# oscilloscope and a function generator and verification of the calibration by badboy920046

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Determination of the line frequency by Lissajous figures using an oscilloscope and a function
generator and verification of the calibration of time/div knob and volts/div knob at a particular
position for different frequencies and voltages.

Theory:

Frequency can be easily measured with an oscilloscope. The unknown frequency (line frequency) is
applied to the vertical input while the reference frequency (signal generator) is applied to the
horizontal input. When two harmonic vibrations, mutually perpendicular to each other, are
superposed on one another, the resultant curve or pattern may take any number of shapes depending
upon the phase difference of the vibrations. These curves are called Lissajous figures. Some typical
patterns are shown in Figure-14.

(a)                             (b)                             (c)
Figure -14: Lissajous figure

The frequency ratio of the two superposed vibrations can be calculated from the relation
LH
fX       f
LV
fX = unknown frequency          f = known frequency
LH = number of loops which touch the horizontal tangent line
LV = number of loops which touch the horizontal tangent line

Signal of different frequencies can be obtained from a signal generator and can be supplied to the
horizontal input of the oscilloscope. The superposition of these signals with the unknown signal (line
signal), which is applied to the vertical input of the oscilloscope, will give rise to curves of given
shapes. From these curves, the frequency of the line signal can be calculated in the manner described
above.

Apparatus:
Oscilloscope, function generator, transformer, battery, multimeter, etc.

Procedure:
1. Switch on the oscilloscope and obtain a bright spot at the centre of the oscilloscope screen by
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adjusting the focus control and the horizontal and vertical switches respectively.

2. Fix the horizontal frequency selector at the line sweep. Fix the vertical input at some suitable
position of the selector control.

3. Switch on the signal generator and apply a signal to the oscilloscope and go on adjusting the
horizontal and vertical gain switches and the frequency of the signal from the generator until a
single loop is obtained on the screen as shown in Figure- 14 (a). Record the corresponding
frequency of the signal.

4. It is a good practice to have the loop rotating slowly rather than being stationary. This
eliminates the possibilities of an error in counting tangent points. If the pattern is stationary a
double image may be formed. In such cases the end of the trace should be counted as one half
a tangent point, rather than a full point. This condition may occur when neither frequency can
be varied.

5. Keeping everything else fixed, go on changing the frequency of the signal generator until two
loops are obtained, first touching the horizontal line and then the vel1ical line.

6. Record the corresponding frequencies. In this way record the frequencies of the signals which
produce a number of loops touching either the horizontal or vertical lines.

7. For each frequency as recorded from the dial of the generator, calculate the line frequency.

Description of the apparatus:

The cathode ray oscilloscope (CRO):
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This is a very important and versatile electrical instrument which uses an electron beam to display
waveforms on a fluorescent screen. The name cathode ray oscilloscope derives from the fact that
electron beams were originally called cathode rays.

The CRO's ability to produce a steady picture of a rapidly varying potential difference( p.d.) is
particularly useful because it allows accurate measurements to be made of transient phenomena. At the
heart of the oscilloscope is the cathode ray tube shown schematically in Figure-1.

Figure -1: The cathode ray tube

The electron gun:

The electron gun shown in Figure - 2 consists of a heated cathode (C), a grid (G), a focusing anode
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(A1) and an accelerating anode (A1). When the cathode is heated by the current from a low voltage
supply, free electrons are thermo-ionic ally emitted from its surface. These electrons are strongly
attracted by the two anodes which are at a positive potential with respect to the cathode.

Figure – 2: Typical electron gun System.

Beam brightness:

The electrons first encounter the grid, which is negative with respect to the cathode and controls the
number of electrons reaching the anodes and screen. Making the grid more negative repels some
electrons, and reduces the number of electrons getting through. Making it less negative increases the
number.

Thus by varying the grid potential we can control the number of electrons which strike the screen and
hence the brightness of the spot on the screen.

