EEN3 Lab Tutorial Script PDF

Christoph Diendorfer Laboratory tutorials Page 1 of 32 Laboratory Tutorials Electrical Engineering III Author...

Christoph Diendorfer Laboratory tutorials Page 1 of 32 Laboratory Tutorials Electrical Engineering III Author Christoph Diendorfer MSc BSc. WS 2023/24 https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 2 of 32 Preface Laboratory exercises will consolidate your knowledge in “Electrical Engineering”. You will get experienced by applying theory and calculus. This script is a guide for the laboratory tutorials “Electrical Engineering III”. It covers the description for the single exercises as well as hints for the organization and the essential organization of the course. Use this script for an optimal preparation for the individual exercises. The goal is to guide you to solve autonomous real “Electrical Engineering” measurement and scientific problem definitions. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 3 of 32 Content 1 Organization......................................................................................................................... 5 1.1 Attendance.................................................................................................................... 5 1.1.1 Second attempt......................................................................................................... 5 1.2 SAFETY ASPECTS..................................................................................................... 5 1.3 Grades........................................................................................................................... 6 1.3.1 Submission of preparation.......................................Error! Bookmark not defined. 1.3.2 Written exam............................................................................................................ 6 1.3.3 Laboratory report...................................................................................................... 6 2 General introduction............................................................................................................. 7 2.1 Laboratory procedure................................................................................................... 7 3 Exercises............................................................................................................................... 8 3.1 Electrostatic field.......................................................................................................... 8 3.1.1 Goal of the exercise.................................................................................................. 8 3.1.2 Theory...................................................................................................................... 8 3.1.2.1 Basic considerations........................................................................................ 8 3.1.2.1.1 The electrostatic field for special geometries........................................... 12 3.1.2.1.1.1 Spherical arrangement....................................................................... 12 3.1.2.1.1.2 Concentric coaxial arrangement........................................................ 12 3.1.2.1.1.3 Plate plate arrangement..................................................................... 12 3.1.3 Exercise guide and instructions.............................................................................. 13 3.1.3.1 Capacitors..................................................................................................... 13 3.1.3.1.1 Circuit and post processing....................................................................... 13 3.1.3.1.1.1.1 AC Measurement........................................................................ 13 3.1.3.1.1.1.2 Pulse Measurement..................................................................... 14 3.1.3.1.2 Arrangements............................................................................................ 14 3.1.3.1.2.1 Plate plate capacitor........................................................................... 14 3.1.3.1.2.2 Coaxial capacitor............................................................................... 15 3.1.3.2 Electric field.................................................................................................. 15 3.1.3.2.1 Circular / circular arrangement................................................................. 16 3.1.3.2.2 Other configurations................................................................................. 16 3.1.4 Typical introductory questions............................................................................... 16 3.2 Magnetic Circuits and Electro Mechanic Actuators.................................................. 17 3.2.1 Goal of the exercise................................................................................................ 17 3.2.2 Theory.................................................................................................................... 17 3.2.2.1 The magnetic circuit...................................................................................... 17 3.2.2.1.1 Ferromagnetic effects............................................................................... 18 3.2.2.2 Electro mechanic actuators........................................................................... 21 3.2.3 Exercise guide and instructions.............................................................................. 24 3.2.3.1 Magnetic hysteresis, current / voltage distortion and in inrush current........ 24 3.2.3.2 Loudspeaker.................................................................................................. 24 3.2.4 Typical introductory question................................................................................ 25 3.3 Electric lines............................................................................................................... 