Outline. Systems and Signals 214 / 244 & Energy Systems 244 / 344. Ideal Inductor. Ideal Inductor (cont... )


 Emerald Pope
 2 years ago
 Views:
Transcription
1 Outline Systems and Signals 214 / 244 & Energy Systems 244 / 344 Inductance, Leakage Inductance, Mutual Inductance & Transformers 1 Inductor revision Ideal Inductor NonIdeal Inductor Dr. P.J. Randewijk Stellenbosch University Dep. of Electrical & Electronic Engineering Copyright c 2015 Stellenbosch University All rights reserved 2 Transformers Ideal Transformers nonideal Transformers Nilsson & Riedel Section 6.5 & Appendix C 1 / 58 2 / 58 Ideal Inductor The typical layout of an ideal inductor, where we assume that all the magnetic flux produced by the coil is confined only to the core, is shown below. Ideal Inductor (cont... ) With the flux in the core, φ c = Ni (1) i φ c l c and the reluctance in the core, = l c µ 0 µ r A c (2) e N A c 3 / 58 4 / 58
2 Ideal Inductor (cont... ) The inductance of the core can thus be calculated as follows: L c = λ i (3) nonideal Inductor In a nonideal inductor, some of the flux will leak through the air, i.e. it will not be confined to the core alone. = Nφ c i = N i (4) Ni (5) = N2 (6) i e N φ φl φ c 5 / 58 6 / 58 nonideal Inductor (cont... ) The total magnetic flux linking the coil is therefore equal to the sum of the flux confined to the core plus the leakage flux through the air. φ = φ c φ l (7) = Ni Ni R l (8) Nφ = N2 i N2 i R l (9) λ = N2 N2 i R l (10) = L c L l (11) nonideal Inductor (cont... ) The total or self inductance of the coils is thus equal to the sum of the inductance due to the flux confined to the core, plus the leakage inductance associated with the leakage flux. L = L c L l (12) 7 / 58 8 / 58
3 Ideal Transformer The typical layout of an ideal transformer, where all the flux produced by the coils are confined only to the core, is shown below. i 1 e 1 φ c =φ m i 2 The flux in the core, φ c, is also referred to as the mutual flux, φ m, because it has is mutual to both coils. If we were to connect an ideal voltage source across coil and we assume that the coil itself does not have any resistance, we will be able to calculate the flux in the core by making use of Faraday s law, with the voltage of the voltage source known. Thus, for a purely sinusoidal voltage, the flux will also be sinusoidal. With the flux being mutual to coil as well, we will be able to calculate the voltage induced in by also making use of Faraday s law. 9 / / 58 Thus from the sketch below, i s (t) φ m v s (t) = 2V s cos(ωt) (13) = e 1 (t) (14) v s (t) e 1 and if the applied voltage is sinusoidal, we can do the following calculations. dφ m = (15) 2Vs φ m (t) = sin(ωt) (16) ω dφ m (t) = ( ) d 2Vs = sin(ωt) ω (17) (18) = e 1 (t) (19) 11 / / 58
4 The current drawn from the supply voltage source can be calculated as follows: φ m (t) = i s (t) (20) i s (t) = φ m (t) (21) = R c 2Vs sin(ωt) (22) ω 2 2Vs = sin(ωt) ωl m (23) = i m (t) (24) The mutual flux, φ m, is sometimes also called the magnetising flux because it magnetises the core and induce the secondary voltage,. Therefore, the current component which is responsible for the magnetising flux is also known as the magnetising current, i m. We would also be able to calculate the magnetising current directly from the inductance of the primary winding. This inductance is therefore also known as the magnetising inductance, L m. L m = 2 (25) 13 / / 58 The magnetising current can thus be calculated directly from the magnetising inductance by making use of phasor. v s (t) = 2V s cos(ωt) (26) V s = V s 0 (27) I s = I m Φ m I m = V s jx m (28) = V s 90 (29) ωl m V s E 1 E 2 i m (t) = = 2Vs cos(ωt 90 ) (30) ωl m 2Vs sin(ωt) (31) ωl m With X m = ωl m known as the magnetising reactance. 15 / / 58
5 The polarity of can be determined by making use of Lenz s law. The polarity of will be such that, if a load were connected over, a current, i 2, will flow so as to oppose the cause of (i.e. will try and oppose φ m ). By looking at the way in which and are wound around the core and using the right hand grip rule, the polarity of w.r.t. e 1 can be determined. v s (t) i s (t) e 1 φ m φ2 i 2 The polarity relationship between e 1 and is usually indicated by dots if the winding configuration self is not shown. With φ 2 which now tries to oppose φ m, it implies that the total flux that sees will now become less / / 58 But from Faraday s law: φ m v s (t) = e 1 (t) = dφ m Thus with v s (t) constant (i.t.o. amplitude and frequency), it implies that the flux which sees must also remain constant. (32) i m (t) i 1 (t) v s (t) e 1 φ1 φ2 i 2 (t) The transformer will now draw an additional current component, i 1, from the supply which will produce an additional flux, φ 1, which will cancel out the effect of φ 2, i.e. φ 1 = φ 2. The nett flux in the core will thus remain constant and equal to φ m. 19 / / 58
