Transformer and Inductor Design Handbook, Fourth Edition by Colonel Wm. T. McLyman

 Transformer and Inductor Design Handbook

If you are not aware of Ferrite, Transformer and Inductor terms and for learning the same if you are looking a book, which along with theory clears your practical ideas then please purchase this book; “Transformer and Inductor Design Handbook, Fourth Edition by Colonel Wm. T. McLyman”.

Links to easily find and to purchase “Transformer and Inductor Design Handbook” with discounts are given at the end of this review.

Transformer and Inductor Design Handbook, Fourth Edition by Colonel Wm. T. McLyman

This book is the best book for learning each and every thing about Transformers and Inductors. It clarifies in depth all meanings, definitions, working and calculations related to Transformer and Inductors. This is practically one to be needed to understand how exactly Transformer and Inductor is working. This book will teach you; transformer design, inductor design, how to design a transformer windings, transformer core size calculation, transformer calculation formulas, transformer core area calculation and many more.

My first introduction with “Transformer and Inductor Design Handbook” is at the time when I started my career as Design & Development Engineer after graduation with a well-known organisation. There we use transformers and inductors in our designs. To understand the ferrite, transformers and inductors well, my seniors suggested to refer this book. He has one copy and initially I referred his copy.

When I read this first time, I found that this book contains all the detail explanations of ferrite selection, transformer & Inductor calculations and their working. It offers what you have to work with ferrite parts. It delivers and clears all the basics so that you can simply use this information when needed. Immediately I planned to purchase my own personal copy. At that time, 3rd edition was available. Till now this book is available with me and till now I am referring it for transformer design and inductor design.

With the time “Transformer and Inductor Design Handbook” flourished and now available in 4th edition, updated and revised by author Colonel Wm. T. McLyman. Because of introduction of new chapters I purchased the 4th edition also.

A new chapter on Autotransformer Design has been included in 4th edition, which focuses on selection and calculations of windings. A chapter on Common Mode Inductor Design has been included which focuses on the selection of ferrite material, winding calculations, cut-off frequency calculations, temperature rise calculations, etc.

The book; “Transformer and Inductor Design Handbook” delivers you, step wise teachings along with reference pictures to clear all the concepts of transformer design and inductor design. This book guides you also on topics like; laminations & its need, tape cores, powder cores & ferrite cores, and iron alloys. This book will guide you for; how to select the right ferrite core size for your design, how to perform calculations, how to design transformer and design inductor and how to perform testing. This book will give you transformer design examples along with step-by-step directions and several tables and visuals for assessment.

The 4th Edition of this book; “Transformer and Inductor Design Handbook” consists of;

• Magnetics fundamentals
• Magnetic materials
• Various features of transformer and inductor design (along with three-phase transformers)
• Transductors for flyback and forward converters
• Input filter design
• Rotary transformer
• Catalogue material on cores
• Autotransformer
• Leakage inductance
• Current transformer
• Planar transformer
• Saturable (magnetic amplifier) transformer design
• Winding capacitance

Table of contents

Chapter 1. Fundamentals of Magnetics
This chapter contains all the terms in basic form. This chapter contains; Magnetic Properties in Free Space, Intensifying the Magnetic Field, Simple Transformer, Fundamental Characteristics of a Magnetic Core, Hysteresis Loop (B-H Loop), Magnetomotive Force (mmf) and Magnetizing Force (H), Air Gap and it’s types, Fringing Flux, etc.

Chapter 2. Magnetic Materials and Their Characteristics
This chapter contains details of; Saturation, Remanence Flux, Coercivity, Permeability, Hysteresis Loss, Resistivity. This chapter also contains; Introduction to Silicon Steel, Introduction to Thin Tape Nickel Alloys, Introduction to Metallic Glass, Introduction to Soft Ferrites, Manganese-Zinc Ferrites, Nickel-Zinc Ferrites, Introduction to Molypermalloy Powder Cores, Introduction to Iron Powder Cores, Core Loss, Selection of Magnetic Materials, Magnetic Material Saturation Theory, Effect of Gapping, etc.

