p.11
High-Gain Feedback in Measurement Systems
What do intelligent instruments do to handle systematic errors?
They contain extra sensors that measure environmental inputs and automatically compensate the output reading.
p.11
Sources of Systematic Errors
Why is it difficult to quantify systematic errors?
Because measurements can be subject to unpredictable environmental conditions.
p.2
Statistical Analysis of Random Errors
How can random errors be minimized?
By taking the same measurement multiple times and averaging the results.
p.8
Techniques for Reducing Systematic Errors
What is the prerequisite for reducing systematic errors in a measurement system?
A complete analysis of the measurement system that identifies all sources of error.
p.7
Techniques for Reducing Systematic Errors
What is one solution to systematic errors caused by wear in instrument components?
Recalibration of the instruments.
p.3
Impact of System Disturbance on Measurements
What happens when a thermometer is plunged into hot water?
It introduces a relatively cold mass, causing heat transfer that lowers the water's temperature.
p.2
Types of Measurement Errors: Systematic and Random
What distinguishes systematic errors from random errors?
Systematic errors are consistent and arise from identifiable sources, while random errors are unpredictable and vary.
p.11
Statistical Analysis of Random Errors
What can be calculated to quantify confidence in mean/median values?
The standard deviation or variance of the data.
p.5
Quantification of Measurement Errors
What is the purpose of applying Thevenin’s theorem in the measurement process?
To find an equivalent circuit for calculating the measurement error.
p.5
Quantification of Measurement Errors
What does a measurement error of 5% indicate about the accuracy of the measurement?
It indicates that the measured value is 5% less than the actual value.
p.12
Statistical Analysis of Random Errors
What are the mean and median values for measurement set A?
Mean = 409.0, Median = 408.
p.4
Introduction to Measurement Errors
What does R_AB represent in the circuit analysis?
The equivalent single resistance.
p.11
Quantification of Measurement Errors
What is the final action required after reducing systematic errors?
To estimate the maximum remaining error that may exist in a measurement due to systematic errors.
What can help rectify errors due to instruments being out of calibration?
Increasing the frequency of recalibration.
p.8
Techniques for Reducing Systematic Errors
What are simple faults in a measurement system that can be easily rectified?
Bent meter needles and poor cabling practices.
p.2
Impact of System Disturbance on Measurements
What is an example of systematic error due to measurement disturbance?
Measuring the temperature of hot water with a thermometer can disturb the system.
p.13
Statistical Analysis of Random Errors
What happens to the confidence in the mean or median value as the spread of measurements decreases?
The smaller the spread of the measurements, the more confidence we have in the mean or median value calculated.
p.12
Statistical Analysis of Random Errors
What is the formula for calculating the mean value of a set of measurements?
x mean = (x1 + x2 + ... + xn) / n.
p.14
Statistical Analysis of Random Errors
How does the number of measurements affect confidence in the mean value?
Confidence in the mean value increases as the number of measurements increases.
p.12
Statistical Analysis of Random Errors
How is the median calculated for an even number of measurements?
It is the average of the two center values.
p.7
Sources of Systematic Errors
What are the three possible reasons for a reading of 1.0 kg on the scales?
1) A 0.9 kg rat in the box (real input), 2) An empty box with a 0.9 kg bias due to temperature change (environmental input), 3) A 0.4 kg mouse in the box with a 0.5 kg bias (real + environmental inputs).
p.7
Techniques for Reducing Systematic Errors
What should be considered when choosing connecting leads for measurement systems?
They should be of adequate cross-section to minimize resistance and adequately screened to prevent induced noise.
p.8
Techniques for Reducing Systematic Errors
What is a key consideration in the design of strain gauges?
Using materials with a very low temperature coefficient.
p.3
Impact of System Disturbance on Measurements
What effect does a voltmeter have when measuring voltage across a resistor?
It acts as a shunt resistance, decreasing the resistance and disturbing the circuit.
p.3
Impact of System Disturbance on Measurements
How can the extent of disturbance in a circuit be assessed?
By calculating the open-circuit voltage and comparing it with the measured voltage.
p.8
High-Gain Feedback in Measurement Systems
What is the benefit of adding high-gain feedback to measurement systems?
It helps to mitigate the effects of environmental inputs on the measurement.
p.13
Statistical Analysis of Random Errors
What is the effect of using n instead of n - 1 in variance and standard deviation calculations?
It produces a value that is statistically less accurate for finite data sets.
p.7
Environmental Inputs and Their Effects on Measurements
Why is it difficult to avoid environmental inputs in measurements?
Because it is often impractical or impossible to control the environmental conditions surrounding the measurement system.
p.7
Sources of Systematic Errors
What common source of error arises from connecting leads in measurement systems?
Failure to account for the resistance of connecting leads.
p.2
Quantification of Measurement Errors
What is the confidence level that can be assigned to measurements affected by random errors?
