UMN EXHIBIT 2027
`LSI Corp. et al. v. Regents of Univ. of Minn.
`IPR2017-01068
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`Page 1 of 80
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`This book may be purchased at a discount from the
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`© 1997 by the Institute of Electrical and Electronics Engineers, Inc.
`3 Park Avenue, 17th Floor, New York, NY 10016-5997
`
`-
`
`All rights reserved. No part of this book may be reproduced in any form,
`nor may it be stored in a retrieval system or transmitted in any form,
`without written permission from the publisher
`
`10987654
`
`ISBN 0-7803-1083-7
`
`IEEE Order Number: PC4374
`
`Library of Congress Cataloging-in-Publication Data
`
`Ashar, Kanu G. (date)
`Magnetic disk drive technology : heads, media, channel, interfaces,
`and integration / Kanu G. Ashar.
`p. cm.
`Includes bibliographical references and index.
`ISBN 0-7803-1083-7
`1. Data disk drives. I. Title
`TK7887.8.D37A83 1996
`621.39’76—dc20
`
`96-14428
`CIP
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`d in any form,
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`Contents
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`PREFACE xv
`
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`ACKNOWLEDGMENTS xvii
`
`
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`LIST OF SYMBOLS, ABBREVIATIONS,
`AND FORMULAS xix
`
`1
`INTRODUCTION 1
`
`1.1 Disk Drive Industry 1
`
`
`
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`1.3 Disk Drive Head Technologies 6
`
`
`1.4 Scope of the Book 8
`
`
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`
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`THE FUNDAMENTALS
`
`
`OF MAGNETISM 13
`
`
`(James C. Suits)
`
`
`
`2.1
`IntroductionfiMagnets and Poles 13
`2.2 Forces between Poles 15
`
`1.2 Disk Drive Technology Development 3
`
`1.5 Outline of Topics Covered 9
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`vi
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`2.3 Magnetic Fields 16
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`2.4 Dipoles, Magnetic Materials,
`and Magnetization 17
`
`2.5 Magnetic Flux Density
`or Magnetic Induction 19
`
`2.6 Demagnetizing Field 21
`
`2.7 Ampere’s Law 23
`
`2.8 Faraday’s Law 23
`
`2.9
`
`Induction 24
`
`2.10 Magnetic Circuits 25
`
`2.11 Units and Conversions 27
`
`2.12 CGS—SI Conversion Table 29
`2.13 Hysteresis Loops and Magnetic Materials 30
`2.14 Magnetic Anisotropy 32
`2.14.1 Magnetocrystalline Anisotropy 33
`2.14.2 Field-Induced Anisotropy 35
`2.14.3 Shape Anisotropy 35
`2.14.4 Magnetostrictive Anisotropy 35
`2.15 Domains 37
`
`2.16 Exchange 38
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`2.17 Magnetoresistanee 41
`
`References 41
`
`
`
`3 DISK DRIVE
`MAGNETIC RECORDING 42
`
`3.1
`
`Introduction 42
`
`3.2 Writing and Reading 44
`
`3.3 Field from the Head 46
`3.4 Example: Head Field Calculation 50
`3.5 Head Efficiency and Field in the Gap 50
`3.6 Reading of Magnetic Disk Data 51
`
`3.7 Reading with Step-Function
`Magnetic Transitions 54
`tangent Magnetic Transitions 55
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`3 .8 Reading Arc
`
`3.9 Transition Parameter a 57
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`Contents
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`Contents
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`vii
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`3.10 Example: Calculations of Transition Parameter a, V1,-” and
`P50 58
`
`3.11 Signal Voltage Parameters
`and Engineering Approximations 59
`
`3.12 Digital Writing Process:
`Discussion and Graphical Illustration 62
`
`3.13 Side Writing, Reading, Erasing,
`and Fringing Fields of Heads 65
`
`3.14 Reading Sinusoidal Magnetic Transitions 67
`References 69
`
`4 FERRITE AND MI_G HEADS 70
`4.1
`Introduction 70
`
`4.2 Ferrite Materials 73
`
`4.3 Recording Head Characteristics 74
`
`4.4 Limitations of Conventional Ferrite Heads 75
`
`4.5 Metal-in—Gap Heads: Motivation 76
`
`4.6 Types of Ferrite and MIG Heads 76
`
`4.7 MIG-Head Construction Steps 77
`
`4.8 Performance Advantages of MIG Heads 81
`4.9 Limitations of MIG Heads 84
`
`4.10 Improvements and Innovations