26 https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 4 of 32 3.3.1 Goal of the exercise................................................................................................ 26 3.3.2 Exercise guide and instructions.............................................................................. 26 3.3.2.1 Determination of the specific line parameter................................................ 26 3.3.2.1.1 Determination of the specific line resistance............................................ 26 3.3.2.1.2 Determination of the specific line conductivity....................................... 26 3.3.2.1.3 Determination of the specific capacity..................................................... 27 3.3.2.2 Determination of the characteristic impedance............................................. 27 3.3.2.3 Determination of the frequency plot of the input impedance of a line......... 27 3.3.2.4 Determination of wave propagation and investigating the reflection at different terminations.................................................................................................................... 27 3.3.2.4.1 Exercises................................................................................................... 28 3.3.3 Typical introductory questions............................................................................... 29 4 Literature............................................................................................................................ 30 5 Appendix............................................................................................................................ 31 5.1 Magnetics Exercise.................................................................................................... 31 5.1.1 Measurement setup hysteresis................................................................................ 31 5.1.2 Desired result.......................................................................................................... 31 5.2 Excel Sheets for Documentation of the Exercise....................................................... 32 https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 5 of 32 1 Organization 1.1 Attendance An attendance of 100% is required. If one exercise will be or has been missed, please check, whether you may attend in another group for the specific exercise. Changing the group for one exercise is possible only in case of urgent reasons (e.g. illness, you need a doctor’s certificate in this case). If one exercise is missed without any attending in any other group, the first attempt of the laboratory tutorial is negative. The student has to take the second attempt automatically. It is highly recommended, to attend the rest of the exercises although the second attempt has to be taken as a form of preparation for the second attempt. 1.1.1 Second attempt For the second attempt all exercises of these laboratory exercises will be covered. The examination procedure will be as listed below Doing a written exam covering all exercises. This exam must be positive (otherwise the whole second attempt is negative and the next steps will not be performed) Selection / definition of a specific problem statement by the examiner The student has to o Develop a measurement circuit o Develop a measurement procedure o Install the circuit o Taking measurements o Interpret the measurements After each step, the examiner has to be consulted. The lecturer will discuss this step with the student. Each discussion will be considered for the final grade. 1.2 SAFETY ASPECTS You have to follow the instructions of the supervisor strictly. In case of any violence an exclusion from the exercise is the consequence. The following fife safety rules have to be considered at any time and have to be memorized: Switch off all poles and all feedings of the circuit which has to be modified Lock against reclosure o Signs, locking, remove fuses,… Check that lines and equipment dead Ground and short circuit phases o Ground at first Cover, partition or screen of adjacent line or other energized sections Additionally all further instructions given in the introductive lecture and before every exercise are absolutely valid. It has to be emphasized, that the universities safety test for laboratory exercises has been passed successfully. Any endangering of the students, or the health of the colleges will cause an exclusion from the course! Also, wanton destruction of equipment will cause an exclusion immediately. Consumption of alcohol before or during the exercise is strictly prohibited! https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 6 of 32 1.3 Grades The grading covers the following items: Written exam before the begin of every exercise (50%) Laboratory report (50%) Both parts have to be completed positively. 1.3.1 Written exam Every student of the group has to write an exam in the begin of the laboratory exercise. It covers the theory of the specific exercise. You find the theory in your scripts of the lectures, skills practice as well as in this document. Also the exercise specific descriptions (theory, handling instructions of the measurement equipment, measurement approach…) and the general instructions and information’s of this document have to be present. Read the exercise instructions carefully, and memorize it. In case of questions ask some days before the exercise starts. Please understand that immediately before the exercise questions cannot be answered anymore, you should have been prepared for this exercise already. 1.3.2 Laboratory report Every group has to prepare one laboratory report per exercise. For every exercise one laboratory report responsible has to be defined by the group. Per semester every group member must have been responsible at least once a time. The report must be submitted via Moodle by the next lab date, and a printed version must be taken to the next lab. Submission after the Moodle deadline causes a grading 5 for all report group members. A new deadline will be set automatically (two weeks). Missing the second deadline, a 5 will be the result for the specific report. The IEEE template is used as the template. Read the guidelines carefully. Any change to the template (graphical etc.) will be judged negatively. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 7 of 32 2 General introduction 2.1 Laboratory procedure For all tutorials please consider the following process: 1. Prepare yourself by studying the instructions of the exercise with sufficient time prior to the exercise at home, prepare the required documents (see chapter Error! Reference source not found.) 2. Written introductory exam 3. At the exercise install the specific circuit 4. Check the circuit 5. Get the approval from the tutor 6. Energize the circuit in case of a positive approval of the lecturer only Violation of this step causes an exclusion from the exercise 7. Carry out the measurements 8. Put your measurement data to your prepared Excel Sheets immediately Compare it to the expected theory results (diagrams and values) 9. In case of a modification of the circuit, de-energize it and get the reenergizing approval from the tutor to energize it again Violation of this step causes an exclusion from the exercise 10. At home do the final data post processing and prepare the report Any violation of this procedure (especially item 5,6, and 9!) causes an immediate exclusion from the exercise because of safety and didactic reasons! https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 8 of 32 3 Exercises 3.1 Electrostatic field 3.1.1 Goal of the exercise The goal of the exercise is to understand the governing effects for the formation of electrostatic fields. This covers especially the electric field distribution for special geometries. A further aspect is the calculation and experimental determination of capacitor values for specific geometries. 3.1.2 Theory The electrostatic field describes the effects of the force observed in between two charged charge carriers. If there is any slow change of the electric field with respect to time, the field is called quasi-static. In case of no time dependency stationary electric or electrostatic field. For one specific moment a quasi-static field may be considered as electrostatic. Further considerations in this document are considering a stationary electric field only. For such type of fields the boundary conditions have to be stationary too. 3.1.2.1 Basic considerations Assuming a plate capacitor in a neutral situation (single plates are uncharged) and removing one electron (with a charge of 𝑄) from one plate, transferring it to the second plate and depositing it there1, a force 𝐹⃗ acting onto the electron will be observed (see Figure 1): 𝐹⃗ = 𝑄𝐸⃗⃗ (1) Force acting onto the electron: Because of the minim energy principle the force onto the electron is acting into a direction to yield a recombination with the plate where the electron has been removed2 After deposition of the electron at the end position, a force between the plates is observed. Its origin may be found in the opposite charge of the two electrodes The definition of an electric field is the observed force per charge carrier (see equation (1)). Since along the path 𝑠⃗ work 𝑊 has to be feed to the system according to the general valid equation (2). Work only has to be invested if there is a path component existing which is parallel to the field vector 𝐸⃗⃗. ⃗⃗⃗⃗ = ∫2 𝐹⃗ ∙ 𝑑𝑠⃗ 𝑊 (2) 1 With growing distance from the plate, where the electron has been removed, the energy level of the electron grows. The energy level is defined by the term “electric potential” 𝜑 and will be indicated by equi-potential lines. Since the energy level changes with a path component parallel to the field vector only, the equipotential lines must be orientated perpendicular to the field lines (see Figure 2). 1 This can be realized by applying a voltage between the two plates; the voltage will charge the capacitor which simply means to shift charge carriers. 2 Compare this effect with the climbing of a hill. The force acting onto the climber tries to bring him into its original position with minimum potential energy. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 9 of 32 Figure 1: Charge displacement at capacitor plates. Figure 2: Equipotential and field lines between parallel capacitor plates (uniform (German “homogenes”) field). Note: since at electrodes the potential is independent from the location at or in the electrode3, a conductive electrode always represent a potential line! In general, electric fields are nonuniform. A simple nonuniform field is the electric field between to equally charged charge carriers with different polarity. Considering such a situation between to spherical charge carriers 𝑄1, 𝑄2 with a given center distance of 𝑟⃗12 4 the observed force can be described by equation (3). 3 In case of any potential difference a force acc. to equation (1) acts onto the charge carriers. Hence they will be displaced as long as there is no electric field anymore. Consequently the electric field in the inner of an electrode must be zero and thus any electrode forms an equipotential area! 4 Pointing from the center 1 to the center 2. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 10 of 32 Figure 3: Resulting force vectors between two equally and oppositely charged charge carriers 𝑸𝟏 and 𝑸𝟐. 1 𝑄 𝑄 𝑟⃗ 𝐹⃗ = 4𝜋𝜀 𝑟1 2 2 |𝑟⃗12 | 5 (3) 12 Introducing the definition (1) the electric field for one charge carrier 𝑄 is given by equation (4). 