Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

-  Mathematics A1, A2, and some parts of A4 (probability theory)

A kötelező előtanulmányi rend az adott szak honlapján és képzési programjában található.

The aim of the course is to provide knowledge on the planning, execution and evaluation of measurements, focusing on the measurement of quantities of particular importance to electrical engineers. The theoretical and practical content of the course emphasizes that measurement is a process of modeling signals and engineering systems, not merely determining the quantitative or qualitative value of a quantity. Students will be able to evaluate the data of any measurement procedure, to give the measurement result with the associated accuracy information (uncertainty), to be familiar with the procedures and instruments for measuring basic quantities in electrical engineering practice, and to apply signal processing tools to solve measurement problems.

Lecture

1. Introduction. Aim of the subject, main topics. Connection between measurement and modeling. Basic measurement methods. Measurement errors: absolute and relative error.
2. Measurement errors: bias and random error. Error propagation (1): mathematical model. Addition of errors. Examples.
3. Error propagation (2), examples. Offset, gain, linearity, hysteresis, and quantization error. Curve fitting. Fitting of line and polynomial.
4. Evaluation of measurement data: mathematical model, averaging, variance of the average, sample standard deviation. Confidence calculus (1). Utilization of normal, chi-square, and Student-t distribution. Derivation of the distributions and formulas.
5. Confidence calculus (2). Chebyshev inequality. Overview of basic confidence problems. Utilization of confidence calculus for error evaluation.
6. Measurement of voltage and current. Structure of analog and digital meters. Extension of the range, input resistance. Errors of the meters and their evaluation.
7. AC measurement. Representation of AC signals: Fourier series, different mean values, dB scale. Comparison of meters of different measurement principles. Description of the noise, signal to noise ratio, noise filtering.
8. Signal transformers: Introduction to non-ideal behavior of passive elements (resistor, capacitance, inductance). Voltage dividers: resistive, inductive, and capacitive divider. Compensated resistive divider.
9. Signal transformers: Voltage and current transformer. Overview in electronics: basic amplifier circuits, instrumentation amplifiers. Application possibilities.
10. Impedance measurement: DC low accuracy methods, series and shunt ohmmeter. AC measurement: impedance models. Connection between mathematical and physical models. AC low accuracy methods. Power measurement.
11. Impedance measurement: voltage comparison method. High accuracy methods, Wheatstone-type bridge circuits. Examples. Ratio transformer and current comparator based bridges. 
12. Canceling parasitic impedances. Disturbance sensitivity of measuring circuits: application of shielding. Canceling of the effect of cabling and stray impedances. 2, 3, 4, and 5 wires methods. In-circuit measurement. Overview of the complete impedance measurement problem.
13. Time and frequency measurement. Counter based frequency, period, and average period meter. Error analysis. Constant gate time period time meter. Digital phase shift measurement.
14. Analog and digital oscilloscope. Conditions for displaying a right graph: the role of trigger logic/circuit. Oscilloscope functions. Signal processing overview: sampling theorem and its applications.
15. Spectrum analysis. Analog methods: parallel, tuned filter, and heterodyne spectrum analyzer. Application of the discrete Fourier transform. Windowing.
16. Analog to digital converters: flash, successive approximation, dual-slope ADCs. Subranging ADC. The role of short time and long time stability. Calculation of conversion time, noise suppression.
17. Digital to analog converters: ladder DACs. Switched capacitor DACs. Comparison of different types of ADCs and DACs. Errors of ADCs and DACs: integral and differential nonlinearity.
18. Quatization error, the noise model of quantization. Effect of sampling on quantization noise. Calculation of effective number of bits. Structure and operation of delta-sigma ADCs and DACs.
19. Simple signal processing tasks: moving average and exponential average filtering. Applications of finite and infinite impulse response (FIR and IIR) filters.
20. Typical structure of measurement equipment, stand-alone, modular and distributed systems.
21. Reserved for compensation of any delay (fallen lectures, slow pace, etc.)

Practice

The 2-hour weekly classroom exercises include the solutions of problems related to the topics covered during lectures.

Laboratory

Laboratory exercises last on average 1 hour per week and are conducted in 4 3-hour long sessions. The topics of each laboratory exercise are as follows:

1. Measurement equipment 1: Introduction to power supplies, multimeters and other voltage and current measuring instruments, function generators, oscilloscopes.
2. Measurement equipment 2:  Continuing the study and practice of the above instruments.
3. Basic measurements: Deepening the knowledge of instruments by measurements on simple circuits.
4. Data loggers: Sampling and recording of a voltage source. Determining the appropriate sampling frequency, displaying the sampled signal, performing simple processing tasks.

During the semester

a. one mid-term exam must be written with at least 40% of the maximum points
b. it is not obligatory to make reports on the laboratory but we expect active participation
c. presence on practice sessions (maximum 4 can be missed)

In the exam period

The exam must be written with at least 40% of the maximum points

The mark will be determined by weighting the results of the mid-term exam and the final exam with a ratio of 1/3 and 2/3, respectively. At least 40% of the total points is required to obtain a pass mark.

The mid-term exam can be repeated on an organized repeated mid-term exam during the semester, and on a 2nd organized repeated mid-term in the repetition period following the semester.

Only one laboratory exercise can be repeated.

[1] Schnell, L. (Ed.): Technology of Electrical Measurements. Wiley, 1993.