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 Elements Smoothen Power Flow
Inductors Inductors are also used as Switch Protection Elements In Switching Aid Networks Inductors Provide Turn-On di/dt Protection
Inductors V L I di V= L dt Electrical Circuit Element Eqaution V, L, I are Electrical Circuit Quantities
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
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
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
Ohm s Law V R I V= IR Bulk Ohm s Law
Ohm s Law at a Point l A I V ρl V= IR= JA = Jρl A V l = Jρ J =σε
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
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
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
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
Magnetic Circuit Relationships I μ N Turns l A F Φ= = (NI) ( l ) Aμ Flux in Magnetic Circuit
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
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
Design of an Inductor I μ N Turns l A μ of a magnetic material varies widely. l is not finely controllable.
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)
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
Popular Geometry of Inductor (EE) EE Cores
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
Definition of Inductance NΦ Flux Linkage Current A Inductance is Defined as Flux Linkage per Ampere Slope of NΦ vs I Curve is Inductance
Saturation Effect NΦ Flux Linkage Current A Flux Linkage Saturates in Most Magnetic Materials Beyond a Certain Level
Saturation Flux Density B m Flux Density B B Field Intensity H A Peak Flux Density in Magnetic Materials is Limited by B m
Saturation Limit l g A W Φ A C LIm= NΦ m= NBmAC Magnetic Path Constraint
Heat Produced in the Conductors Q = 2 I Rt I 2 R Heating in the Conductors
Thermal Limit l g A W Φ A C N I = k A J rms W W Current Carrying Capacity Constraint
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
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
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
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
Sample Core Selection Type Number A C A W A C A W mm 2 mm 2 mm 4 E16/8/5 20.1 37.6 755.8 E21/9/5 21.6 66.0 1425.6 E20/10/6 32.1 57.4 1842.5 E25.4/10/7 38.2 80.0 3056.0 E25/13/7 52.5 87.0 4567.5 Core Data Sheet Select Core E25.4/10/7
No. of Turns Type Number A C mm 2 A W mm 2 A C A W mm 4 E25.4/10/7 38.2 80.0 3056.0 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
Wire Size Type Number A C mm 2 A W mm 2 A C A W mm 4 E25.4/10/7 38.2 80.0 3056.0 L 2.00E-05 I 5 N 13 a W mm 2 1.67 a W I 5 = = = 1.67 mm J 3 Select a W 1.67 mm 2 which is 16 SWG 2
Air Gap Type Number A C mm 2 A W mm 2 A C A W mm 4 E25.4/10/7 38.2 80.0 3056.0 L 2.00E-05 I 5 N 13 a W mm 2 1.67 l g mm 0.41 2 N Aμ l g = L Select Airgap of 0.205 mm on each limb
A Few Other Geometries (EE) Low Profile Cores ELP Low Profile Cores EFD Pot Cores P
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 0.205 mm x 2
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
Back to the Design l g A W Φ A C Assumptions: Core Reluctance << Gap Reluctance Fringing Field at Gap is Negligible
Core Reluctance : Gap Reluctance l g A W Φ A C ( l ) << l μ m m 47.2 0.031 0.205 1510 = << g
Fringing Effect l g A W Φ A C ( l A ) g<< C 0.205 << 6.2
Parasitic Resistance of Inductor l g A W Φ A C ωl@ 20kHz is 2.51Ω R l ρl = a 6 1 1.76*10 *13* 40*10 Rl = Ω= 5.5mΩ 2 1.67*10 W W
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%.
Measurement of L V L I di V= L dt V(t) I(t) t Pulsed Voltage and Current Rise
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
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)]
Inductors Devices for Efficient Power Conversion Switches Inductors Transformers Capacitors