Chapter 3. Magnetic Cores
This chapter contains in detail following terms; Core Type and Shell Type Construction, Types of Core Materials, Eddy Currents & Insulation, Laminations, Annealing and Stress-Relief, Stacking Laminations and Polarity, Flux Crowding, Exciting Current, Tape Wound C, EE, and Toroidal Cores, Stacking Factors, Design and Dimensional Data for different type of Laminations, Dimensional Data for different type of ferrite cores, Dimensional Data for different type of powder cores, etc.

Chapter 4. Window Utilization, Magnet Wire and Insulation
This chapter contains; Window Utilization Factor, Wire Insulation, Fill Factor, Effective Window, Insulation Factor, Window Utilization Factor for bobbin ferrites, Magnet Wire, Base Film Insulation, Bonding Methods, Multistrand Wire and Skin Effect, Multistrand Litz Wire, Proximity Effect, Different types of wires, Standard Foils, etc.

Chapter 5. Transformer Design Trade-Offs
This chapter contains; Power Handling Ability, Transformer Area Product, Transformer Volume and the Area Product, Transformer Weight and the Area Product, Transformer Surface Area and the Area Product, Transformer Current Density and the Area Product, Transformer Core Geometry and the Area Product, etc.

Chapter 6. Transformer-Inductor Efficiency, Regulation, and Temperature Rise
This chapter contains all the details about; Transformer Efficiency, Transformer Dissipation by Radiation and Convection, Temperature Rise Versus Surface Area Dissipation, Surface Area Required for Heat Dissipation, Required Surface Area, Regulation as a Function of Efficiency, etc.

Chapter 7. Power Transformer Design
This chapter contains details about; Power-Handling Ability, Output Power Versus Apparent Power Capability, Transformers with Multiple Outputs, Regulation, Relationship of Kg to Power Transformer Regulation Capability, Relationship of Ap to Transformer Power Handling Capability, Different Cores Same Area Product, 250 Watt Isolation Transformer Design, 38 Watt 100kHz Transformer Design, etc.

Chapter 8. DC Inductor Design, Using Gapped Cores
It contains all the details about; Critical Inductance for Sine Wave Rectification, Critical Inductance for Buck Type Converters, Core Materials used in PWM Converters, Fringing Flux, Inductors, Relationship of Ap to Inductor's Energy-Handling Capability, Relationship of Kg to Inductor's Energy-Handling Capability, Gapped Inductor Design Example Using the Core Geometry Kg, Gapped Inductor Design Example Using the Area Product Ap, etc.

Chapter 9. DC Inductor Design, Using Powder Cores
This chapter contains all the details about; Molybdenum Permalloy Powder Cores, High Flux Powder Cores, Sendust Powder Cores, Iron Powder Cores, Inductors, Relationship of Ap to Inductor's Energy-Handling Capability, Relationship of Kg to Inductor's Energy-Handling Capability, Toroidal Powder Core Design Using the Core Geometry Kg, Toroidal Powder Core Inductor Design, Using the Area Product Ap, etc.

Chapter 10. AC Inductor Design
It contains; Relationship of Ap to the Inductor Volt-Amp Capability, Relationship of Kg to the Inductor Volt-Amp Capability, Fringing Flux, AC Inductor Design Example, etc.

Chapter 11. Constant Voltage Transformer (CVT)
This chapter contains; Constant-Voltage Transformer’s Regulating Characteristics, Electrical Parameters of a CVT Line Regulator, Design equations & examples of Constant-Voltage Transformer, Design example of Series AC Inductor, etc.

Chapter 12. Three-Phase Transformer Design
It contains; Primary Circuit of Three-Phase transformer, comparison according to physical size, Phase Current, Line Current & Voltage in a Delta System and Wye system, Comparing Multiphase & Single-Phase Power, Multiphase Rectifier Circuits, Area Product Ap and Core Geometry Kg for Three-Phase Transformers, Output Power Versus Apparent Pt Capability, Relationship Kg to Power Transformer Regulation Capability, Relationship Ap to Transformer Power Handling Capability, Design example of three-phase Transformer, etc.

