# Study notes on Error Analysis & Oscilloscope For Electrical Engineering Students

By Ankita Srivastava|Updated : July 6th, 2023

Error analysis is a process used to identify and quantify the sources of error or uncertainty in a measurement or experimental data. It involves examining various factors that can contribute to discrepancies between the measured values and the true values or expected results.

When it comes to using an oscilloscope, error analysis can be applied to understand and minimize the sources of error in the measurements taken with the oscilloscope.

In this article, you will find the study notes on Error Analysis & Oscilloscope which will cover the topics such as Errors and Statistical Analysis, Classification of Errors, Gross Errors, Instrumental Errors, Environmental Errors, Absolute Errors/Limiting Errors/Static Errors, Percentage Error, Combination of Quantities With Limiting Errors, The Cathode Ray Oscilloscope, Component of C.R.O, Deflection of Electron Beam, Deflection Sensitivity, Deflection Factor, Velocity of Electron Beam, Electrostatic Deflection, Frequency limit of CRO & Rising Time of Vertical Amplifier.

Error Analysis

Errors: It is defined as the deviation of the true value from the desired value.

Classification of Errors

Gross Errors

• Mistake by observer
• Calculation mistake

Systematic Errors

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

Instrumental Errors

These errors arises due to following reasons

• Due to the inherent defect in the instrument.
• Due to mishandling or misuse of the instrument.

Environmental Errors

These errors occur due to change in the environmental parameters such as temperature, humidity, pressure etc.

Observational Errors

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.

Static Correction

δC = AT - Am = -δA

Percentage Error

The relative error may be quoted as a fraction e.g., 5 parts in 1000 or may be expressed as a percentage.

Shortcut

Combination of Quantities With Limiting Errors

The following cases will be considered

Case 1 Sum of Quantities

Let A=A1+A2+A3+...+An

Where, δA1, δA2... = relative increment in quantity A1, A2…..

relative limiting error in quantity A1, A2…….

Case 2 Difference of Quantities

Let

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

Deflection

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)

Deflection Sensitivity

Deflection Factor

Velocity of Electron Beam

in m/s

Where, e = charge of electron = 16 × 10-19 C

m = mass of electron = 9.1 × 10-31 kg

Electrostatic Deflection

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## FAQs

• Error analysis is the process of identifying, quantifying, and understanding the uncertainties or errors that occur in experimental measurements in electrical engineering.

• Error analysis is crucial because it helps assess the reliability and accuracy of experimental results, enables comparisons between different measurements, and guides the optimization of measurement setups.

• The two main types of errors encountered in electrical measurements are systematic errors (or determinate errors) and random errors (or indeterminate errors). Systematic errors arise from faulty equipment, calibration issues, or flawed measurement techniques, while random errors result from inherent fluctuations and limitations in the measurement process.

• An oscilloscope is an electronic test instrument used to measure and display voltage waveforms over time. It is widely used in electrical engineering for analyzing signals, troubleshooting circuits, and verifying system performance.

• An oscilloscope captures electrical signals using probes connected to its input channels. It samples the voltage at regular intervals and displays the waveform on its screen, representing voltage on the vertical axis and time on the horizontal axis.

• Oscilloscopes are used for various applications, including waveform analysis, circuit debugging, signal characterization, timing analysis, frequency analysis, and modulation analysis.

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