ELECTRICAL POWER TRANSFORMER AND INDUCTOR DESIGNBASIC PRINCIPLES, THEORY, CALCULATION 

Before discussing the calculation of magnetic components for switching power supplies, let's just quickly go over the basic concepts and definitions. Transformer is a passive device which transfers alternating (AC) electric energy from one circuit into another through electromagnetic induction. 
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It normally consists of a ferromagnetic core and two or more coils (windings). A changing current in the primary winding creates an alternating magnetic field in the core. The core multiplies this field and couples most of the flux through the secondary windings. This in turn induces alternating voltage (electromotive force, or emf) in each of the secondary coil according to Faraday's law. Power transformer in SMPS is designed to change amplitude of highfrequency pulses by the turns ratio and to provide isolation between circuits. Note that it can't transfer a DC component of a pulse: in a steady state mode net voltseconds across each winding should be zero, otherwise the core will saturate. In general, ideal SMPS transformers need to transfer all energy instantaneously from one winding to another while storing no or little energy in the process. However, some topologies do need certain amount of energy stored in magnetizing inductance for a proper operation. Conversely, a power inductor is used in SMPS as an energy storage device. It accumulates energy in the magnetic field as current flows through it, and then transfers it into another circuit during the alternate part of the switching cycle. In power supplies, the inductors are also used for filtering out high frequency currents (in which case they are often called chokes). 
Function  Waveform  Bmax, gauss 
Sine wave  Vrms×10^{8}/4.44N×Ac×F  
Square wave  Vpk×10^{8}/4N×Ac×F  
Bipolar pulses with D=Ton/T=Ton×F (0<D<0.5) 
Vpk×D×10^{8}/2N×Ac×F  
Unipolar pulses with passive reset 
Br+Vpk×Ton×10^{8}/N×Ac  
In these and other equations: V  voltage (volts), N  coil's turns, Ac  core's crosssectional area (sq.cm), F frequency (hertz), Br  remanence (gauss) 
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UNITRODE SEMINAR MAGNETICS HANDBOOK
Introduction and magnetics basics (design for switching power supplies)(MAG 100A) Magnetic core characteristics Windings data and skin effect Power supply transformer design Inductor and flyback transformer design Magnetic core properties Eddy current losses in transformer windings Equivalent electrical circuit The effect of leakage inductance Coupled filter inductors How to design a power supply transformer with fractional turns 
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Designing magnetic components for high frequency dcdc converters (by W.T.McLyman)  pdf downloadEQUATIONS, TUTORIALS The following three guides are instructor's slides: see their author's terms of use Basic transformer theory SMPS transformer design procedure and equations Inductor design procedure Planar power transformers basics and design guide Electrical transformer: how it works and physical principles 

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