Beam focus:

Apart from accelerating the electron beam towards the screen, the anodes also have a focusing effect
on the beam. The sharpness of the spot produced on the screen is controlled by adjusting the potential
of anode (A1) with respect to the cathode. This alters the angle of the cone of electrons issuing from
the grid, so that the apex of the cone falls on the screen to give the finest possible spot.
Anode (A2) is at zero potential, and its main function is to accelerate the electrons.

The deflection system:

The beam deflection system consists of two pairs of parallel plates at right angles to each other, as
shown in Figure - 3 .When a p.d.. is applied across a pair of plates, the electric field created exerts a
force on the electrons. The electric field between the Y-plates causes vertical deflection of the beam
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and that between the X-plates produces horizontal deflection.

Figure -3: X and Y deflection system

X and Y shift:

If the oscilloscope is switched on (with the time-base off, a stationary spot should be visible on the
screen where the electron beam strikes it. By varying the steady p.d. between the X- or Y-plates, the
horizontal and vertical position of the spot on the screen can be controlled. On the oscilloscope these
are called the X- and Y-shift controls.

X. and Y-inputs:

When the oscilloscope is being used for observing and measuring, the voltages being studied are
applied to either or both of the X- and Y-inputs. This causes changes in the position of the spot on the
screen, and enables measurements to be made.

It is also possible to use Helmholtz coils to provide a deflection system. In this case the electron beam
would be deflected by the magnetic field between the coils which would also be positioned at right
angles to each other

The display system:

Figure - 4 shows a typical cathode ray tube. The zinc sulphide gives a glow of light when electrons
collide with it. The atoms of the coating become excited by absorbing the energy of the incoming
electrons, and this energy is re-released as a burst of light.
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Thus the motion of the spot, produced by the electron beam on the screen, is seen as a C glowing
trace. The addition of other chemicals can produce different colors.

Figure - 4: CRO display system
There is a graphite coating inside the tube which ends close to the screen. This is at earth potential (0
V) and provides a return path for electrons which strike the screen as well as for secondary electrons
produced from the impact of electrons with the zinc sulphide. Otherwise there would be a large build-
up of static charge on the tube.

The graphite also shields the electron beam from external electric fields which would give unwanted
deflections.

A mumetal screen surrounds the tube and shields it from external magnetic fields.

Using the CRO – the time base:
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Figure 5: Basic controls on a laboratory CRO

Figure - 5 shows the essential features and controls found on a basic oscilloscope. Input p.d.s to be
studied are applied to the Y-input terminals (one of which is earthed) and go through an amplifier
before reaching the Y-plates. The amplification is altered by the Y-GAIN control. This enables a very
wide range of potential differences to be measured.
When the oscilloscope is switched on with the time base off and no p.d. applied to the input, the spot
appears in the centre of the screen.
If a steady direct potential difference is applied to the Y-input (e.g. from a cell) the spot will move up
or down to a new stationary position from its central position by an amount depending on the size of
the p.d. and on the Y-GAIN setting (see Figure- 6). If the non-earthed terminal is made positive, the
spot moves upwards.
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Figure -6: Spot deflection produced by steady D.C. potential difference (time-base off)

If an alternating p.d. is applied to the input terminals the spot moves vertically up and down at the
frequency of the applied p.d. as shown in Figure -7. This produces a vertical straight line trace on the
screen whose length represents the peak-to-peak value of the p.d. applied.

Figure-7: Trace produced by an alternating           Figure-8: Time-base potential difference(saw-
p.d. (time-base off)                    tooth     waveform)
In order to see how the alternating p.d. varies with time, the X-plates are connected to an internal
circuit called the time-base which applies a saw-tooth p.d. as shown in Figure- 8.

This moves the spot horizontally across the screen at a constant rate which is controlled by the time-
base setting. The cycle of the time-base p.d. starts off with a negative value, which pulls the spot to the
extreme left of the screen. The p.d. becomes positive at a constant rate, which sweeps the spot at a
constant speed across the screen. At the end of the cycle, the saw-tooth p.d. changes back to its initial
negative value in a very short time (called the fly back time) and this returns the spot to its starting
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position, and the cycle repeats.