6 The relationship between i 1 and i 2 can now be calculated as follow: φ 2 = i 2 (t) (33) φ 1 = i 1 (t) (34) φ 1 = φ 2 (35) i 1 (t) = i 2 (t) (36) i 1 (t) = i 2 (t) (37) i 1 (t) = i 2 (t) (38) The transformer can also be represented completely electrical, with out the need to refer to its magnetic circuit, by making use of the electrical symbol for an ideal transformer as shown below, i s i 1 i 2 i m L m :N2 v s e 1 21 / / 58 with the following relationship between the primary and the secondary s currents and voltages: i 1 = i 2 (39) = e 1 (40) For a transformer to really be considered ideal, the relative permeability of, µ r, of the magnetic core of the transformer must tend to infinity. And that would imply that the reluctance of the core will tend to zero. This in turn would imply that the magnetising inductance of the transformer will tend to infinity. As a result, the magnetising current will tend to zero. The ideal transformer in the time domain, can thus electrically be shown as only: i s = i 1 i 2 :N2 v s = e 1 23 / / 58
7 This is also true for the phasor domain : to rather work with the winding ration 1 : a, so that: V s I s = I 1 I 2 1:a E 1 E 2 Z load a = N2 (41) E 2 = ae 1 (42) I 2 = I 1 a (43) The load can thus be defined as: Another simplification is to, instead of using the winding ratio : N2, Z load = E 2 I 2 (44) = a 2 E 1 I 1 (45) 25 / / 58 The load, as referred to the supply side of the transformer, Z load, can be defined as follows: nonideal Transformers For a nonideal transformer, not all the flux from coil 1 couples with coil 2 and reverse. I s = I 1 φ m i 1 φ1 i 2 V s E 1 Z load a 2 e 1 φl1 φl2 φ2 Z load = Z load a 2 = Z load ( ) 2 (46) 27 / / 58
8 N.B. φ 1 and φ 2 are now defined differently as in the previous section and are now directly associated with and respectively. φ 1 is the total magnetic flux that links coil 1 due to the current in coil1, i 1, and the current in coil 2, i 2. Similarly is φ 2 the total magnetic flux that links coil 2 due to the current in coil 1, i 1, and the current in coil 2, i 2. Not all the flux that is linking coil 1, links with coil 2 and reverse. The portion of the flux from coil 1 that also links with coil 2 (i.e. which is common to both coils) is known as the mutual flux, φ m. The portion of the flux from coil 1 which does not link with coil 2, is known as the leakage flux, φ l1. Similarly, φ l2 is the leakage flux of coil 2, i.e. the portion of the flux that links coil 2, but which does not link with coil 1. The total flux of coils 1 & 2 can thus mathematically be expressed as: φ 1 = φ l1 φ m (47) φ 2 = φ l2 φ m (48) 29 / / 58 Or in terms of the different reluctance values: φ 1 = i 1 R l1 i 1 i 2 (49) φ 2 = i 2 R l2 i 1 i 2 (50) In order to obtain the flux linkages of coils 1 & 2, we multiply (49) with and (50) with. φ 1 = 2 i 1 2 i 1 i 2 (51) R l1 2 i 2 φ 2 = 2 i 2 i 1 (52) R l2 R ( ) c 2 λ 1 = ( ) 1 i 1 i 2 (53) R l1 ( ) ( ) 2 N2 λ 2 = i 1 2 i 2 (54) R l2 31 / / 58
9 Or in matrix format: with: [ λ1 λ 2 ] [ ] [ ] L1 M i1 = M L 2 i 2 (55) L 1 = 2 1 R l1 (56) = L l1 L m1 (57) The self inductance of coil 1 is equal to the leakage inductance of coil 1 plus the mutual inductance as referred to coil 1 (i.e. the primary side) L 2 = 2 2 R l2 (58) = L l2 L m2 (59) The self inductance of coil 2 is equal to the leakage inductance of coil 2 plus the mutual inductance as referred to coil 2 (i.e. the secondary side) M = (60) The mutual inductance, as seen from the primary and secondary side, i.e. not referred to any specific side. 33 / / 58 The coupling factor, k, can be defined as the mutual flux linking coil 2, φ m, divided by the total flux linking coil 1, φ 1, due to the current in coil 1, i 1. k = φ m φ 1 (61) φ m = φ l1 φ m (62) = = i 1 i 1 R l1 N 1i 1 2 i 1 ( ) (63) 2 i 1 R l1 2 i 1 (64) = L m1 L l1 L m1 (65) = L m1 L 1 (66) Similarly, the coupling factor (due to the current in coil 2, i 2 ) can also be expressed as : Which implies that: k = L m2 L 2 (67) k 2 = L m1 L 1 Lm2 L 2 (68) M = k L 1 L 2 (69) 35 / / 58
