+ |
300 |
-0.8660 |
- |
|
135 |
0.7071 |
+ |
315 |
-0.7071 |
- |
|
150 |
0.5000 |
+ |
330 |
-0.5000 |
- |
|
165 |
0.2588 |
+ |
345 |
-0.2588 |
- |
|
180 |
0.0000 |
zero |
360 |
0.0000 |
zero |
The reason why an electromechanical
alternator outputs sine-wave AC is due to the physics of its operation. The
voltage produced by the stationary coils by the motion of the rotating magnet
is proportional to the rate at which the magnetic flux is changing
perpendicular to the coils (Faraday’s Law of Electromagnetic Induction).
That rate is greatest when the
magnet poles are closest to the coils, and least when the magnet poles are
farthest away from the coils.
Mathematically, the rate of
magnetic flux change due to a rotating magnet follows that of a sine function,
so the voltage produced by the coils follows that same function.
Period vs Frequency
If we were to follow the
changing voltage produced by a coil in an alternator from any point on the sine
wave graph to that point when the wave shape begins to repeat itself, we would
have marked exactly one cycle of that wave.
This is most easily shown by
spanning the distance between identical peaks, but may be measured between any
corresponding points on the graph.
The degree marks on the
horizontal axis of the graph represent the domain of the trigonometric sine
function, and also the angular position of our simple two-pole alternator shaft as it rotates: Figure below
Alternator
voltage as function of shaft position (time). Since
the horizontal axis of this graph can mark the passage of time as well as shaft
position in degrees, the dimension marked for one cycle is often measured in a
unit of time, most often seconds or fractions of a second. When expressed as a
measurement, this is often called the period of a wave.
The period of a wave in degrees
is always 360, but the amount of time one period occupies depends on
the rate voltage oscillates back and forth.
A more popular measure for describing the
alternating rate of an AC voltage or current wave than period is the rate of that
back-and-forth oscillation. This is called frequency. The modern unit for frequency is the Hertz (abbreviated
Hz), which represents the number of wave cycles completed during one second of
time.
●
In
the United States of America, the standard power-line frequency is 60 Hz,
meaning that the AC voltage oscillates at a rate of 60 complete back-and-forth
cycles every second.
●
In
Europe, where the power system frequency is 50 Hz, the AC voltage only
completes 50 cycles every second. A radio station transmitter broadcasting at a
frequency of 100 MHz generates an AC voltage oscillating at a rate of
100 million cycles every second.
Prior to the canonization of the
Hertz unit, frequency was simply expressed as “cycles per second.” Older meters
and electronic equipment often bore frequency units of “CPS” (Cycles Per
Second) instead of Hz. Many people believe the change from self-explanatory
units like CPS to Hertz constitutes a step backward in clarity. A similar
change occurred when the unit of “Celsius” replaced that of “Centigrade” for
metric temperature measurement. The name Centigrade was based on a 100-count
(“Centi-”) scale (“-grade”) representing the melting and boiling points of H2O,
respectively. The name Celsius, on the other hand, gives no hint as to the
unit’s origin or meaning.
Period and frequency are
mathematical reciprocals of one another. That is to say, if a wave has a period
of 10 seconds, its frequency will be 0.1 Hz, or 1/10 of a cycle per second:
Usage of an Oscilloscope:
An
instrument called an oscilloscope, Figure below
is
used to display a changing voltage over time on a graphical screen.
You may be familiar with the appearance of
an ECG or EKG (electrocardiograph) machine, used by
physicians to graph the oscillations of a patient’s heart over time. The ECG is
a special-purpose oscilloscope expressly designed for medical use.
General-purpose
oscilloscopes have the ability to display voltage from virtually any voltage
source, plotted as a graph with time as the independent variable. The
relationship between period and frequency is very useful to know when
displaying an AC voltage or current waveform on an oscilloscope screen. By measuring the period of the
wave on the horizontal axis of the oscilloscope screen
and reciprocating that time value (in seconds), you can determine the frequency in Hertz.