1 𝑄 𝑟⃗ 𝐸⃗⃗ = 4𝜋𝜀 𝑟 2 |𝑟⃗12 | (4) 12 Considering this equation, the field plot of such a single charge carrier results in Figure 4. Figure 4: Electrostatic field of a single spherically charge. Note, that according to equation (4) the change of the electric field is larger (with growing distance from the charge center) close to the space charge center. Consequently, the iso-potential lines must be denser close to the charge carrier compared to the iso-potential line inter distance far from the center. Considering the discussions above, that iso-potential lines always have to intersect perpendicular to the field lines the field lines must show increasing spacing density with lower distance to the charge center. Thus it is a general valid and very essential conclusion, that densely spaced field lines indicate a high electric field and vice versa6. This can be derived from an analogy between electrostatic and electric flow fields too: Considering a total electric charge 𝑄𝑡 as a source for an electric flux density 𝐷 ⃗⃗ the conservation law for flux indicates, that in the inner of a so called “flux tube”, indicating that volume, where the absolute electric flux 𝑄 is constant, the flux density must be higher with lower cross section of the flux tube (see equation (5) and Figure 5). ⃗⃗ ∙ 𝑑𝐴⃗ 𝑄𝑡 = ∫ 𝑑𝐷 (5) 5 Note: this equation is analogue to the force equation in a gravity field. 6 NOTE: analyze the field plots in the field simulation results document “LaboratoryTutorialElectricalEngineeringIII_FieldSimulation” which corresponds to this document, with respect to the appearance of the field and iso-potential lines. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 11 of 32 Since the correlation between a flux and the corresponding field is assumed to be linear (see the equation connecting the current density 𝑆⃗, the electrical conductivity 𝜎 and the electrical field 𝐸⃗⃗ ⃗⃗ represent the field lines 𝐸⃗⃗ too, according to equation (7). in equation (6)) the flux density lines 𝐷 𝑆⃗ = 𝜎𝐸⃗⃗ (6) ⃗⃗ = 𝜀𝐸⃗⃗ 𝐷 (7) Note that for the dielectric flux density the term “dielectric displacement” is common too! The (material property!) constant 𝜀 is called (dielectric) permittivity or dielectric constant of matter7. Figure 5: Flux tube, covering a constant electric flux 𝑸. Based on the considerations above the closed surface integral along any surface must yield the total charge 𝑄𝑡 enclosed by the surface according to equation (5). This integral law is known as the “Gauss’s Law”. A further consideration is a “macroscopic” definition describing the relation between the electric resulting electric flux 𝑄 excited by a given potential difference 𝑈. The relation is linear with a constant 𝐶 called capacitance (which is influenced by the material and geometry only!) according to equation (9). Relation (9) is an arbitrary definition! 𝑄 = 𝐶𝑈 (9) Additionally, any potential difference (voltage 𝑈) can be considered as the work 𝑊 which has to be in invested if a charge 𝑄 is displaced from the potential 𝜑1 to 𝜑2 according to equation (10). 2 2 − ∫1 𝐹⃗ ∙𝑑𝑠⃗ − ∫1 𝑄𝐸⃗⃗∙𝑑𝑠⃗ 2 𝑈= = = − ∫1 𝐸⃗⃗ ∙ 𝑑𝑠⃗ (10) 𝑄 𝑄 7 For more details see the lecture Electrical Engineering III. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 12 of 32 3.1.2.1.1 The electrostatic field for special geometries 3.1.2.1.1.1 Spherical arrangement The integral (8) may be solved by introducing the surface value 𝐴 of a sphere with a radius 𝑟 according to equation (11) considering, that the dielectric strength must be constant for a constant distance from the charge center which results in equation (12): 𝐴 = 4𝑟 2 𝜋 (11) 𝑄 = 4𝑟 2 𝜋𝐷 (12) Introducing relation (7) and restructuring the result yields equation (13) 𝑄 𝐸 = 4𝜋𝑟 2𝜀 (13) Introducing (13) into (10) and solving the integral yields 𝑄 1 1 𝑈= ( − ) (14) 4𝜋𝜀 𝑟1 𝑟2 describing the voltage difference between the radii 𝑟1 and 𝑟2 caused by a given charge carrier. Considering two opposite charged electrodes of spherical shape centered arranged and with the definition of the capacitance (9) the capacitance between these two spherical electrodes yields 4𝜋𝜀 𝐶= 1 1 (15) ( − ) 𝑟1 𝑟 2 3.1.2.1.1.2 Concentric coaxial arrangement Considering a constant electric field in a constant distance from the center of the cylinder, the surface value of a cylinder with a given length, and longish shaped geometries similar considerations as in chapter 3.1.2.1.1.1 yields 𝑄 𝐸 = 𝑙2𝜋𝑟𝜀 (16) 𝑄 𝑟 𝑈 = 𝑙2𝜋𝜀 ln (𝑟2) (17) 1 𝑙2𝜋𝜀 𝐶= 𝑟 (18) ln( 2 ) 𝑟1 3.1.2.1.1.3 Plate plate arrangement It can be derived very easy that equations (19) to (21) cover a plate plate arrangement where the lateral extension of the electrode, with an area of 𝐴 is large compared to the distance between the plates 𝑄 𝐸 = 𝐴𝜀 (19) 𝑑𝑄 𝑈= (20) 𝐴𝜀 𝐴𝜀 𝐶= (21) 𝑑 https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 13 of 32 3.1.3 Exercise guide and instructions 3.1.3.1 Capacitors 3.1.3.1.1 Circuit and post processing The capacitance should be measured by charging the unknown capacitor 𝐶𝑥 via a known resistor 𝑅 according to Figure 6. Figure 6: Electric circuit for capacitance measurement. NOTE: The voltage probe of the scope must be adjusted to a probe ratio of 1:10! Otherwise the input impedance of the measurement circuit will cause a high measurement error.8 Record the voltages 𝑢𝑖𝑛 (𝑡), and 𝑢𝑅 (𝑡) with an oscilloscope and store the single measurements as csv files. After the exercise (or may be during the exercise by means of prepared excel files) analyze the csv files for AC and (rectangular) pulse function generator adjustments: With AC signals the impedance of the capacitor may be determined and thus the capacitance can be derived With the pulse signals the capacitance from the exponential charging time constant may be derived Consider the general recommendations for operating the oscilloscope. Don’t forget to adjust (compensate) the voltage probes if a probe ratio different form 1:1 is adjusted! Try to realize your test setup with very short connectors! Otherwise parasitic capacitances and impedances will cause a high systematic measurement error. Connect the scope via the insulation transformer. The input coupling mode for the single channels must be adjusted to DC! 3.1.3.1.1.1.1 AC Measurement From the total voltage 𝑢𝑖𝑛 (𝑡), the voltage at the resistor 𝑢𝑅 (𝑡) and the exact resistor value 𝑅, the impedance of the capacitor may be derived. From the frequency the capacitor value can be calculated. 