Transformer's Book

We have already finished our book of transformers called  "Transformers Book" is a product of 46 years of experience in the field and the achievement of many projects with a lot of different good results.Transformers book is not a theoretical work but a theoretic/practical work of Years of labor, despite it´s strong mathematical and physical background.

    We know that a big part of this book is not found in any similar work, because We had been looking for those subjects by many years without any success. We gathered many papers of the IRE, IEE, IEEE and other societies of same importance in combination with our own work through many years to make possible its construction.

We could had written it in our own language  but We tried to write  it in English, with the intention to reach more people like possible, around the world.

 

The content:

The content is distributed in three volumes. The first one is currently availlable at Amazon.com with the ISBN 978-85-920396-0-8 at location:

https://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=ISBN+978-85-920396-0-8

the second and third volumes are coming soon.

There are two versiom sthe paperback and the electronics book version (Kindle) that can be obtained quicly at any part of the world.

The content of the first volume:

Index:

A  Brief History

What Is a Transformer?

The physics behind the scenes

Structure of the Matter and a brief view over atomic physics

Magnetism and Magnetic Materials

Magnetism

Ferromagnetic Materials

The ferromagnetic domains.

Ferromagnetic Domains and domain walls.

Initial Concepts.

Ampere´s Law.

Magnetization.

Flux Density B:

Matlab Model

Permeability.

Measurement of permeability:

Amplitude permeability.

Initial Permeability, Rayleigh Constant and Rayleigh law.

Absolute and relative permeability.

Complex permeability.

Apparent permeability.

Differential permeability.

Magnetostriction.

Inductance and Inductors.

What is Inductance?

Reluctance.

Losses in Magnetics Materials.

Losses.

The measurement of losses:

Representation of losses.

General Losses.

Hysteresis losses:

Classical losses:

Excess Losses.

Facts affecting the total losses

Loss behavior in different magnetic materials

Soft ferrites for high frequency applications:

Searching for a general loss model which could include harmonics and DC currents:

The MSE Approach - (Modified Steinmetz Equation)

The GSE Approach (General Steinmetz Equation)

Combination of fields.

Ampere´s Law in depth.

For the Sake of simplicity.

Magnetic field produced by currents in endless sheets.

Addition of fields in two parallel plates.

Infinite Solenoid.

Addition of fields in several layers:

Two overlapping solenoids.

Simulation by FEA (Finite Element Analysis)

Equivalent Circuit of a transformer:

Leakage Inductance.

What is leakage Inductance.

The definition of a fundamental inductance equation departing from the energy stored in magnetic field:

Inductance formula definition (Toroidal Case):

Inductance Formula definition (Leakage inductance Case):

The equivalent circuit of a transformer and measurements of AC Resistance:

The equivalent circuit:

AC resistance Measurement

Measurement of DC resistance.

High frequencies response:

Medium frequencies Response.

Low frequencies response.

Skin Depth and Proximity Effect

Skin Depth.

Ampere Law in more Detail:

Diffusion of magnetic field in a Conductor

Simple Rules in order to handle fields and currents in a single face.

Direction of the current.

Simple Rules.

Diffusion interrupted by change of field or current direction.

Proximity Effect:

The proximity effect develops considerable losses.

Proximity Effect three-dimensional configurations.

Simplifying assumptions.

Consequences:

Transformation from a round conductor winding to metal plate or sheet.

Dowell transformed circular wire windings into an "Equivalent Sheet" as follows.

Eddy Currents.

Forming a unique sheet:

Square of the current.

Second Layer

Determination of Fr for the entire coil:

Sample Calculation of AC resistance for primary and secondary windings due to skin and proximity effect

Dowell Relations – Simplifying the figure:

Expanding in series for simplification:

Applicability.

Skin and Proximity effects facing complex waveforms.

Behavior for complex waveforms.

We need to treat the problem through losses:

Determination of the Kr Curve.

Using Kr for loss calculation.

Further simplification with harmonics.

First Example: Calculation of a 4 Layers transformer with Copper sheet in the two coils.

Second example: Calculating ht losses:

Another method for the calculation of Fr.

Solution other than for paper and pencil:

Calculation in the design of a 20Kva inverter filter inductor.

Design of a ferrite 3Kva 200Khz power transformer for a ZVS-QRC telecommunication SMPS.

The Gap Losses - The approach.

The visual effect of the gaps.

Determination of losses by finite elements:

The calculation of losses in Litz Wires.

The End Effect 

The problem of the size.

The definition of the equation that determines the flux density B, departing from frequency, voltage and magnetic cross sectional area of the core:

EI Core transformer:

Calculating over a single Phase EI lamination transformer

Design of a sample E I transformer:

Determination of the better cost for a three phase transformer.

K Factor and K Factor transformers.

The problem of the loads and the current spectrum.

The K Factor definition:

Different topologies of non linear loads and the K Factor:

A simplified but full precision, Matlab-Simulink K Factor Calculator.

The IEC 62040 standard for UPS systems and the non linear input interface power supply for personal computers.

The effect on the neutral current.

Classification of K factor according to loads and lines.

Formulas group:

Sample project of a 50Kva three Phase distribution transformer for Kfactor = 13. 260

Solutions for skin depth.

Conductor plate or foil.

Interleaving winding.

Winding Construction for Minimum Losses:

Planar Windings.

REFERENCES.

Index of all volumes.

 

The content of the Second Volume:

Index of Vol II

A survey of different magnetic materials and cores

E I Cores for small Transformers

Pulverization and lamination needs for Eddy currents reduction and skin depth partial solution.