CATHODE RAY OSCILLOSCOPE:
The CRO stands for a cathode ray
oscilloscope. It is typically divided into four sections which
are display, vertical controllers, horizontal controllers, and Triggers. Most
of the oscilloscopes are used the probes and they are used for the input of any
instrument. We can analyze the waveform by plotting amplitude along with the
x-axis and y-axis. The applications of CRO’s mainly involve in the radio, TV
receivers, also in laboratory work involving research and design. In modern
electronics, the CRO plays an important
role in the electronic circuits.
What is a CRO?
The cathode ray oscilloscope is an
electronic test instrument, it is used to obtain waveforms when
the different input signals are given. In the early days, it is called as an
Oscillograph. The oscilloscope observes the changes in the electrical signals
over time, thus the voltage and time describe a shape and it is continuously
graphed beside a scale. By seeing the waveform, we can analyze some properties
like amplitude, frequency, rise time, distortion, time interval and etc.
This is a cathode ray oscilloscope.
Block Diagram of CRO
The following block diagram shows the
general purpose CRO contraction. The CRO recruit the cathode ray tube
and acts as a heat of the oscilloscope. In an oscilloscope, the CRT produces
the electron beam visible spot where the electron beam strikes with it. By
detecting the beam above the screen in reply to the which is accelerated to a
high velocity and brings to the focal point on a fluorescent screen. Thus, the
screen produces a electrical signal, the electrons can act as an electrical
pencil of light which produces a light where it strikes.
To complete this task, we need various electrical signals and voltages.
This
provides the power supply circuit of the oscilloscope. Here we will use
high voltage and low voltage.
●
The low voltage
is used for the heater of the electron gun to generate the electron beam.
●
The high voltage
is required for the cathode ray tube to speed up the beam.
● The normal voltage supply is necessary for
other control units of the oscilloscope.
Working of CRO
The following circuit diagram shows the basic
circuit of a cathode ray oscilloscope. In this, we will discuss
important parts of the oscilloscope.
Vertical
Deflection System:
The main
function of this amplifier is to amplify the weak signal so that the amplified
signal can produce the desired signal. To examine the input signals are
penetrated to the vertical deflection plates through the input attenuator and
number of amplifier stages.
Horizontal
Deflection System:
The vertical and horizontal
system consists of horizontal amplifiers to amplify the weak input signals, but
it is different to the vertical deflection system. The horizontal deflection
plates are penetrated by a sweep voltage that gives a time base. By seeing the
circuit diagram, the sawtooth sweep generator is triggered by the synchronizing
amplifier while the sweep selector switches in the internal position. So, the
trigger saw tooth generator gives the input to the horizontal amplifier by
following the mechanism. Here we will discuss the four types of sweeps.
RECURRENT SWEEP:
As the name,
itself says that the saw tooth is respective that is a new sweep is started
immodestly at the end of the previous sweep.
Triggered Sweep:
Sometimes the waveform should be
observed that it may not be predicted, thus the desired that the sweep circuit
remains inoperative and the sweep should be initiated by the waveform under the
examination. In these cases, we will use the triggered sweep.
Driven Sweep:
In general, the
drive sweep is used when the sweep is a free running but it is a triggered by
the signal under the test.
Non-Saw Tooth Sweep:
This sweep is used to find the
difference between the two voltages. By using the non-sawtooth sweep, we can
compare the frequency of the input voltages.
Synchronization:
The synchronization is done to
produce the stationary pattern. The synchronization is between the sweep and
the signal should measure. There are some sources of synchronization which can
be selected by the synchronization selector. Which are discussed below.
Internal:
In this the signal is measured
by the vertical amplifier and the trigger is abstained by the signal.
External:
In the external trigger, the
external trigger should be present.
Line
The line trigger is produced by
the power supply.
Intensity Modulation:
This
modulation is produced by inserting the signal between the ground and cathode.
This modulation
causes by brightening the display.
Positioning Control
By applying the small
independent internal direct voltage source to the detecting plates through the
potentiometer the position can be controlled and also, we can control the
position of the signal.