Chapter 13. Flyback Converter, Transformer Design
It contains; Energy Transfer, Discontinuous and Continuous Current Mode, Continuous and Discontinuous Boundary, The Buck Converter, Discontinuous and Continuous Current Buck Converter Design Equations, The Boost Converter, Discontinuous and Continuous Current Boost Converter Design Equations, The Inverting Buck-Boost Converter, Discontinuous and Continuous Current Inverting Buck-Boost Design Equations, The Isolated Buck-Boost Converter, Discontinuous and Continuous Current Isolated Buck-Boost Design Equations, Design Example of Buck-Boost Isolated Converter for Discontinuous Current, Design Example of Boost Converter for Discontinuous Current, Designing Boost Inductors for Power Factor Correction, Standard Boost Flyback Converter, Boost PFC Converter, Design Example of (PFC) Boost Converter for Continuous Current, etc.

Chapter 14. Forward Converter, Transformer Design, and Output Inductor Design
It contains; Circuit Operation, Comparing the Dynamic B-H Loops, Forward Converter Waveforms, Transformer Design Using the Core Geometry Kg Approach, Forward Converter Output Inductor Design, Output Inductor Design Using the Core Geometry Kg Approach, etc.

Chapter 15. Input Filter Design
It contains details about; Capacitor, Inductor, Oscillation, Applying Power, Resonant Charge, Input Filter Inductor Design Procedure, Input Filter Design Specification, etc.

Chapter 16. Current Transformer Design
This chapter contains; Analysis of the Input Current Component, Unique to a Current Transformer, Current Transformer Circuit Applications, Current Transformer Design Example, etc.

Chapter 17. Winding Capacitance and Leakage Inductance
This chapter contains details about; Parasitic Effects, Leakage Flux, Minimizing Leakage Inductance, Winding Capacitance, Winding Capacitance Turn-to-Turn, Winding Capacitance Layer-to-Layer, Capacitance Winding-to-Winding, Stray Capacitance, etc.

Chapter 18. Quiet Converter Design
This chapter contains; The Voltage-fed Converter, Regulating and Filtering, The Current-fed Converter, The Quiet Converter, Regulating and Filtering, Quiet Converter Waveforms, Technology on the Move, Window Utilization Factor Ku, Temperature Stability, Calculating the Apparent Power Pt, Quiet Converter Design Equations, Transformer Design using the Core Geometry Kg Approach, etc.

Chapter 19. Rotary Transformer Design
This chapter contains; Basic Rotary Transformer, Square Wave Technology, Rotary Transformer Leakage Inductance, Current-fed Sine Wave Converter Approach, Rotary Transformer Design Constraints, etc.

Chapter 20. Planar Transformers and Inductors

This chapter contains; Planar Transformer and Inductors Basic Construction, Planar Integrated PC Board Magnetics, Core Geometries, Planar Transformer and Inductor Design Equations, Window Utilization Ku, Current Density J, Printed Circuit Windings, Calculating the Mean Length Turn, Winding Resistance & Dissipation, PC Winding Capacitance, Planar Inductor Design, Winding Termination, PC Board Base Materials, Core Mounting and Assembly, etc.

Chapter 21. Derivations for the Design Equations
This chapter contains; Output Power P0 vs Apparent Power Pt Capability, Transformer Derivation for the Core Geometry Kg, Transformer Derivation for the Area Product Ap, Inductor Derivation for the Core Geometry Kg, Inductor Derivation for the Area Product Ap, Transformer Regulation, etc.

Chapter 22. Autotransformer Design
This chapter contains; windings and other details for the design of autotransformer. It is clearly explained with the calculations.

Chapter 23. Common-Mode Inductor Design
This chapter contains; windings and selection details for the design of Common-Mode Inductor Design. It is clearly explained with the help of calculations.

