ELECTRICAL POWER TRANSFORMER AND INDUCTOR



DESIGN PRINCIPLES, CALCULATION, THEORY, TUTORIALS,
AND OTHER INFORMATION




Magnetic components (transformers and inductors) are necessary parts of all power supply circuits.

Transformer is a passive device which transforms alternating (AC) electric energy from one circuit into another through electromagnetic induction. 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 the 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.

An SMPS power transformer is used to change amplitude of high-frequency pulses by the turns ratio and to provide isolation between circuits. Note that it can't transfer a DC component of the pulses: in a steady state mode net volt-seconds across each winding should be zero, otherwise the core will saturate. DC output voltage is obtained only by using rectifiers. Note that an average voltage across a real coil's terminals can be non-zero due to non-zero coil's resistance. This DC voltage can be used for lossless sensing of an average current across an inductor or a transformer winding: in an RC network parallel to the coil the voltage across the capacitor is proportional to the coil's average current. For better thermal stability the wire can be made of low TCR material, such as a copper alloy.

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 (although some topologies do need some energy stored in magnetizing inductance for 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 all or portion of this energy into another circuit during the alternate part of the switching cycle. In power supplies inductors are also used for filtering high frequency ripple (in which case they are often called chokes).
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FIND POWER TRANSFORMER BY SPEC
Function Waveform Bmax, gauss
Sine wave Sinewave voltage Vrms×108/4.44N×Ac×F
Square wave Square wave voltage Vpk×108/4N×Ac×F
Bipolar pulses with D=Ton/T=Ton×2F
(0<D<1)
PWM voltage Vpk×D×108/4N×Ac×F
Unipolar pulses
with passive reset
Unidirectional voltage pulse Br+Vpk×Ton×108/N×Ac
In this equations: V - voltage (volts), N - winding's turns, Ac - core's cross-sectional area (sq.cm), F- frequency (hertz), Br - remanence (gauss)
The magnetics designing normally involves tradeoffs between size, cost and losses. The main constraint in all cases (except for saturable inductors) is that peak magnetic flux density should not reach the core material's saturation flux value. In a "voltage-driven" coil the flux change is related to the applied volt-seconds and does not depend on the core's properties or air gaps. This table provides the formulas for maximum flux density Bmax for common voltage waveforms.

For "current-driven" coils: Bmax=L×I×108/N×Ac,
where L - inductance (in henrys), I - peak current in amps.

Below you will find magnetics theory, design information, tools and other free downloads. Note that most textbook's design procedures are written for natural convection cooling. For applications with forced airflow or conduction cooling these procedures may result in over-designed coils because of an overestimated temperature rise.

FREE INDUCTOR
AND POWER TRANSFORMER
DESIGN SOFTWARE


UNITRODE SEMINAR MAGNETICS HANDBOOK
(MAG 100A)


MAGNETISM PRINCIPLES,


EQUATIONS, TUTORIALS


Transformer turns and wire calculator
(includes skin effect)

SMPS PFC inductor calculation tool

Transformer calculation for various switching regulator topologies

Software to design electrical inductors using powder cores

Output inductor calculation tool

Current transformer design software

Ferrite magnetic
design tool (includes skin and proximity effects)

Core loss calculator
for non-sinusoidal waveforms

Introduction and Basic Magnetics (Design for Switching Power Supplies)

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


Magnetic field unit conversion and equations - online calculator and table

Basic transformer theory (instructor's slides- see terms of use)

SMPS transformer design procedure and equations (instructor's slides- see terms of use)

Inductor design procedure

Planar power transformers basics and design guide

Electrical transformer: physical principles and how it works




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