`in MIG Head Structures 86
`
`References 89
`
`5 THIN FILM HEADS 90
`
`Introduction and Historical Perspective 90
`5.1
`5.2 Film Head Structure 92
`
`5.3 Film Head Construction 93
`
`5.4 Thin and Thick Pole Heads 97
`
`5.5 Writing and Reading with Film Heads 100
`
`5.6 Film Head Writing 100
`
`5.7 Equivalent Circuit of Inductive
`and MR Heads
`101
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`”raw‘
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`Contents
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`10 HEAD-DISK INTERFACE 268
`(Roger F. Hoyt)
`
`10.1 Introduction 268
`
`10.2 Air-Bearing Sliders 270
`
`10.6 Head—Disk Tribology 288
`10.6.1 Flying Height and Glide Height 288
`10.6.2 Friction, Stiction,
`and Contact Start-Stops 289
`
`10.7 Novel Slider Designs 291
`10.7.1 Simulated Comparison
`of Various ABS Designs 292
`10.7.2 Novel Slider Designs 295
`10.7.3 Tripad Slider Design 299
`
`10.8 Environment, Particles,
`and Chemical Contamination 300
`
`10.9 Contact Recording Approaches 300
`10.9.1 Head Spacing Controller 301
`10.9.2 Taildragger Head 302
`10.9.3 Continuous Contact 303
`10.9.4 Integrated Head Suspension Design 304
`References 304
`
`10.3 Self-Acting Air Bearings 271
`10.3.1 Cylindrical Crown Bearings 271
`10.3.2 Winchester Slider 271
`10.3.3 Taper Flat Slider 272
`10.3.4 ”Self-Loading” Slider 273
`10.3.5 Miniaturized Designs 274
`10.4 Gas Lubrication for Air Bearings 276
`10.5 Characterization and Test Measurements
`of the Air—Bearing Interface 278
`10.5.1 Capacitance Measurement Technique
`for Air—Bearing Separation 279
`10.5.2 Optical Interference Method to Evaluate
`Slider Flying Characteristics 280
`10.5.3 Piezoelectric Technique to Measure
`Head-Disk Interactions 285
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`ll FUTURE TRENDS IN TECHNOLOGY 306
`11.1
`Introduction 306
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`11.2 Projections and Predictions
`of Technology Parameters 307
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`11.3 Multigigabit Density Demonstrations 309
`
`11.4 Giant Magnetoresistance
`and Spin-Valve Magnetic Head 313
`11.4.1 GMR 313
`11.4.2 Spin Valve 315
`11.4.3 Spin-Valve Read Head 317
`
`11.5 Optical Servo for Magnetic Recording 319
`
`11.6 Application of Discrete Tracks for Servo
`and Recording 321
`
`11.7
`
`Perpendicular Recording
`and Contact Recording 322
`
`11.8 Applications of Disk Drives 324
`
`11.9 Multispindle Arrays or RAIDS
`(Redundant Arrays of Independent Drives) 325
`11.9.1 Mirroring, or RAID-1 325
`11.9.2 RAID-3 326
`11.9.3 RAID-5 327
`
`11.10 Small-Form—Factor Drives 328
`
`11.11 Summary: Disk Drive R&D Directions 329
`11.11.] Heads 329
`11.112 Media 329
`11.113 Signal Processing Electronics 330
`11.11.4 Serve and Track-Following Mechanics 330
`References 331
`
`INDEX 335
`
`AUTHOR’S BIOGRAPHY 341
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`ix
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`Contents
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`Contents
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`6.15 Topics Related to Reliability of MR Heads 148
`
`‘
`
`6.16 Yoke-Type MR-Head Structures 149
`6.17 Novel MR—Head Structures 150
`
`6.18 Modeling of Shielded
`and Biased MR Heads 152
`
`6.18.1 MR Head Equivalent Circuit 157
`6.19, Medium Field Distribution
`of a Shielded MR Head 157
`
`6.20 Sinusoidal Transition Response '
`of the Shielded MR 158
`
`6.21 Asymmetric Track Reading-
`of the Shielded-Biased MR Head 158
`
`References .160
`
`7 THIN FILM MEDIA 163
`
`(Kenneth E. Johnson)
`
`Introduction and Historical Perspective 163
`7.1
`7.2 Particulate Media 164
`
`7.3 Thin Film Media Structure
`and Manufacture 165
`7.3.1 Disk Structure 165
`7.3.2 Disk Manufacture 169
`
`7.4 Disk Magnetics 171
`7.4.1 Macromagnetics 173
`7.4.2 Micromagnetics 174
`7.4.3 Low—Noise Fabrication Techniques 174
`7.5 Disk Tribology 179
`
`7.6 Disk Testing and Characterization 182
`7.6.1 Materials Characterization 182
`7.6.2 Finished Disk Testing 187
`7.6.3 Mechanical Testing 188
`7.7 Disk Technology Directions 190
`7.7.1 Substrates 190
`7.7.2 Magnetic Film 191
`7.7.3 Head/Medium Interaction 194
`References 195
`.