Chapter 24. Series Saturable Reactor Design
This chapter contains; Terms related to Reactor, controlling of magnetization, etc.

Chapter 25. Self-Saturating, Magnetic Amplifiers
This chapter contains; feedback windings, gain of magnetic amplifier, etc.

Chapter 26. Designing Inductors for a Given Resistance
This chapter contains; detail design procedure for Inductor design respect to resistance.

Positive points of “Transformer and Inductor Design Handbook”

• The book covers much practical information.
• Step-by-step instruction.
• Detail explanation along with calculations.
• Detail explanation for selection of ferrite cores.
• Easy to understand language.
• Detail derivation of equations.
• Availability of reference pictures for easy understanding.

Negative points of “Transformer and Inductor Design Handbook”

• Fewer contents for the reader, who’s seeking a detail understanding of the necessary in-depth of magnetics and its application in power converter circuits.
• There are fewer explanations of some valuable methods like; how to wind transformers in different configurations and with several layers.

About the author

Colonel Wm. T. McLyman – Colonel McLyman has 47 years of experience in the field of Magnetics. He holds fourteen United States Patents on Magnetics associated conceptions. He worked and retired as a Senior Member of the Avionics Equipment Section of the Jet Propulsion Laboratory (JPL) associated with the California Institute of Technology, California.

He has written above seventy JPL Technical Documents and Technology Reports on the subject of Magnetics and circuit designs for power converters when he worked thirty years at JPL as the Magnetics Specialist. NASA has published many of his technical works. He has done many seminars in the United States, Mexico, Canada and Europe on the design and construction of magnetic components.

Colonel Wm. T. McLyman

He is the President of his company called Kg Magnetics, Inc., which focuses on magnetic design. Through his company, Kg Magnetics, Inc., he markets transformers and inductors design and analysis computer program.

He is the writer of four famous books: "Transformer and Inductor Design Handbook, Fourth Edition", "Magnetic Core Selection for Transformers and Inductors, Second Edition", "Designing Magnetic Components for High-Frequency DC-DC Converters", "High Reliability Magnetic Devices: Design and Fabrication".

Details about this book, “Transformer and Inductor Design Handbook, Fourth Edition by Colonel Wm. T. McLyman”

Paperback: 667 pages

Publisher: CRC Press; 4 edition (April 26, 2011)

Language: English

ISBN-10: 9781439836873

ISBN-13: 978-1439836873

ASIN: 1439836876

Product Dimensions: 8 x 1.5 x 11 inches

Conclusion

This book, “Transformer and Inductor Design Handbook” is like a bible of Transformer design and Inductor design learning and must have book for all transformer & inductor design enthusiasts. This book will develop your transformer & inductor design knowledge and develop the skills essential to develop and construct your own transformer and inductors for your designed circuit. It is a reliable guide for the engineers and other professionals; who usually design, develop and tests transformers and inductors.

Purchase links for “Transformer and Inductor Design Handbook”

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Also eBook format of this book is available.

You can read this book on Kindle e-Readers, Fire Tablets, Fire Phones, Kindle reading apps, Kobo e-Readers, Kobo reading apps, Nook e-Readers and Nook reading apps.

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*If you didn't find your country name above, then please contact me (check Contact page), I will try to find where and how you can get this book easily in your home country.

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Power Factor Correction (PFC) – Biasing Circuitry of L6562

We know very well what is, "Power Factor Correction" and why it is needed.
More details on "Power Factor and Power Factor Correction", you can find on my previous blog and link for the same is;
https://www.powerelectronicstalks.com/2018/09/what-is-power-factor-correction.html

More details on "Power Factor Correction (PFC) - Critical Conduction Mode Boost Converter Calculations using L6562", you can find on my previous blog and link for the same is;
https://www.powerelectronicstalks.com/2018/11/power-factor-correction-critical-conduction-mode-boost-converter-calculations-using-L6562.html

Below picture is of assembled boost circuit in a 120W power converter.