8 Probe setting 1:1 1 M and 95 pF, 1:10 10 M and 16 pF! https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 14 of 32 Another approach would be, to activate following measurements on the oscilloscope: Phase shift between the sinusoidal signals Amplitudes of the signals (Peak peak) Frequency of the signals Noting these values the approach above may be applied without any storage of a csv file. A third and most simple approach is to adjust a frequency where a phase angle of 45° between the signals is measured. This exactly represents the limiting / cut off frequency of the low pass represented by the circuit in Figure 6. The cut of frequency can be determined (according to the theory introduced in Electrical Engineering I) by 1 1 𝜔𝑐 = 𝜏 = 𝑅𝐶 (22). 𝑥 Knowing the frequency 𝑓 the unknown capacitance may be derived. 3.1.3.1.1.1.2 Pulse Measurement In case of a square pulse of sufficient long pulse length the voltage at the resistor will be 𝑡 ̂ 𝑒 −𝜏 𝑢𝑅 (𝑡) = 𝑈 (23). From the stored csv data, a voltage time plot in EXCEL may be generated. This time plot can be compared to a theoretical charging plot according to equation (23). Function (23) may be approximated to the measured function by adjusting the parameter 𝑈 ̂ and 𝜏. If the best fit has been identified the capacitance may be derived from the time constant 𝜏 (see equation (22). The best fit is yield if the sum of the quadratic errors is a minimum. This means the sum of the quadratic errors has to be evaluated in the EXCEL Sheet too. 3.1.3.1.2 Arrangements Two arrangements a plate plate and a coaxial arrangement should be investigated. 3.1.3.1.2.1 Plate plate capacitor Determine the relative permittivity of the provided insulation material. Assemble different plate capacitors and prove, that laminated capacitors acting like single series interconnected capacitors. As an example for a laminated capacitor see Figure 7. Figure 7: Laminated capacitor arrangement. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 15 of 32 3.1.3.1.2.2 Coaxial capacitor Determine the permittivity of the insulation material of a 20 m long coaxial line. Compare the capacity of a coaxial capacitor model with the theoretical value. Determine the capacitance of a coaxial capacitor according to Figure 8. Figure 8: Coaxial capacitor arrangement. Fill the coaxial capacitor with water, determine the capacity and compare the result with theoretical considerations. Derive the permittivity of water and compare it with values from the literature. Note: There is a thin insulation layer at the inner conductor9. Hence the coaxial capacitor hast to be considered as a laminated one! 3.1.3.2 Electric field Since the electric field is directly proportional to the flow field acc. to equation (6), the electric field will be determined by means of an electrolytic tray (see Figure 9). Figure 9: Electrolytic tray. 9 This layer prevents from any current flow between the inner and outside conductor through the water https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 16 of 32 Electrodes will be placed in a salt water filled tray. The potential between the electrodes should be measured and compared to calculations (see document “LaboratoryTutorialElectricalEngineeringIII_FieldSimulation”). NOTE: AC has to be applied in order to avoid any electrolytic reaction! 3.1.3.2.1 Circular / circular arrangement For the theory see lectures and skills practice of Electrical Engineering III. Measure the potential for three different distances and compare it with the theoretical models from the lecture and the skills practice (capacitance of two parallel wires!). The potential is the superimposition of the electric potential of opposite charged cylinders. 3.1.3.2.2 Other configurations For fife other configurations the potential should be measured according to the simulation results of the field simulations (see extra document). 3.1.4 Typical introductory questions This is not a complete list of all possible questions! Coaxial capacitor, derivation of the capacity and field distribution Spherical capacitor, derivation of the capacity and field distribution Plate capacitor, derivation of the capacity and field distribution o Same for laminated plate capacitor ▪ Note the dielectric flux has to be assumed as constant between the two plates, from this the ratio between the field strength’s in the different dielectrics may be derived! How the capacitance may be measured by means of a scope, one resistor and a pulse generator? How the capacitance may be measured by means of a resistor, a scope and a sine generator? Typical permittivity for water, insulation, air Interpretation of the field simulations of the word document “LaboratoryTutorialElectricalEngineeringIII_FieldSimulation” Typical structure of field and potential plots Measurement principles for capacitors Electrolytic tray measurement principle What type of current should be applied (AC or DC) for the measurement of the field distribution in the electrolytic tray? https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 17 of 32 3.2 Magnetic Circuits and Electro Mechanic Actuators 3.2.1 Goal of the exercise The goal of the exercise is to investigate the magnetic hysteresis of a magnetic core and to analyze and understand the electric characteristics of different electro mechanic actuators. 3.2.2 Theory This is a summary of the magnetic theory only. The basic governing principles and formulas are content of the lecture. 3.2.2.1 The magnetic circuit Magnetic circuits are applied to “conduct” the magnetic flux to a volume where the desired magnetic induction should be generated. Air is a very poor magnetic conductor whereas ferromagnetic materials provide very good magnetic conduction performance. Considering equation (24) the magnetic resistance 𝑅𝑚 of a magnetic conductor with a characteristic length 𝑙 a cross section of 𝐴 and a magnetic permeability of 𝜇 yields 𝑙 𝑅𝑚 = 𝜇𝐴 (24)10. Any magnetic flux 𝜙 causes a magnetic voltage drop 𝑉 across a magnetic resistance according to the “Ohms Law of Magnetic Circuits” (see equation (25)). 