`
`8 RECORDING CHANNEL 197
`
`
`g
`g
`
`Introduction 197
`8.1
`8.2 Functions of a Channel 198
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`8.3
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`8.4
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`8.5
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`8.6
`
`8.7
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`8.8
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`8.9
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`8.10
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`8.11
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`8.12
`
`8.13
`
`8.14
`
`8.15
`
`Peak Shift or Bit Shift
`from Intersymbol Interference 200
`Peak Detection Window 202
`
`Coding in a Disk Drive Channel 202
`
`NRZI, MFM,
`and Run Length—Limited Codes 204
`86.1 FM 204
`8.6.2 MFM 205
`8.6.3 RLL Codes 207
`
`Write Precompensation 208
`
`Am Electronics Module 208
`
`Automatic Gain Control Module 209
`
`Filter and Equalizer 210
`
`Peak Detection Process 213
`
`Variable Frequency Oscillator
`or Phase—Locked Oscillator 214
`
`Partial Response Maximum
`Likelihood Channel 214
`8.13.1 Motivation 215
`8.13.2 Explanation of PRML and Comparison
`with Peak Detection Channel 215
`8.13.3 Partial Response 217
`8.13.4 Maximum Likelihood 220
`Extended PRML and (1, 7) Maximum
`Likelihood Channels 221
`
`Magnetic Recording Measurements of Write
`and Read Parameters 222
`
`8.16 Overwrite and Its Measurements 223
`8.17
`
`Write Current Optimization
`for Recording 225
`
`8.18
`
`Linear Density Roll-Off Curve
`and Resolution 227
`
`8.19 Noise Sources in Recording Processes 230
`8.19.1 Random Noise 232
`
`8.20 Head Equivalent Circuit Noise 232
`
`8.21 Head Preamplifier Noise 233
`
`8.22 Thin Film Medium Noise 234
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`Contents
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`:71
`‘l.1
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`Contents
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`Contents
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`8.23 Signal—to-Noise Ratio
`and On—Track Error Rates 235
`
`References 237
`
`9 MAGNETIC DISK
`
`RECORDING INTEGRATION 238
`
`9.1
`
`Introduction 238
`
`9.2 Disk Drive Design Considerations 240
`9.2.1 The Form Factor 240
`
`9.2.2 Capacity (in Megabytes or Gigabytes)
`and Price 240
`9.2.3 Access Time 240
`9.2.4 Data Rate 241
`9.2.5 Reliability 241
`
`9.3 Track Density and Storage Capacity
`of a Disk 242
`
`9.4 Track Misregistration 243
`9.4.1 Thermal Effects 246
`9.4.2 Spindle Bearing Runouts 247
`9.4.3 Mechanical Vibrations 247
`9.4.4 Servo Loop Electronic Noise 247
`
`9.5 Disk Drive Servo 247
`
`9.6 Sector, or Embedded, Servo 249
`
`9.7
`
`Integration of Head, Medium,
`and Channel 250
`
`9.8 Track Profile and Microtraek Profile 252
`
`9.9 Off—track or 01 Measurement 255
`
`9.10 Estimation of the System Error Rate 257
`
`9.11 Track Pitch Determination, “Squeeze,"
`and the “747" Curve 257
`
`9.12 Application of Integration Procedures 259
`
`9.13 Window Margin Integration Procedures 261
`9.13.1 Window Margin Analysis 264
`9.13.2 Channel Optimization 264
`9.13.3 Off-Track Analysis and Track—Pitch
`Determination Using Peak
`Jitter Measurements 265
`9.13.4 Head—Disk Assembly Qualification 266
`References 267
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`5.9 Thin Film Head Efficiency
`
`5.10 Applications of Film Head
`
`5.12 Processes and Materials
`for Thin Film Heads 111
`
`513' Progress and Research on Thin Film Heads 112
`5.14 Instability, Wiggles, and Multidomains
`in Film Heads
`113
`
`5.15 Silicon Planar Thin Film Head 115
`
`References 119
`
`
`
`of Inductive Heads 103
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`5.8 Number of Turns and Resonance Frequency
`
`
`and Inductance Modeling 105
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`
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`Inductance Measurements 109
