GATE Biomedical Engineering Measurements and Control Systems Syllabus

Measurements and Control Systems syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Measurements and Control Systems in GATE Biomedical Engineering, not a summary of it.

1. 1

   SI Units

   overview

   Examined as a single unit within Measurements and Control Systems — no further topic split in the official outline.

2. 2

   Systematic and Random Errors in Measurement

   2 topics

   • Expression of Uncertainty - Accuracy and Precision Index
   • Propagation of Errors
3. 3

   PMMC, MI and Dynamometer Type Instruments

   overview

   Examined as a single unit within Measurements and Control Systems — no further topic split in the official outline.

4. 4

   DC Potentiometer

   overview

   Examined as a single unit within Measurements and Control Systems — no further topic split in the official outline.

5. 5

   Bridges for Measurement of R, L and C

   overview

   Examined as a single unit within Measurements and Control Systems — no further topic split in the official outline.

6. 6

   Q-Meter

   overview

   Examined as a single unit within Measurements and Control Systems — no further topic split in the official outline.

7. 7

   Basics of Control System - Transfer Function

   overview

   Examined as a single unit within Measurements and Control Systems — no further topic split in the official outline.

Measurements and Control Systems flashcards for GATE Biomedical Engineering

19 of 50 cards from the Measurements and Control Systems deck — real questions with worked answers.

1. Define the "true value" of a measurand in metrology.

   The true value is the actual, exact value of the quantity being measured. In practice it is unknowable; it can only be estimated, since every real measurement carries some uncertainty.

2. What is measurement error? Give its defining equation.

   Measurement error is the difference between a measured value and the true value: $$\varepsilon = x_{\text{measured}} - x_{\text{true}}$$

3. Distinguish between accuracy and precision.

   Accuracy is closeness of a measured value to the true value (low systematic error). Precision is closeness of repeated measurements to one another (low random scatter), regardless of how close they are to the true value.

4. In the dartboard analogy, what do "high accuracy, low precision" and "low accuracy, high precision" look like?

   High accuracy, low precision: darts scattered widely but centered on the bullseye (mean is correct, large spread). Low accuracy, high precision: darts tightly clustered but off the bullseye (small spread, biased).

5. What is a systematic error and how does it affect a measurement?

   A systematic (bias) error is a consistent, repeatable error that shifts all readings in the same direction by roughly the same amount. It degrades accuracy but not precision, and cannot be reduced by averaging.

6. What is a random error and how can its effect be reduced?

   A random error causes unpredictable scatter in repeated readings, varying in sign and magnitude. It degrades precision and can be reduced by averaging many readings, since its mean tends toward zero.

7. Define absolute error of a measurement.

   Absolute error is the magnitude of the difference between the measured value and the true value: $$E_{\text{abs}} = |x_{m} - x_{t}|$$ It carries the same units as the measured quantity.

8. Define relative (fractional) error and percentage error.

   Relative error: $$E_{r} = \frac{|x_{m} - x_{t}|}{x_{t}}$$ Percentage error: $$E_{\%} = \frac{|x_{m} - x_{t}|}{x_{t}} \times 100\%$$

9. How is the arithmetic mean of $n$ measurements $x_1, x_2, \dots, x_n$ defined?

   $$\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_{i}$$ The mean is the best estimate of the true value when only random errors are present.

10. Define the deviation of an individual reading from the mean.

    The deviation of the $i$-th reading is $$d_{i} = x_{i} - \bar{x}$$ The algebraic sum of all deviations about the mean is always zero: $\sum_{i} d_{i} = 0$.

11. What is the average (mean) deviation as a measure of precision?

    $$\bar{d} = \frac{1}{n}\sum_{i=1}^{n} |x_{i} - \bar{x}|$$ A smaller average deviation indicates higher precision.

12. Give the formula for the population standard deviation $\sigma$ of a set of measurements.

    $$\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_{i} - \bar{x})^{2}}$$

13. Give the formula for the sample standard deviation $s$ and explain the $n-1$ factor.

    $$s = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_{i} - \bar{x})^{2}}$$ The divisor $n-1$ (Bessel's correction) accounts for the one degree of freedom lost in estimating $\bar{x}$, giving an unbiased estimate of the population variance.

14. What is the variance of a set of measurements?

    Variance is the square of the standard deviation, $\sigma^{2}$ (or $s^{2}$ for a sample): $$\sigma^{2} = \frac{1}{n}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}$$

15. Define the standard deviation of the mean (standard error of the mean) and its formula.

    It quantifies the uncertainty in the estimated mean: $$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$$ Averaging $n$ readings reduces the uncertainty of the mean by a factor of $\sqrt{n}$.

16. By what factor must the number of readings increase to halve the standard error of the mean?

    Since $\sigma_{\bar{x}} = \sigma/\sqrt{n}$, halving it requires $\sqrt{n}$ to double, i.e. $n$ must increase by a factor of $4$ (four times as many readings).

17. What is meant by the "uncertainty" of a measurement result?

    Uncertainty is a parameter associated with a measurement result that characterizes the dispersion of values that could reasonably be attributed to the measurand. It defines an interval, e.g. $x = \bar{x} \pm u$, within which the true value is expected to lie.

18. Distinguish Type A and Type B evaluation of uncertainty (GUM classification).

    Type A uncertainty is evaluated by statistical analysis of repeated observations (e.g. standard deviation of the mean). Type B uncertainty is evaluated by non-statistical means: manufacturer specs, calibration certificates, instrument resolution, or experience.

19. What is standard uncertainty $u(x)$?

    Standard uncertainty is an uncertainty expressed as a standard deviation. For Type A it is $s/\sqrt{n}$; for Type B it is derived from an assumed distribution (e.g. dividing a half-width by $\sqrt{3}$ for a rectangular distribution).

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