Analog and Digital Systems for Measurement, Measuring Instruments for Different Applications

The normal form of a CRO uses a horizontal input voltage which is an internally generated ramp voltage called 'time base'. The horizontal voltage moves the luminous spot periodically in a horizontal direction from left to right over the display area or screen. The vertical input to the CRO is the voltage under investigation. The vertical input voltage moves the luminous spot up and down in accordance with the instantaneous value of the voltage. The luminous spot thus traces the waveform of the input voltage with respect to time. When the input voltage repeats itself at a fast rate, the display on the screen appears stationary on the screen. The CRO thus provides a means of visualising time-varying voltages. As such, the CRO has become a universal tool in all kinds of electrical and electronic investigation.

2.BLOCK DIAGRAM OF A CATHODE RAY TUBE (CRT)

The main part of the CRO is Cathode Ray Tube (CRT). It generates the electron beam, accelerates the beam to a high velocity, deflects the beam to create the image and contains a phosphor screen where the electron beam eventually becomes visible. The phosphor screen is coated with 'Aquadag' to collect the secondary emitted electrons. For accomplishing these tasks, various electrical signals and voltages are required, which are provided by the power supply circuit of the oscilloscope. The low voltage supply is required for the heater of the electron gun for generation of electron beam and high voltage, of the order of a few thousand volts, is required for cathode ray tube to accelerate the beam. A normal voltage supply, say a few hundred volts, is required for other control circuits of the oscilloscope.

Horizontal and vertical deflecting plates are fitted between the electron gun and screen to deflect the beam according to the input signal. The electron beam strikes the screen and creates a visible spot. This spot is deflected on the screen in the horizontal direction (X-axis) with a constant time-dependent rate. This is accomplished by a time base circuit provided in the oscilloscope. The signal to be viewed is supplied to the vertical deflection plates through the vertical amplifier, which raises the potential of the input signal to a level that will provide usable deflection of the electron beam. Now electron beam deflects in two directions, horizontal on X-axis and vertical on Y-axis. A triggering circuit is provided for synchronising two types of deflections so that horizontal deflection starts at the same point of the input vertical signal each time it sweeps. A basic block diagram of a general-purpose oscilloscope is shown in Figure 1 and a schematic of internal parts of a CRT is shown in Figure 2.

3.ELECTROSTATIC DEFLECTION

Above Figure 2 shows a general arrangement for electrostatic deflection. There are two parallel plates with a potential applied between. These plates produce a uniform electrostatic field in the Y direction. Thus any electron entering the field will experience a force in the Y direction and will be accelerated in that direction. There is no force either in X-direction or Z direction and hence there will be no acceleration of electrons in these directions.

Let,     E_a = voltage of pre-accelerating anode; (volt)

e = charge of an electron; (Coulomb)

m = mass of electron; (kg)

θ = deflection angle of the electron beam

v_ox = velocity of electron when entering the field of deflecting plates; (m/s)

E_d = potential difference between deflecting plates; (volt)

d = distance between deflecting plates; (m)

l_d = length of deflecting plates; (m)

L = distance between the screen and the centre of the deflecting plates; (m)

y = displacement of the electron beam from the horizontal axis at time t and   D = deflection of the electron beam on the screen in Y direction; (m)

The loss of potential energy (PE) when the electron moves from cathode to accelerating anode;

PE = eE_a                                                                               ……(i)

The gain in kinetic energy (KE) by an electron

                                               …(ii)

Equating the two energies, we have

                                    …(iii)

                        ……(iv)

Therefore, deflection sensitivity   

                                     ………(v)

The deflection factor of a CRT is defined as the reciprocal of sensitivity

Therefore, deflection factor  

4.TIME BASE GENERATOR

Generally, oscilloscopes are used to display a waveform that varies as a function of time. For the waveform to be accurately reproduced, the beam must have a constant horizontal velocity. Since the beam velocity is a function of the deflecting voltage, the deflecting voltage must increase linearly with time. A voltage with this characteristic is called a ramp voltage. If the voltage decreases rapidly to zero with the waveform repeatedly reproduced, as shown in Figure 3, the pattern is generally called a sawtooth waveform.

Generally, oscilloscopes are used to display a waveform that varies as a function of time. For the waveform to be accurately reproduced, the beam must have a constant horizontal velocity. Since the beam velocity is a function of the deflecting voltage, the deflecting voltage must increase linearly with time. A voltage with this characteristic is called a ramp voltage. If the voltage decreases rapidly to zero with the waveform repeatedly reproduced, as shown in Figure 3, the pattern is generally called a sawtooth waveform.

