Switched Mode Power Conversion

Transcription

1 Inductors Devices for Efficient Power Conversion Switches Inductors Transformers Capacitors

2 Inductors Inductors Store Energy Inductors Store Energy in a Magnetic Field In Power Converters Energy Storage Elements Smoothen Power Flow

3 Inductors Inductors are also used as Switch Protection Elements In Switching Aid Networks Inductors Provide Turn-On di/dt Protection

4 Inductors V L I di V= L dt Electrical Circuit Element Eqaution V, L, I are Electrical Circuit Quantities

5 Inductors V Φ N turns dφ V= N dt Electromagnetic Equation Faraday s Law V is Electrical Circuit Quantity N, Φ are Magnetic Circuit Quantities

6 Inductors V L V Φ I di V= L dt N turns dφ V= N dt LI = NΦ Relationship Between L, I & N, Φ NΦ is also defined as Flux Linkage in the Inductor

7 Inductors V L V Φ di V= L LI= NΦ dt I N turns dφ V= N dt How to Relate the Electrical Circuit V, L, I and The Magnetic Circuit of the Inductor N, Φ, I & R

8 Ohm s Law V R I V= IR Bulk Ohm s Law

9 Ohm s Law at a Point l A I V ρl V= IR= JA = Jρl A V l = Jρ J =σε

10 Ohm s Law at a Point l A I V J=σE In a Conducting Material Electrical Current Density (J) is Proportional to (σ), and Electrical Field Intensity (Ε) σ is the conductivity of the material

11 Magnetic Ohm s Law at a Point l A Φ F B=μ H In a Magnetic Material Magnetic Flux Density (B) is Proportional to (μ), and Magnetic Field Intensity (Η) μ is the permeability of the material

12 Dielectric Ohm s Law at a Point l A D V D=ε E In a Dielectric Material Dielectric Flux Density (D) is Proportional to (ε), and Electrical Field Intensity (Ε) ε is the permittivity of the material

13 Magnetic Ohm s Law l Φ A F NI NI F BA =μ A l =Φ= l Aμ = Φ = F Bulk Magnetic Ohm s Law

14 Magnetic Circuit Relationships I μ N Turns l A F Φ= = (NI) ( l ) Aμ Flux in Magnetic Circuit

15 Inductance of an Electromagnetic Circuit I μ N Turns l A 2 2 NΦ N N A L= = = I ( l ) Aμ Inductance of a Magnetic Circuit l μ

16 Conceptual Design of an Inductor I μ N Turns l A For the desired L and I, To select a magnetic core (A, μ, l), number of turns N and conductor size a

17 Design of an Inductor I μ N Turns l A μ of a magnetic material varies widely. l is not finely controllable.

18 Practical Design of an Inductor I μ A N Turns l m l g Magnetic path is made of: Large Path of High Permeability and a Small Controlled Path of Low Permeability (Air)

19 Practical Design of an Inductor I μ A N Turns l m l g 2 NΦ N L= = I l l m g + Aμμ o m Aμ o 2 N A Inductance is Independent of Core Material (μ) Inductance is Independent of Core Shape (l m ) l g μ o

20 Popular Geometry of Inductor (EE) EE Cores

21 Popular Geometry of Inductor (EE) l g A W A C A C is the area of Magnetic Path supporting the Flux A W is the area of Window Supporting the Electric Current

22 Definition of Inductance NΦ Flux Linkage Current A Inductance is Defined as Flux Linkage per Ampere Slope of NΦ vs I Curve is Inductance

23 Saturation Effect NΦ Flux Linkage Current A Flux Linkage Saturates in Most Magnetic Materials Beyond a Certain Level

24 Saturation Flux Density B m Flux Density B B Field Intensity H A Peak Flux Density in Magnetic Materials is Limited by B m

