We now turn to one of the most fundamentally important devices found in any high school physics lab: the Cathode ray oscilloscope. At Harrison College in Barbados, we regularly used this device to precisely measure voltages, as well as analyze, diagnose and record rapidly changing electrical phenomena whose frequencies often varied from less than 1 c/s (cycle per second, or Hz) to thousands of megacycles per second (Mc/s, or MHz). The versatility of the 'CRO' is such that it can be used in everything from electronics, to missile technology, though many of these have been displaced in the modern era. Nevertheless, the CRO remains a highly useful teaching tool!
The front face of one oscilloscope is shown in Fig.1. with its circular screen (and grid) as well as controls below. Basically, the heart of the machine is a cathode ray tube, which is sketched from my old Harrison College notes in Fig. 2. This is an elongated vacuum tube with an electron gun at one end (left) which acts as a supply for high velocity electrons. By means of an electron 'lens' system these electrons are brought to a focus (e.g. into a narrow beam) and accelerated along the axis of the tube. From there various controls are used (along with differentially applied voltages) to alter the outputs. (A power supply provides the necessary voltages to operate the electron gun and focus the beam).
In reference to the components of the CRO illustrated in Fig. 2:
- The cathode is raised to a high temperature by a heated filament
- the accelerating anode is maintained at a high positive potential relative to the cathode, so a storng E-field obtains between the two.
-The control grid regulates the number of electrons leaving the anode.
- The focussing anode ensures electrons leaving the anode arrive at the same spot on the screen.
- X and Y plates (pairs) are used for deflection. Separately, the Y -plates are used for up and down motions and the X-plates for side to side motions'
- The amplitude scale is along the vertical scale and the time along the base.
Fig. 3 shows the arrangement of the X and Y -plates in a frontal view and their grounding. The graph in 3(b) shows the linear relationship between the magnitude of deflection (vertical axis) and the voltage applied.
Our CROs at Harrison College typically had a sensitivity of 50V/cm (of course all CROs have amplifiers built in to amplify signals too small to be read otherwise). In performing calibrations, typically a vertical line 1 cm long would be produced by this a.c. input of 50 V (peak-to-peak) thus, 25V peak maximum so the rms voltage (root mean square voltage) would be: V(max)/[2]^½ = 18 V. Students found that on setting the gain to 0.1 the gain of the amplifier was greatest and small potential differences could be measured.
Some initial observations:
a) Connect the Y1 plate to a positive d.c. potential, the spot observed in Fig. 4 appears.
b) Connect the same Y1 plate to an a.c. potential and the vertical motion of the spot depicted in Fig. 5 is seen.
Calibrating the instrument
1. Connect the output of an audio signal generator to the Y input terminal.
2. Set the signal generator at 100 Hz (c/s) and by adjusting the sweep frequency controls, obtain one complete cycle on the oscilloscope screen.
3. Repeat with the signal generator set at 250 and then 500 cycles/s.
4. With the signal generator set at 100 c/s set its output at 2.0 V.
5. With the (scaled) grid in place over the oscilloscope face, set the vertical gain control to give a 20-unit vertical amplitude.
6. Reduce the signal generator output so the amplitude is now 10 units.
For Displaying General Waveforms
The signal to be examined is connected to the Y-plates (e.g. via the audio signal generator) and the time base to the X-plates. As the CRO spot is drawn horizontally across by the time base it is deflected vertically by the alternating signal potential. (Time base must have a linear sweep of the waveforms will suffer distortion).
The ratio of the frequency for the signal amplitude to the time base will be:
f(a) / f(tB) = 1
Lissajous Figures
The creation and examination of Lissajous Figures (see Fig. 6) is also very popular with H.C. students. The particular pattern formed depends on the frequency, amplitude, and phase relationship of the two inputs (X and Y). Basically, these figures are formed when two differing signal generators (generating different frequencies) are connected to the vertical and horizontal inputs. (The controls must be changed so that the oscilloscope accepts the output of the signal generator instead of the horizontal sweep!)
The objective is mainly such that the frequency ratio of the two inputs, (e.g. f(v)/f(h)) can be determined from an analysis of the Lissajous figure produced. If enclosed in a rectangle whose sides are parallel to the formation axes of the figure the frequency ratio is determined by counting the points of tangency to the sides of the rectangle enclosing the pattern. The ratio of the tangency points is the inverse ratio of the input frequencies.
Practical Problem:
Fig. 6 shows the Lissajous pattern produced when the frequency ratio = 2/3.
if the frequency of the vertical input is 300 Hz, then what is the frequency of the horizontal input?
We first confirm the frequency ratio is correct, and note there are 3 vertical tangency points along the sides of the rectangle - made by the figure. There are two horizontal tangency points, so the T-points ratio = 3/2.
The actual frequency ratio f(v)/f(h) is the inverse of this so:
f(v)/f(h) = 1 /(3/2) = 2/3
Now, we have f(v) = 300 Hz, then:
f(v) = 2/3 (f(h)) or
f(h) = 3/2 (300 Hz) = 450 Hz
Other problems:
1) If in a test of an oscilloscope the Y2 plate is connected to a positive (d.c.)potential, sketch what would be observed.
2) The time base is connected to a positive potential (X-plates only involved). Sketch what would be observed.
3) When the time variation of a quantity is to be studied, an alternating p.d. representing the quantity is applied to the Y-plates via the Y-amplifier to the time -base. This generates a "saw-tooth" pattern. Illustrate such a pattern, and label its "sweep" and "flyback" aspects.
(Hints: The sweep must be linear so the deflection of the beam is proportional to the time. The 'saw-tooth' results from a combination of the alternating input p.d. and the steady speed of the image spot going left to right)
4) Say a 2 cm long line (peak-to-peak, from above to below reference horizontal) is generated on the screen in a lab oscilloscope by an a.c. input of 60V. What would the peak voltage be? What will the rms voltage be?
5) A signal generator producing 1,000 Hz is connected to the vertical Y-input of an oscilloscope while a 2nd signal generator producing 500 Hz is connected to the horizontal. Sketch the Lissajous figure that would be produced. Explain why you sketched it as you did.
6) The frequency ratio analyzed from a Lissajous figure is found to be:
f(v)/f(h) = 1
Sketch how this pattern would appear on the oscilloscope screen.
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