Assembled boost circuit in a 120W power converter

While designing the Critical Conduction Mode boost converter we have to also focus on biasing circuitry i.e. the components which will control the working of L6562 we can say it in another words as;

Biasing Circuitry of L6562

Figure 1 shows the internal block diagram of L6562.

Internal block diagram of L6562

Let’s discuss it more in detail pin by pin.

·        Pin 1 (INV): Internal schematic of L6562 shows that this pin is connected both to the inverting input of the error amplifier and to the DIS circuit block. Externally we have to connect a resistive divider between the boost regulated output voltage and this pin. The internal reference on the non-inverting input of the E/A is 2.5 V (typ), while the DIS intervention threshold is 27 µA (typ). RoutH and RoutL are then selected as follows:

RoutH = ΔVovp / 27µA = 55V / 27µA = 2.03MΩ = 2MΩ

RoutH / RoutL = Vout / 2.5V    ·    – 1 = 400V / 2.5V   ·    – 1   = 159

RoutL = RoutH / 159 = 2MΩ / 159 = 12.6kΩ

To get RoutL 12.6kΩ place 15kΩ parallel to 82kΩ.

For RoutH a resistor with a voltage rating >400 V is needed otherwise more resistors in series have to be used.

This pin can also be used as an ON/OFF control input if tied to GND by an open collector or open drain.

·        Pin 2 (COMP): This pin is the output of the error amplifier that is fed to one of the two inputs of the multiplier. Place a feedback compensation network in between this pin and INV (pin 1) having a narrow bandwidth in order to avoid the output voltage ripple (100 Hz) that would bring high distortion of the input current waveform.

We can find the capacitance value by setting the bandwidth (BW) from 20 to 30 Hz so, a capacitor can provide a low-frequency pole as well as a high DC gain.

Below equation can be use for calculating the value of single capacitor.

Ccompensation = 1 / [2π · (RoutH // RoutL) · BW]

A CRC network providing 2 poles and a zero is more suitable for constant power loads like a downstream converter.

                       The transfer functions of compensation networks are shown in Figure 2 and Figure 3;

Transfer functions of compensation networks

In our design we used combination of two capacitors and one resistor network.

CcompP = 150nF

CcompS = 2.2µF

RcompS = 22kΩ

·        Pin 3 (MULT): Internal schematic of L6562 shows that this pin is also a multiplier input. It is connected both to the output of the error amplifier and to the inverting input of PWM comparator. In application it is connected through a resistive divider, to the rectified mains to get a sinusoidal voltage reference.

The multiplier can be described by the relationship:

VCS = k · (VCOMP – 2.5V) · VMULT

Where,

VCS = It is the multiplier output. It is the reference for the current sense.

k = 0.38 (typ) is the multiplier gain.

VCOMP = It is the voltage available on Pin 2; i.e. Output of error amplifier.

VMULT = It is the voltage on pin 3.

The linear operation of the multiplier is guaranteed within the range 0 to 3 V of VMULT and the range 0 to 1.16 V (typ) of Vcs.

The procedure to properly set the operating point of the multiplier is;

First, the maximum peak value for VMULT, VMULTmax is selected. This value, which occurs at maximum mains voltage, should be 3V or nearly so in wide-range mains and less in case of single mains. The sense resistor selected is Rs = 0.55Ω and it is described in the detail about pin 4 of this section. The maximum peak value, occurring at maximum mains voltage is:

VMULTmax = [(ILpk · RS) / 1.1] · [VACmax / VACmin]

                     = [(1.812 · 0.55) / 1.1] · [265V/ 85V]

                     = 2.82V

Where, 1.1 V/V is the multiplier maximum slope.

The maximum required divider ratio is calculated as;

kp = (VMULTmax) / (√2 · VACmax)

     = 2.82 / (1.414 · 265V)

     = 0.00752

     = 7.52 X 10¯³

Suppose a 200 μA current flowing into the multiplier divider, the lower resistor value can be calculated as;

RmultH = [(1-kp)/kp]RmultL

            = [(1 - 7.52 X 10¯³) / 7.52 X 10¯³] · 15kΩ

            = 1.97MΩ

In this application example RmultH = 2 MΩ and RmultL = 15 kΩ have been selected. Please note that for RmultH a resistor with a suitable voltage rating (>400 V) is needed, or more resistors in series must be used.

