R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

Size: px
Start display at page:

Download "R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder"

Transcription

1 R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

2 Chapter 14 Inductor Design 14.1 Filter inductor design constraints 14.2 A step-by-step design procedure 14.3 Multiple-winding magnetics design using the K g method 14.4 Examples 14.5 Summary of key points 1

3 14.1 Filter inductor design constraints Objective: i L R Design inductor having a given inductance L, which carries worst-case current I max without saturating, and which has a given winding resistance R, or, equivalently, exhibits a worst-case copper loss of P cu = I rms 2 R Example: filter inductor in CCM buck converter L i i I i L + 0 DT s T s t 2

4 Assumed filter inductor geometry Core reluctance R c Φ i + n v turns Air gap reluctance ni + R g F c + R c Φ R g Solve magnetic circuit: l c R c = µ c A c l g R g = µ 0 A c ni = Φ R c + R g Usually R c < R g and hence ni ΦR g 3

5 Constraint: maximum flux density Given a peak winding current I max, it is desired to operate the core flux density at a peak value B max. The value of B max is chosen to be less than the worst-case saturation flux density B sat of the core material. From solution of magnetic circuit: ni = BA c R g Let I = I max and B = B max : ni max = B max A c R g = B max l g µ 0 This is constraint #1. The turns ratio n and air gap length l g are unknown. 4

6 Constraint: inductance Must obtain specified inductance L. We know that the inductance is L = n2 R g = µ 0A c n 2 l g This is constraint #2. The turns ratio n, core area A c, and air gap length l g are unknown. 5

7 Constraint: winding area Wire must fit through core window (i.e., hole in center of core) core Total area of copper in window: na W Area available for winding conductors: wire bare area A W core window area W A K u W A Third design constraint: K u W A na W 6

8 The window utilization factor K u also called the fill factor K u is the fraction of the core window area that is filled by copper Mechanisms that cause K u to be less tha: Round wire does not pack perfectly, which reduces K u by a factor of 0.7 to 0.55 depending on winding technique Insulation reduces K u by a factor of 0.95 to 0.65, depending on wire size and type of insulation Bobbin uses some window area Additional insulation may be required between windings Typical values of K u : 0.5 for simple low-voltage inductor 0.25 to 0.3 for off-line transformer 0.05 to 0.2 for high-voltage transformer (multiple kv) 0.65 for low-voltage foil-winding inductor 7

9 Winding resistance The resistance of the winding is R = ρ l b A W where is the resistivity of the conductor material, l b is the length of the wire, and A W is the wire bare area. The resistivity of copper at room temperature is cm. The length of the wire comprising an n-turn winding can be expressed as l b = n (MLT) where (MLT) is the mean-length-per-turn of the winding. The meanlength-per-turn is a function of the core geometry. The above equations can be combined to obtain the fourth constraint: R = ρ n (MLT) A W 8

10 The core geometrical constant K g The four constraints: ni max = B max A c R g = B max l g µ 0 L = n2 R g = µ 0A c n 2 l g K u W A na W These equations involve the quantities R = ρ n (MLT) A W A c, W A, and MLT, which are functions of the core geometry, I max, B max, µ 0, L, K u, R, and, which are given specifications or other known quantities, and n, l g, and A W, which are unknowns. Eliminate the three unknowns, leading to a single equation involving the remaining quantities. 9

11 Core geometrical constant K g Elimination of n, l g, and A W leads to A 2 c W A (MLT) ρl2 2 I max 2 B max RK u Right-hand side: specifications or other known quantities Left-hand side: function of only core geometry So we must choose a core whose geometry satisfies the above equation. The core geometrical constant K g is defined as K g = A c 2 W A (MLT) 10

12 Discussion K g = A 2 cw A (MLT) ρl2 2 I max 2 11 B max RK u K g is a figure-of-merit that describes the effective electrical size of magnetic cores, in applications where the following quantities are specified: Copper loss Maximum flux density How specifications affect the core size: A smaller core can be used by increasing B max use core material having higher B sat R allow more copper loss How the core geometry affects electrical capabilities: A larger K g can be obtained by increase of A c more iron core material, or W A larger window and more copper

13 14.2 A step-by-step procedure The following quantities are specified, using the units noted: Wire resistivity ( -cm) Peak winding current I max (A) Inductance L (H) Winding resistance R ( ) Winding fill factor K u Core maximum flux density B max (T) The core dimensions are expressed in cm: Core cross-sectional area A c (cm 2 ) Core window area W A (cm 2 ) Mean length per turn MLT (cm) The use of centimeters rather than meters requires that appropriate factors be added to the design equations. 12

14 Determine core size K g ρl2 2 I max (cm 5 ) RK u B max Choose a core which is large enough to satisfy this inequality (see Appendix D for magnetics design tables). Note the values of A c, W A, and MLT for this core. 13

15 Determine air gap length l g = µ 2 0LI max A c B max (m) with A c expressed in cm 2. µ 0 = H/m. The air gap length is given in meters. The value expressed above is approximate, and neglects fringing flux and other nonidealities. 14

16 A L Core manufacturers sell gapped cores. Rather than specifying the air gap length, the equivalent quantity A L is used. A L is equal to the inductance, in mh, obtained with a winding of 1000 turns. When A L is specified, it is the core manufacturer s responsibility to obtain the correct gap length. The required A L is given by: A c 2 A L = 10B 2 max 2 (mh/1000 turns) LI max L = A L n (Henries) Units: A c cm 2, L Henries, B max Tesla. 15

17 Determine number of turns n n = LI max B max A c

18 Evaluate wire size A W K uw A n (cm 2 ) Select wire with bare copper area A W less than or equal to this value. An American Wire Gauge table is included in Appendix D. As a check, the winding resistance can be computed: R = ρn (MLT) A w ( ) 17

19 Boost filter inductor example

20 Boost filter inductor example Fixed input voltage of 25 V, fixed power = 200 W Variable duty cycle: 0 to 50%, variable output voltage Switching frequency 100 khz, L = 30 µh PQ 26/20 core, TSC 50ALL ferrite material 10 turn winding, two layers, solid copper magnet wire #15 AWG φ = 6.2, M = 2 Calculate dc copper loss, proximity loss, and core loss vs. duty cycle In a dc filter inductor having small current ripple, we normally expect core and proximity losses to be small

21 Loss vs. duty cycle, boost filter inductor

22 14.3 Multiple-winding magnetics design using the K g method The K g design method can be extended to multiplewinding magnetic elements such as transformers and coupled inductors. This method is applicable when Copper loss dominates the total loss (i.e. core loss is ignored), or The maximum flux density B max is a specification rather than a quantity to be optimized To do this, we must Find how to allocate the window area between the windings Generalize the step-by-step design procedure 18