Intensity Control:
The intensity has a difference
by changing the grid potential with respect to the cathode.
RMS Value of an AC Waveform:
For a
pure sinusoidal waveform this effective or R.M.S. value will always be equal
too: 1/√2*Vmax which
is equal to 0.707*Vmax and this relationship holds true for RMS values of current. The RMS value
for a sinusoidal waveform is always greater than the average value except for a
rectangular waveform. In this case the heating effect remains constant so the
average and the RMS values will be the same.
One
final comment about R.M.S. values. Most multimeters, either digital or analogue
unless otherwise stated only measure the R.M.S. values of voltage and current
and not the average. Therefore, when using a multimeter on a direct current
system the reading will be equal to I = V/R and for an alternating current system the reading will be equal to Irms = Vrms/R.
Also,
except for average power calculations, when calculating RMS or peak voltages,
only use VRMS to find IRMS values, or peak
voltage, Vp to find peak current, Ip values. Do not mix them together as
Average, RMS or Peak values of a sine wave are completely different and your
results will definitely be incorrect.
Form Factor and Crest Factor:
Although
little used these days, both Form Factor and Crest
Factor can be used to give information about the actual shape of the AC
waveform. Form Factor is the ratio between the average value and the RMS value
and is given as.
For a pure
sinusoidal waveform, the Form Factor will always be equal to 1.11. Crest Factor is
the ratio between the R.M.S. value and the Peak value of the waveform and is given
as.
For a pure sinusoidal waveform, the Crest Factor
will always be equal to 1.414.
EXPERIMENT:
AIM: To
determine the parameters of AC sine wave using a cathode ray oscilloscope….
APPARATUS AND SPCIFICATIONS:
Cathode ray oscilloscope (20 MHz_dual channel_Two trace_Input 220-230V AC/50
Hz), Function generator(Frequency range
20 Hz to 20 Mz_amplitude 0 to 5V AC_Wave forms sine/triangular/square)
FORMULA:
Vpeak = Vpeak_to_ peak * 0.5
Vrms =
Vpeak * 0.07071
Vavg = 0.637
* Vpeak
Form factor
= RMS VALUE / AVERAGE VALUE
Crest factor
= Peak value / RMS VALUE
Frequency =
1/T Hz
PROCEDURE:
1. First switch on the CRO and
setup the system with function generators.
2. Now set the wave form to
sine wave and then keep a constant amplitude and find the number of divisions,
values of peak value and peak to peak value and RMS value of the sine wave.
3. Now keep a certain frequency
and maintain constant time period switch the wave forms to sine wave and find
out the number of divisions, time sensitivity and time period, frequency etc.
Parameters for AC sine wave and finally determine the parameters.
4. Do the same procedure for
different frequencies and find out the corresponding values.
5. Note down the observations
in a tabular form and do the calculations using the respective formulae.
PRECAUTIONS:
1. The beam spot on the CRO screen
should be highly intense and it is required to be focused exactly on the center
of the screen.
2. Keep the intensity at a low
value because high intensity may damage the CRO.
3. Handle the switches gently as
they very sensitive and they may result in wrong values.
RESULT:
From the experiment we have
concluded the different parameters of AC sine wave.
RESULT ANALYSIS:
1. For different values of
frequencies at same time the corresponding frequencies for different wave forms
do not change.
2. For a constant amplitude the
voltages of different wave forms changes because the voltage in AC circuit
changes drastically.
Applications of CRO
·
Voltage
measurement
·
Current
measurement
·
Examination
of waveform
·
Measurement
of phase and frequency
Uses of CRO
In laboratory,
the CRO can be used as
·
It
can display different types of waveforms
·
It
can measure short time interval
·
In
voltmeter, it can measure potential difference
REFERENCES :
·
https://www.allaboutcircuits.com/textbook/alternating-current/chpt-1/ac-waveforms/
·
https://www.elprocus.com/cro-cathode-ray-oscilloscope-working-and-application/
·
http://courses.washington.edu/phys431/scope_ex/scope_ex.pdf
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