·        Pin 4 (CS): It is the inverting input of the current sense comparator. Instantaneous inductor current is sensed by L6562 by this pin, which is converted to a proportional voltage by an external sense resistor (Rs). As this signal crosses the threshold set by the multiplier output, the PWM latch is reset and the power MOSFET is turned off. The MOSFET stays in OFF-state until the PWM latch is reset by the ZCD signal. The pin is equipped with 200 ns leading-edge blanking to improve noise immunity.

                For 50W PFC the sense resistor value (Rs) can be calculated as follows;

RS < (VCSmin / ILpk)

RS < (1.0V / 1.812A) = 0.55Ω

Where;

ILpk = Inductor’s maximum peak current. It is already calculated for 50W PFC solution. Please refer “Critical Conduction Mode Boost Converter Calculations using L6562”.

VCSmin = 1.0 V is the minimum voltage allowed on the L6562 current sense. It is given in the datasheet.

As the internal current sense clamping sets the maximum current that can flow in the inductor, the maximum peak of the inductor current is calculated considering the maximum voltage Vcsmax allowed on the L6562.

ILpkx = Vcsmax / RS = 1.16V / 0.55Ω = 2.10A

Where;

Vcsmax = 1.16V. It is given in the datasheet.

The calculated ILpkx is the limit at which the boost inductor saturates and it is used for calculating the inductor number of turns and air gap length.

The power dissipated in RS is given by;

PS = RS · (ISWRMS)² = 0.55 · (0.638A)² = 0.223W

As per the result two parallel resistors of 1.1Ω with 0.25 W of power rating have been selected.

·        Pin 5 (ZCD): It is the input of the zero current detector circuit. In transition mode PFC, the ZCD pin is connected, through a limiting resistor, to the auxiliary winding of the boost inductor. The ZCD circuit is negative-going edge triggered. When the voltage on the pin falls below 0.7V, it sets the PWM latch and the MOSFET is turned on. Prior to falling below 0.7V, because of MOSFET’s turnoff the voltage on pin 5 must experience a positive-going edge exceeding 1.4V.

The maximum main-to-auxiliary winding turn ratio is given by;

nmax = nprimary / nauxiliary

           = [Vout – (√2 · VACmax)] / 1.4V · 1.15

           = [400 – (√2 · 265V)] / 1.4V · 1.15

           = 15.7

If the winding is also used for supplying the IC, the above criterion may not be well-suited with the Vcc voltage range; we have to design a self supply network.

The minimum value of the limiting resistor can be found considering the maximum voltage across the auxiliary winding with a selected turn ratio = 10 and assuming 0.8 mA current through the pin.

R1 = [(Vout/naux) – VZCDH] / 0.8mA

      = [(400V/10) – 5.7V] / 0.8mA  =  42.9kΩ

R2 = [(√2 · VACmax/naux) – VZCDL] / 0.8mA

      = [(√2 · 265V/10) – 0V] / 0.8mA = 46.8kΩ

VZCDH = 5.7 V and VZCDL = 0 V are the upper and lower ZCD clamp voltages of the L6562.

               Considering the higher value between the two calculated, RZCD = 47 kΩ has been selected as the limiting resistor.

·        Pin 6 (GND): This pin acts as the current return both for the signal internal circuitry and for the gate drive current. When laying out the printed circuit board, these two paths should run separately.

·        Pin 7 (GD): It is the output of the L6562. The pin is able to drive an external MOSFET with 600 mA source and 800 mA sink capability. The high-level voltage of this pin is clamped at about 12 V to avoid excessive gate voltages in case the pin is supplied with a high Vcc. An internal pull-down circuit holds the pin low to avoid undesired switch-on of the external MOSFET because of some leakage current when the supply of the L6562 is below the UVLO threshold.