𝑉 = 𝑅𝑚 𝜙 (25) All single magnetic voltage drops 𝑉𝑖 of a magnetic circuit have to be compensated by a magneto motoric force Θ. This is leading to the Kirchhoff’s voltage law of magnetic circuits: Θ = ∑𝑁 𝑖=1 𝑉𝑖 (26) The same equation may be written if the magnetic field strength 𝐻 is introduced ⃗⃗ ∙ 𝑑𝑙⃗ (27) Θ = ∮𝐻 A magneto motoric force may be excited by means of a coil with 𝑁 turns excited by a current 𝐼 according to equation (28). Θ = 𝑁𝐼 (28) Based on the equations above and analogy considerations with the electric flow field the magnetic flux density (magnetic induction) 𝐵 are defined: 𝑑𝜙 𝐵 = 𝑑𝐴 (29) 𝐵 = 𝜇𝐻 (30) 10 Note: This formula is valid for very long geometries with a constant cross section. For complex geometries the geometric parameter may not be determined. Therefore numerical simulations for magnetic circuits are applied. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 18 of 32 For magnetic circuits the Kirchhoff’s current law is applicable according to equation (31). Kirchhoff’s current law: ∑𝑁 𝑖=1 𝜙𝑖 = 0 (31) Any change of a magnetic flux is linked to a change of the magnetic energy. According to the general laws of inertia11 and specific for magnetic fields according to the Lenz’s law any change of a magnetic flux will cause an induction of a voltage 𝑢(𝑡) 𝑑𝜙 𝑢(𝑡) = − 𝑑𝑡 (32) The magnetic energy 𝑊𝑚 of a volume 𝑆 penetrated by a magnetic field may be calculated by ⃗⃗∙𝐻 𝐵 ⃗⃗ 𝑊𝑚 = ∫𝑆 𝑑𝑆 (33) 2 3.2.2.1.1 Ferromagnetic effects Ferromagnetic materials provide a high magnetic permeability. However the materials characteristics shows strong non linearity as well as a hysteresis effect according to Figure 10. Figure 10: Characteristics of ferromagnetic material. The hysteresis causes extra losses: The area of the hysteresis is proportional to the absorbed energy in case of a full magnetization cycle. Thus materials for electric machines should show a very small hysteresis whereas permanent magnets should show a wide hysteresis (the higher the residual flux density 𝐵𝑟 and the coercive field strength 𝐻𝐶 the more magnetic flux will be sustained in a magnetic circuit). A second (undesired) effect is the distortion of the current or voltage if electric machines with ferromagnetic materials are energized. 11 Any change of an energy state causes a counter reaction which is known as the laws of inertia (e.g. accelerating and decelerating of a car causes a counteracting force) https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 19 of 32 Assuming a simple magnetic circuit according to Figure 11 the application of Kirchhoff’s voltage law yields: 𝑁𝑖 𝐻= (34) 𝑙 Hence the magnetic field strength is directly proportional to the electric current 𝑖. The induced voltage in the second coil may be derived from the Lenz’s law of induction (32). This equation may be solved after the magnetic induction which yields: 1 𝐵 = 𝐴 ∫ 𝑢(𝑡)𝑑𝑡 (35) Figure 11: Simple magnetic circuit. Neglecting the integration constant of the integral (35) i.e. assuming stationary conditions where all transient effects have been dissipated, the magnetic induction is proportional to the induced voltage in the measuring coil. Assuming a sinusoidal voltage the current will be distorted according to Figure 1212. Hence at an inductor with ferromagnetic material either the current or the voltage can be sinusoidal only, the other parameter MUST be distorted. The distortions of either the current or the voltage cause harmonics which will cause extra losses in the electric grid and electric machines. Considering the integration constant of the integral (35) at sinusoidal excitation the magnetic flux in the core yields ̂ ̂ sin(𝜔𝑡) 𝑑𝑡 = 𝑈 cos(𝜔𝑡) + 𝑐 𝜙 = −∫𝑈 (36) 𝜔 And specially for a start point of the integration of 𝑡1 : 𝑡 ̂ 𝜙 = − ∫𝑡 𝑈̂ sin(𝜔𝑡) 𝑑𝑡 = 𝑈 {cos(𝜔𝑡) − cos(𝜔𝑡1 )} (37) 1 𝜔 12 This consideration is valid for one coil too. In the considerations Figure 12 the hysteresis is neglected. In case of considering any hysteresis the distortion will become more intensive. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 20 of 32 Figure 12: Current distortion at a ferromagnetic material. The influence of the starting time point of the integration of a sinusoidal function is illustrated in Figure 13. Figure 13: Effect of the starting time point onto the integration constant of a sinusoidal function. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 21 of 32 Starting the integration at 0° or 180° electrically the integration constant becomes a maximum value of the amplitude value of the sinusoidal function. Hence the maxima in such a case are double of the amplitude. Considering (37) it can be concluded, that double of the magnetic flux (and magnetic flux density) will be excited in case a magnetic circuit is energized (switched on) at 0° and 180° electrically (at any zero crossing of the sinusoidal function). A magnetic circuit is designed in a way that the nominal flux density shows a magnitude of the knee point value of the magnetization curve (typically 1,5 T). Corresponding to this induction the nominal magneto motoric force and based on (31) the nominal current will be measured (see Figure 14). In case of doubling the flux density and because of the saturation of the magnetic characteristics of the ferromagnetic core incredible high current will appear in case of switching on the circuit in the zero crossings of the source voltage. This current is called inrush current and can reach a value of typically ten times of the nominal value. Figure 14: Excitation current of a magnetic circuit as a function of the magnetic flux or magnetic flux density respectively. 