23 Window area allocation Given: application with k windings having known rms currents and desired turns ratios v 1 = v 2 n 2 = = v k n k rms current I 1 : n 2 rms current I 2 Core Window area W A Core mean length per turn (MLT) Wire resistivity ρ Fill factor K u : n k rms current I k Q: how should the window area W A be allocated among the windings? 19

24 Allocation of winding area Winding 1 allocation α 1 W A Winding 2 allocation α 2 W A etc. { { Total window area W A 0<α j <1 α 1 + α α k =1 20

25 Copper loss in winding j Copper loss (not accounting for proximity loss) is P cu, j = I j 2 R j Resistance of winding j is with R j = ρ l j A W,j l j = n j (MLT) A W, j = W AK u α j n j length of wire, winding j wire area, winding j Hence R j = ρ n2 j (MLT) W A K u α j 21 P cu,j = n j 2 i j 2 ρ(mlt) W A K u α j

26 Total copper loss of transformer Sum previous expression over all windings: P cu,tot = P cu,1 + P cu,2 + + P cu,k = ρ (MLT) W A K u k Σj =1 n 2 2 j I j α j Need to select values for 1, 2,, k such that the total copper loss is minimized 22

27 Variation of copper losses with 1 Copper loss Pcu,1 P cu,tot P cu,2 + P cu, P cu,k For 1 = 0: wire of winding 1 has zero area. P cu,1 tends to infinity For 1 = 1: wires of remaining windings have zero area. Their copper losses tend to infinity 0 1 α 1 There is a choice of 1 that minimizes the total copper loss 23

28 Method of Lagrange multipliers to minimize total copper loss Minimize the function P cu,tot = P cu,1 + P cu,2 + + P cu,k = ρ (MLT) W A K u k Σj =1 n 2 2 j I j α j subject to the constraint α 1 + α α k =1 Define the function where f (α 1, α 2,, α k, )=P cu,tot (α 1, α 2,, α k )+ g(α 1, α 2,, α k ) g(α 1, α 2,, α k )=1 α j Σj =1 is the constraint that must equal zero and is the Lagrange multiplier k 24

29 Lagrange multipliers continued Optimum point is solution of the system of equations f (α 1, α 2, α 1, α k, ) =0 f (α 1, α 2, α 2, α k, ) =0 f (α 1, α 2, α k, α k, ) =0 f (α 1, α 2,, α k, ) =0 Result: = ρ (MLT) W A K u α m = n mi m Σ n j I j n =1 An alternate form: α m = V mi m Σ V j I j n =1 k Σj =1 n j I j 2 = P cu,tot 25

30 Interpretation of result α m = Apparent power in winding j is where V j I j V mi m Σ V j I j n =1 V j is the rms or peak applied voltage I j is the rms current Window area should be allocated according to the apparent powers of the windings 26

31 Example PWM full-bridge transformer i 1 i 2 I turns { } n 2 turns } n 2 turns i 1 n 2 I i Note that waveshapes (and hence rms values) of the primary and secondary currents are different Treat as a threewinding transformer i 2 i 3 I 0 n 2 I 0.5I 0.5I 0 I 0.5I 0.5I 0 DT s T s T s +DT s 2T s t 27

32 Expressions for RMS winding currents i 1 n 2 I I 1 = 1 2Ts I 2 = I 3 = 1 2Ts see Appendix A 2T s i 2 1 dt = n 2 I 0 D 2T s i 2 2 dt = 1 2 I 1+D 0 i 2 i 3 I n 2 I 0.5I 0.5I 0 I 0.5I 0.5I 0 DT s T s T s +DT s 2T s t 28

33 Allocation of window area: α m = V mi m Σ V j I j n =1 Plug in rms current expressions. Result: α 1 = D D Fraction of window area allocated to primary winding α 2 = α 3 = D 1+D Fraction of window area allocated to each secondary winding 29

34 Numerical example Suppose that we decide to optimize the transformer design at the worst-case operating point D = Then we obtain α 1 = α 2 = α 3 = The total copper loss is then given by P cu,tot = ρ(mlt) W A K u 3 Σj =1 n j I j 2 = ρ(mlt)n 2 2 I 2 W A K u 1+2D +2 D(1 + D) 30

35 Coupled inductor design constraints Consider now the design of a coupled inductor having k windings. We want to obtain a specified value of magnetizing inductance, with specified turns ratios and total copper loss. i 1 + v 1 i M L M : n 2 + v 2 i 2 Magnetic circuit model: R c R 1 R 2 i M + Φ R g + v k i k : n k R k 31

36 Relationship between magnetizing current and winding currents : n 2 i 1 + i M + i 2 v 1 L M v 2 R 1 R 2 Solution of circuit model, or by use of Ampere s Law: i M =i 1 + n 2 i n k i k + v k i k : n k R k 32

37 Solution of magnetic circuit model: Obtain desired maximum flux density R c Assume that gap reluctance is much larger than core reluctance: i M + Φ R g i M =BA c R g Design so that the maximum flux density B max is equal to a specified value (that is less than the saturation flux density B sat ). B max is related to the maximum magnetizing current according to I M,max = B max A c R g = B max l g µ 0 33

38 Obtain specified magnetizing inductance By the usual methods, we can solve for the value of the magnetizing inductance L M (referred to the primary winding): L M = n = n µ 0 A c R 1 g l g 34

39 Copper loss Allocate window area as described in Sectio As shown in that section, the total copper loss is then given by P cu = ρ(mlt)n2 2 1I tot W A K u with I tot = k Σ j =1 n j I j 35

40 Eliminate unknowns and solve for K g Eliminate the unknowns l g and : P cu = ρ(mlt)l 2 MI 2 2 tot I M,max 2 B max A 2 c W A K u Rearrange equation so that terms that involve core geometry are on RHS while specifications are on LHS: A 2 c W A (MLT) = ρl 2 MI 2 2 tot I M,max 2 B max K u P cu The left-hand side is the same K g as in single-winding inductor design. Must select a core that satisfies K g ρl 2 MI 2 2 tot I M,max 2 B max K u P cu 36

41 Step-by-step design procedure: Coupled inductor The following quantities are specified, using the units noted: Wire resistivity ( -cm) k n Total rms winding currents I tot = Σ j n I j (A) (referred to winding 1) 1 j =1 Peak magnetizing current I M, max (A) (referred to winding 1) Desired turns ratios n 2 /. n 3 /n 2. etc. Magnetizing inductance L M (H) (referred to winding 1) Allowed copper loss P cu (W) Winding fill factor K u Core maximum flux density B max (T) The core dimensions are expressed in cm: Core cross-sectional area A c (cm 2 ) Core window area W A (cm 2 ) Mean length per turn MLT (cm) The use of centimeters rather than meters requires that appropriate factors be added to the design equations. 37

42 1. Determine core size K g ρl 2 MI 2 2 tot I M,max (cm 5 ) P cu K u B max Choose a core that satisfies this inequality. Note the values of A c, W A, and MLT for this core. The resistivity of copper wire is cm at room temperature, and cm at 100 C. 38