·        Pin 8 (VCC): At this pin supply is applied to make run L6562. This pin is externally connected to the startup circuit and to the self-supply circuit. To start the L6562, the voltage must exceed the startup threshold (typically 12.5 V). High value startup resistors (in the hundreds kΩ), should be use for reducing power consumption and optimizes system efficiency at low load. If the Vcc voltage exceeds 25V, an internal clamping circuitry, is activated in order to clamp the voltage.

Below figure shows location of biasing components in PFC Boost circuit using L6562.

Location of biasing components in PFC Boost circuit using L6562

Below pictures are of a boost circuit assembly on general board and it’s measured output voltage on Agilent DSO-X 2024A.

L6562A based boost circuit assembled on general board for testing

Output of the Boost Circuit using L6562 measured on Agilent DSO-X 2024A

Reference : Referred STMicroelectronics "Solution for designing a transition mode PFC preregulator with the L6562A". Link is embed in title.

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Hysteresis loop or B-H curve and Hysteresis loss

What is Hysteresis loop or B-H curve?

Hysteresis loop gives information about the magnetic properties of a material. By studying hysteresis loop all the magnetic properties related information of a material can be easily traced out.

In another word’s we can define Hysteresis loop as, “When a ferromagnetic material is magnetized in a one direction, it will not come back to zero magnetization when the applied magnetizing field is taken out. It must be driven back to zero by a magnetizing field in the opposite or reverse direction. If an alternating magnetic field is applied to the material, its magnetization will trace out a loop (in the form of curve graph) called a hysteresis loop.

The absence of re-traceability of the magnetization curve (H) is the property called as hysteresis and it is associated with the presence of magnetic domains in the material.

A hysteresis loop shows the relationship between the induced magnetic flux density (B) and the magnetizing force (H). This is the reason it is also called as the B-H curve. Below figure shows an example of hysteresis loop;

Hysteresis loop or B-H curve

Below points explains the Hysteresis loop or B-H curve;

• The loop is produced by measuring the magnetic flux (B) of a ferromagnetic material when the applied magnetizing force is changed (H).
• A ferromagnetic material which has been never before magnetized or demagnetized ferromagnetic material will trail the dashed line (see the figure) as magnetizing force (H) is increased.
• The dashed line shows that, the larger the quantity of current applied (H+), the stronger the magnetic field in the component (B+).
• At "a" point nearly all of the magnetic domains are aligned and an extra increase in the magnetizing force will generate very little increase in magnetic flux.
• The magnetic saturation point has been reached for the material.
• When magnetizing force (H) is decreased to zero, the curve will move or change from "a" point to "b" point.
• At this point, we can notice that some magnetic flux leftovers in the material even though the magnetizing force (H) is zero. This is called as the point of retentivity on the graph and shows the remanence or level of remaining magnetism in the material. Some of the magnetic domains stay aligned, but some magnetic domains lose their alignment.
• With the application of magnetizing force in reverse direction, the curve moves to "c" point, where the flux has been decreased to zero. This point is called as coercivity point on the curve or loop. The reversed magnetizing force has reversed plenty of the domains, so that the remaining flux within the material is zero.
• To remove the residual magnetism from the material a force has to be apply, this required force is called as the coercive force or coercivity of the material.
• In the negative direction when magnetizing force is increased, the material will become again magnetically saturated or material under goes in saturation, but in the opposite or reverse direction i.e. towards "d" point.
• Decreasing magnetizing force (H) to zero brings the curve to "e" point. The available level of remaining magnetism is equal to that achieved in the other direction.
• Increasing magnetizing force (H) back in the positive direction will return or bring back the magnetic flux (B) to zero.
• We can notice that, the curve did not return back to the beginning or origin of the graph because some magnetizing force is needed to remove the remaining or residual magnetism.
• Now the curve in the graph will take a diverse or different path from “f” point back to the saturation point, here at this point it with complete the loop.

