Electrostatic Focusing and Electrostatic Lens Principle: A stream of electron experiences a change in direction of motion when it passes through non-uniform electric field. Construction: It consists of two cylindrical metal tubes T1 & T2 separated by a small distance held at different potential V1& V2 such that V2 > V1. A high equipotential ring 1MM’ is placed in the gap between the two tubes. The shape of the equipotential lines will be curved on the cylindrical surface of the tubes T1& T2. The electric lines of forces are acting perpendicular at each point on the equipotential surface directed from the tube T2 to T1 thus the curved equipotential planes form an electrostatic lens. WORKING Consider a bundle of electron entering through the tube T1. The electron moves from a lower potential region to a higher potential region.. As the electron approached the gap between the tubes it comes across the equipotential surface. Convex surface at point A the electric field is along the axis without any deviation. Electrons labelled 2 reaching at point B on the convex. Equipotential surface experiences an electric force that acts at an angle to the direction of motion of the electron thus the force can be resolved along two rectangular components F and Fll. F force (vertical component) causes the electron to deflect downwards towards the axis and Fll (horizontal components) to be accelerated towards tube T2 hence such electrons are continually bent down. Similarly electron three reaching ‘C’ on the equipotential surface are continually deflected up towards the axis and are also accelerated thus all three electron path tend to converge towards a point on the axis. The focal length of such a lens is altered by adjusting potentials V1 and V2 Electron travels from T1 of low potential V1 at velocity v1 to a region of T2 of higher potential V2 and velocity v2 The electron emerging from the concaved equipotential surface in Tube T2 tends to diverge however the potential is higher in T2 than T1as a result the electrons travel faster hence the electron are diverged less in Tube T2 than the Tube T1 Magnetostatic Lens, Magnetostatic Focusing Principle: Magnetic field which is axially symmetric has a focusing effect on an electron beam passing through it. Construction It consists of a non-uniform magnetic field along the axis of a short solenoid which behaves as a magnetic lens. AB is a section of soft iron shielded coil of electromagnet separated by a narrow gap in the form of a ring. P and q are diametrically opposite gaps across which there is a strong magnetic field. The arrangement is such that the electron emerging from the source ‘o’ are focused at a point ‘I’. Due to the magnetic lens point I can be changed by changing the magnetic field, which is the required criteria for magnification in an electron microscope where an intense and a very fast beam of electron is needed and mainly Magnetic focusing system is used. Working: Magnetic field has a focusing effect on an electron beam passing through them. Which are produced by short solenoid by encasing coils in a hollow iron shields, which forms a magnetic lens. Thus, when an electron travels in a magnetic field follows a helical path. As the electrons move from weaker to the stronger region at the magnetic field, the radius of the loop goes on decreasing, and the electron path is twisted into tighter loops and the turns become smaller and ultimately appear on the screen as a sharp spot. Determination of focal length Let ‘O’ be the position of an electron inside a uniform magnetic field of intensity B moving with a velocity v along OP making an angle θ with the field. The velocity v is resolved along 2 components. vCosθ along B (x direction) vSinθ perpendicular to B (y direction) If there was only one component vSinθ the electron would move in a circular V along y direction. ∴ π = π£ πππθ ∴ the centripetal force experienced by the electron πΉ= ππ£ 2 πππ2 θ π − − − − − − − − − −(1) ∴ the force experienced by the electron in the external magnetic field πΉ = πππ΅ππππ − − − − − − − − − −(2) From (1) & (2) ππ£ 2 πππ2 θ = πππ΅ππππ π ∴ π£ππππ = ππ΅π π The time taken for the electron to complete one circle of radius r with velocity vSinθ is π‘= = 2πππ ππ΅π = 2ππ ππ΅ 2ππ π£ππππ -------------------- (3) However, since the electron possesses both x and y component it will not follow a circular path but will move along a helical path along ox with pitch (l= OR) will be the distance travelled by the electron parallel to the field in time. π = π£π‘ πΆππ π = π= π£ 2ππ πΆππ π π΅π Substituting t from (3) π£ 2ππ πΆππ π π΅π OP gives the direction of motion of electron in the absence of the electric field. l = (OR) = focal length of the field which can be altered by changing the magnetic field B thus the magnetic beam acts as a lens to bring the divergent electron beam to focus at point ‘l’. CRO It is a device that allows us to measure the amplitude of electrical signals such as voltage or current as a function of time CRT (CATHODE RAY TUBE) The CRT constitutes the central part of CRO. The CRT produces a trace on its fluorescent screen. An electron gun located at one end of the CRT produces a sharp electron beam due to which a small luminous spot caused on the fluorescent coating indicates the position of the electron beam. The brightness and sharpness of the luminous spot on the screen are adjusted with the help of intensity and focus controls. When voltage is not applied to the x and y plates, the luminous spot stays at the center of the screen. When a voltage is applied to the y-plate, an electric field is produced in the vertical direction and the electron beam passing through the filed is deflected upwards or downwards. Similarly, when a voltage is applied to the x-plate, an electric field is produced horizontally and the electron beam passing through the field deflects sideways (right or left) Time Base Generator The sweep generator uses the charging characteristics of a capacitor ‘C’ to generate linear rise time voltages to fled the πβππππ ππ π£πππ‘πππ πΌ horizontal amplifier. The rate of voltage rise is: =πΆ π‘πππ Thus there is a gradual increase in voltage across C, when