43 2. Determine air gap length l g = µ 2 0L M I M,max (m) A c B max (value neglects fringing flux, and a longer gap may be required) The permeability of free space is µ 0 = H/m 39

44 3. Determine number of turns For winding 1: = L MI M,max B max A c 10 4 For other windings, use the desired turns ratios: n 2 = n 2 n 3 = n 3 40

45 4. Evaluate fraction of window area allocated to each winding α 1 = I 1 I tot α 2 = n 2I 2 I tot α k = n ki k I tot Winding 1 allocation α 1 W A Winding 2 allocation α 2 W A etc. { { 0<α j <1 α 1 + α α k =1 Total window area W A 41

46 5. Evaluate wire sizes A w1 α 1K u W A A w2 α 2K u W A n 2 See American Wire Gauge (AWG) table at end of Appendix D. 42

47 14.4 Examples Coupled Inductor for a Two-Output Forward Converter CCM Flyback Transformer 43

48 Coupled Inductor for a Two-Output Forward Converter v g + + i 1 v 1 Output 1 28 V 4 A f s = 200 khz n 2 turns i 2 + v 2 Output 2 12 V 2 A The two filter inductors can share the same core because their applied voltage waveforms are proportional. Select turns ratio n 2 / approximately equal to v 2 /v 1 = 12/28. 44

49 Coupled inductor model and waveforms v M + i 1 + i M i M L M v 1 I M i M Coupled inductor model : n 2 i 2 + v 2 0 v M 0 D T s V 1 Secondary-side circuit, with coupled inductor model Magnetizing current and voltage waveforms. i M is the sum of the winding currents i 1 + i 2. 45

50 Nominal full-load operating point Design for CCM operation with D = 0.35 v g + + i 1 v 1 Output 1 28 V 4 A i M = 20% of I M f s = 200 khz f s = 200 khz n 2 turns i 2 + v 2 Output 2 12 V 2 A DC component of magnetizing current is I M = I 1 + n 2 I 2 = (4 A) + 12 (2 A) 28 = 4.86 A 46

51 Magnetizing current ripple i M = V 1D T s 2L M i M I M i M To obtain i M = 20% of I M choose L M = V 1D T s 2 i M (28 V)(1 0.35)(5 µs) = 2(4.86 A)(20%) = 47 µh 0 v M 0 D T s V 1 This leads to a peak magnetizing current (referred to winding 1) of I M,max = I M + i M = 5.83 A 47

52 RMS winding currents Since the winding current ripples are small, the rms values of the winding currents are nearly equal to their dc comonents: I 1 = 4 A I 2 = 2 A Hence the sum of the rms winding currents, referred to the primary, is I tot = I 1 + n 2 I 2 = 4.86 A 48

53 Evaluate K g The following engineering choices are made: Allow 0.75 W of total copper loss (a small core having thermal resistance of less than 40 C/W then would have a temperature rise of less than 30 C) Operate the core at B max = 0.25 T (which is less than the ferrite saturation flux density of 0.3 ot 0.5 T) Use fill factor K u = 0.4 (a reasonable estimate for a lowvoltage inductor with multiple windings) Evaluate K g : K g ( cm)(47 µh) 2 (4.86 A) 2 (5.83 A) 2 (0.25 T) (0.75 W)(0.4) = cm 5 49

54 Select core It is decided to use a ferrite PQ core. From Appendix D, the smallest PQ core having K g cm 5 is the PQ 20/16, with K g = cm 5. The data for this core are: A 1 A c = 0.62 cm 2 W A = cm 2 MLT = 4.4 cm 2D 50

55 Air gap length l g = µ 2 0L M I M,max A c B max = (4π 10 7 H/m)(47 µh)(5.83 A) 2 (0.25 T) 2 (0.62 cm 2 ) = 0.52 mm

56 Turns = L MI M,max 10 B max A 4 c (47 µh)(5.83 A) = (0.25 T)(0.62 cm 2 ) 104 = 17.6 turns n 2 = n 2 = (17.6) = 7.54 turns Let s round off to = 17 n 2 = 7 52

57 Wire sizes Allocation of window area: α 1 = I 1 I tot = α 2 = n 2I 2 I tot = (17)(4 A) (17)(4.86 A) = (7)(2 A) (17)(4.86 A) = Determination of wire areas and AWG (from table at end of Appendix D): A w1 α 1K u W A = (0.8235)(0.4)(0.256 cm2 ) = cm 2 (17) use AWG #21 A w2 α 2K u W A = (0.1695)(0.4)(0.256 cm2 ) = cm 2 n 2 (7) use AWG #24 53

58 Example 2: CCM flyback transformer i M Transformer model I M i M V g i 1 i M + L M + v M : n 2 D 1 i 2 C R + V 0 i 1 I M 0 i 2 Q 1 I n M 2 0 v M V g 0 DT s 54

59 Specifications Input voltage Output (full load) Switching frequency Magnetizing current ripple V g = 200V 20 V at 5 A 150 khz Duty cycle D = 0.4 Turns ratio n 2 / = 0.15 Copper loss 20% of dc magnetizing current 1.5 W Fill factor K u = 0.3 Maximum flux density B max = 0.25 T 55

60 Basic converter calculations Components of magnetizing current, referred to primary: I M = n 2 1 D V R = 1.25 A RMS winding currents: I 1 = I M D i M I M 2 = A i M = 20% I M = 0.25 A I 2 = n 2 I M D i M I M 2 = 6.50 A I M,max = I M + i M = 1.5 A Choose magnetizing inductance: I tot = I 1 + n 2 I 2 = 1.77 A L M = V g DT s 2 i M = 1.07 mh 56

61 Choose core size K g ρl 2 MI 2 2 tot I M,max P cu K u B max = cm H A A T W 0.3 = cm The smallest EE core that satisfies this inequality (Appendix D) is the EE30. A 57

62 Choose air gap and turns l g = µ 2 0L M I M,max A c B max = 4π 10 7 H/m H 1.5 A T cm = 0.44 mm = L MI M,max B max A c 10 4 = H 1.5 A 0.25 T 1.09 cm = 58.7 turns Round to = n 2 = n 2 = = 8.81 n 2 =9

63 Wire gauges α 1 = I 1 I tot = A 1.77 A = 0.45 α 2 = n 2I 2 I tot = A A = 0.55 A W1 α 1K u W A = cm 2 use #28 AWG A W2 α 2K u W A n 2 = cm 2 use #19 AWG 59

64 Core loss CCM flyback example B-H loop for this application: B B sat B max B The relevant waveforms: B B max V g B H c Minor B H loop, CCM flyback example B H loop, large excitation 0 v M 0 A c V g DT s B vs. applied voltage, from Faraday s law: db dt = v M A c For the first subinterval: db dt = V g A c 60

