Xformer_Converters_102213

Xformer_Converters_102213 - EE152 Green Electronics...

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EE152 Green Electronics Transformers Transformer Converters 10/22/13 Prof. William Dally Computer Systems Laboratory Stanford University
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Course Logistics Lab 4 signed off this week Lab 5 out this week Homework 4 out this week Quizzes back today
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Agenda Review of Magnetics and Inductors • Transformers Transformer Design Transformer Converters
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Magnetics Summary Inductors and transformers are key components of Green Electronic systems Governed by Lentz’s and Ampere’s Laws Gap cores to give required reluctance while avoiding saturation Magnetic materials Characterized by μ , B sat , and losses Use ferrites for high-frequency applications, Si Steel for low Wires have resistivity and suffer from skin effect Inductor design Iterate on core selection and parameters to minimize losses V = N d φ dt φ = F R = NI R L = N 2 R
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Recap of Inductor Design Example Specified L, I max , f, B, R, P Initial core uses too little of the window Select core to just fill the window – But P w >> P c Remove B, R constraints, optimize for P – Lower power with a smaller core
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Transformers
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Why Transformers? Galvanic isolation – Cannot tie DC GND to either side of AC line – Sometimes output must “float” Large step-down or step-up – More efficient to use transformer when ratio is more than about 5:1 – Reduced switching losses – Switches don’t see both high current and high voltage Multiple outputs – Not restricted to just two windings
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Transformers Suppose I have two windings on a core – One with N 1 turns, and one with N 2 turns
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Transformers Suppose I have two windings on a core – One with N 1 turns, and one with N 2 turns – We know V 1 = N 1 d φ dt V 2 = N 2 d φ dt V 2 = N 2 N 1 V 1
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Equivalent Magnetic Circuit If reluctance were zero we would have N 1 i 1 = N 2 i 2 i 2 = N 1 N 2 ! " # $ % & i 1
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Equivalent Magnetic Circuit With reluctance we have N 1 i 1 = N 2 i 2 + R φ i 2 = N 1 N 2 ! " # $ % & i 1 + R N 1 2 V dt
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Model as Ideal Transformer in Parallel with Magnetizing Inductance (Superposition) L m = N 1 2 R
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Transformer Saturation Transformer can pass high current from primary to secondary without saturating Saturation is due to magnetizing inductance Magnetizing flux is proportional to VT (volt-seconds) Choose N (number of turns) for required VT at specified max B VT must be balanced (sum to zero each cycle). V = N d φ dt V T = N φ V T = NBA N = V T BA
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Leakage Inductance Flux that is not linked by both windings results in leakage inductance – Typically 1-5% of total inductance – Larger for gapped cores (due to fringing) – Can be reduced by ‘interleaving’ windings Can be reflected to primary or secondary – Just one leakage inductance
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Model with Leakage Inductance
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SPICE Model of a Transformer * Transformer Model * Does not include core loss * Make Ls very large (1000x Lm) * N:1 primary:secondary * Lx is leakage Lm is magnetizing inductance .subckt xfrmr PP PN SP SN RP PP X {Rs*N*N} LM X Y {Lm} LP X Y {N*N*Ls} LX Y PN {Lx} LS SP Z {Ls} RS Z SN {Rs} K LP LS 1 .ends
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