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 } Conventional transformer } Coupled inductor } Flyback transformer } SEPIC transformer } Magnetic amplifier } Saturable reactor } Filter inductor design constraints } The core geometrical constant Kg } Step-by-step design procedure } Summary 3/39

Types of magnetic devices } Choice of maximum operating flux density B max } Choose B max to avoid saturation of core } Further reduce B max, to reduce core losses } Different design procedures are employed in the two cases } Types of magnetic devices } Filter inductor } Ac inductor } Conventional transformer } Coupled inductor } Flyback transformer } SEPIC transformer } Magnetic amplifier } Saturable reactor 4/39

Filter inductor } CCM buck example منحني B-H براي فیلتر سلفي منحني B-H براي تحریك كامل i L 6/39

Filter inductor } Negligible core loss, negligible proximity loss } Loss dominated by dc copper loss } Flux density chosen simply to avoid saturation } Air gap is employed } Could use core materials having high saturation flux density (and relatively high core loss), even though converter switching frequency is high Φ Φ(t) 7/39

ج( ب( Ac inductor منحني B-H براي سلف ac (الف) حلقه B-H هسته ( ( 9/39

Ac inductor } Core loss, copper loss, proximity loss are all significant } An air gap is employed } Flux density is chosen to reduce core loss } A high-frequency material (ferrite) must be employed 10/39

Conventional transformer } منحني B-H مربوط به ترانس قراردادي حلقه B-Hهسته 12/39

Conventional transformer } Core loss, copper loss, and proximity loss are usually significant } No air gap is employed } Flux density is chosen to reduce core loss } A high frequency material (ferrite) must be employed 13/39

Coupled inductor } Two-output forward converter example D2 n 1 i 1 + D3 C1 R1 v 1 v g - Q D1 D4 D5 n 2 C2 i 2 R2 + v 2 - منحني B-H براي سلف تزویجي منحني B-H براي تحریك كامل 15/39

Coupled inductor } A filter inductor having multiple windings } Air gap is employed } Core loss and proximity loss usually not significant } Flux density chosen to avoid saturation } Low-frequency core material can be employed 16/39

Flyback transformer } DCM Flyback transformer i 1 n 1 n 2 D حلقة B-H براي مبدل فلاي بك مد جریان نا پیوسته i mp i 2 + L mp C R v حلقة B-Hهسته v g - Q 0 Ton T 0 Ton Toff 18/39 0 Ton Toff T

Flyback transformer } Core loss, copper loss, proximity loss are significant } Flux density is chosen to reduce core loss } Air gap is employed } A high-frequency core material (ferrite) must be used 19/39

Filter inductor design constraints } 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 worstcase copper loss of P =RI cu 2 rms i(t) L R 21/39

Filter inductor design constraints } Assumed filter inductor geometry l c R= c μa c c l g R g = μ 0 A g ni= Φ(R +R ) ΦR c g g Φ Φ(t) 22/39

Filter inductor design constraints } 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 worstcase saturation flux density of the core material } From solution of magnetic circuit ni=ba R c g ni =B AR = B max max c g max l g μ 0 } This is constraint #1. The turns ratio n and air gap length l g are unknown 23/39

Filter inductor design constraints } Inductance } Must obtain specified inductance L } We know that the inductance is L 2 n = = R g μ na l 2 0 c g } This is constraint #2 } The turns ratio n, core area A c, and air gap length l g are unknown 24/39

Filter inductor design constraints } Winding area } Wire must fit through core window (i.e., hole in center of core) } Total area of copper in window na W } Area available for winding conductors KW } Third design constraint KW na u A W u A 25/39

Filter inductor design constraints } 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 than 1 } 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 26/39

Filter inductor design constraints } Winding resistance lb } The resistance of the winding is R = ρ AW } where ρ 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 -6 1.724 10 Ω -cm.the length of the wire comprising an n-turn winding can be expressed as lb = n(mlt) where (MLT) is the mean-length-per-turn of the winding. The mean-length-per-turn is a function of the core geometry. The above equations can be combined to obtain the fourth constraint n(mlt) R = ρ A W 27/39

The core geometrical constant Kg } The four constraints 2 lg μ0nac ni L = max = Bmax μ l 0 g n(mlt) KW u A naw R = ρ AW } These equations involve the quantities } A c, W A, and MLT, which are functions of the core geometry } I max, B max, µ 0, L, K u, R, and ρ, which are given specifications or other known quantities } n, l g, and A W, which are unknowns } Eliminate the three unknowns, leading to a single equation involving the remaining quantities 29/39

The core geometrical constant Kg } Elimination of n, l g, and A W leads to 2 2 2 AW c A ρl Imax 2 (MLT) B RK max 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 Kg is defined as K g 2 AW c A = (MLT) 30/39

The core geometrical constant Kg } Discussion } Kg 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 Kg can be obtained by increase of A c more iron core material W A larger window and more copper 31/39

A step-by-step procedure } The following quantities are specified } Wire resistivity ρ (Ω-cm) } Peak winding current I max (A) } Inductance L (H) } Winding resistance R ( Ω) } 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 33/39

A step-by-step procedure } Determine core size 2 2 ρlimax Kg 10 (cm 2 B RK max u 8 5 ) } Choose a core which is large enough to satisfy this inequality } Note the values of A c, W A, and MLT for this core 34/39

A step-by-step procedure } Determine air gap length 2 µ 0LImax 4 l g = 10 (m) 2 BmaxA c } with A c expressed in cm 2 } µ 0 = 4Π10-7 H/m } The air gap length is given in meters } The value expressed above is approximate, and neglects fringing flux and other nonidealities 35/39

A step-by-step procedure } Determine number of turns n LImax n = 10 B A max c 4 36/39

A step-by-step procedure } Evaluate wire size A W KW u n A (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 } As a check, the winding resistance can be computed ρn(mlt) R = ( Ω) A W 37/39

Summary } A variety of magnetic devices are commonly used in switching converters } These devices differ in their core flux density variations, as well as in the magnitudes of the ac winding currents } When the flux density variations are small, core loss can be neglected } Alternatively, a low-frequency material can be used, having higher saturation flux density } The core geometrical constant Kg is a measure of the magnetic size of a core, for applications in which copper loss is dominant } In the Kg design method, flux density and total copper loss are specified 39/39