10 with: M 2 = L m1 L m2 (70) L m1 L m2 = 2 2 (71) The equivalent circuit diagram of the transformer, shown earlier, can be drawn with dots to indicate the winding direction and relationship between the primary and secondary windings. i 1 i 2 The voltages over both coils can be obtained by differentiating both sides: d [ λ1 λ 2 [ e1 ] = d [ ] [ ] L1 M i1 M L 2 i 2 ] = d [ ] [ ] L1 M i1 M L 2 i 2 (72) (73) M e 1 L 1 L 2 37 / / 58 Dot Definition If the current flows into a dot of a coil, it will induce a voltage in the other coil which will be positive at that coil s dot. The Kirchoff voltage mesh equations for the primary and secondary side of the transformer can thus be written as: Alternative Dot Definition If a current flow out of a dot of a coil, it will induce a voltage in the other coil which will be negative at that coil s dot. L 1 di 1 L 2 di 2 M di 2 M di 1 e 1 = 0 (74) = 0 (75) If we were to write the equations in matrix format, it will be identical to (73). 39 / / 58
11 If we were to reverse the winding direction of the secondary coil of the transformer, the polarity of the induced voltage in the secondary will also reverse. The equivalent circuit diagram of the transformer can now be drawn as follows with the dots once again indicating the winding direction relationship. φ m i 1 i 2 i 1 φ1 i 2 M e 1 φl1 φl2 e 1 L 1 L 2 φ2 41 / / 58 The Kirchoff voltage mech equations for the primary and secondary side of the transformer can now be written as: L 1 di 1 L 2 di 2 Or in matrix format: [ e1 M di 2 M di 1 ] = d [ ] [ ] L1 M i1 M L 2 e 1 = 0 (76) = 0 (77) i 2 (78) Equation (73) (or (78)) can also be seen as the equivalent twoport network zparameters matrix equations of the transform and thus also be represented as an equivalent T circuit. i 1 L 1 M L 2 M i 2 e 1 M 43 / / 58
12 See Nilsson & Riedel Appendix C.1, Fig. C.2 For a representative model of the transformer, it should make sense that the equivalent circuit should include an ideal transformer model. i 1?? í 2 i 2 e 1? é 2 45 / / 58 Another advantage that the ideal transformer have, is that it eliminates the negative inductances in the equivalent T model, especially for stepup transformers see Nilsson & Riedel Appendix C.2. The new unknown circuit elements in the T equivalent circuit can be calculated as follows. With the relationship between é 2 and, and í2 and i 2 on both sides of the ideal transformer known, é 2 = (79) í 2 i 2 = (80) (73) can thus be rewritten as: [ ] ( e 1 ) é N2 = d [ ] [ ] L1 M ( i 1 ) 2 M L 2 í 2 [ ] [ ] [ ] e1 = d ( L 1 ) ( M ) ( i 1 ) é2 M L 2 í 2 ( ) = d L 1 M [ N ( ) ( 2 ) 2 i1í2] M L 2 [ ] = d [i1 ] L 1 Ḿ Ḿ Ĺ2 í 2 (81) (82) (83) (84) 47 / / 58
13 with: Ḿ = M ( = ) ( ) (85) (86) = N2 1 (87) = L m1 (88) ( ) 2 Ĺ 2 = L 2 (89) N ( 2 ) 2 = ( ) 2 2 (90) R l2 = 2 1 (91) R l2 = L l2 L m1 (92) The mutual inductance as referred to the primary side. The leakage inductance of the secondary coil, as referred to the primary side. 49 / / 58 This implies that the twoport zparameters of (84), can be represented by the equivalent T circuit as shown below. Which is basically the same as shown in Fig. C.13 of Appenidx C.2 from Nilsson & Riedel. i 1 L l1 L í 2 i 2 l2 e 1 é 2 L m1 with a = (93) 51 / / 58
14 In Nilsson & Riedel Section 6.5, the different magnetic flux components are defined somewhat different. The total magnetic flux that links coil 1, φ 1, is divided in the flux produced by the current in coil 1 itself, φ 11, as well as the flux produced by the current in coil 2, φ 12. Similarly, the total magnetic flux linking coil 2 can be divided into the flux produced by the current in coil 1, φ 21, as well as the flux produced by the current in coil 2 itself, φ 22. φ 1 = φ 11 φ 12 (94) φ 2 = φ 21 φ 22 (95) The mutual flux, φ m, as defined earlier, can be written as the sum of φ 12 and φ 21 (with the winding direction as shown earlier). φ m = φ 12 φ 21 (96) The leakage flux of coil 1 can thus be defined as the magnetising flux produced by the current in coil 1 minus the portion of the flux that links with coil 2. φ l1 = φ 11 φ 21 (97) Similarly, the leakage flux of coil 2 can be defined as the flux produced by the current in coil 2, minus the portion of the flux that links with coil 1. φ l2 = φ 22 φ 12 (98) 53 / / 58 The relationship between φ 11, φ 21, φ 12 & φ 22 and φ m, φ l1 & φ l2 can thus graphically be depicted as follows: This implies that both Fig & Fig in Nillson & Riedel is wrong. φ m =φ 21 φ 12 i 1 φ1 i 2 e 1 φl1=φ11φ21 φl2=φ22φ12 φ2 55 / / 58
15 The inductance associated with the different magnetic flux components can be calculated exactly the same as previously. φ 1 = φ 11 φ 12 (99) φ 2 = φ 21 φ 22 (100) [ λ1 λ 2 λ 1 = λ 11 λ 12 (101) λ 2 = λ 21 λ 22 (102) ] [ ] [ ] L11 L = 12 i1 L 21 L 22 i 2 (103) d [ λ1 λ 2 ] = d [ ] [ ] L11 L 12 i1 L 21 L 22 i 2 [ e1 ] = d [ ] [ ] L11 L 12 i1 L 21 L 22 i 2 (104) (105) The zparameter matrix equation is basically equivalent to (73), which thus implies that: L 1 = L 11 (106) L 2 = L 22 (107) M = L 12 = L 21 (108) 57 / / 58