Below image shows B-H curve measurement on Oscilloscope;

B-H curve measurement on Oscilloscope

Advantages of Hysteresis loop or B-H curve

The outcome of magnetic hysteresis loop shows;

• The magnetisation process of a ferromagnetic core.
• The part of the curve the ferromagnetic core is magnetised decides flux density because this depends on the circuits previous history which gives the core a form of “memory”.
• Ferromagnetic materials have memory because they stay magnetised after the external magnetic field has been taken out.
• Relays, solenoids and transformers can be easily magnetised and demagnetised because, they are made up of Soft ferromagnetic materials such as silicon steel or iron, which have very narrow magnetic hysteresis loops resulting in very small amounts of residual magnetism.
• Residual magnetism can be overcome by a coercive force; energy which is in use is dissipated as heat in the magnetic material. This heat is known as hysteresis loss, the material’s value of coercive force decides the amount of loss.
• A very small coercive force can be made that have a very narrow hysteresis loop by adding additive’s to the iron metal such as silicon. Magnetisation and demagnetisation of soft magnetic materials with narrow hysteresis loops are easy.

Hysteresis loop for Soft and Hard Material

Applications of Hysteresis

There are varieties of applications of the hysteresis in ferromagnets. Many of the applications make use of their capability to hold a memory; like magnetic tape, computer hard disks and debit cards - credit cards. In these applications, hard magnets which have high coercivity like chromium and iron are required so the memory is not easily removed. Let understand it in detail;

Because of presence of magnetic domains in the material the magnetization curve is not re-traceable (which is termed as hysteresis). After re-orientation of magnetic domains, it will take some magnetizing field or energy to turn them back again. This characteristic of ferromagnetic materials is useful as a magnetic "memory". Some configurations of ferromagnetic materials will maintain a forced magnetization forever and are useful as "permanent magnets". The magnetic memory features of chromium and iron oxides are useful in audio tape recording and also for the magnetic storage of data on computer hard disks.

Soft magnets which have low coercivity for example iron oxide is used for the ferrite cores in electromagnets. The low coercivity decreases that energy loss related with hysteresis. This low energy loss at the time of hysteresis loop is the main reason of using soft iron for electric motors and transformer cores.

Hysteresis loss

As current flows in the forward and reverse directions the magnetization and demagnetization of the core happens which result in Hysteresis loss.

When we apply external magnetizing force to a material and as we increase the magnetizing force (current), the magnetic flux also increases, but when the magnetizing force (current) is decreased, the magnetic flux decreases gradually and not at the same rate. So, when the magnetizing force touches zero, the flux density didn’t come to zero and still has a positive value. Now the magnetizing force must be applied in the negative direction so the flux density reaches zero.

The link between the magnetizing force (H) and the magnetic flux density (B) is shown on a hysteresis loop or curve. The energy required for completing a full cycle of magnetizing and de-magnetizing is shown by the area of the hysteresis loop. Also this area of the loop characterizes the energy lost during this magnetisation process.

Below is the equation for hysteresis loss;

Where;

Pb = hysteresis loss (W)

η = Steinmetz hysteresis coefficient, depending on material (J/m³)

Bmax = maximum flux density (Wb/m²)

n = Steinmetz exponent, ranges from 1.5 to 2.5, depending on material

f = frequency of magnetic reversals per second (Hz)

V = volume of magnetic material (m³)

The hysteresis loss results in wasted energy which is proportional to the area of the magnetic hysteresis loop.

In AC transformers, hysteresis loss is always a problem where the current is continually changing the flow of direction and by this the magnetic poles continually flows in reverse direction and causes loss in the core.

Conclusion

Hysteresis loop provides information about the magnetic properties of a material. It is important that the B-H hysteresis loop is as small as possible so loss will be less because shape of B-H curve decides the loss. Bigger the area then more is the loss and vice-versa. The shape of hysteresis loop depends upon the nature of the material used i.e. iron or steel.

More details on Ferrite you can find in my previous blog;

“Ferrite,Ferrite structure and Ferrite properties”.

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