25 Saturation Limit l g A W Φ A C LIm= NΦ m= NBmAC Magnetic Path Constraint

26 Heat Produced in the Conductors Q = 2 I Rt I 2 R Heating in the Conductors

27 Thermal Limit l g A W Φ A C N I = k A J rms W W Current Carrying Capacity Constraint

28 Energy Equation A W l g N I = k A J rms W W Φ A C LIm= NΦ m= NBmAC LImI k B J w rms m Energy (Area Product) Equation for Inductor Design = AA C W

29 Size of Magnetic Core LImI k B J w rms m = AA C W The Magnetic Core has to be Big Enough to Handle the Stored Energy in the Core The Core Size is Inversely Proportional to Saturation Flux Density B m Peak Current Carrying Capacity J Window Space factor k W

30 Typical Design Constraints The Core Size is Inversely Proportional to Saturation Flux Density B m B m = 0.2 T for Ferrite Cores Peak Current Carrying Capacity J J = 3 A/mm 2 for Copper, Natural Cooling Window Space factor k W k W = 0.35 for round Conductors

31 Sample Core Selection L = 20 μh; DC Current of 5 A; High Frequency (20 khz) Application I m = 5 A; I rms = 5 A; L = 20 μh A A 20 μ*5*5 = = 2381mm 0.35*0.2*3*10 C W 6 4

32 Sample Core Selection Type Number A C A W A C A W mm 2 mm 2 mm 4 E16/8/ E21/9/ E20/10/ E25.4/10/ E25/13/ Core Data Sheet Select Core E25.4/10/7

33 No. of Turns Type Number A C mm 2 A W mm 2 A C A W mm 4 E25.4/10/ L 2.00E-05 I 5 N 13 6 LI 20*10 *5 N = = B A 0.2*38.2*10 m C 6 Select 13 Turns

34 Wire Size Type Number A C mm 2 A W mm 2 A C A W mm 4 E25.4/10/ L 2.00E-05 I 5 N 13 a W mm a W I 5 = = = 1.67 mm J 3 Select a W 1.67 mm 2 which is 16 SWG 2

35 Air Gap Type Number A C mm 2 A W mm 2 A C A W mm 4 E25.4/10/ L 2.00E-05 I 5 N 13 a W mm l g mm N Aμ l g = L Select Airgap of mm on each limb

36 A Few Other Geometries (EE) Low Profile Cores ELP Low Profile Cores EFD Pot Cores P

37 Back to the Design l g A W Φ A C L = 20 μh; DC Current of 5 A; 13 Turns of 16 SWG Core Type E25.4/10/7 Airgap mm x 2

38 Practical Design of an Inductor I μ A N Turns l m l g 2 NΦ N L= = I l l m g + Aμμ o m Aμ o 2 N A Inductance is Independent of Core Material (μ) Inductance is Independent of Core Shape (l m ) l g μ o

39 Back to the Design l g A W Φ A C Assumptions: Core Reluctance << Gap Reluctance Fringing Field at Gap is Negligible

40 Core Reluctance : Gap Reluctance l g A W Φ A C ( l ) << l μ m m = << g

41 Fringing Effect l g A W Φ A C ( l A ) g<< C << 6.2

42 Parasitic Resistance of Inductor l g A W Φ A C ωl@ 20kHz is 2.51Ω R l ρl = a *10 *13* 40*10 Rl = Ω= 5.5mΩ *10 W W

43 Losses in the Inductor l g A W Φ A C 0.36 W per set If the DC Output Voltage is 7.5 V, This loss is 0.1%.

44 Measurement of L V L I di V= L dt V(t) I(t) t Pulsed Voltage and Current Rise

45 Measurement of L with LCR Meter V L r I I ur r V I= j ω L V I =ωl V ur Sinusoidal Voltage and Current

46 Impedance as a Function of ω V L I ur ur V Z= r = jωl I dbω ω = 1/L 20 dbω/dec log (ω) Impedance Plot [dbω vs log (ω)]

47 Inductors Devices for Efficient Power Conversion Switches Inductors Transformers Capacitors