Typically 95% or 99%, but never 100%.
p.7
Impact of System Disturbance on Measurements
How did changing the routing of cables affect induced noise in the author's experience?
It reduced the magnitude of the induced noise by a factor of about ten.
p.10
High-Gain Feedback in Measurement Systems
What is the significance of the gain constants Ka, Km, and Ks in the context of environmental inputs?
Their sensitivity to environmental inputs becomes irrelevant with high-gain feedback.
p.12
Statistical Analysis of Random Errors
What is the median value for a set of 9 measurements arranged in order?
x5 (the fifth measurement).
p.11
Techniques for Reducing Systematic Errors
How can a measurement technician reduce errors in output readings?
By calculating the effect of systematic errors and making appropriate corrections to the instrument readings.
Why is instrument calibration important in measurement systems?
Instruments suffer drift in their characteristics, affecting accuracy.
p.3
Impact of System Disturbance on Measurements
How does the measurement process generally affect the system being measured?
It always disturbs the system and alters the values of the physical quantities being measured.
p.8
Techniques for Reducing Systematic Errors
What does the method of opposing inputs do in a measurement system?
It introduces an equal and opposite environmental input to cancel out the effect of an environmental input.
p.1
Types of Measurement Errors: Systematic and Random
What are systematic errors?
Errors that consistently occur on one side of the correct reading, either all positive or all negative.
p.12
Statistical Analysis of Random Errors
Which measurement set should we have more confidence in and why?
Measurement set B, because the measurements are much closer together.
p.2
Types of Measurement Errors: Systematic and Random
What are random errors?
Perturbations of the measurement either side of the true value caused by random and unpredictable effects.
p.2
Sources of Systematic Errors
What is a common source of random errors in measurements?
Human observation of an analogue meter, especially during interpolation.
p.11
Statistical Analysis of Random Errors
What are random errors in measurements?
Unpredictable variations in the measurement system that result in small perturbations around the correct value.
p.6
Measurement and Instrumentation Principles
What is one way to overcome the sensitivity issue in a moving-coil voltmeter?
By changing the spring constant of the restraining springs.
p.6
Measurement and Instrumentation Principles
What is a consequence of changing the spring constant in a voltmeter?
It reduces the ruggedness of the instrument and requires better pivot design.
p.6
Errors due to environmental inputs
Why must calibration conditions be closely reproduced?
Because deviations can cause measurement errors due to variations in instrument characteristics.
p.1
Sources of Systematic Errors
How are inherent errors in instruments quantified?
By the accuracy figure quoted in the instrument's published specifications.
p.4
Introduction to Measurement Errors
What is the purpose of the circuit in Fig. 3.1(a)?
To measure the voltage across R5.
p.4
Introduction to Measurement Errors
How is R_AB calculated according to the provided formula?
R_AB = (R4 + R_CD) || R5.
p.10
High-Gain Feedback in Measurement Systems
What is a potential drawback of using high-gain feedback?
It may cause instability in the measurement system.
p.1
Quantification of Measurement Errors
What is the importance of reducing errors in measurement systems?
To minimize errors to the lowest possible level and quantify the maximum remaining error.
p.6
Errors due to environmental inputs
What is an environmental input in a measurement system?
An input caused by a change in the environmental conditions surrounding the measurement system.
p.1
Sources of Systematic Errors
What can cause systematic errors in measurement instruments?
Bent meter needles, uncalibrated instruments, drift in instrument characteristics, and poor cabling practices.
p.13
Statistical Analysis of Random Errors
How is the variance (V) calculated?
V = (d1² + d2² + ... + dn²) / (n - 1).
p.13
Statistical Analysis of Random Errors
Why do the expressions for variance and standard deviation differ from formal mathematical definitions?
Because they are for finite data sets, using n - 1 instead of n in the denominator.
p.10
High-Gain Feedback in Measurement Systems
What is the primary function of high-gain feedback in measurement systems?
To reduce the system's sensitivity to environmental inputs.
What factors influence the rate of drift in instrument characteristics?
Environmental conditions and frequency of use.
p.8
Techniques for Reducing Systematic Errors
How can careful instrument design help in reducing systematic errors?
By reducing the sensitivity of an instrument to environmental inputs.
p.8
Techniques for Reducing Systematic Errors
How does the compensating resistance work in a milli-voltmeter?
It has a temperature coefficient that is equal in magnitude but opposite in sign to that of the coil.
p.1
Sources of Systematic Errors
What are two major sources of systematic errors?
System disturbance during measurement and environmental changes.
p.13
Statistical Analysis of Random Errors
What does the median value tend towards as the number of measurements increases?
The median value tends towards the mean value.
p.6
Errors due to environmental inputs
What challenge arises when modifying inputs are present in a measurement system?