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`5.11 Reading with Thin Film Heads 110
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`6 MR HEADS 121
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`6.5 Biasing of an MR Head 131
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` 6.6 Permanent—Magnethiased Shielded
`MR Head 133
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`6.9
`Soft-Adjacent—Layer Bias for the MR Head 138
` 6.10 Barber—Pole Biasing for an MR Sensor 140
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`6.11 Dual-Striped MR—Head Biasing 142
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`Appendix: Head Gap Field
`for a Thin Film Head 118
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`6.1
`
`Introduction 121
`
`,
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`6.2 Principles of the MR Sensor Operation 124
`
`6.3
`
`Shielded MR Heads 128
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`6.4 Structure and Processing Considerations
`of the MR Head 129
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`6.7
`
`Shunt-Biased Shielded MR Head 134
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`6.8 Shielded Shunt—Biased MR Head
`for 2 Gb/in.2 Density 136
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`6.12 Barkhausen Noise and Instabilities
`in MR Sensors 143
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`6.13 Prevention of Barkhausen Noise:
`Longitudinal Biasing of MR Heads 144
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`. g“
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`6.14 Electromigration in MR Sensors 147
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`Disk Drive Magneti
`Recordin
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`
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`3.1 INTRODUCTION
`
`Multitrack magnetic audio recording in cassette and open—reel form is universallfi
`
`well known. The drawback of this form of recording is a long access time t
`selected section on the tape. In the past, phonograph recording and, now, comp
`
`discs are preferred for quick access to a desired selection. In the 19505, digi
`magnetic tapes predominated in providing on—line data storage although, for a
`
`years in the late 19503, expensive and complex drums were employed for criti
`applications requiring fast access to the data. For reasons analogous to those f?
`
`the audio recording-—that is, access to random data—~the evolution of the rigid dis
`drive began in 1956. In a sense, the disk drive is a hybrid of a digital tape reco
`and a phonograph jukebox. Figure 3.1 'shows the parts of a disk drive. The dis
`often referred to as a platter. Disk drive parts and their functions are given in t
`
`list that follows.
`I The purpose of the disk drive is to store data over a long period of time
`
`retrieve it reliably.
`I The head writes and reads data from the disk.
`I The head is part of a slider. A slider has a flexible connection to the actu
`and it has a profiled surface facing the medium that forms an air—bearing
`face (ABS) allowing the head to “fly” at a close distance from the med
`
`I An actuator provides a means of moving the head/slider from one tra
`another and produces motions to retain the head in the center of the
`under servo electronics commands.
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`Sec. 3.1 I Introduction
`
`43
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`Electronics
`
`Spindle
`
`Head slider
`
`
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`ActuatorVoice coil motor
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`Base plate
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`Two disks
`
`Figure 3.1 Schematic drawing of a disk drive and its parts.
`
`I A channel converts the digital data to be stored into write currents and sup—
`plies them to the head coil. It receives signals read by the head from the
`medium and translates them to data or usable bit patterns.