Time-base settings can range from several
seconds per cm, where the spot moves very
slowly across the screen, to microseconds per
cm. In practice, with time-base settings of
shorter than around 10 ms per cm, the trace
looks like a continuous line rather than a
moving spot.

The combined effects of the alternating p.d.
applied to the Y-p1ates and the time-base p.d.
applied to the X-plates produces the
alternating trace shown in Figure- 9.

Figure -9: Trace obtained with alternating

Measuring potential difference:

Both a.c. and d.c. voltages can be measured by connecting to the Y- input terminals of the CRO.

D.c. potential difference:

With the time-base switched off the spot is displaced vertically by an amount which depends on the
size of the p.d. and the Y-GAIN setting (Figure – 10).
With no p.d. applied to the Y-input, use the Y-shift control to position the spot on one of the grid
lines. Apply the p.d. to be measured, the spot will be deflected vertically. Use the Y-GAIN control to
produce the maximum possible deflection (improves accuracy by reducing the percentage error in
Measure the deflection of the spot (in cm) and multiply by the Y-GAIN setting (in V cm-1). This gives
the p.d. in volts.
Spot

Figure -10: Measuring d.c. potential difference
A.C. potential difference:

With the time-base switched off, the length of the vertical trace obtained represents the peak to peak
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value of the applied potential difference (V) as shown in the figure-11.

To determine the peak to peak potential difference, measure the length of the trace (in cm) and
multiply by the Y-GAIN setting (in V cm-1).

To determine the amplitude of an alternating p.d., it is usual to have the time-base switched on, when
a sinusoidally varying trace is obtained, as shown in Figure -12.

Figure-11: Measuring an alternating potential             Figure- 12: Measurement of amplitude of
difference                                                            alternating current

Use the Y-shift control to centre the trace on the screen. Measure the height of the peaks above the
centre line (in cm). Multiplying by the Y-GAIN setting (in V cm-1) gives the amplitude (or peak value)
of the alternating potential difference.

The CRO is a very useful form of voltmeter because:

Both d.c. and a.c. voltages can be measured the electron beam is a virtually weightless pointer with an
almost instantaneous response.
It has a very high resistance to d.c. and a very high impedance to a.c. - hence it draws very little
current from the circuit it is connected to.

Measuring time intervals:

Since the time-base is marked in (time cm-1), it is possible to determine the time interval between two
events, as long as the two events produce visible changes in the trace seen on the CRO screen. Two
extra controls not shown in Figure- 5 must be used now:
The fine (or variable) time-base control must be set to CAL. This ensures that the trace takes an exact
number of milliseconds to cross each cm on the screen.
The X-GAIN must be set to minimum, again to ensure that the time-base setting accurately represents
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the movement of the spot on the screen.

Example: A microphone beside a starting pistol detects the initial sound of the gun and, a short time
later, the echo of the sound from a cliff some distance away. These events are seen on the CRO screen

Figure-12: Trace obtained on the CRO.                 Figure-13: Heart trace on CRO screen
as voltage peaks which are separated by a horizontal distance of 6.0 cm: as shown in Figure -12.

If the time-base setting is 100 ms cm-1, then the time interval between making the sound and
receiving the echo is:
6 x 100 = 600 ms = 0.6 s

Measuring frequency:

Since frequency = l /(time period), measuring frequency using a CRO involves using the above
method to measure the time interval between successive cycles of the alternating waveform, and using
this to calculate the frequency. In hospitals, CROs are used to monitor heart beat. The muscles of the
heart are triggered to contract by electrical signals carried through the nerve fibers. These electrical
signals can be received through electrodes stuck to the skin of the chest, enabling medical staff to
study the rhythm and behavior of the heart's contractions.

Suppose the heart trace shown in Figure -13 is obtained with the time-base setting at 0.5 s cm-1

Clearly each beat of the heart is slightly irregular, but an average heart rate can be calculated by
measuring the time taken for several beats, and calculating an average period.