65 Calculation of ac flux density and core loss Solve for B: B = V g A c DT s Plug in values for flyback example: 200 V µs B = cm 2 =0.041 T From manufacturer s plot of core loss (at left), the power loss density is 0.04 W/cm 3. Hence core loss is P fe = 0.04 W/cm 3 A c l m = 0.04 W/cm cm cm = 0.25 W 61 Power loss density, Watts/cm W/cm 3 400kHz 200kHz 150kHz 100kHz 50kHz 20kHz B, Tesla

66 Comparison of core and copper loss Copper loss is 1.5 W does not include proximity losses, which could substantially increase total copper loss Core loss is 0.25 W Core loss is small because ripple and B are small It is not a bad approximation to ignore core losses for ferrite in CCM filter inductors Could consider use of a less expensive core material having higher core loss Neglecting core loss is a reasonable approximation for this application Design is dominated by copper loss The dominant constraint on flux density is saturation of the core, rather than core loss 62

Chapter 14: Inductor design

Chapter 14: Inductor design Chapter 14 Inductor Design 14.1 Filter inductor design constraints 14.2 A step-by-step design procedure 14.3 Multiple-winding magnetics design using the K g method 14.4 Examples 14.5 Summary of key points

More information

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder 15.3.2 Example 2 Multiple-Output Full-Bridge Buck Converter Q 1 D 1 Q 3 D 3 + T 1 : : n 2 D 5 i

More information

15.1 Transformer Design: Basic Constraints. Chapter 15: Transformer design. Chapter 15 Transformer Design

15.1 Transformer Design: Basic Constraints. Chapter 15: Transformer design. Chapter 15 Transformer Design Chapter 5 Transformer Design Some more advanced design issues, not considered in previous chapter: : n Inclusion of core loss Selection of operating flux density to optimize total loss Multiple winding

More information

In The Name of GOD. Switched Mode Power Supply

In The Name of GOD. Switched Mode Power Supply In The Name of GOD Switched Mode Power Supply Switched Mode Power Supply Lecture 9 Inductor Design Φ Adib Abrishamifar EE Department IUST Outline } Types of magnetic devices } Filter inductor } Ac inductor

More information

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder Part III. Magnetics 13 Basic Magnetics Theory 14 Inductor Design 15 Transformer Design 1 Chapter

More information

Part III. Magnetics. Chapter 13: Basic Magnetics Theory. Chapter 13 Basic Magnetics Theory

Part III. Magnetics. Chapter 13: Basic Magnetics Theory. Chapter 13 Basic Magnetics Theory Part III. Magnetics 3 Basic Magnetics Theory Inductor Design 5 Transformer Design Chapter 3 Basic Magnetics Theory 3. Review of Basic Magnetics 3.. Basic relationships 3..2 Magnetic circuits 3.2 Transformer

More information

Switched Mode Power Conversion Prof. L. Umanand Department of Electronics System Engineering Indian Institute of Science, Bangalore

Switched Mode Power Conversion Prof. L. Umanand Department of Electronics System Engineering Indian Institute of Science, Bangalore Switched Mode Power Conversion Prof. L. Umanand Department of Electronics System Engineering Indian Institute of Science, Bangalore Lecture - 39 Magnetic Design Good day to all of you. Today, we shall

More information

6.3. Transformer isolation

6.3. Transformer isolation 6.3. Transformer isolation Objectives: Isolation of input and output ground connections, to meet safety requirements eduction of transformer size by incorporating high frequency isolation transformer inside

More information

Elements of Power Electronics PART I: Bases

Elements of Power Electronics PART I: Bases Elements of Power Electronics PART I: Bases Fabrice Frébel (fabrice.frebel@ulg.ac.be) September 21 st, 2017 Goal and expectations The goal of the course is to provide a toolbox that allows you to: understand

More information

Section 8: Magnetic Components

Section 8: Magnetic Components Section 8: Magnetic omponents Inductors and transformers used in power electronic converters operate at quite high frequency. The operating frequency is in khz to MHz. Magnetic transformer steel which

More information

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder . W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder 2.4 Cuk converter example L 1 C 1 L 2 Cuk converter, with ideal switch i 1 i v 1 2 1 2 C 2 v 2 Cuk

More information

Switched Mode Power Conversion

Switched Mode Power Conversion Inductors Devices for Efficient Power Conversion Switches Inductors Transformers Capacitors Inductors Inductors Store Energy Inductors Store Energy in a Magnetic Field In Power Converters Energy Storage

More information

ET4119 Electronic Power Conversion 2011/2012 Solutions 27 January 2012

ET4119 Electronic Power Conversion 2011/2012 Solutions 27 January 2012 ET4119 Electronic Power Conversion 2011/2012 Solutions 27 January 2012 1. In the single-phase rectifier shown below in Fig 1a., s = 1mH and I d = 10A. The input voltage v s has the pulse waveform shown

More information

Lecture 17 Push-Pull and Bridge DC-DC converters Push-Pull Converter (Buck Derived) Centre-tapped primary and secondary windings

Lecture 17 Push-Pull and Bridge DC-DC converters Push-Pull Converter (Buck Derived) Centre-tapped primary and secondary windings ecture 17 Push-Pull and Bridge DC-DC converters Push-Pull Converter (Buck Derived) Centre-tapped primary and secondary windings 1 2 D 1 i v 1 v 1s + v C o R v 2 v 2s d 1 2 T 1 T 2 D 2 Figure 17.1 v c (

More information

Chapter 1 Magnetic Circuits

Chapter 1 Magnetic Circuits Principles of Electric Machines and Power Electronics Third Edition P. C. Sen Chapter 1 Magnetic Circuits Chapter 1: Main contents i-h relation, B-H relation Magnetic circuit and analysis Property of magnetic

More information

Chapter 3. Steady-State Equivalent Circuit Modeling, Losses, and Efficiency

Chapter 3. Steady-State Equivalent Circuit Modeling, Losses, and Efficiency Chapter 3. Steady-State Equivalent Circuit Modeling, Losses, and Efficiency 3.1. The dc transformer model 3.2. Inclusion of inductor copper loss 3.3. Construction of equivalent circuit model 3.4. How to

More information

Review of Basic Electrical and Magnetic Circuit Concepts EE

Review of Basic Electrical and Magnetic Circuit Concepts EE Review of Basic Electrical and Magnetic Circuit Concepts EE 442-642 Sinusoidal Linear Circuits: Instantaneous voltage, current and power, rms values Average (real) power, reactive power, apparent power,

More information

Chapter 15 Magnetic Circuits and Transformers

Chapter 15 Magnetic Circuits and Transformers Chapter 15 Magnetic Circuits and Transformers Chapter 15 Magnetic Circuits and Transformers 1. Understand magnetic fields and their interactio with moving charges. 2. Use the right-hand rule to determine

More information

Lecture 30: WED 04 NOV

Lecture 30: WED 04 NOV Physics 2113 Jonathan Dowling Lecture 30: WED 04 NOV Induction and Inductance II Fender Stratocaster Solenoid Pickup F a r a d a y ' s E x p e r i m e n t s I n a s e r i e s o f e x p e r i m e n t s,