Mutual Inductance and Transformers F3 3. r L = ω o
utual Inductance and Transformers F3 1 utual Inductance & Transformers If a current, i 1, flows in a coil or circuit then it produces a magnetic field. Some of the magnetic flux may link a second coil
More informationCoupled Inductors. Introducing Coupled Inductors
Coupled Inductors From power distribution across large distances to radio transmissions, coupled inductors are used extensively in electrical applications. Their properties allow for increasing or decreasing
More informationSolution Derivations for Capa #11
Solution Derivations for Capa #11 Caution: The symbol E is used interchangeably for energy and EMF. 1) DATA: V b = 5.0 V, = 155 Ω, L = 8.400 10 2 H. In the diagram above, what is the voltage across the
More informationElectrical Machines II. Week 1: Construction and theory of operation of single phase transformer
Electrical Machines II Week 1: Construction and theory of operation of single phase transformer Transformers Overview A transformer changes ac electric power at one frequency and voltage level to ac electric
More informationES250: Electrical Science. HW7: Energy Storage Elements
ES250: Electrical Science HW7: Energy Storage Elements Introduction This chapter introduces two more circuit elements, the capacitor and the inductor whose elements laws involve integration or differentiation;
More informationEE 221 Circuits II. Chapter 13 Magnetically Coupled Circuits
EE Circuits II Chapter 3 Magnetically Coupled Circuits Magnetically Coupled Circuits 3. What is a transformer? 3. Mutual Inductance 3.3 Energy in a Coupled Circuit 3.4 inear Transformers 3.5 Ideal Transformers
More informationSlide 1 / 26. Inductance. 2011 by Bryan Pflueger
Slide 1 / 26 Inductance 2011 by Bryan Pflueger Slide 2 / 26 Mutual Inductance If two coils of wire are placed near each other and have a current passing through them, they will each induce an emf on one
More informationRLC Resonant Circuits
C esonant Circuits Andrew McHutchon April 20, 203 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. The format followed in this document
More information8 Speed control of Induction Machines
8 Speed control of Induction Machines We have seen the speed torque characteristic of the machine. In the stable region of operation in the motoring mode, the curve is rather steep and goes from zero torque
More informationNZQA registered unit standard 20431 version 2 Page 1 of 7. Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians
NZQA registered unit standard 0431 version Page 1 of 7 Title Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians Level 3 Credits 7 Purpose This unit standard covers
More informationModule 7. Transformer. Version 2 EE IIT, Kharagpur
Module 7 Transformer Version EE IIT, Kharagpur Lesson 4 Practical Transformer Version EE IIT, Kharagpur Contents 4 Practical Transformer 4 4. Goals of the lesson. 4 4. Practical transformer. 4 4.. Core
More informationModule 22: Inductance and Magnetic Field Energy
Module 22: Inductance and Magnetic Field Energy 1 Module 22: Outline Self Inductance Energy in Inductors Circuits with Inductors: RL Circuit 2 Faraday s Law of Induction dφ = B dt Changing magnetic flux
More informationChapter 30 Inductance
Chapter 30 Inductance  Mutual Inductance  SelfInductance and Inductors  MagneticField Energy  The R Circuit  The C Circuit  The RC Series Circuit . Mutual Inductance  A changing current in
More informationW03 Analysis of DC Circuits. Yrd. Doç. Dr. Aytaç Gören
W03 Analysis of DC Circuits Yrd. Doç. Dr. Aytaç Gören ELK 2018  Contents W01 Basic Concepts in Electronics W02 AC to DC Conversion W03 Analysis of DC Circuits (self and condenser) W04 Transistors and
More informationImpedance Matching. Using transformers Using matching networks
Impedance Matching The plasma industry uses process power over a wide range of frequencies: from DC to several gigahertz. A variety of methods are used to couple the process power into the plasma load,
More informationThe Flyback Converter
The Flyback Converter Lecture notes ECEN4517! Derivation of the flyback converter: a transformerisolated version of the buckboost converter! Typical waveforms, and derivation of M(D) = V/! Flyback transformer
More informationEEE1001/PHY1002. Magnetic Circuits. The circuit is of length l=2πr. B andφ circulate
1 Magnetic Circuits Just as we view electric circuits as related to the flow of charge, we can also view magnetic flux flowing around a magnetic circuit. The sum of fluxes entering a point must sum to
More informationEdmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H).
