Errors: It is defined as the deviation of the true value from the desired value.
Classification of Errors
- Mistake by observer
- Reading and recording error
- Calculation mistake
These errors occur due to short comings of the instruments such as defective or worn parts or aging or effects of the environment on the instrument. Systematic errors are classified as
These errors arises due to following reasons
- Due to the inherent defect in the instrument.
- Due to mishandling or misuse of the instrument.
- Due to loading effect.
These errors occur due to change in the environmental parameters such as temperature, humidity, pressure etc.
The most common errors is the parallax error introduced in reading a meter scale and the error of estimation.
Absolute Errors/Limiting Errors/Static Errors
It is the difference between measured value and a true value of a quantity.
δA = Am - AT
where, Am = Measured value or actual value
AT = True value or nominal value
Relative Static Errors
It is the ratio of absolute static error (δA) to true value (AT) of the quantity under measurement.
δC = AT - Am = -δA
The relative error may be quoted as a fraction e.g., 5 parts in 1000 or may be expressed as a percentage.
Combination of Quantities With Limiting Errors
The following cases will be considered
Case 1 Sum of Quantities
Where, δA1, δA2... = relative increment in quantity A1, A2…..
relative limiting error in quantity A1, A2…….
relative limiting error in A
Case 2 Difference of Quantities
Case 3 Multiplication or Quotient of More than Two Quantities
Case 4 Composite Errors
The Cathode Ray Oscilloscope
The main part of the C.R.O. is a highly evacuated glass tube housing parts which generate a beam of electrons, accelerates them, shapes them into a narrow beam, and provides external connections to the sets of plates described m above for changing the direction of the beam.
Component of C.R.O
- K, an indirectly heated cathode which provides a source of electrons for the beam by “boiling” them out of the cathode.
- P, the anode (or plate) which is circular with a small central hole. The potential of P creates an electric field which accelerates the electrons, some of which emerge from the hole as a fine beam. This beam lies along the central axis of the tube.
- G, the grid. Controlling the potential of the grid controls the number of electrons for the beam, and hence the intensity of the spot on the screen where the beam hits.
- F, the focusing cylinder. This aids in concentrating the electron beam into a thin straight line much as a lens operates in optics.
- X, Y, deflection plate pairs. The X plates are used for deflecting the beam left to right (the x-direction) by means of the “ramp” voltage.The Y plates are used for deflection of the beam in the vertical direction. Voltages on the X and Y sets of plates determine where the beam will strike the screen and cause a spot of light.
- S, the screen. This is coated on the inside with a material which fluoresces with green light (usually) where the electrons are striking.
As well as this tube, there are several electronic circuits required to operate the tube, all within the C.R.O. along with the tube explained below
- A power supply, operated from the 110 volts 60 cycle per second electrical “mains”. This supply provides all the voltages required for the different circuits within the C.R.O. for operation of the tube.
- A “sawtooth”, or “ramp” signal generator which makes the spot move left to right on the screen. External controls for this circuit allow variation of the sweep width, and the frequency of the sweep signal. Because of the persistence of our vision, this sweep is often fast enough that what we see on the screen is a continuous horizontal line.
- Amplifiers for the internally generated ramp signal, and for the “unknown” signal which we hook up to the C.R.O. for the purpose of displaying it.
- Shift devices which allow us to control the mean position of the beam; up or down, or left to right.
- The synchronizer circuit. This circuit allows us to synchronize the “unknown” signal with the ramp signal such that the resulting display is a nice clear signal like a snapshot of the unknown voltage vs. time.
CRO (Cathode Ray Oscilloscope) and Q-meter
CRO is a device which provides accurate time and amplitude of voltage signals over a wide range of frequencies.
Deflection of Electron Beam
Where, L = distance between screen and the center of deflecting plates (m)
Id = length of deflecting plates (m)
Ed = potential between deflecting plates (V)
d = distance between deflecting plates (m)
Ea = voltage of pre-accelerating anode (V)
Velocity of Electron Beam
Where, e = charge of electron = 16 × 10-19 C
m = mass of electron = 9.1 × 10-31 kg
Where, y = displacement in y-direction (m)
e = charge of an electron (C)
m = mass of electron (kg)
x = displacement in X-direction (m)
Ey = electric field intensity in y-direction (V/m)
Vox = velocity of electron when entering in the fields of deflecting plates (m/s)
Frequency limit of CRO
Where, Vox = velocity of the electron beam in X-direction before it enters in deflecting plates
Id = length of vertical deflection plates
Rising Time of Vertical Amplifier
Where, BW = Bandwidth of oscilloscope (CRO)