JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III ELECTRICAL AND ELECTRONICS INSTRUMENTATION Previous Question Paper (November/December - 2020 - R16)

Measurement error is defined as the difference between the measured value and the true value of a quantity. These errors are broadly classified into three categories based on their source and nature:

• Gross Errors: These are primarily caused by human mistakes in reading, recording, or calculating results. They occur due to improper use of instruments or misinterpretation of data. Example: Reading a pressure gauge as 5.2 bar when the actual reading is 2.5 bar due to parallax error or misreading the scale. These errors cannot be treated mathematically and are minimized by taking multiple readings and ensuring careful observation.
• Systematic Errors: These errors occur due to shortcomings in the instrument, environmental effects, or observational methods. They are consistent and repeatable. They are subdivided into:
  • Instrumental Errors: Inherent defects in the instrument, such as friction in bearings, improper spring tension, or calibration drift. Example: A voltmeter reading 105V when the actual voltage is 100V due to a weak permanent magnet.
  • Environmental Errors: External conditions such as temperature, pressure, humidity, or magnetic fields affecting the instrument. Example: A change in ambient temperature causing the resistance of a copper coil to change, thereby altering the calibration of a galvanometer.
  • Observational Errors: Errors introduced by the observer, such as parallax error while reading a pointer on a scale.
• Random Errors: These are unpredictable errors that remain after gross and systematic errors have been eliminated. They are caused by small, transient fluctuations in experimental conditions like voltage spikes, mechanical vibrations, or thermal noise. Example: Minor fluctuations in the reading of a digital multimeter caused by electromagnetic interference in the laboratory environment. Since these are random, they are analyzed using Statistical Analysis, such as calculating the arithmetic mean and standard deviation of a large number of observations to estimate the most probable value.

Pulse Code Modulation (PCM) is a digital representation of an analog signal where the magnitude of the signal is sampled at uniform intervals and then quantized to a discrete level, which is subsequently encoded into a binary code.

The process involves three primary stages:

• Sampling: The continuous-time analog signal is converted into a discrete-time signal by taking samples at a rate f_s, which must satisfy the Nyquist criterion (f_s ≥ 2f_m) to avoid aliasing.
• Quantization: Each sample is mapped to the nearest value from a finite set of discrete levels. The difference between the original sample value and the quantized value is known as Quantization Noise or Quantization Error.
• Encoding: The quantized levels are converted into a sequence of binary digits (bits). For N quantization levels, each sample is represented by n = log₂(N) bits.

Block Diagram Description:

The Low Pass Filter ensures the signal is band-limited. The Sampler performs periodic sampling. The Quantizer rounds off the amplitude, and the Encoder assigns a unique binary word to each level. PCM is highly favored in instrumentation and communication systems due to its high Signal-to-Quantization-Noise Ratio (SQNR) and robustness against channel noise, as digital signals can be regenerated easily compared to analog signals.