INDUCTANCE MUTUAL INDUCTANCE If we consider two neighbouring closed loops and with bounding surfaces respectively then a current through will create a magnetic field which will link with as the flux passes
More informationMutual inductance. Resources and methods for learning about these subjects (list a few here, in preparation for your research):
Mutual inductance This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More informationEðlisfræði 2, vor 2007
[ Assignment View ] [ Print ] Eðlisfræði 2, vor 2007 30. Inductance Assignment is due at 2:00am on Wednesday, March 14, 2007 Credit for problems submitted late will decrease to 0% after the deadline has
More informationREPORT ON CANDIDATES WORK IN THE CARIBBEAN ADVANCED PROFICIENCY EXAMINATION MAY/JUNE 2008 ELECTRICAL AND ELECTRONIC TECHNOLOGY (TRINIDAD AND TOBAGO)
CARIBBEAN EXAMINATIONS COUNCIL REPORT ON CANDIDATES WORK IN THE CARIBBEAN ADVANCED PROFICIENCY EXAMINATION MAY/JUNE 2008 ELECTRICAL AND ELECTRONIC TECHNOLOGY (TRINIDAD AND TOBAGO) Copyright 2008 Caribbean
More informationFunctions, variations and application areas of magnetic components
Westring 18 3314 Büren Germany T +49 951 60 01 0 F +49 951 60 01 3 www.schaffner.com energy efficiency and reliability 1.1 Transformers The transformer is one of the traditional components of electrical
More informationLast time : energy storage elements capacitor.
Last time : energy storage elements capacitor. Charge on plates Energy stored in the form of electric field Passive sign convention Vlt Voltage drop across real capacitor can not change abruptly because
More informationInduced voltages and Inductance Faraday s Law
Induced voltages and Inductance Faraday s Law concept #1, 4, 5, 8, 13 Problem # 1, 3, 4, 5, 6, 9, 10, 13, 15, 24, 23, 25, 31, 32a, 34, 37, 41, 43, 51, 61 Last chapter we saw that a current produces a magnetic
More informationLecture 24. Inductance and Switching Power Supplies (how your solar charger voltage converter works)
Lecture 24 Inductance and Switching Power Supplies (how your solar charger voltage converter works) Copyright 2014 by Mark Horowitz 1 Roadmap: How Does This Work? 2 Processor Board 3 More Detailed Roadmap
More informationCoupling Factor Calculation of Low Frequency RFID Systems by the Mutual Inductance Effective Permeability Method
Coupling Factor Calculation of Low Frequency RFID Systems by the Mutual Inductance Effective Permeability Method P. Csurgai, M. Kuczmann Szécheny István University, Lab. Of Electromagentic Fields, Dept.
More informationChapter 30 Inductance
Chapter 30 Inductance In this chapter we investigate the properties of an inductor in a circuit. There are two kinds of inductance mutual inductance and selfinductance. An inductor is formed by taken
More informationBasic Electrical Technology Dr. L. Umanand Department of Electrical Engineering Indian Institute of Science, Bangalore. Lecture  33 3 phase System 4
Basic Electrical Technology Dr. L. Umanand Department of Electrical Engineering Indian Institute of Science, Bangalore Lecture  33 3 phase System 4 Hello everybody. So, in the last class we have been
More informationAlternating Current RL Circuits
Alternating Current RL Circuits Objectives. To understand the voltage/current phase behavior of RL circuits under applied alternating current voltages, and. To understand the current amplitude behavior
More information1. Title Electrical fundamentals II (Mechanics Repair and Maintenance)
1. Title Electrical fundamentals II (Mechanics Repair and Maintenance) 2. Code EMAMBG429A 3. Range The knowledge is needed for a wide range of aircraft repair and maintenance works,e.g. applicable to aircrafts,
More informationChapter 12: Three Phase Circuits
Chapter 12: Three Phase Circuits 12.1 What Is a Three Phase Circuit? 12.2 Balance Three Phase Voltages 12.3 Balance Three Phase Y to Y Connection 12.4 Other Balance Three Phase Connections 12.5 Power in
More informationLCR Parallel Circuits
Module 10 AC Theory Introduction to What you'll learn in Module 10. The LCR Parallel Circuit. Module 10.1 Ideal Parallel Circuits. Recognise ideal LCR parallel circuits and describe the effects of internal
More informationE.G.Strangas MSU Electrical Machines and Drives Laboratory
Notes for an Introductory Course On Electrical Machines and Drives E.G.Strangas MSU Electrical Machines and Drives Laboratory Contents Preface ix 1 Three Phase Circuits and Power 1 1.1 Electric Power
More information7.1 POWER IN AC CIRCUITS
C H A P T E R 7 AC POWER he aim of this chapter is to introduce the student to simple AC power calculations and to the generation and distribution of electric power. The chapter builds on the material
More informationCurrent Probes, More Useful Than You Think
Current Probes, More Useful Than You Think Training and design help in most areas of Electrical Engineering Copyright 1998 Institute of Electrical and Electronics Engineers. Reprinted from the IEEE 1998
More informationInductors & Inductance. Electronic Components
Electronic Components Induction In 1824, Oersted discovered that current passing though a coil created a magnetic field capable of shifting a compass needle. Seven years later, Faraday and Henry discovered
More informationApplication Notes. Magnetics. Determining L min for Buck/Boost Converters
Application Notes Magnetics etermining min for Buck/Boost onverters Fundamental oncepts 172 alculating Minimum nductance Buck Type onverters 174 Boost Type onverters 177 BuckBoost onverters 180171 APPATON
More informationChapter 11. Inductors ISU EE. C.Y. Lee
Chapter 11 Inductors Objectives Describe the basic structure and characteristics of an inductor Discuss various types of inductors Analyze series inductors Analyze parallel inductors Analyze inductive
More informationHomework #11 20311721 Physics 2 for Students of Mechanical Engineering
Homework #11 20311721 Physics 2 for Students of Mechanical Engineering 2. A circular coil has a 10.3 cm radius and consists of 34 closely wound turns of wire. An externally produced magnetic field of
More informationElectromagnetic Induction
Electromagnetic Induction "Concepts without factual content are empty; sense data without concepts are blind... The understanding cannot see. The senses cannot think. By their union only can knowledge
More informationExtra Questions  1. 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A
Extra Questions  1 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A 2. A current of 500mA flows in a resistance of 12Ω. What power is dissipated
More information2. A conductor of length 2m moves at 4m/s at 30 to a uniform magnetic field of 0.1T. Which one of the following gives the e.m.f. generated?
