EC 217 MEASUREMENTS AND INSTRUMENTATION Chapter #1 Measurement and Error

Introduction Measurement is the process of comparing unknown quantity with an accepted standard quantity. It involves connecting a measuring instrument into the system under consideration and observing the resulting response of the instrument.

Basic definitions Instrument: It is a device for determining the value or magnitude of a quantity. Accuracy: It is the closeness of the measured value with the true value. Precision: It is the degree of agreement within a group of readings Sensitivity, S: The ratio of the output signal or response of the instrument to a change in the input variable. Resolution , R : Smallest change in a measured value to which the instrument will respond (can identify it). Error, e: Deviation of the measured value from the true one e = measured value – true value 1.1

Basic Definitions (cont.) Absolute error, ea : ea = e = xm – xt 1.2 where ea = absolute error. xt = expected value (true value). xm = measured value. Percentage relative error : 1.3

Accuracy and Precision Accuracy: refers to the degree of closeness or conformity to the true value of the quantity under measurement. Precision: refers to the degree of agreement within a group of measurement or instruments. Good accuracy: means good precision. Good precision: does not have to mean good accuracy. The accuracy, precision and error depend on the instrument and the person. But the sensitivity and resolution depend on the instrument only.

Significant Figures An indication of the precision of the measurement is obtained from the number of significant figure in whish the result is expressed. For example if a resistor is specified as having a resistance of 68 Ω then the number of significant figure is two. But if a resistor is specified as having a resistance of 68.0 Ω then the number of significant figure is three. Case 1 : 67 Ω, 68 Ω, 69 Ω Error = 1 Ω Case 2 : 67.9 Ω, 68.0 Ω, 68.1 Ω Error = 0.1 Ω

Notes In addition or subtraction, the integer number must not changed and the number of decimals in the output must be equal to the lowest one after round, i.e. the result is only as accurate as the least acceptable measurement . For multiplication or division, the significant figure of the product must be equal to the significant figure of the least one of coefficients.

Types of Errors Any measurement is affected by many variables therefore the results is deviated from the expected value for example connecting the measuring instruments into the circuit under consideration always disturbs (changes) the circuit causing the measurement to differ from the expected value. Some factors that affect measurements are related to the instruments themselves, other factors are related to the person using the instrument, i.e. errors may come from different sources.

Types of Errors (cont.) Gross errors. Systematic errors. Random errors.

Gross Errors Covers human mistakes in reading or bad usage of the instruments or incorrect calculating the measurement results. Also covers the incorrect adjustment for the instruments. (Zero adjustment).

Systematic Errors 1. Instrumental errors: Which are inherent in measuring instruments because of their mechanical structure such as movement friction in the bearing, irregular spring tension, reduction in tension or overloading. These errors may be avoided by selecting a suitable instrument, applying correction factors after determining the amount of instrumental error and calibrating the instrument against standard.

Systematic Errors (cont.) 2. Environmental errors These errors are due to the external conditions such as temperature, magnetic field, and humidity that can effect in the reading. These errors may be avoided by shielding the measuring instrument.

Random Errors These errors are due to unknown reasons and occur even when all systematic errors have been accounted for. The only way to avoid or decrease these errors is by increasing the number of reading and using statistical analysis to obtain best approximation.