the critical voltage is reached the capacitor returns to zero voltage by discharging. So the electrons are deflected linearly with time in the horizontal direction for a time T and then the beam returns to the starting point on the screen very quickly, as the sawtooth voltage rapidly falls to its initial value at the end of each period. Thus, the time base generator is a variable oscillator which produces an output voltage of sawtooth shape. Trigger circuit Synchronization: it is a method of locking the frequency of a time base generator to the frequency of the input signal so that a stationary display of wave pattern is seen on the CRO screen. Synchronization is achieved trigger circuit. In this method a part of the output obtained from the vertical amplifier is fed to the trigger generator. Trigger generator is sensitive to the level of the voltage applied to its input. The circuit monitors the input signal and detects the point when it reaches a selected level while moving towards polarity. When the predetermined level is reached the circuit produces a trigger pulse which is fed to the time base generator which acts as a command to the time base generator that starts one sweep cycle of the time base. The sweep voltage is not developed in the trigger mode if the input signal is not given. Vertical circuit It consists mainly of an attenuator and a voltage amplifier. The signal applied to the y- input goes to the input of the attenuator. The signal amplitude is increased or decreased by changing the amount of attenuation and then fed to the input of the voltage amplifier to obtain adequate attenuation on the screen. Horizontal Circuits It mainly consists of a voltage amplifier when the sweep voltage is applied to the horizontal amplifier the output of the amplifier is fed to the x-plates and a linear trace is produced on the screen. However if the sweep voltage is not applied to the amplifier at this position the electron beam remains stationary and produces a luminous spot at the center of CRO. OR The function of each block of CRO is mentioned below. ο· Vertical Amplifier − It amplifies the input signal, which is to be displayed on the screen of CRT. ο· Delay Line − It provides some amount of delay to the signal, which is obtained at the output of vertical amplifier. This delayed signal is then applied to vertical deflection plates of CRT. ο· Trigger Circuit − It produces a triggering signal in order to synchronize both horizontal and vertical deflections of electron beam. ο· Time base Generator − It produces a sawtooth signal, which is useful for horizontal deflection of electron beam. ο· Horizontal Amplifier − It amplifies the sawtooth signal and then connects it to the horizontal deflection plates of CRT. ο· Power supply − It produces both high and low voltages. The negative high voltage and positive low voltage are applied to CRT and other circuits respectively. ο· Cathode Ray Tube (CRT) − It is the major important block of CRO and mainly consists of four parts. Those are electron gun, vertical deflection plates, horizontal deflection plates and fluorescent screen. Advantages of CRO 1) It is the only device that can give the visual display of the actual shape of the signal. 2) CRO is used to test and display signals of frequencies up to a few 100 Mega Hz, since electron due to negligible mass can respond instantaneously to the variation of signal rapidly. Applications of CRO 1. Measurement of Frequency (i) Time Period measurement method A sine wave whose frequency is to be determined is applied to the input signal and a time base control is adjusted to obtain a two or three cycles covering a large area on the CRO screen. The horizontal distance of one cycle is noted and multiplied with the value of the time division knob and hence the time period of the cycle is obtained and thus frequency can be calculated, which is the frequency of the signal given by the relation 1 π= π (ii) Determination of frequency using Lissajous figures. A more accurate method is to use CRO as a frequency comparator. The signal of the unknown frequency is applied to the vertical input and a voltage of known frequency is given to the horizontal input. By varying the frequency of the known source, a stable loop pattern known as Lissajous pattern is obtained on the screen. The nu,ber of points at which the loop touches the horizontal and vertical tangents is noted. If LH and LV are number of points touching the horizontal and vertical inputs respectively than the unknown frequency is ππ¦ = ππ₯ πΏπ» πΏπ ππ₯ is known frequency 2. Measurement of Phase difference (i) Dual sweep method When two sinusoidal waves are started at different time then there will be a phase difference or phase shift will occur between them, expressed in terms of degrees. Phase shift between two AC signals of same amplitude and frequency can be measured with a dual trace CRO. When two Ac signals with a phase difference Ο is applied in two different channel. If the distance (time delayed T D) between the same points of two waveforms is (in time) t then phase difference between them will be: π‘ π = = 360° π (ii) Lissajour’s Figures Phase shift between two AC signals can be calculated by Lissajour’s figures (pattern) by using CRO in an X-Y mode. When two sinusoidal waves of same frequency and amplitudes but with a phase difference (Ο) are applied to x and y plates. The plot obtained is a general ellipse. x and y AC signals are given as: ππ₯ = π πππππ‘ ππ¦ = π πππ(ππ‘ + Ο) at t = 0, Vx = 0, Vy = Vx = 0, Vy = V.SinΟ similarly from the given figure at t = 0, Vx = 0, Vy = h Thus h = V.SinΟ h = V.SinΟ ππππ = π = β π£ πππ−1 β π When h = V, Ο = 90°, Lissajour’s figure is a circle. 3. Measurement of AC/DC voltage CRO is a voltage measuring device. Since voltage is shown as am amplitude on CRO screen for AC signal along vertical axis , which can be controlled by volts/Div. knob. So amplitude of unknown AC voltage is Amplitude (V) = Amp. × Volts/div.knob position = cm.V/cm = Volts In case of a DC Voltage, the distance between the spot before and after the DC voltage applied is proportional to the applied voltage, which is also controlled by Volts/div knob.
