EET 423 POWER ELECTRONICS -2 Prof R T Kennedy POWER ELECTRONICS 2

ELECTRIC - MAGNETIC ANALOGY ELECTRIC CIRCUIT CURRENT I VOLTAGE (EMF) V (E) RESISTANCE R CONDUCTANCE G CONDUCTIVTY POWER limits current density P Ohm’s Law Prof R T Kennedy POWER ELECTRONICS 2

ELECTRIC - MAGNETIC ANALOGY MAGNETIC CIRCUIT (N turns) FLUX wb (webers) MMF F A-T (ampere turns) RELUCTANCE R A-T/wb PERMEANCE P PERMEABILITY FLUX DENSITY saturation limited Tesla Ampere’s Law FIELD INTENSITY H A-T/m Faraday’s Law  Prof R T Kennedy POWER ELECTRONICS 2

Permeance is comparable to Conductance (SI system) permeance is the inductance of a single turn Reluctance is comparable to Resistance Don’t equating these they’re not the same thing !!!! Resistance is a power-dissipating element Reluctance is an energy storage element Reluctance: convenient way to describe magnetic elements Prof R T Kennedy POWER ELECTRONICS 2

current contained within circuit elements circuit conductivity >>conductivity of air Prof R T Kennedy POWER ELECTRONICS 2

permeance of magnetic circuit only a few orders > air air frequently forms part of magnetic circuit flux leaves magnetic circuit (LEAKAGE FLUX) Prof R T Kennedy POWER ELECTRONICS 2

SMPS MAGNETICS INTENTIONAL: inductors and transformers UNINTENTIONAL (PARASITIC): leakage inductance Prof R T Kennedy POWER ELECTRONICS 2

INDUCTORS and INDUCTANCE The FUNCTION of the SMPS ‘filter’ inductor is to STORE ENERGY in one interval and return it to the circuit during a later interval; a process that smoothes the current waveform. Inductance (L), the primary functional parameter of an inductor, is a measure of the magnetic flux linking a coil and is the flux linkage per ampere Prof R T Kennedy POWER ELECTRONICS 2

core geometry and materials scaling factor core geometry and materials Prof R T Kennedy POWER ELECTRONICS 2

electromagnetic interference (EMI) AIR CORED INDUCTORS A low inductance m = mo = 4 p 10-7 electromagnetic interference (EMI) Prof R T Kennedy POWER ELECTRONICS 2

due to ease of winding and assembly MAGNETIC CORES E I Cores E Cores the most common in use due to ease of winding and assembly but are not self shielding Prof R T Kennedy POWER ELECTRONICS 2

MAGNETIC CORES Pot Cores almost completely surround the windings thereby reducing EMI but difficulty in bringing the winding outside core Prof R T Kennedy POWER ELECTRONICS 2

MAGNETIC CORES Toroids high flux density possible  smaller lighter cores high flux density possible  smaller lighter core reduced EMI: windings shield core! Prof R T Kennedy POWER ELECTRONICS 2

mcore  mr= mcore  L  Prof R T Kennedy POWER ELECTRONICS 2

ASSEMBLIES Prof R T Kennedy POWER ELECTRONICS 2

MAGNETICS and ENERGY (J) LOW ENERGY STORAGE Prof R T Kennedy POWER ELECTRONICS 2

core material characteristics depend on sample temperature flux level  inductor design unpredictable Prof R T Kennedy POWER ELECTRONICS 2

AIR GAPS N I A F = NI Prof R T Kennedy POWER ELECTRONICS 2

independent of core material: gap counteracts Dm with current reduced inductance larger gap linear inductor Prof R T Kennedy POWER ELECTRONICS 2

Inductor Energy –Air Gap Virtually all of the inductor’s energy is stored in the gap Prof R T Kennedy POWER ELECTRONICS 2

Prof R T Kennedy POWER ELECTRONICS 2

LEAKAGE FLUX I L Lleakage N F = NI Prof R T Kennedy POWER ELECTRONICS 2

reluctance R is now even lower Fringing N I F = NI reluctance R is now even lower  increased inductance Prof R T Kennedy POWER ELECTRONICS 2

minimal external field large external field minimal external field Prof R T Kennedy POWER ELECTRONICS 2

FERROMAGNETIC MATERIALS magnetisation curve (hysteresis loop) binternal bexternal Prof R T Kennedy POWER ELECTRONICS 2

FERROMAGNETIC MATERIALS magnetisation curve (hysteresis loop) bexternal binternal Remanence (retentivity) b when H is zero Coercivity H when b is zero Prof R T Kennedy POWER ELECTRONICS 2

b-H characteristic f-F characteristic b flux density v magnetic field intensity slope: permeability F f f-F characteristic total flux v magnetomotive force slope: permeance characteristic defines equivalent electrical characteristic (core + N turns) slope: inductance Prof R T Kennedy POWER ELECTRONICS 2

HYSTERESIS CURVE and ENERGY MAGNETIC SYSTEM ENERGY INPUT HYSTERESIS LOSS STORED ENERGY RETURNED . Prof R T Kennedy POWER ELECTRONICS 2

HYSTERESIS CURVE and ENERGY MAGNETIC SYSTEM ENERGY INPUT HYSTERESIS LOSS STORED ENERGY RETURNED . Prof R T Kennedy POWER ELECTRONICS 2

CORE DATA SHEET + saturation SMPS major loop SMPS minor loop sinusoidal driven - saturation Prof R T Kennedy POWER ELECTRONICS 2

IDEAL MAGNETIC CORE Prof R T Kennedy POWER ELECTRONICS 2

‘REAL’ MAGNETIC CORE LOW ENERGY STORAGE HIGH ENERGY LOSS HIGH L Prof R T Kennedy POWER ELECTRONICS 2

AIR GAPPED CORE HIGHER ENERGY STORAGE reduced L reduced energy loss characteristic linearised Prof R T Kennedy POWER ELECTRONICS 2

PARAMETER DESIGN CHOICES INCREASE FLUX DENSITY ‘b’ increase b  reduced turns N  reduced winding loss  increased efficiency  reduced size increase b  increased core loss  increased core temperature  reduced efficiency Prof R T Kennedy POWER ELECTRONICS 2

PARAMETER DESIGN CHOICES INCREASE TURNS ‘N’ increase N  reduced b  reduced core loss  increased efficiency increase N  increased winding loss  increased winding temperature  reduced efficiency increase N  increased size Prof R T Kennedy POWER ELECTRONICS 2

PARAMETER DESIGN CHOICES INCREASE AREA ‘A’ increase A  reduced b  reduced core loss  increased efficiency increase A  increased winding length  increased winding loss  increased winding temperature  reduced efficiency increase A  reduced efficiency increase A  increased weight  increased size Prof R T Kennedy POWER ELECTRONICS 2

PARAMETER DESIGN CHOICES INCREASE FREQUENCY increase f  reduced b  possible reduced core loss increase f  smaller size due to N /A reduction Prof R T Kennedy POWER ELECTRONICS 2