Extra Questions  2 1. A straight length of wire moves through a uniform magnetic field. The e.m.f. produced across the ends of the wire will be maximum if it moves: a) along the lines of magnetic flux
More informationPHASOR DIAGRAMS HANDSON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER  BPA
PHASOR DIAGRAMS HANDSON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER  BPA What are phasors??? In normal practice, the phasor represents the rms maximum value of the positive half cycle of the sinusoid
More informationEMI and t Layout Fundamentals for SwitchedMode Circuits
v sg (t) (t) DT s V pp = n  1 2 V pp V g n V T s t EE core insulation primary return secondary return Supplementary notes on EMI and t Layout Fundamentals for SwitchedMode Circuits secondary primary
More informationCircuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49
Circuits with inductors and alternating currents Chapter 20 #45, 46, 47, 49 RL circuits Ch. 20 (last section) Symbol for inductor looks like a spring. An inductor is a circuit element that has a large
More informationThe March/April Morseman Problem
The Problem as stated was: The March/April Morseman Problem A toroidal transformer is used in directional coupler versions of an SWR bridge. The primary winding is the single wire running through the toroid,
More informationExperiment A5. Hysteresis in Magnetic Materials
HYSTERESIS IN MAGNETIC MATERIALS A5 1 Experiment A5. Hysteresis in Magnetic Materials Objectives This experiment illustrates energy losses in a transformer by using hysteresis curves. The difference betwen
More informationFall 12 PHY 122 Homework Solutions #10
Fall 12 PHY 122 Homework Solutions #10 HW10: Ch.30 Q5, 8, 15,17, 19 P 1, 3, 9, 18, 34, 36, 42, 51, 66 Chapter 30 Question 5 If you are given a fixed length of wire, how would you shape it to obtain the
More informationDC Circuits: Operational Amplifiers Hasan Demirel
DC Circuits: Operational Amplifiers Hasan Demirel Op Amps: Introduction Op Amp is short form of operational amplifier. An op amp is an electronic unit that behaves like a voltage controlled voltage source.
More informationEE301 Lesson 14 Reading: 10.110.4, 10.1110.12, 11.111.4 and 11.1111.13
CAPACITORS AND INDUCTORS Learning Objectives EE301 Lesson 14 a. Define capacitance and state its symbol and unit of measurement. b. Predict the capacitance of a parallel plate capacitor. c. Analyze how
More informationThe Ideal Transformer. Description and Circuit Symbol
The Ideal Transformer Description and Circuit Symbol As with all the other circuit elements, there is a physical transformer commonly used in circuits whose behavior can be discussed in great detail. However,
More informationCoupling Magnetic Signals to a SQUID Amplifier
SQUID Application Note 1050 Coupling Magnetic Signals to a SQUID Amplifier Matching the effective inductances of the Pickup Coil and the Input Coil to detect and couple magnetic flux maximizes the sensitivity
More informationPower measurement in balanced 3 phase circuits and power factor improvement. 1 Power in Single Phase Circuits. Experiment no 1
Experiment no 1 Power measurement in balanced 3 phase circuits and power factor improvement 1 Power in Single Phase Circuits Let v = m cos(ωt) = cos(ωt) is the voltage applied to a RL circuit and i =
More informationLinear DC Motors. 15.1 Magnetic Flux. 15.1.1 Permanent Bar Magnets
Linear DC Motors The purpose of this supplement is to present the basic material needed to understand the operation of simple DC motors. This is intended to be used as the reference material for the linear
More informationChapter 12 Driven RLC Circuits
hapter Driven ircuits. A Sources... . A ircuits with a Source and One ircuit Element... 3.. Purely esistive oad... 3.. Purely Inductive oad... 6..3 Purely apacitive oad... 8.3 The Series ircuit...
More informationAlternatingCurrent Circuits
hapter 1 Alternatingurrent ircuits 1.1 A Sources... 11. Simple A circuits... 13 1..1 Purely esistive load... 13 1.. Purely Inductive oad... 15 1..3 Purely apacitive oad... 17 1.3 The Series ircuit...