3.2.2.2 Electro mechanic actuators The purpose of electro mechanic actuators is to convert electric energy into mechanic energy and vice versa. Typically this conversion is realized via magnetic circuits13. Generally a feedback of the mechanic system to the electric system is observed at electro mechanic actuators. A very simple electro mechanic actuator is a loud speaker. A cross section of a loudspeaker is given in Figure 15. A diaphragm is driven by a coil (excited electrically by the output power of any music amplifier). The magnetic force is counteracting a spring mechanism (see Figure 15 “surround” and “spider”) which drags the diaphragm into the direction of its original position. A permanent magnet is sustaining a magnetic flux density in order to generate a current proportional force in the cylindrically shaped air gap. 13 Electric converter making use of the electrostatic force are applied for micro mechanic systems or sensors only https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 22 of 32 Figure 15: Cross section of a loudspeaker. Figure 16 shows the relevant components to analyze the magnetic circuit and the magnetic force of the loudspeaker. Figure 16: Magnetic circuit of a loudspeaker. The force acting onto the membrane can be derived from the Lorentz’s force rule in correspondence to Figure 16. 𝐹 = 𝐵𝑁𝑖(𝑡)𝑑𝜋 (38) Introducing the deflection 𝑥 of the diaphragm the mass of the moving parts 𝑚, the spring constant 𝑘 of the spring system, and a speed proportional friction 𝑟 the counteracting mechanic force yields 𝐹𝑚 = 𝑚𝑥̈ + 𝑟𝑥̇ + 𝑘𝑥 (39) Introducing the speed 𝑣 of the membrane equation (39) may be written as 𝐹𝑚 = 𝑚𝑣̇ + 𝑟𝑣 + 𝑘 ∫ 𝑣𝑑𝑥 (40) The electric system may be modeled as a resistive part 𝑅 considering the resistance of the coil, and inductive part 𝐿𝜎 considering the inductivity of the coil and the induced voltage in the coil (caused by the moving coil in the magnetic field in the air gap) corresponding to Figure 17. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 23 of 32 Figure 17: Electric circuit of a loudspeaker. For further considerations a linear magnetic circuit is assumed. Hence Kirchhoff’s voltage law yields 𝑑𝑖(𝑡) 𝑢(𝑡) = 𝑅𝑖(𝑡) + 𝐿𝜎 − 𝐵𝑣𝑑𝜋𝑁 (41) 𝑑𝑡 Assuming sinusoidal excitation with an angular frequency of 𝜔 (41) may be written as14 𝑈 = 𝑅𝐼 + 𝑗𝜔𝐿𝜎 𝐼 − 𝐵𝑣𝑑𝜋𝑁 (42) The force equations (38) and (40) can be transformed into the complex plain and set to be equal (mechanic equilibrium). 𝑘 𝑁𝐵𝐼𝑑𝜋 = 𝑗𝜔𝑚𝑣 + 𝑟𝑣 + 𝑗𝜔 𝑣 (43) Equation (43) can be resolved after the speed. 𝑁𝐵𝐼𝑑𝜋 𝑣= 𝑘 (44) 𝑗𝜔𝑚+𝑟+ 𝑗𝜔 Introducing (44) into (42) yields (𝐵𝑑𝜋𝑁)2 𝑈 = 𝑅𝐼 + 𝑗𝜔𝐿𝜎 𝐼 − 𝐼 𝑘 (45) 𝑗𝜔𝑚+𝑟+ 𝑗𝜔 Restructuring the last term of (45) yields (𝐵𝑑𝜋𝑁)2 𝑈 = 𝑅𝐼 + 𝑗𝜔𝐿𝜎 𝐼 − 𝐼 1 1 1 (46) 1 + 1 + 𝑗𝜔 𝑗𝜔𝑚 𝑟 𝑘 The last term of (46) indicates that the mechanic part is acting as a parallel circuit of a capacitor, inductor and a resistor. The friction of the system is corresponding to the resistive part, the stored kinetic energy is corresponding to a capacitive component, and the actual compression energy of the spring system is considered by the inductive part of equation (46). 14 For the transformation of differentials and integrals see electrical engineering I. If the excitation is sinusoidal the velocity must be sinusoidal too. Hence the velocity is a complex parameter too. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 24 of 32 Hence the loudspeaker can be modeled according to Figure 18. Figure 18: Equivalent circuit of a loudspeaker. Analog to the considerations above any electro mechanic system can be modeled based on 3.2.3 Exercise guide and instructions 3.2.3.1 Magnetic hysteresis, current / voltage distortion and in inrush current At the exercise two magnetic cores will be provided. Core exactly corresponding to Figure 11 The magnetic hysteresis should be determined for different excitations and the hysteresis loops should be plotted in one diagram The measurement setup is given in the appendix 5.1.1 The desired hysteresis loop result is given in 5.1.2 For one excitation the distortion of the current should be derived according to Figure 12 The inrush current should be derived according to Figure 14 and compared to measurement results NOTE: you must transfer the recorded data to via a csv file to an Excel Sheet. There you can perform the required integration. Prepare an appropriate EXCEL sheet, there will be not time for that in the exercise. Inductance with one coil and unknown core: Demonstrate the inrush current and the hysteresis. Try to measure a hysteresis by considering the resistance of the winding. 3.2.3.2 Loudspeaker Based on a Bode Diagram and appropriate measurements the electric model of two different loudspeakers should be derived and compared with the measurement results. Determine the electric resistance of the coil with a proper DC measurement. Determine the frequency plot of the loudspeaker’s impedance (absolute value and angle, shunt around 100 ). Try to adjust the equivalent values in the Excel theory plot to optimize the agreement between the measurement and the theory. Hint: observe which type of resonance is measured. Analyzing the corresponding theoretical impedance resonant peak and the impedance value for low and high frequency values help to identify proper equivalent values (are any equivalent values are dominant at these frequency values?). Repeat the procedure for a second loudspeaker and analyze the change of the impedance plot with respect to the loudspeaker’s dimensions. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 25 of 32 3.2.4 Typical introductory question Theory of the introductory chapter 3.2.2 and the corresponding theory from the lectures and skills practice. The goals and approaches of the single exercises must be known. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 26 of 32 3.3 Electric lines 3.3.1 Goal of the exercise The goal of the exercise is to investigate wave propagation effects on lines as well as reflection effects. The students should learn how to determine the characteristic impedance, and the specific line values. The frequency plot of the input impedance (absolute value and phase) of a coaxial line in open loop and short circuit termination should be measured. 