Inductance r balanced over each cycle r volt seconds

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Unformatted text preview: mm^2 609 Turns 15 Strands 2.83E+00 m 1.58E- 02 Ohms 1.58 W 3.16 W Core Loss Pc 4.63 4.23 4.00 2.18 W Total Loss Pt 10.23 8.60 8.86 5.35 Max flux density Primary turns Secondary turns Primary magne*zing inductance Fill factor Window frac*on for primary Area for primary Number of wires that will fit Parallel strands per turn Length of each strand E36/21 core has lower loss than E41/17 core due to larger window area Core loss VT =N N= V = N BA MagneticsT Summary VT BA NI F VT •  Inductors and transformers are key components of Green Electronic = = N= R R systems BA •  Governed by Lentz’s and Ampere’s Laws N2 NI F d L= = = V =N R R R dt •  Gap cores to give required reluctance while avoiding saturation d V =N •  Magnetic materials = N VT dt –  Characterized by µ, Bsat, and losses –  Use ferrites for high-frequency applications, Si Steel for low V T = and suffer from skin effect V T = N •  Wires have resistivity N BA •  Inductor design VT V T = N BA N= BA –  Iterate on core selection and parameters to minimize losses •  Transformers NI F –  Have magnetizing inductance and leakage inductance = = R balanced over each cycle R –  Volt-seconds must be N= VT BA NI F = = R R Transformer Converters Transformer Converters •  Use a transformer to provide step-up/step-down –  Still also require an inductor for energy storage •  Flyback converter –  Like a buck/boost –  Uses magnetizing inductance for energy storage –  Primary and secondary conduct during different phases •  Forward converter –  Like a buck –  Inductor in secondary circuit •  Bridge converters (full-bridge and half-bridge) –  Voltage-fed – like a buck –  Current-fed – like a boost Analyzing Transformer Converters •  Divide cycle into phases •  In each phase determine which winding sets the transformer voltage •  Voltage across each inductor (including Lm and Ll) determines current slope Flyback Converter Flyback Converter Flyback Converter With Lm and Ll Auxiliary circuit to deal with energy stored in leakage inductance Flyback Converter With Lm and Ll and Transformer Eliminated Flyback Operates in 4 Phases DCM Shown Here Flyback Phase 1: Primary Conduction Phase 1: Current ramps in Lm+Ll ΔI = VinΔt/(Lm+Ll) Flyback Phase 2: Commutation Phase 2: Commutation Diode clamps junction to Vin+NVout Aux circuit applys voltage across Ll Current ramps down in Ll ΔI = -VyΔt/Ll Secondary current ramps up by same amount Flyback Phase 3: Secondary Conducts Phase 3: Secondary Conducts Diode clamps ju...
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