More informationChapter 14: Inductor design
Chapter 14 Inductor Design 14.1 Filter inductor design constraints 14.2 A stepbystep design procedure 14.3 Multiplewinding magnetics design using the K g method 14.4 Examples 14.5 Summary of key points
More informationAnalysis of Dynamic Circuits in MATLAB
Transactions on Electrical Engineering, Vol. 4 (2015), No. 3 64 Analysis of Dynamic Circuits in MATLAB Iveta Tomčíková 1) 1) Technical University in Košice/Department of Theoretical and Industrial Electrical
More informationG019.A (4/99) UNDERSTANDING COMMON MODE NOISE
UNDERSTANDING COMMON MODE NOISE PAGE 2 OF 7 TABLE OF CONTENTS 1 INTRODUCTION 2 DIFFERENTIAL MODE AND COMMON MODE SIGNALS 2.1 Differential Mode signals 2.2 Common Mode signals 3 DIFFERENTIAL AND COMMON
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT 4 Understand singlephase alternating current (ac) theory Single phase AC
More informationCapacitors in Circuits
apacitors in ircuits apacitors store energy in the electric field E field created by the stored charge In circuit apacitor may be absorbing energy Thus causes circuit current to be reduced Effectively
More informationRevision Calcs. 1. The flux produced by a magnet is 10mWb. Determine the flux density if the area of the pole is 250 mm 2
EMA Revision Calcs Miller College Revision Calcs Revision Calcs 1. The flux produced by a magnet is 10mWb. Determine the flux density if the area of the pole is 250 mm 2 2. For the magnet in the previous
More informationTransformer Modeling for Simulation of Low Frequency Transients
IEEE PES General Meeting July 1317, 23, Toronto Transformer Modeling for Simulation of Low Frequency Transients J.A. MARTINEZVELASCO Univ. Politècnica Catalunya Barcelona, Spain B.A MORK Michigan Tech..
More information13 ELECTRIC MOTORS. 13.1 Basic Relations
13 ELECTRIC MOTORS Modern underwater vehicles and surface vessels are making increased use of electrical actuators, for all range of tasks including weaponry, control surfaces, and main propulsion. This
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3. OUTCOME 3  MAGNETISM and INDUCTION
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 3  MAGNETISM and INDUCTION 3 Understand the principles and properties of magnetism Magnetic field:
More informationPHY2049 Exam #2 Solutions Fall 2012
PHY2049 Exam #2 Solutions Fall 2012 1. The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r) and radial segments. The circuits
More informationIf there is no fault, then with proper connections account for the CT polarity, we should obtain circulatory current through CT secondary.
Module 10 : Differential Protection of Bus, Transformer and Generator Lecture 39 : Transformer Protection Introduction Differential protection of transformer was introduced in lecture 2. Traditionally,
More information7 Testing of Transformers
7 Testing of Transformers The structure of the circuit equivalent of a practical transformer is developed earlier. The performance parameters of interest can be obtained by solving that circuit for any
More informationDigital Energy ITI. Instrument Transformer Basic Technical Information and Application
g Digital Energy ITI Instrument Transformer Basic Technical Information and Application Table of Contents DEFINITIONS AND FUNCTIONS CONSTRUCTION FEATURES MAGNETIC CIRCUITS RATING AND RATIO CURRENT TRANSFORMER
More informationThree phase circuits
Three phase circuits THREE PHASE CIRCUITS THREEPHASE ADVANTAGES 1. The horsepower rating of threephase motors and the kva rating of threephase transformers are 150% greater than singlephase motors
More informationLecture 22. Inductance. Magnetic Field Energy. Outline:
Lecture 22. Inductance. Magnetic Field Energy. Outline: Selfinduction and selfinductance. Inductance of a solenoid. The energy of a magnetic field. Alternative definition of inductance. Mutual Inductance.
More informationChapter 17 11/13/2014
Chapter 17 Voltage / Current source conversions Mesh and Nodal analysis in an AC circuit Balance conditions and what elements are needed in a bridge network ECET 207 AC Circuit Analysis, PNC 2 1 Magnitude
More informationMotor Fundamentals. DC Motor
Motor Fundamentals Before we can examine the function of a drive, we must understand the basic operation of the motor. It is used to convert the electrical energy, supplied by the controller, to mechanical
More informationInductors. AC Theory. Module 3
Module 3 AC Theory What you ll learn in Module 3. Section 3.1 Electromagnetic Induction. Magnetic Fields around Conductors. The Solenoid. Section 3.2 Inductance & Back e.m.f. The Unit of Inductance. Factors
More informationCALCULATION OF POWER TRANSFORMERS EQUIVALENT CIRCUIT PARAMETERS USING NUMERICAL FIELD SOLUTIONS
www.arpapress.com/volumes/vol17issue1/ijrras_17_1_03.pdf CALCULATION OF POWER TRANSFORMERS EQUIVALENT CIRCUIT PARAMETERS USING NUMERICAL FIELD SOLUTIONS Antônio Flavio Licarião Nogueira Santa Catarina
More informationTopic Suggested Teaching Suggested Resources
Lesson 1 & 2: DC Networks Learning Outcome: Be able to apply electrical theorems to solve DC network problems Electrical theorems and DC network problems Introduction into the unit contents, aims & objectives
More informationEquipment: Power Supply, DAI, Transformer (8341), Variable resistance (8311), Variable inductance (8321), Variable capacitance (8331)
Lab 5: Singlephase transformer operations. Objective: to examine the design of singlephase transformers; to study the voltage and current ratios of transformers; to study the voltage regulation of the
More informationAC RL and RC Circuits
AC RL and RC Circuits When a sinusoidal AC voltage is applied to an RL or RC circuit, the relationship between voltage and current is altered. The voltage and current still have the same frequency and