3.3.2 Exercise guide and instructions 3.3.2.1 Determination of the specific line parameter The specific resistance 𝑅′, the specific capacitance 𝐶′, the specific conductivity 𝐺′ should be measured by measuring the total values and dividing them by the length of the line. The specific inductivity may be derived from the characteristic impedance measurement. In the report the specific values should be documented and checked by theoretical considerations and / or datasheets 3.3.2.1.1 Determination of the specific line resistance The exercise should be performed for three coaxial lines (10 m, 20 m, 40 m) a twisted pair line, and a power chord. Short circuit the end of the line and select a proper measurement method15 to measure the resistance of the system with DC; apply a current less than 0,1 A. The specific resistance is the total resistance divided by the length of the line. 3.3.2.1.2 Determination of the specific line conductivity The exercise should be performed for three coaxial lines (10 m, 20 m, 40 m) a twisted pair line, and a power chord. Operate the line in open loop condition and select a proper measurement method16 to measure the conductivity (resistance) of the system with DC. The specific conductivity is the total conductivity divided by the length of the line. 15 Current or voltage correct method, consider the correct arrangement of current and potential terminals, see Electrical Engineering 1! 16 Current or voltage correct method, see Electrical Engineering 1! https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 27 of 32 3.3.2.1.3 Determination of the specific capacity The exercise should be performed for three coaxial lines (10 m, 20 m, 40 m) a twisted pair line, and a power chord. Terminate the line in open loop condition. Supply the line by means of a HAMEG pulse generator via a shunt in the range between 1 k and 10 k. Determine the total capacitance by means of the exponential charging of the line (see exercise 3.1.3.1). The specific capacitance is the total capacitance divided by the length of the line. 3.3.2.2 Determination of the characteristic impedance The characteristic impedance may be derived from the measured input impedance of the short- circuited line 𝑍𝑆 and the line in open loop termination 𝑍𝑂 according to equation (44). 𝑍 = √𝑍𝑆 𝑍𝑂 (47) The input impedance may be measured by measuring the current and the voltage at the line input at AC. Therefore, a shunt of 47  and a frequency of around 50 kHz should be selected. For the connection of the shunt the setup given in Figure 19 should be applied. Figure 19: Recommended arrangement to connect the shunt for the impedance measurement. 3.3.2.3 Determination of the frequency plot of the input impedance of a line Adjust different frequencies and prove the hyperbolic behavior of a short circuited and open loop operated coaxial line. 3.3.2.4 Determination of wave propagation and investigating the reflection at different terminations The speed of light should be determined by means of a HAMEG pulse generator. In order to avoid any unwanted reflections, apply the setup given in Figure 20. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 28 of 32 Figure 20: Recommended arrangement for wave propagation measurement. 3.3.2.4.1 Exercises The setups given in Table 1 should be investigated with a single pulse and the echo of the pulse. Line type Termination Documentation Coaxial Open loop Store a representative screenshot from the 50  scope, you should see the propagation time Potentiometer of the pulse, the reflection factor, and the Short circuit voltage at the line input and output. Twisted pair Open loop The attenuation factor of the line should be 50  determined. Potentiometer What typical reflections may be adjusted Short circuit with the potentiometer at which Power cord Open loop potentiometer values? 50  Potentiometer Short circuit Table 1: Test parameter for wave propagation experiments. In the report the results should be checked by a wave propagation plot. Additionally the attenuation of the line in dB/m should be indicated. Adjust the potentiometer in a way that no reflections may be observed. Disconnect the potentiometer and measure the adjusted value with an ohmmeter. Compare the measured value with the characteristic impedance. For a coaxial cable a recording according to Figure 21 should be adjusted. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 29 of 32 Figure 21: Desired input voltage. Document in the report the settings, show the plot of the input voltage and the voltage at the end of the line. Discuss the input voltage function by means of a wave propagation diagram. 3.3.3 Typical introductory questions Line theory from the lectures and skills practice: Line input impedance of a terminated line and a non terminated line as a function of the frequency Ferranti effect Characteristic impedance Reflection factor Speed of light Wave propagation diagrams https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 30 of 32 4 Literature http://www.tonmeister.ca/wordpress/2014/01/31/bo-tech-how-to-make-a-loudspeaker- driver-a-primer/, last access: 2.1.2017 https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 31 of 32 5 Appendix 5.1 Magnetics Exercise 5.1.1 Measurement setup hysteresis 5.1.2 Desired result https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx Christoph Diendorfer Laboratory tutorials Page 32 of 32 5.2 Excel Sheets for Documentation of the Exercise See also the document for the report guidelines! The Excel sheet must cover at least the following columns Measurement (entering Error Calculation Theory (for plotting the measurement results) theory) Parameter Result Result % Parameter Result Result 1 2 1 2 Nr. Unit Unit Unit Deviation from Unit Unit Unit 1 the theory 2 … … Such an EXCEL sheet must be submitted for every task of an exercise! It must be prepared in a way that any graph will be plotted at the exercise automatically i.e. the measurement results are added to the plots immediately while entering the value. All charts and diagrams must be in one EXCEL file (use the tabs of the EXCEL documents). Reasonable and clear formatting and headlines, descriptions must be used. https://fhooe- my.sharepoint.com/personal/p24941_fhooe_at/Documents/Lehre/Lehre/002_Lehre/003_Labor/2020_WS/EEN3/20193012_LabTutorialScript. docx