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# Electrostatic Focusing in CRT

### Electrostatic Focusing System of CRT:

The focusing used in a cathode ray oscilloscope is analogous to the refraction of light beam, through a compound lens system. As light beam can be focused varying the focal length of the system, the electron beam also can be focused on to the screen, to offer a fine spot of illumination. To understand the electronic lens system it is necessary to know the nature of the electro static field lines and the equipotential lines in the CR Tube.

Let us consider an electron situated at rest in an electric field. From the definition of electric field intensity we know that the force on a unit positive charge at any point in an electric field is the electric field intensity at that point.

Hence Ɛ = f/q V/m --------------------------- (1)
Where Ɛ = electric field intensity in V/m
f = force on the charge in N
q = charge in C
The charge of an electron is Ɛ = 1,602 x 10-19 C -------------------------- (2)
The force on the electron in an electric field is fe= -eƐN from equation (1) ------------------ (3)

The negative sign indicates that the force is acting in a direction opposite to the direction of the electric field. Figure illustrates the electron situated in the electric field. The electric field lines have been shown in figure with directions from positive plate to negative plate. The field lines experience lateral repulsion. This results in spreading of the space between the lines. Therefore the field lines will be curved at the ends of the plates. Hence the density of the field lines will be less at the ends of the plates. A line joining points of equal potentials is called an equipotential line. When such lines are drawn, they are obtained as shown in Figure.

As the force on an electron acts in a direction opposite to the direction of the field, it can also be stated that the force on an electron is in the direction normal to the equipotential surfaces or equipotential lines. The following figure illustrates the shape of the equipotential lines between two cylinders placed end to end. Shape of field and equiipotential lines for two cylinders placed end to end
Since the density of the electric field varies in the area between the two cylinders, the equipotential lines are curved. Let us now consider regions on both sides of the equipotential surface S as shown in Figure. The potential to the left of S is negative and to the right of it is positive. An electron entering the area in the direction AB at an angle with the normal to the equipotential surface will experience a force at the surface. The velocity of the electron is taken as v1. The force acts in a direction normal to the equipotential surface. Hence the velocity of the electron increases to a new value v2; after it passes S. The tangential component, vt of the velocity on both sides of S remains the same. The normal component of the velocity vn only increases by the force at the equipotential surface to a new value v1n. From the figure we have

Vt = V1 sin θi = V2 sin θr,
θi, is the angle of incidence and θr is the angle of refraction of the electron ray.
Rearranging equation (4).
sin θi/ sin θr = V2/V1

We find that the equation (5) is identical to the expression relating the refraction of a light beam in geometrical optics. Therefore we conclude saying that the refraction or bending of an electron beam at an equipotential surface is governed by the same laws of refraction of a light beam. This is the reason for calling the electrostatic focusing system as electron lens system.

Having established the fact that the refraction or bending of the electron beam follows the laws of refraction of light, we will consider the electrostatic focusing system of the CR Tube.

The pre-accelerating electrode or anode, the focusing anode and the accelerating anode are shown along with the grid structure and the supply voltages in the following diagram.

In the above diagram we find the pre-accelerating anode, called as A1. It is hollow cylindrical in structure with metal discs placed to make the structure compartmental. There are holes in the metal discs. Electrons will be entering this structure through the hole in the left side. Immediately after this electrode we find the focusing anode. This is a hallow metal cylinder. After the focusing anode we have the accelerating anode called A2. In some constructions the focusing anode may not be there. Anode A1 and Anode A2 are arranged to give the focusing.

The pre-accelerating anode A1 and the accelerating anode A2 are connected in common to a high positive potential, supplied by the EHT. The focusing anode is connected to a lower + ve potential. As the focusing anode is negative with respect to the two accelerating anodes A1A2, the electric field lines are non-uniformly placed. The equipotential lines are only shown in the figure. The field distribution and hence the shape of the equipotential surfaces/ lines, can be altered by varying the potential difference between the focusing anode and the two accelerating anodes A1 and A2. As shown in the figure the potentiometer connected in the potential divider network that supplies voltage to the electrodes does this job of varying the voltage and hence is called the focus control. This control is made available on the front panel of the CRO as a user control. Varying this voltage changes the focal length of the electron lens. Therefore the beam of electrons can be accurately focused on the screen by proper adjustment of the voltage on the focusing anode.

The electron beam on entering the pre-accelerating anode will be under the influence of a high positive potential the electrons will be accelerated towards the screen. The discs with centrally located holes aid their travel in the form of a beam. However some electrons will be attracted by the pre-accelerating anode, that contribute the A1 current. The electrons being negative charges repel each other. Therefore we will not get a close beam of electrons. Right from the grid they travel in a diverging beam pass through the pre-accelerating anode with increased velocities and encounter the electric field between the focusing anode and the anode A1, As their paths are not normal to the equipotential lines (surfaces) the electrons undergo refraction through the electric field between the anode A1 and the focusing electrode. Later again they encounter the electric field between the focusing anode and the second anode while they travel towards the screen. The high voltage accelerates them and at the same time due to the electric field distribution they are again refracted through the field. Thus the electrons undergo refraction through the double concave lens system. The result is that they enter the region between A1 and focusing electrode with an inclination, travel parallel to the axis of the CR Tube in side focusing electrode structure latter undergo refraction and finally arrive on the screen as a fine spot. As mentioned earlier the size of the spot (beam) striking the screen is determined by the relative potential difference between A1, A2 and the focusing electrode (anode).

It must be noted that the second anode may not attract electrons due to their velocities. The A2 current is mostly by the secondary electrons from the screen.