More information

Lecture 24. April 5 th, Magnetic Circuits & Inductance

Lecture 24. April 5 th, Magnetic Circuits & Inductance Lecture 24 April 5 th, 2005 Magnetic Circuits & Inductance Reading: Boylestad s Circuit Analysis, 3 rd Canadian Edition Chapter 11.1-11.5, Pages 331-338 Chapter 12.1-12.4, Pages 341-349 Chapter 12.7-12.9,

More information

Lecture Set 1 Introduction to Magnetic Circuits

Lecture Set 1 Introduction to Magnetic Circuits Lecture Set 1 Introduction to Magnetic Circuits S.D. Sudhoff Spring 2017 1 Goals Review physical laws pertaining to analysis of magnetic systems Introduce concept of magnetic circuit as means to obtain

More information

ELECTRO MAGNETIC INDUCTION

ELECTRO MAGNETIC INDUCTION ELECTRO MAGNETIC INDUCTION 1) A Circular coil is placed near a current carrying conductor. The induced current is anti clock wise when the coil is, 1. Stationary 2. Moved away from the conductor 3. Moved

More information

Chapter 11 AC and DC Equivalent Circuit Modeling of the Discontinuous Conduction Mode

Chapter 11 AC and DC Equivalent Circuit Modeling of the Discontinuous Conduction Mode Chapter 11 AC and DC Equivalent Circuit Modeling of the Discontinuous Conduction Mode Introduction 11.1. DCM Averaged Switch Model 11.2. Small-Signal AC Modeling of the DCM Switch Network 11.3. High-Frequency

More information

Analysis of Thermal Behavior of High Frequency Transformers Using Finite Element Method

Analysis of Thermal Behavior of High Frequency Transformers Using Finite Element Method J. Electromagnetic Analysis & Applications, 010,, 67-63 doi:10.436/emaa.010.1108 ublished Online November 010 (http://www.scirp.org/ournal/emaa) Analysis of Thermal Behavior of High Frequency Transformers

More information

Chapter 21. Derivations for the Design Equations

Chapter 21. Derivations for the Design Equations Chapter 21 Derivations for the Design Equations The author would like to thank Richard Ozenbaugh of Linear Magnetics for his help with the derivations. Table of Contents 1. Output Power, P 0, Versus Apparent

More information

Cross Regulation Mechanisms in Multiple-Output Forward and Flyback Converters

Cross Regulation Mechanisms in Multiple-Output Forward and Flyback Converters Cross Regulation Mechanisms in Multiple-Output Forward and Flyback Converters Bob Erickson and Dragan Maksimovic Colorado Power Electronics Center (CoPEC) University of Colorado, Boulder 80309-0425 http://ece-www.colorado.edu/~pwrelect

More information

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder . W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder 8.1.7. The low-q approximation Given a second-order denominator polynomial, of the form G(s)= 1

More information

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder . W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder Part II" Converter Dynamics and Control! 7.!AC equivalent circuit modeling! 8.!Converter transfer

More information

Mutual Inductance: This is the magnetic flux coupling of 2 coils where the current in one coil causes a voltage to be induced in the other coil.

Mutual Inductance: This is the magnetic flux coupling of 2 coils where the current in one coil causes a voltage to be induced in the other coil. agnetically Coupled Circuits utual Inductance: This is the magnetic flux coupling of coils where the current in one coil causes a voltage to be induced in the other coil. st I d like to emphasize that

More information

Force and Displacement Measurement

Force and Displacement Measurement Force and Displacement Measurement Prof. R.G. Longoria Updated Fall 20 Simple ways to measure a force http://scienceblogs.com/dotphysics/200/02/diy_force_probe.php Example: Key Force/Deflection measure

More information

Reactor Characteristic Evaluation and Analysis Technologies of JFE Steel

Reactor Characteristic Evaluation and Analysis Technologies of JFE Steel JFE TECHNICAL REPORT No. 21 (Mar. 2016) Reactor Characteristic Evaluation and Analysis Technologies of HIRATANI Tatsuhiko *1 NAMIKAWA Misao *2 NISHINA Yoshiaki *3 Abstract: Reactor characteristic evaluation

More information

The initial magnetization curve shows the magnetic flux density that would result when an increasing magnetic field is applied to an initially

The initial magnetization curve shows the magnetic flux density that would result when an increasing magnetic field is applied to an initially MAGNETIC CIRCUITS The study of magnetic circuits is important in the study of energy systems since the operation of key components such as transformers and rotating machines (DC machines, induction machines,

More information

Electromagnetic Induction & Inductors

Electromagnetic Induction & Inductors Electromagnetic Induction & Inductors 1 Revision of Electromagnetic Induction and Inductors (Much of this material has come from Electrical & Electronic Principles & Technology by John Bird) Magnetic Field

More information

Tutorial Sheet IV. Fig. IV_2.

Tutorial Sheet IV. Fig. IV_2. Tutorial Sheet IV 1. Two identical inductors 1 H each are connected in series as shown. Deduce the combined inductance. If a third and then a fourth are similarly connected in series with this combined

More information

Electric Circuits I. Inductors. Dr. Firas Obeidat

Electric Circuits I. Inductors. Dr. Firas Obeidat Electric Circuits I Inductors Dr. Firas Obeidat 1 Inductors An inductor is a passive element designed to store energy in its magnetic field. They are used in power supplies, transformers, radios, TVs,

More information

[22.1 (2)(0.42) (3.38 / 2)] At/Wb

[22.1 (2)(0.42) (3.38 / 2)] At/Wb Transformers and Inductors for Power Electronics Theory, Design and Applications p. xiii: In Hurley bio add He received the IEEE Power Electronics Society Middlebrook Award for technical achievement in

More information

Modellierung von Kern- und Wicklungsverlusten Jonas Mühlethaler, Johann W. Kolar

Modellierung von Kern- und Wicklungsverlusten Jonas Mühlethaler, Johann W. Kolar Modellierung von Kern- und Wicklungsverlusten Jonas Mühlethaler, Johann W. Kolar Power Electronic Systems Laboratory, ETH Zurich Motivation Modeling Inductive Components Employing best state-of-the-art

More information

ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT

ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT Chapter 31: ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT 1 A charged capacitor and an inductor are connected in series At time t = 0 the current is zero, but the capacitor is charged If T is the

More information

Scheme I SAMPLE QUESTION PAPER I

Scheme I SAMPLE QUESTION PAPER I SAMPLE QUESTION PAPER I Marks : 70 Time: 3 Hours Q.1) A) Attempt any FIVE of the following. a) Define active components. b) List different types of resistors. c) Describe method to test following passive

More information

The output voltage is given by,

The output voltage is given by, 71 The output voltage is given by, = (3.1) The inductor and capacitor values of the Boost converter are derived by having the same assumption as that of the Buck converter. Now the critical value of the