C Cores and C Composed cores for medium Power transformers

The problems of composition

Composed lamination for high power transformers

Cruciform cored transformers, optimization and the minimum degree

Simulations essays using FEA to see the behavior of the compositions

The importance of the definition of lamination standards

The Ferrite cores

The Powder Cores

 MPP

High FluX

Kool Mu

X Flux

Vitroperm cores for High frequency transformers

Nanocrystaline cores for MagAmp

Metglass Magnetic Alloys

MicroMetals Powder Cores

 

The Exciting current of a transformer.

The magnetizing current (inductive part)

The real part

 

 

The problem of the inrush current

 

The effect of magnetic memory of the core

The problem of the initial value

The value of the saturation and the slope of the curve

The profile of the inrush current

The sympathetic inrush current

The magnetic pulse outside the transformer due to the inrush (Dangerous Consequences)

Transformers like a Voltage or Current power supply.

Transformer as a voltage source

The problem of the voltage regulation

The voltage accuracy as a potential measurement transformer

The transformer as a current source

The problem of the current regulation

The current accuracy as a current measurement transformer

 

The problem of Temperature

The external area approach (Average temperature)

The weight and loss approach (Average Temperature)

Calculation of temperature drop between layers

Temperature measurement of power transformers

Temperature measurement at light load and nominal voltage

Temperature measurement at nominal load and low voltage

The size and weight versus temperature time constant and the transient thermal impedance.

The complete thermal model of a transformer. Involving power losses, dissipation and thermal feedback. Using Simulink, Simscape and Thermal elements

The hot spots ant their measurement.

The forced cooling of transformers

 

Power Transformer optimization

The point of maximum efficiency

The curve of maximum point efficiency: maximum copper weight side or maximum core weight side.

Optimization constraints

By temperature

By Voltage Regulation

By special dimensions

By Cost

By efficiency

By impedance

 

The problem of skin and proximity effect in high power transformers

The orthogonality between proximity and skin effect

The exact calculation of proximity effect

The exact calculation of skin effect

Th simplified approach

 

Polyphase Transformers and High power polyphase Rectifiers

Three Phase Transformers

The rectification

The commutation principle

The commutation angle calculation for different configurations

Delta open and scott Transformers

Zig-Zag Topologies

Multiple Zig-Zag Topologies

Extended delta topologies

The transformers for high power industrial rectifiers and multiple topologies

The problem of multiple waveforms in the windings for polyphase topologies

The calculations of additional losses due to proximity skin effect in multiple windings at different waveforms.

 

The end Effect

 

Demonstration of the end effect by FEA (Finite Elements Analysis)

Causes

A thermographic photo showing the end effect

The difficulty to find a solution

A difficulty for partial solution

 

The strange effect

 

Who is the strange?

Strange effect Calculation

Definitions

Solutions

 

Planar Transformers and inductors

The planar approach

The windings problems and solutions

The printed circuit winding

Multiple printed circuit winding and flexible printed circuits

Interleaving coil and its effects over the H profile and the improvement of losses

Calculations of Additional losses due to skin proximity effect

Copper or aluminum Foil for high power solutions

The planar inductor, limitation by the fixed H profile

Planar solutions

 

REFERENCES. Of the Vol II

 

The Content of Volume three

 

Index of Volume III

 

 Designing mains medium power Transformer (500KVA) using the (Cost Constraint algorithm). 

The problems involved

Concluding; the usage of copper or aluminum.

Optimizing the height of the coil.

One simple mathematical, Matlab and Simulink Model for power transformers calculations

 

Designing a power choke of various tenths of KVAR using planar topology to solve gaps problems.

 

The geometric problem

Construction problems

Calculation of losses

Demonstrating the results by FEA

 

Designing a selective 500Khz power supply inductor with 2 different conductors.

 Designing the inductor with Wire

Designing the inductor with foils

Calculating the inductor and concluding the impossibility to go ahead.

Installing a very thin conductor in parallel that solves the problem

Calculations to see the solution

Designing the same 500Khz power supply inductor with Printed circuit planar multilayer solution.

 

Transductors and magnetic Amplifiers (MagAmp)

The transductor – The revival from the grave - A forgotten theory

Mean voltage and flux changes

Addition of mean fluxes

Energy Storage in magnetic Cores

Summary of useful relationships

Basic operation of the transductors

Characteristic of a transductor

Control Ratio

Free magnetization transductor.

Forced magnetization transductor.

Supply Voltage

Power Output

Power amplification

Sel-Excited transductor

AC Magnetization Curve

Form Factor and waveforms of load current

Efficiency

 

Transient and steady-state operation of idealized transductors

Simplification of the magnetization curve

Voltage-time integral

Basic circuit equations

The self excitation

Mean fluxes and transductor Voltages

 

The self excited Transductors

 

            Limitations of the simplified treatment

            Action of the self excitation rectifier

            Amplification of the self excited transductor in the steady state

The amperes turn ratio

The control characteristic

 

 

Transductors with auto excitation

 

Circuit operation of auto excited transductors

Singularity theorem for auto excited transductors.

Ampere turn ratio of auto excited transductors

 

 

Transductors with reactive Loads

 

Transient and frequency response of transductors

 

High speed transductors and magnetic amplifiers

 

Multi stage Magnetic Amplifiers

 

The new solutions for SMPS.

            The regulation and control circuits

            The simplicity of the regulation circuits

 

 

Appendix A

Appendix B

Appendix C

Appendix D

 

REFERENCES Of Vol III