`
`
`
`
`
`For disk drives equal to or larger than 130 mm (5.25 in.) in diameter, linear actuators
`with comblike head accessing arrangements have been used. For disk diameters
`
`of 95 mm (3.5 in.) and smaller, rotary actuators are utilized. Figure 3.1 shows a
`3 and open—reel form is universa
`
`rotary actuator. To shorten the latency or time of accessing on a given'track, the
`cording is a long access time t
`
`drive rotates between 1800 and 7200 revolutions per minute (RPM). The relative
`graph recording and, now, comp
`
`velocity between head and disk is in tens of meters per second. For instance, for
`:ed selection. In the 1950s, dig
`
`a 76 mm diameter track of a disk rotating at 7200 RPM, relative velocity between
`ine data storage although, for af
`
`head and disk is about 29 m/sec (64 mi/hr). To ensure sufficiently long life for the
`x drums were employed for c
`
`head and magnetic medium on the disk, the head slider attached to the actuator
`For reasons analogous to tho
`aerodynamically “flies” at close distance of less than 100 nm (4 microinches).
`data—the evolution of the rigid]
`
`After reviewing the principles of writing and reading, we shall focus on the
`,
`:he parts of a disk drive. The dis
`, magnetic writing of data by the head on the medium (magnetic thin layer on a sub-
`
`and their functions are glVfin 111.
`strate). The magnetic writing process is strongly tied to the recording performance
`of the disk drive system. Because of its importance, the discussion on writing is
`
`‘
`divided into parts. The beginning part is simple and fairly intuitive, yet it points out
`
`e data over along P3?10d 0f “m
`,
`the limitations of the head and medium components, which has led to the evolution
`
`of recording technology. Additional topics on writing are described inthe last two
`
`sections of the chapter. These issues are important for the comprehensive under-
`
`standing of disk drive recording. The middle sections are dedicated to the reading
`; a flexible connection to the ac
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`processes. The significant aspects of reading are how the signal voltages and signal
`medium that forms an air—bean ,
`,
`
`pulse widths vary with the head and medium parameters and the spacing between
`at a close distance from the In
`
`head and medium. The principles and procedures used in deriving useful equations
`
`_ are explained. As much as possible, simple equations are used for illustrations and
`
`_ Clarification of concepts. More complex equations are not derived here, but their
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`applications and simplifications are reviewed and references are pointed out whet
`
`n inductive head is assumed for most of the discussion
`more details can be found. A
`Where appropriate, the comparison of inductive and MR heads is considered, bu
`details of the MR signal characteristics are treated in Chapter 6.
`
`Chap. 3 I Disk Drive Magnetic Recordin
`
`: Sec. 3.2 I
`
`3.2 WRITING AND READING
`
`
`
`s the medium a
`
`
`
`First, we shall review the writing and reading processes. Figure 3.2 shows
`
`' schematic of a ring head and a disk. The head consists of a ring or yoke of mag
`netic material with a coil of wire wrapped on the core. The coil is connected to th
`
`channel electronics. There is a gap at the bottom of the head, close to the medium /
`The writing sequence is as follows:
`
`ata to be stored from the computer, and after som
`1. The channel receives d
`tes currents in circuits calle
`processing (explained in Chapter 8), genera
`write drivers.
`
`2. The write driver supplies current to the head coil.
`
`f the head. Ne
`3. The coil current results in magnetization of the “core” 0
`the gap, the magnetic field spreads out. '
`4. Some of the fringe or stray field near the gap reache
`magnetizes it in one direction as seen in Figure 3.2.
`As the data changes, depending on the coding rules, the current in the coil is
`versed, and the field near the gap reverses, reversing the magnetic poles in
`
`medium. The sequence ofdata from the channel electronics thus gets translated in
`magnetized poles in the medium. During reading, the write drivers are switched
`
`and are virtually isolated from the head coil. The reading preamplifier is connect
`
`to the head. Assuming that the disk track has previously written data, the follow'
`its.
`sequence of events or reading converts them into user b
`
`the core of the head becom
`1. As the magnetic poles pass near the head gap,
`magnetized.
`
`11 depend on the direction
`2. The direction of magnetization of the core wi
`the magnetization of the medium.
`
`3. The change in magnetization in the core results in avoltage across the h
`coil.
`
`Note that only a change in magnetization in the medium and, hence, a‘chang
`magnetic flux through the coil, produces a voltage. According to Faraday’s
`
`(Sec. 2.8), V = —dd>/dt or voltage is generated if the flux changes with time.
