UNIT-I ELECTRON DYNAMICS AND CRO: Motion of charged particles in electric and magnetic fields. Simple problems involving electric and magnetic fields only. Electrostatic and magnetic focusing. Principles of CRT, deflection sensitivity (Electrostatic and magnetic deflection), parallel and perpendicular electric and magnetic fields
Deflection of Electrons in a Uniform Electric Field Consider an electron beam directed between two oppositely charged parallel plates as shown below. With a constant potential difference between the two deflecting plates, the trace is curved towards the positive plate. + - d
Deflection of Electrons in a Uniform Electric Field The force acting on each electron in the field is given by where E = electric field strength, V = p.d. between plates, d = plate spacing. p
Deflection of Electrons in a Uniform Electric Field The vertical displacement y is given by This is the equation for a parabola.
Deflection of Electrons in a Uniform Magnetic Field The force F acting on an electron in a uniform magnetic field is given by Since the magnetic force F is at right angles to the velocity direction, the electron moves round a circular path.
Deflection of Electrons in a Uniform Magnetic Field The centripetal acceleration of the electrons is Hence which gives
Cathode Ray Oscilloscope (CRO) The structure of the cathode ray tube
Cathode Ray Oscilloscope Controls Y-Gain Time Base
Y-Gain amplifies the Y-deflection small input voltages are amplified by built-in amplifiers before applying to the Y-plates. Y- Gain = 0.5 V/div –0.5 volt will cause a vertical deflection of 1 division
Time Base is a saw-tooth voltage applied internally across the X-plates. time volts
Time Base controls the speed at which the spot sweeps across the screen horizontally from left to right. Time taken for spot to move across the screen and back Fly back volts time 0 spot at centre of screen spot on left side of screen spot on right side of screen
volts time 0 Screen spot on left side of screen spot at centre of screen spot on right side of screen Fly back
Time Base it helps to display the actual waveform of any a.c. applied across the Y-plates normally calibrated in –s/cm –ms/cm – s/cm gives the time required for the spot to sweep 1 cm horizontally across the screen.
Time Base: How It Works Time taken for spot to move across the screen and back time volts Fly back 0 spot at centre of screen spot on left side of screen spot on right side of screen A B C
Uses of c.r.o. Measure potential difference –d.c. –a.c. Display waveforms of alternating p.d. Measure short intervals of time, and Compare frequencies
Measuring d.c. Potential Difference switch off the time-base a spot will be seen on the c.r.o. screen d.c. to be measured is applied to the Y- plates spot will either deflected upwards or downwards deflection of the spot is proportional to the d.c. voltage applied
Measuring d.c. Potential Difference Y-input y If the Y-gain control is set at 2 volts/division And the vertical deflection, y, is 1.5 Then d.c. voltage =1.5 x 2 =3.0 V
Measuring a.c. voltage switch off the time-base a spot will be seen on the c.r.o. screen a.c. to be measured is applied to the Y-plates spot will move up and down along the vertical axis at the same frequency as the alternating voltage –spot moves to the top when the voltage increases to its maximum (positive) –spot moves to the bottom when the voltage decreases to its lowest (negative)
Measuring a.c. voltage When the frequency is high –the spot will move so fast that a vertical line is seen on the screen Length of the vertical line gives the peak- to-peak voltage (V pp ) applied to the Y-plate The peak voltage (V p ) is =V pp /2
C.R.O. as a Voltmeter it has nearly infinite resistance (between the X- and Y-plates), therefore draws very little current; it can be used to measure both d.c. and a.c. voltages; and it has an immediate response.
Displaying Waveforms Set the time-base to a suitable frequency, Apply the input to the Y-plate –a steady waveform of the input will be displayed on the c.r.o.
Displaying Waveforms When input voltage frequency is the same as the time-base frequency Input Voltage c.r.o. screen
Displaying Waveforms When input voltage frequency is the twice the time-base frequency Input Voltage c.r.o. screen
Measuring Short Time Intervals Set time-base to its lowest frequency range Connect microphone to the Y-input Blow two short whistles into the microphone –two short pulses, at short interval apart will be displayed on the c.r.o. screen
Measuring Short Time Intervals t divisions If the time-base is 10 ms/division and if the separation between pulses is t divisions then time interval is 10t ms c.r.o. screen
Lissajous Figures Lissajous figure can be displayed by applying two a.c. signals simultaneously to the X-plates and Y-plates of an oscilloscope. As the frequency, amplitude and phase difference are altered, different patterns are seen on the screen of the CRO.
Lissajous Figures Same amplitude but different frequencies