More information

Tutorial Sheet Fig. Q1

Tutorial Sheet Fig. Q1 Tutorial Sheet - 04 1. The magnetic circuit shown in Fig. Q1 has dimensions A c = A g = 9 cm 2, g = 0.050 cm, l c = 30 cm, and N = 500 turns. Assume the value of the relative permeability,µ r = 70,000

More information

Suppose two uniform bars meet at an abrupt plane and there is a magnetic field induced by an extended core and coil structure off stage as in:

Suppose two uniform bars meet at an abrupt plane and there is a magnetic field induced by an extended core and coil structure off stage as in: Class Notes Week of 1/9 /3/017 ENGN1931F The magnetic structures that are central to the design of generators, transformers, motors, inductors, solenoids, etc. can be complex. We need a way to make approximate

More information

Design and analysis of the ferrite air-gapped cores for a resonant inductor

Design and analysis of the ferrite air-gapped cores for a resonant inductor ARCHIVES OF ELECTRICAL ENGINEERING VOL. 67(3), pp. 579 589 (2018) DOI 10.24425/123664 Design and analysis of the ferrite air-gapped cores for a resonant inductor JIANFEN ZHENG, CHUNFANG WANG, DONGWEI XIA

More information

Power Electronics

Power Electronics Prof. Dr. Ing. Joachim Böcker Power Electronics 3.09.06 Last Name: Student Number: First Name: Study Program: Professional Examination Performance Proof Task: (Credits) (0) (0) 3 (0) 4 (0) Total (80) Mark

More information

EE 3324 Electromagnetics Laboratory

EE 3324 Electromagnetics Laboratory EE 3324 Electromagnetics Laboratory Experiment #3 Inductors and Inductance 1. Objective The objective of Experiment #3 is to investigate the concepts of inductors and inductance. Several inductor geometries

More information

9-3 Inductance. * We likewise can have self inductance, were a timevarying current in a circuit induces an emf voltage within that same circuit!

9-3 Inductance. * We likewise can have self inductance, were a timevarying current in a circuit induces an emf voltage within that same circuit! /3/004 section 9_3 Inductance / 9-3 Inductance Reading Assignment: pp. 90-86 * A transformer is an example of mutual inductance, where a time-varying current in one circuit (i.e., the primary) induces

More information

Magnetic Quantities. Magnetic fields are described by drawing flux lines that represent the magnetic field.

Magnetic Quantities. Magnetic fields are described by drawing flux lines that represent the magnetic field. Chapter 7 Magnetic fields are described by drawing flux lines that represent the magnetic field. Where lines are close together, the flux density is higher. Where lines are further apart, the flux density

More information

magneticsp17 September 14, of 17

magneticsp17 September 14, of 17 EXPERIMENT Magnetics Faraday s Law in Coils with Permanent Magnet, DC and AC Excitation OBJECTIVE The knowledge and understanding of the behavior of magnetic materials is of prime importance for the design

More information

ROEVER COLLEGE OF ENGINEERING & TECHNOLOGY ELAMBALUR, PERAMBALUR DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING ELECTRICAL MACHINES I

ROEVER COLLEGE OF ENGINEERING & TECHNOLOGY ELAMBALUR, PERAMBALUR DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING ELECTRICAL MACHINES I ROEVER COLLEGE OF ENGINEERING & TECHNOLOGY ELAMBALUR, PERAMBALUR-621220 DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING ELECTRICAL MACHINES I Unit I Introduction 1. What are the three basic types

More information

Regulated DC-DC Converter

Regulated DC-DC Converter Regulated DC-DC Converter Zabir Ahmed Lecturer, BUET Jewel Mohajan Lecturer, BUET M A Awal Graduate Research Assistant NSF FREEDM Systems Center NC State University Former Lecturer, BUET 1 Problem Statement

More information

Thermal vs. Power Loss Efficiency Considerations for Powder Core Materials. Christopher Oliver Nien Teng Micrometals, Incorporated

Thermal vs. Power Loss Efficiency Considerations for Powder Core Materials. Christopher Oliver Nien Teng Micrometals, Incorporated Thermal vs. Power Loss Efficiency Considerations for Powder Core Materials Christopher Oliver Nien Teng Micrometals, Incorporated Outline Powder Cores Description What properties change with temperature

More information

Chapter 7 DC-DC Switch-Mode Converters

Chapter 7 DC-DC Switch-Mode Converters Chapter 7 DC-DC Switch-Mode Converters dc-dc converters for switch-mode dc power supplies and dc-motor drives 7-1 Block Diagram of DC-DC Converters Functional block diagram 7-2 Stepping Down a DC Voltage

More information

Magnetism & Electromagnetism

Magnetism & Electromagnetism Magnetism & Electromagnetism By: Dr Rosemizi Abd Rahim Click here to watch the magnetism and electromagnetism animation video http://rmz4567.blogspot.my/2013/02/electrical-engineering.html 1 Learning Outcomes

More information

CERN ACCELERATOR SCHOOL Power Converters. Passive components. Prof. Alfred Rufer

CERN ACCELERATOR SCHOOL Power Converters. Passive components. Prof. Alfred Rufer CERN ACCELERATOR SCHOOL Power Converters Passive components Prof. Alfred Rufer Overview Part 1: (to be designed) Part 2: Capacitors (to be selected) Part 3: A new component: The Supercapacitor, component

More information

Physics 1c Practical, Spring 2015 Hw 3 Solutions

Physics 1c Practical, Spring 2015 Hw 3 Solutions Physics 1c Practical, Spring 2015 Hw 3 Solutions April 16, 2015 1 Serway 31.79 (5 points) By Lenz s Law, current will flow in each of the two sub-loops to oppose the change in flux. One can easily see

More information

LECTURE 8 Fundamental Models of Pulse-Width Modulated DC-DC Converters: f(d)

LECTURE 8 Fundamental Models of Pulse-Width Modulated DC-DC Converters: f(d) 1 ECTURE 8 Fundamental Models of Pulse-Width Modulated DC-DC Converters: f(d) I. Quasi-Static Approximation A. inear Models/ Small Signals/ Quasistatic I V C dt Amp-Sec/Farad V I dt Volt-Sec/Henry 1. Switched

More information

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder . W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder Objective of Part II! Develop tools for modeling, analysis, and design of converter control systems!

More information

Electromagnetic Induction

Electromagnetic Induction Faraday s Discovery Faraday found that there is a current in a coil of wire if and only if the magnetic field passing through the coil is changing. This is an informal statement of Faraday s law. Electromagnetic

More information

Transformer. Transformer comprises two or more windings coupled by a common magnetic circuit (M.C.).