More informationDrive circuit basics + V. τ e. Industrial Circuits Application Note. Winding resistance and inductance
ndustrial Circuits Application Note Drive circuit basics For a given size of a stepper motor, a limited space is available for the windings. n the process of optimizing a stepper motor drive system, an
More informationPower supplies. EE328 Power Electronics Assoc. Prof. Dr. Mutlu BOZTEPE Ege University, Dept. of E&E
Power supplies EE328 Power Electronics Assoc. Prof. Dr. Mutlu BOZTEPE Ege University, Dept. of E&E EE328 POWER ELECTRONICS Outline of lecture Introduction to power supplies Modelling a power transformer
More informationSERIESPARALLEL DC CIRCUITS
Name: Date: Course and Section: Instructor: EXPERIMENT 1 SERIESPARALLEL DC CIRCUITS OBJECTIVES 1. Test the theoretical analysis of seriesparallel networks through direct measurements. 2. Improve skills
More informationBASIC ELECTRONICS AC CIRCUIT ANALYSIS. December 2011
AM 5202 BASIC ELECTRONICS AC CIRCUIT ANALYSIS December 2011 DISTRIBUTION RESTRICTION: Approved for Pubic Release. Distribution is unlimited. DEPARTMENT OF THE ARMY MILITARY AUXILIARY RADIO SYSTEM FORT
More informationExperiment 1 The DC Machine
Experiment 1 The DC Machine ECEN 4517 R. W. Erickson and D. Maksimovic The purpose of this experiment is to become familiar with operating principles, equivalent circuit models, and basic characteristics
More informationFull representation of the real transformer
TRASFORMERS EQVALET CRCT OF TWOWDG TRASFORMER TR Dots show the points of higher potential. There are applied following conventions of arrow directions: for primary circuit the passive sign convention
More informationLecture  4 Diode Rectifier Circuits
Basic Electronics (Module 1 Semiconductor Diodes) Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati Lecture  4 Diode Rectifier Circuits
More informationDiodes have an arrow showing the direction of the flow.
The Big Idea Modern circuitry depends on much more than just resistors and capacitors. The circuits in your computer, cell phone, Ipod depend on circuit elements called diodes, inductors, transistors,
More informationEXPERIMENT 1.2 CHARACTERIZATION OF OPAMP
1.17 EXPERIMENT 1.2 CHARACTERIZATION OF OPAMP 1.2.1 OBJECTIVE 1. To sketch and briefly explain an operational amplifier circuit symbol and identify all terminals 2. To list the amplifier stages in a typical
More information1 Introduction. 2 Two Phases. J.L. Kirtley Jr.
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.061 Introduction to Power Systems Class otes Chapter 3 Polyphase etworks J.L. Kirtley Jr. 1 Introduction
More informationAlternating Current Circuits and Electromagnetic Waves
Arecibo, a large radio telescope in Puerto Rico, gathers electromagnetic radiation in the form of radio waves. These long wavelengths pass through obscuring dust clouds, allowing astronomers to create
More informationUsing the Impedance Method
Using the Impedance Method The impedance method allows us to completely eliminate the differential equation approach for the determination of the response of circuits. In fact the impedance method even
More informationIntroduction to the Smith Chart for the MSA Sam Wetterlin 10/12/09 Z +
Introduction to the Smith Chart for the MSA Sam Wetterlin 10/12/09 Quick Review of Reflection Coefficient The Smith chart is a method of graphing reflection coefficients and impedance, and is often useful
More informationStudent Name Instructor Name. High School or Vocational Center Grade. COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Electronics
Student Name Instructor Name High School or Vocational Center Grade COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Electronics Please check below each skill the student has mastered as described,
More informationFor these various types, the electrical configurations that are available are:
RF Transformers RF transformers are widely used in lowpower electronic circuits for impedance matching to achieve maximum power transfer, for voltage stepup or stepdown, and for isolating dc from two
More informationINDUCTION REGULATOR. Objective:
INDUCTION REGULATOR Objective: Using a wound rotor induction motor an Induction Regulator, study the effect of rotor position on the output voltage of the regulator. Also study its behaviour under load
More informationApril 1. Physics 272. Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html. Prof. Philip von Doetinchem philipvd@hawaii.
Physics 272 April 1 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272  Spring 14  von Doetinchem  164 Summary Gauss's
More informationNetwork Theory Question Bank
Network Theory Question Bank UnitI JNTU SYLLABUS: Three Phase Circuits Three phase circuits: Phase sequence Star and delta connection Relation between line and phase voltages and currents in balanced
More information12. Transformers, Impedance Matching and Maximum Power Transfer
1 1. Transformers, Impedance Matching and Maximum Power Transfer Introduction The transformer is a device that takes AC at one voltage and transforms it into another voltage either higher or lower than
More informationDirection of Induced Current
Direction of Induced Current Bar magnet moves through coil Current induced in coil A S N v Reverse pole Induced current changes sign B N S v v Coil moves past fixed bar magnet Current induced in coil as
More informationDIODE CIRCUITS CHAPTER 2
CHAPTER 2 DIODE CIRCUITS As discussed in the previous section, diodes are essentially oneway valves. They carry current in one direction, but block current in the other. In addition, in the forward conduction
More informationElectromagnetism Laws and Equations
Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E and Dfields............................................. Electrostatic Force............................................2
More information