During the sweep time, T5, the beam moves from left to right across the CRT screen. The beam is deflected to the right by the increasing amplitude of the ramp voltage and the fact that the positive voltage attracts the negative electrons. During the retrace time or flyback time, Tr, the beam returns quickly to the left side of the screen. This action would cause a retrace line to be printed on the CRT screen. To overcome this problem the control grid is generally 'gated off', which blanks out the beam during retrace time and prevents an undesirable retrace pattern from appearing on the screen.

The vertical sector consists of a wideband preamplifier and power amplifier combination that drivers the CRT vertical deflection plates. The vertical amplifier has a high gain, so large signals must be passed through an attenuator or, in low cost oscilloscopes, a vertical gain controller.

5.MEASUREMENT OF ELECTRICAL QUANTITIES WITH CRO

Basic Oscilloscope Patterns Assume that a sinusoidal voltage is applied to the horizontal deflecting plates without any voltage signal to the vertical deflecting plates, as shown in Figure 6. One horizontal line will appear on the screen of the CRO. This line would be in the central position on the screen vertically.

If a sinusoidal voltage signal is applied to the vertical deflecting plates without applying any voltage signal to the horizontal deflecting plates then we get a vertical line on the screen of CRO, as shown in Figure 7. This line would be in the central position on the screen horizontally.

Now we would discuss what happens when both vertical and horizontal deflection plates are supplied with sinusoidal voltage signals simultaneously. Let us consider when two sinusoidal signals equal in magnitude and frequency and in phase with each other are applied to both of the horizontal and vertical deflection plates, as shown in Figure 8. Here we get a straight line inclined at 45° to the positive X-axis.

6.MEASUREMENT OF VOLTAGE AND CURRENT

The expression for electrostatic deflection is , where

L = distance between screen and the centre of the deflecting plates

I_d = length of deflecting plates

E_d = potential between deflecting plates

d = distance between deflecting plates

E_a = voltage of pre accelerating anode

So deflection is proportional to the deflecting-plate voltage. Thus, the cathode ray tube will measure voltage. It is used to calibrate the tube under the given operating conditions by observing the deflection produced by a known voltage. Direct voltage may be obtained from the static deflection of the spot, alternating voltage from the length of the line produced when the voltage is applied to Y-plates while no voltage is applied to X-plates. The length of the line corresponds to the peak to peak voltage. While dealing with sinusoidal voltages, the rms value is given by dividing the peak to peak voltage by .

For measurement of current, the current under measurement is passed through a known non inductive resistance and the voltage drop across it is measured by CRO, as mentioned above. The current can be determined simply by dividing the voltage drop measured by the value of non-inductive resistance. When the current to be measured is of very small magnitude, the voltage drop across noninductive resistance (small value) is usually amplified by a calibrated amplifier.

7.MEASUREMENT OF FREQUENCY

It is interesting to consider the characteristics of patterns that appear on the screen of a CRO when sinusoidal voltages are simultaneously applied to the horizontal and vertical plates. These patterns are called Lissajous patterns. Lissajous patterns may be used for accurate measurement of frequency. The signal, whose frequency is to be measured, is applied to the Y-plates. An accurately calibrated standard variable frequency source is used to supply voltage to the X-plates, with the internal sweep generator switched off. The standard frequency is adjusted until the pattern appears as a circle or an ellipse, indicating that both signals are of the same frequency. Where it is not possible to adjust the standard signal frequency to the exact frequency of the unknown signal, the standard is adjusted to a multiple or submultiple of the frequency of the unknown source so that the pattern appears stationary. Let us consider an example. Suppose sine waves are applied to X and Y plates as shown in Figure 9. Let the frequency of wave applied to Y plates is twice that of the voltage applied to the X plates. This means that the CRT spot travels two complete cycles in the vertical direction against one of the horizontal direction. The two waves start at the same instant. A Lissajous pattern may be constructed in the usual way and a 8 shaped pattern with two loops is obtained. If the two waves do not start at the same

instant we get different pattern for the same frequency ratio. The Lissajous pattern for the other frequency ratios can be similarly drawn. 

It can be shown that for all the above cases, the ratios of the two frequencies is

Where f_y = Frequency of signal applied to Y plates

          f_x = Frequency of signal applied to X plates

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