Transformer. Transformer comprises two or more windings coupled by a common magnetic circuit (M.C.). . Transformers Transformer Transformer comprises two or more windings coupled by a common magnetic circuit (M.C.). f the primary side is connected to an AC voltage source v (t), an AC flux (t) will be

More information

SYLLABUS(EE-205-F) SECTION-B

SYLLABUS(EE-205-F) SECTION-B SYLLABUS(EE-205-F) SECTION-A MAGNETIC CIRCUITS AND INDUCTION: Magnetic Circuits, Magnetic Materials and their properties, static and dynamic emfs and dforce on current carrying conductor, AC operation

More information

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder Sampled-data response: i L /i c Sampled-data transfer function : î L (s) î c (s) = (1 ) 1 e st

More information

Some Important Electrical Units

Some Important Electrical Units Some Important Electrical Units Quantity Unit Symbol Current Charge Voltage Resistance Power Ampere Coulomb Volt Ohm Watt A C V W W These derived units are based on fundamental units from the meterkilogram-second

More information

EDEXCEL 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 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 information

ENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL 16 - INDUCTANCE

ENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL 16 - INDUCTANCE ENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL 16 - INDUCTANCE On completion of this tutorial you should be able to do the following. Explain inductance and inductors. Explain

More information

Introduction to AC Circuits (Capacitors and Inductors)

Introduction to AC Circuits (Capacitors and Inductors) Introduction to AC Circuits (Capacitors and Inductors) Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/

More information

MAGNETIC CIRCUITS. Magnetic Circuits

MAGNETIC CIRCUITS. Magnetic Circuits Basic Electrical Theory What is a magnetic circuit? To better understand magnetic circuits, a basic understanding of the physical qualities of magnetic circuits will be necessary. EO 1.8 EO 1.9 EO 1.10

More information

Mutual Inductance. The field lines flow from a + charge to a - change

Mutual Inductance. The field lines flow from a + charge to a - change Capacitors Mutual Inductance Since electrical charges do exist, electric field lines have a starting point and an ending point. For example, if you have a + and a - change, the field lines would look something

More information

Different Techniques for Calculating Apparent and Incremental Inductances using Finite Element Method

Different Techniques for Calculating Apparent and Incremental Inductances using Finite Element Method Different Techniques for Calculating Apparent and Incremental Inductances using Finite Element Method Dr. Amer Mejbel Ali Electrical Engineering Department Al-Mustansiriyah University Baghdad, Iraq amerman67@yahoo.com

More information

Revision Guide for Chapter 15

Revision Guide for Chapter 15 Revision Guide for Chapter 15 Contents tudent s Checklist Revision otes Transformer... 4 Electromagnetic induction... 4 Generator... 5 Electric motor... 6 Magnetic field... 8 Magnetic flux... 9 Force on

More information

Tactics: Evaluating line integrals

Tactics: Evaluating line integrals Tactics: Evaluating line integrals Ampère s law Whenever total current I through passes through an area bounded by a closed curve, the line integral of the magnetic field around the curve is given by Ampère

More information

Preliminary Sizing Design of a 1 MW Low Duty Cycle Switched Reluctance Generator for Aerospace Applications

Preliminary Sizing Design of a 1 MW Low Duty Cycle Switched Reluctance Generator for Aerospace Applications Preliminary Sizing Design of a 1 MW Low Duty Cycle Switched Reluctance Generator for Aerospace Applications Jin-Woo Jung, Ph. D. Student Advisors: Prof. Ali Keyhani Adjunct Prof. Tomy Sebastian Oct. 25,

More information

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder 1.. Averaged switch modeling with the simple approximation i 1 (t) i (t) i (t) v g (t) v 1 (t)

More information

Part 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is

Part 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is 1 Part 4: Electromagnetism 4.1: Induction A. Faraday's Law The magnetic flux through a loop of wire is Φ = BA cos θ B A B = magnetic field penetrating loop [T] A = area of loop [m 2 ] = angle between field

More information

RADIO AMATEUR EXAM GENERAL CLASS

RADIO AMATEUR EXAM GENERAL CLASS RAE-Lessons by 4S7VJ 1 CHAPTER- 2 RADIO AMATEUR EXAM GENERAL CLASS By 4S7VJ 2.1 Sine-wave If a magnet rotates near a coil, an alternating e.m.f. (a.c.) generates in the coil. This e.m.f. gradually increase

More information

Capacitor. Capacitor (Cont d)

Capacitor. Capacitor (Cont d) 1 2 1 Capacitor Capacitor is a passive two-terminal component storing the energy in an electric field charged by the voltage across the dielectric. Fixed Polarized Variable Capacitance is the ratio of

More information

Fachgebiet Leistungselektronik und Elektrische Antriebstechnik. Test Examination: Mechatronics and Electrical Drives

Fachgebiet Leistungselektronik und Elektrische Antriebstechnik. Test Examination: Mechatronics and Electrical Drives Prof. Dr. Ing. Joachim Böcker Test Examination: Mechatronics and Electrical Drives 8.1.214 First Name: Student number: Last Name: Course of Study: Exercise: 1 2 3 Total (Points) (2) (2) (2) (6) Duration:

More information

Magnetic Fields

Magnetic Fields Magnetic circuits introduction Becomes aware of the similarities between the analysis of magnetic circuits and electric circuits. Develop a clear understanding of the important parameters of a magnetic

More information

ASSOCIATE DEGREE IN ENGINEERING RESIT EXAMINATIONS SEMESTER 1. "Electrical Eng Science"

ASSOCIATE DEGREE IN ENGINEERING RESIT EXAMINATIONS SEMESTER 1. Electrical Eng Science ASSOCIATE DEGREE IN ENGINEERING RESIT EXAMINATIONS SEMESTER 1 COURSE NAME: "Electrical Eng Science" CODE: GROUP: "[ADET 2]" DATE: December 2010 TIME: DURATION: 9:00 am "Two hours" INSTRUCTIONS: 1. This

More information

Lecture 47 Switch Mode Converter Transfer Functions: Tvd(s) and Tvg(s) A. Guesstimating Roots of Complex Polynomials( this section is optional)

Lecture 47 Switch Mode Converter Transfer Functions: Tvd(s) and Tvg(s) A. Guesstimating Roots of Complex Polynomials( this section is optional) Lecture 47 Switch Mode Converter Transfer Functions: T vd (s) and T vg (s) A. Guesstimating Roots of Complex Polynomials( this section is optional). Quick Insight n=. n th order case. Cuk example 4. Forth

More information

SECTION 3 BASIC AUTOMATIC CONTROLS UNIT 12 BASIC ELECTRICITY AND MAGNETISM

SECTION 3 BASIC AUTOMATIC CONTROLS UNIT 12 BASIC ELECTRICITY AND MAGNETISM SECTION 3 BASIC AUTOMATIC CONTROLS UNIT 12 BASIC ELECTRICITY AND MAGNETISM Unit Objectives Describe the structure of an atom. Identify atoms with a positive charge and atoms with a negative charge. Explain

