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EXPERIMENT NO. 2

Electrostatic and Magnetic Deflection of Electrons in a Cathode Ray Tube

Part A. Motion of electrons in an electric field:

Introduction

The heart of an oscilloscope is the cathode-ray tube (CRT). The electrode structure

(electron gun) of a CRT is shown schematically in Fig. 1.

Figure 1: Electrode structure of the CRT

Figure 2: The electrical connections of the CRT

Electrons are emitted from the cathode and are accelerated and focused onto a screen by

an assembly of electrodes. Some of the energy of these electrons is converted into visible light

when they hit the fluorescent screen, producing a small bright spot. The spot can be moved

around on the face of the screen by applying voltages to the deflecting plates.

2

If the electrons accelerated by the gun fall through a total potential difference VA, they will have

a velocity component, vz, along the axis of the gun (the z direction) given by the energy equation

Az Vemv 2

2

1 (1)

Ideally, the electrons will have zero velocity in the x and y directions perpendicular to the z axis

on leaving the gun, but the earth’s magnetic field may give the beam some deflection. Electrons

can be accelerated transversely by applying potential differences between the deflecting plates.

Let us consider one set of plates only, those that can cause vertical deflections.

Figure 3: Electron deflection in a CRT.

On the assumption that the electrostatic field is uniform between the plates and extends only over

the distance , the field between these plates is the applied voltage divided by the plate separation. Therefore:

Ey = Vy /d , (2)

and an electron will be in this field for a time

t = zv/ (3)

The force on the electron during this time interval is Fy = e·Ey and the vertical component of

acceleration will be given by

md

Ve

m

Ee

m

F a

yyy

y

(4)

This can be used to obtain the change of velocity in the vertical direction,

z

y

yy vd

V

m

e tav

(5)

3

The tangent of the deflection angle, , is given by the ratio of the velocity components,

A

y

z

y

z

y

V

V

dmdv

eV

v

v

2 tan

2

(6)

If D is the deflection of the beam on the screen, and L is the distance from the centre of the

deflection plates, making the approximation L >> , Fig. 3 shows that

D L tan A

y

V

V

d

L

2

(7)

The dependence of D on Vy and VA

The lab instructor will acquaint you with the apparatus, instruments and their operation.

After this is done, start with the case of a high accelerating potential by setting the VC- adjustment of the large power supply to its maximum output position (100%) and then adjust the

VB+ dial to obtain a well focussed spot on the CRT tube face. Measure your CRT’s accelerating

potential VA (= CB VV ) using a multi-meter. You may find it convenient to rotate the CRT

on the desktop to obtain an orientation for which the spot lies on the axis when the deflecting

plate voltage is absent.

* What do you suspect is the origin of this spot motion when the tube is rotated?

Answer all questions beginning with * in your report as well as other questions in the text.

Once this orientation is achieved, the CRT must be kept in this position for the rest of this part of

the experiment.

With your small power supply connected to the vertical deflection plate leads and your

voltmeter on the appropriate range, deflect the spot vertically in increments of the major vertical

divisions and note the voltage Vy, required to do this. Your deflections should span the entire

vertical scale, which will require you to reverse the polarity of the plate voltage in order to

deflect the spot in the opposite direction. This is achieved by simply removing, reversing and re-

inserting the leads plug to the Vy source. The major divisions of the graticule scale on the tube

face are ¼ inch units (=0.635 cm) and must be converted to centimetres for your analysis.

Repeat this procedure for a lower VA value by setting VC- to approximately 50% of its maximum

output and again adjusting VB+ to obtain a well-focussed spot.

Tabulate all the data obtained such that upward (or +D) deflections are associated with

+Vy voltages and downward (or –D) deflections are associated with –Vy voltages. Plot D against

Vy for both values of VA on one graph.

*Are your graphical results as expected?

4

Calculate Vy/VA for both sets of VA values and plot D against Vy /VA on a second graph.

*Are your graphical results in the second plot as expected?

Determine the Deflection Coefficient, DC, for the tube where DC = Vy /D (Volts/ugd ). The

deflection coefficient tells you the required input voltage to vertical deflection plates necessary

to produce a unit vertical displacement of the spot on the tube face.

Equation (7) provides the basis for understanding the oscilloscope as an instrument which will

measure voltage, time and hence, frequency and phase. To emphasize the close connection

between the CRT itself and the oscilloscope, consider the following diagram of the input

connection to a CRT. The resistor R2 is a “bleed resistance” across the vertical deflection plates.

Its purpose is to remove charge from the plates to neutralize them. Your input wires to the

deflection plates have such a resistor.

Creation of an Adjustable Calibrated Voltage Scale

a) Find an expression for the Deflection Coefficient for the tube, DC, in terms of the slope of

graph D vs. Vy/VA.

b) What VA must your CRT have to achieve a Deflection Coefficient, DC, equal to 1 volt/ugd?

[ugd = unit graticule division]

c) Assuming you have a DC for your tube equal to 1 volt/ugd, what values of R1 are required to

achieve an effective deflection coefficient,

(as shown in the figure

above) of 1, 2, 5 and 10 volts/ugd? Give details.

d) Why is it not possible to obtain all these values with your CRT?

ugd = unit graticule division

5

e) The correction for the problem of part (d) is to raise the accelerating potential across the

electron gun, VA. Assuming the answer to (b) is 40 volts, let’s assume we set the VA to 400

volts. What is the new DC as a result of these changes? If 1 volt is now placed across R2 what

spot displacement results? What voltage must be placed across the plates to now achieve a spot

displacement of one ugd?

f) The solution to the higher VA value which retains the resistor divider values computed in (c) is

to have an amplifier with voltage gain, AV = vout/vin inserted between the output voltage across

R2 and the input voltage to the deflection plates as shown below. What is the required value of

AV?

The relationship which permits one to measure the input voltages to such a system should be

seen to be:

Vi = DC ∙ Dy

where Vi is the input voltage across R1 and R2 and Dy is the deflection of the spot in ugd’s. This

equation indicates that the vertical (or horizontal) size of the trace is controllable by the

magnitude of the DC of the system and/or that of the input voltage, Vi.

6

Creation of an Adjustable Calibrated Time Base

A time base, like that possessed by an oscilloscope in the x-axis direction, is based on the

achievement of an adjustable constant speed of the beam spot in the direction from left to right

across the CRT tube face. An electronic circuit is designed to achieve such a result.

To understand how this can be accomplished, consider the DC expression in the form

below where D and Vx are divided by the common time interval t. Vx implies that the

voltage is to be placed across the horizontal deflection plates. Recognizing that D / t equals

the speed of the spot in the x-direction, vx,

D

DC V v

D

t DC

V

t x x

x 1 1

a) Assuming that VA is 400 volts and that the DC for the horizontal deflections plates is the

same, how must Vx vary with time in order to achieve a constant speed? What must Vx/t be in

order for vx to be 1 ugd/sec? What is the Time Equivalent/ugd, TC, under this circumstance for

the motion of the spot in the x-direction? If two points on a trace of a displayed voltage, Vy(t),

are measured to be 4.6 ugd’s apart, what is the time interval between these two points?

b) What magnitudes of