Time for three beats = 6.6×0.5 =3.3 sec

Period, T = 3.3 / 3 =1.1 sec

 Frequency, f = 1 / T = 1/ 1.1 = 0.909 beats per seconds (Hz)
 Heart rate = 0.909 × 60 = 55 beats per minute.
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DATA SHEET:        Determining DC and AC voltage and Line Frequency by using an Oscilloscope.

Table -1: Determining DC voltage:
Number of        Volts per Division         Number of Divisions     Voltage of the Battery
Observations               A                          B                       A×B
Volts                                                Volts
1
2
3

Table -2: Determining AC voltage:

Number of         Volts per Division      Number of Divisions from    Voltage of the signal
Observations               A                   top to bottom                  A×B
Volts                        B                       Volts
1
2
3

Table -3: Determining line Frequency:
Number of        Sweep time          Number of        Time period      Frequency of the
Observations      per Division      Divisions for one       T                 signal
A             wave length          A×B                     1
ms                  B                ms                f 
T
Hz
1
2
3

Table -4: Determining line Frequency by Lissajous figure:
Number       Known frequency from        Number of      Number of         Line frequency
of          function generator         vertical      horizontal                LH
Obs.                  f                  loops          loops            fX       f
LV
Hz                    LV             LH
Hz
1
2
3
4
5
6
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Results:

(i)        DC voltage =

(ii)       AC voltage =

(iii)      Line frequency =

Discussions:

(i)        As mentioned in the procedure, it is better to have the Lissajous pattern slowly rotating.

(ii)       It is difficult to record the number of both the horizontal and vertical loops at the same
time. It is better to fix the number of either vertical or horizontal loops constant and then
vary the number or the other and note the corresponding frequency of the signal from the
signal generator.
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PHY-109 LAB
Sample oral Questions and Answers
Experiment No: 04
Name of the experiment:
Determination of the Power frequency (Line frequency) by Lissajous figures using an
oscilloscope and a function generator and verification of the calibration of time/div knob at a
particular position for different frequencies.

1. What are oscilloscope and function generator( signal generator)?
Ans: An oscilloscope (abbreviated sometimes as scope or O-scope) is a type of electronic test
instrument that allows signal voltages to be viewed, usually as a two-dimensional graph of one or
more electrical potential differences (vertical axis) plotted as a function of time or of some other
voltage (horizontal axis).
A function generator is a piece of electronic test equipment or software used to generate
electrical waveforms
2. What are frequency, time period, wavelength, speed of wave?
Ans: Frequency is defined as a number of cycles per unit time. In SI units, the unit of
frequency is hertz (Hz), named after the German physicist Heinrich Hertz. For example, 1 Hz
means that an event repeats once per second. Time Period(T) is the duration of one cycle in a
repeating event, so the period is the reciprocal of the frequency.
Wavelength(λ) of a sinusoidal wave is the spatial period of the wave –
the distance over which the wave's shape repeats. It is usually
determined by considering the distance between consecutive
corresponding points of the same phase, such as crests, troughs, or zero
crossings.

Speed(v) is the distance traveled by a given point on the wave (such as a                 
crest) in a given interval of time (Time Period).                                   
T
3. What is power frequency (line frequency)?

Ans : The utility frequency, (power) line frequency (American English) or mains frequency
(British English) is the frequency at which alternating current (AC) is transmitted from a power
plant to the end user. In most parts of the world this is 50 Hz, although in the America it is
typically 60 Hz.

4. What are A.C. and D.C. currents?

Ans: In alternating current (AC, also ac) the
movement (or flow) of electric charge
periodically reverses direction. An electric
charge would for instance move forward, then
backward, then forward, then backward, over and
over again.

In direct current (DC), the movement (or flow) of
electric charge is only in one direction.
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Pre-Lab Exercise:

1. An electric fan rotates 360 cycles per minute. What are its time period and frequency?

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2. What are the peak to peak voltage and frequency of the sine wave shown below?

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3. What are the peak to peak voltage and frequency of the square wave shown below?

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4. What are the peak to peak voltage and frequency of the triangle wave shown below?

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