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 highfrequency 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
– Voltseconds must be N= VT
BA NI
F
=
=
R
R Transformer Converters Transformer Converters
• Use a transformer to provide stepup/stepdown
– 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 (fullbridge and halfbridge)
– Voltagefed – like a buck
– Currentfed – 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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 Fall '13
 Leakage inductance, Transformer Converters

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