It becomes difficult to determine the cause of output changes—whether from the measured variable or environmental conditions.
p.12
Statistical Analysis of Random Errors
How is the median value determined from a set of measurements?
It is the middle value when the measurements are arranged in ascending order.
p.1
Techniques for Reducing Systematic Errors
What is the starting point to reduce measurement errors?
A detailed analysis of all error sources in the system.
p.10
High-Gain Feedback in Measurement Systems
What does the equation X0 = Ei / Kf signify in the context of high-gain feedback?
It shows the relationship between output X0 and input Ei, simplified to involve only Kf.
p.6
Measurement and Instrumentation Principles
What is a key constraint in designing a moving-coil voltmeter?
Achieving high internal resistance can decrease measurement sensitivity.
p.6
Measurement and Instrumentation Principles
What is the effect of increasing the coil turns on the current in a moving-coil voltmeter?
It decreases the current flowing in the coil, leading to less magnetic torque.
p.5
Impact of System Disturbance on Measurements
What is the relationship between current (I) and the resistances in a circuit with a measuring instrument?
I = E0 / (RAB + Rm), where Rm is the resistance of the measuring instrument.
p.3
Impact of System Disturbance on Measurements
What is the first step in calculating equivalent resistance in a circuit?
Identifying series and parallel resistances and calculating their equivalent resistances.
p.13
Statistical Analysis of Random Errors
What are the two better ways to express the distribution of measurements?
Variance and standard deviation.
p.4
Introduction to Measurement Errors
What does the formula for R_AB indicate about the relationship between resistances?
It shows how resistances combine in parallel and series.
p.6
Measurement and Instrumentation Principles
How can the input impedance of a moving-coil voltmeter be increased?
By increasing the number of turns in the coil or using higher-resistance material.
p.3
Impact of System Disturbance on Measurements
What is a significant example of measurement disturbance?
The use of an orifice plate in a fluid-carrying pipe, which causes permanent pressure loss.
p.11
Statistical Analysis of Random Errors
How can random errors be minimized?
By calculating the average of a number of repeated measurements.
p.5
Techniques for Reducing Systematic Errors
How does increasing the resistance of the measuring instrument (Rm) affect the measurement ratio (Em/E0)?
As Rm gets larger, the ratio Em/E0 gets closer to unity, minimizing disturbance.
p.12
Statistical Analysis of Random Errors
Under what condition is the mean value considered the most likely true value?
When measurement errors are distributed equally about the zero error value.
p.13
Statistical Analysis of Random Errors
What is the standard deviation (σ) in relation to variance?
The standard deviation is the square root of the variance.
p.4
Introduction to Measurement Errors
What is the expression used to substitute for R_CD in the calculation of R_AB?
R_CD = [(R1 + R2)R3] / (R1 + R2 + R3 + R4).
p.1
Types of Measurement Errors: Systematic and Random
What are the two main categories of errors in measurement systems?
Systematic errors and random errors.
p.3
Impact of System Disturbance on Measurements
What is Th´evenin’s theorem used for in electric circuits?
It helps analyze system disturbance during measurements by simplifying the circuit.
p.1
Quantification of Measurement Errors
What complicates the final output from a measurement system?
The final output is calculated by combining measurements of separate physical variables.
p.2
Sources of Systematic Errors
What is the effect of parallax in manual measurements?
It can introduce a systematic error if the observer consistently reads from one side of the scale.
p.3
Impact of System Disturbance on Measurements
What is the purpose of defining equivalent resistance using Th´evenin’s theorem?
To simplify the analysis of complex circuits by replacing them with a single resistance and voltage source.
p.6
Errors due to environmental inputs
What are sensitivity drift and zero drift?
Constants that quantify variations in instrument characteristics due to environmental changes.
p.13
Statistical Analysis of Random Errors
Why is using the range between the largest and smallest value not a good way to examine measurement distribution?
It does not effectively express how the measurement values are distributed about the mean value.
p.14
Statistical Analysis of Random Errors
What happens to V and σ as the spread in measurement sets decreases?
Greater confidence that the calculated mean or median value is close to the true value.
p.2
Sources of Systematic Errors
What can cause systematic errors in instruments?
Manufacturing tolerances, wear in components, environmental disturbances, and measurement disturbances.
p.5
Impact of System Disturbance on Measurements
What happens to the voltage across AB when a measuring instrument is connected?
The voltage across AB is reduced by the ratio given by Em/E0 = Rm / (RAB + Rm).
p.12
Statistical Analysis of Random Errors
What are the two ways to express the average value of a set of measurements?
Mean value and median value.
p.12
Statistical Analysis of Random Errors
As the number of measurements increases, what happens to the difference between the mean and median values?
The difference becomes very small.
p.12
Statistical Analysis of Random Errors
What are the mean and median values for measurement set B?
Mean = 406.0, Median = 407.