More information

Electronic Power Conversion

Electronic Power Conversion Electronic Power Conersion Switch Moe DC-DC Conerters with Isolation Challenge the future Switch moe c-c conerters Frequent requirements: regulate output isolation (safety) multiple outputs Solutions:

More information

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY /$ IEEE

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY /$ IEEE IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007 195 Analysis of Half-Turn Effect in Power Transformers Using Nonlinear-Transient FE Formulation G. B. Kumbhar, S. V. Kulkarni, Member,

More information

Wireless charging using a separate third winding for reactive power supply

Wireless charging using a separate third winding for reactive power supply Wireless charging using a separate third winding for reactive power supply Master s thesis in Energy and Environment IAN ŠALKOIĆ Department of Energy and Environment Division of Electric Power Engineering

More information

Lecture Notes ELEC A6

Lecture Notes ELEC A6 Lecture Notes ELEC A6 Dr. Ramadan El-Shatshat Magnetic circuit 9/27/2006 Elec-A6 - Electromagnetic Energy Conversion 1 Magnetic Field Concepts Magnetic Fields: Magnetic fields are the fundamental mechanism

More information

SECOND ENGINEER REG III/2 MARINE ELECTRO-TECHNOLOGY. 1. Understands the physical construction and characteristics of basic components.

SECOND ENGINEER REG III/2 MARINE ELECTRO-TECHNOLOGY. 1. Understands the physical construction and characteristics of basic components. SECOND ENGINEER REG III/ MARINE ELECTRO-TECHNOLOGY LIST OF TOPICS A B C D Electric and Electronic Components Electric Circuit Principles Electromagnetism Electrical Machines The expected learning outcome

More information

Part II Converter Dynamics and Control

Part II Converter Dynamics and Control Part II Converter Dynamics and Control 7. AC equivalent circuit modeling 8. Converter transfer functions 9. Controller design 10. Ac and dc equivalent circuit modeling of the discontinuous conduction mode

More information

Magnetic Induction Faraday, Lenz, Mutual & Self Inductance Maxwell s Eqns, E-M waves. Reading Journals for Tuesday from table(s)

Magnetic Induction Faraday, Lenz, Mutual & Self Inductance Maxwell s Eqns, E-M waves. Reading Journals for Tuesday from table(s) PHYS 2015 -- Week 12 Magnetic Induction Faraday, Lenz, Mutual & Self Inductance Maxwell s Eqns, E-M waves Reading Journals for Tuesday from table(s) WebAssign due Friday night For exclusive use in PHYS

More information

Capacitors. Charging a Capacitor. Charge and Capacitance. L05: Capacitors and Inductors

Capacitors. Charging a Capacitor. Charge and Capacitance. L05: Capacitors and Inductors L05: Capacitors and Inductors 50 Capacitors 51 Outline of the lecture: Capacitors and capacitance. Energy storage. Capacitance formula. Types of capacitors. Inductors and inductance. Inductance formula.

More information

7.3 State Space Averaging!

7.3 State Space Averaging! 7.3 State Space Averaging! A formal method for deriving the small-signal ac equations of a switching converter! Equivalent to the modeling method of the previous sections! Uses the state-space matrix description

More information

Measurements in Mechatronic design. Transducers

Measurements in Mechatronic design. Transducers Measurements in Mechatronic design Transducers Quantities Current Voltage Torque Force Magnetic flux Distance Temperature Measurement system Physical quanties Transducer Signal conditioning Measurement

More information

MAGNETISM. Magnetism. Magnetism is a result of electrons spinning on their own axis around the nucleus (Figure 18). Basic Electrical Theory

MAGNETISM. Magnetism. Magnetism is a result of electrons spinning on their own axis around the nucleus (Figure 18). Basic Electrical Theory Basic Electrical Theory Certain metals and metallic oxides have the ability to attract other metals. This property is called magnetism, and the materials which have this property are called magnets. Some

More information

Power Electronics Notes 30A Review of Magnetics

Power Electronics Notes 30A Review of Magnetics Power Electronics Notes 30A Review of Magnetics Marc T. Thompson, Ph.D. Thompson Consulting, Inc. 9 Jacob Gates Road Harvard, MA 01451 Phone: (978) 456-7722 Fax: (240) 414-2655 Email: marctt@thompsonrd.com

More information

HighpowerfactorforwardAC-DC converter with low storage capacitor voltage stress

HighpowerfactorforwardAC-DC converter with low storage capacitor voltage stress HAIT Journal of Science and Engineering B, Volume 2, Issues 3-4, pp. 305-326 Copyright C 2005 Holon Academic Institute of Technology HighpowerfactorforwardAC-DC converter with low storage capacitor voltage

More information

6.013 Lecture 11: Inductors and Transformers

6.013 Lecture 11: Inductors and Transformers 6.013 Lecture 11: Inductors and Transformers A. Inductors All circuits carry currents that necessarily produce magnetic fields and store magnetic energy. Thus every wire and circuit element generally has

More information

Revision Guide for Chapter 15

Revision Guide for Chapter 15 Revision Guide for Chapter 15 Contents Revision Checklist Revision otes Transformer...4 Electromagnetic induction...4 Lenz's law...5 Generator...6 Electric motor...7 Magnetic field...9 Magnetic flux...

More information

6.014 Lecture 11: Inductors and Transformers

6.014 Lecture 11: Inductors and Transformers 6.014 Lecture 11: Inductors and Transformers A. Inductors All circuits carry currents that necessarily produce magnetic fields and store magnetic energy. Thus every wire and circuit element generally has

More information

Solution for Fq. A. up B. down C. east D. west E. south

Solution for Fq. A. up B. down C. east D. west E. south Solution for Fq A proton traveling due north enters a region that contains both a magnetic field and an electric field. The electric field lines point due west. It is observed that the proton continues

More information

LECTURE 12 Lossy Converters (Static State Losses but Neglecting Switching Losses) HW #2 Erickson Chapter 3 Problems 6 & 7 A.

LECTURE 12 Lossy Converters (Static State Losses but Neglecting Switching Losses) HW #2 Erickson Chapter 3 Problems 6 & 7 A. ETUE 12 ossy onverters (Static State osses but Neglecting Switching osses) HW #2 Erickson hapter 3 Problems 6 & 7 A. General Effects Expected: (load) as (load) B. Switch and esistive osses hange M(D) Modified

More information

Transformer Fundamentals

Transformer Fundamentals Transformer Fundamentals 1 Introduction The physical basis of the transformer is mutual induction between two circuits linked by a common magnetic field. Transformer is required to pass electrical energy

More information

Pretest ELEA1831 Module 11 Units 1& 2 Inductance & Capacitance

Pretest ELEA1831 Module 11 Units 1& 2 Inductance & Capacitance Pretest ELEA1831 Module 11 Units 1& 2 Inductance & Capacitance 1. What is Faraday s Law? Magnitude of voltage induced in a turn of wire is proportional to the rate of change of flux passing through that

More information