`is what happens during changing of the magnetization pattern under the head
`At transitions, where the magnetizations in the medium change, voltage outp
`
`result. Depending on the data, there are two types of transitions possible: no,
`poles facing north poles or south poles facing south poles. These transitions cr
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`positive- or negative-going voltage pulses in the head coil. These voltage pu
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`ap. 3 I Disk Drive Magnetic Recording
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`sec. 3.2 I Writing and Reading
`
`45
`
`
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`Magnetic medium.
`of thickness. 5
`
`Disk substrate
`
`Figure 3.2 Head gap region and head
`fields.
`
`get amplified and, after a series of detection steps (discussed in Chapter 8), result
`in usable data supplied to the computing processor.
`Figure 3.3 illustrates write and read sequences. Figure 3.3a shows a sequence
`of data in the form of a series of “ones” and “zeros.” In one method of storing this
`sequence of data, the current through the head coil must reverse at each “one” and
`not reverse at each “zero” (Fig. 3.3b). When this is done during disk rotation, the
`magnetization of the disk medium along a disk track looks as in Figure 3.30. A
`magnetic transition occurs at each “one” and not at each “zero.”
`Let’s turn now from writing data to reading data. The operation occurs in
`reverse. As a written transition passes under the head, a small change in the yoke
`magnetization occurs (Fig. 3.3d). This change in yoke magnetization induces a volt—
`age in the coil that is sensed by the disk drive electronics (Fig. 3.3e). This occurs
`each time a transition passes under the head.
`
`
`
`
`
`
`
`Writing
`(a) Information data ———i—l—~l*+l
`(b) Writingcurrents :F:}:;
`
`(c) Medium magnetizations
`
`'1
`
`
`
`
`1 references are pointed out where ‘
`ssumed for most of the discussmn
`and MR heads is considered, bu
`ed in Chapter 6.
`
`
`
`
`
`
`
`1g processes. Figure 3.2 shows
`
`consists of a ring or yoke of mag
`
`e core. The coil is connected to th
`
`n of the head, close to the medium
`
`
`from the computer, and after som
`
`generates currents in circuits calle
`
`
`
`:ion of the “core” of the head. Ne
`
`
`rr the gap reaches the medium an
`
`in Figure 3.2.
`g rules, the current in the coil'is r
`
`reversing the magnetic poles in.
`:1 electronics thus gets translated in
`
`.ng, the write drivers are switched
`“be reading preamplifier is connect
`
`)reviously written data, the follow
`
`into user bits.
`
`ead gap, the core of the head bec "
`
`
`
`
`
`ore results in a voltage across the h
`
`
`
`Reading
`(d) Magnetic flux changes
`in read head
`
`'
`
`'\~
`
`(e) Waveformsofread voltage __A——VA_—
`
`
`
`. the medium and, hence, a Chang
`voltage. According to Faraday’s.
`
`rted if the flux changes with time
`gnetization pattern under the hea .,
`
`l the medium change, voltage out
`vo types of transitions possible: _
`
`1g south poles. These transrtions c,
`Figure 3.3 Writing and reading data.
`in the head coil. These voltage p__
`
`
`
`Page 15 of 80
`
`

`

`
`
`
`
`
`
`
`
`From an energy standpoint, the writing and reading of information in the disk driv
`is highly inefficient. For writing, one needs currents——on the order of a few tens o
`
`milliamperes—so that the writing field at the disk medium is high enough to write
`
`On the other hand, for reading, one only has voltages in the range 0.1 to l millivolts
`
`and this requires complex external detection and amplification to extract usable dat
`
`out of such low signals. However, the merit of this technology lies in its ability t
`
`store data indefinitely without power, and retrieve it inexpensively and reliably.
`
`
`
`
`The preceding discussion gave a qualitative picture of how data are written to an
`read from a disk. However, to understand general design principles as well as re
`
`cent improvements in head and disk designs, one needs to have a quantitative u
`
`derstanding of the factors involved in the writing and reading processes.
`A sufficient writing field must be applied to the disk medium to write magnet‘
`
`transitions. More specifically, the field produced by the head at the medium must
`
`least exceed the coercivity of the medium. However, applying a field equal to H6:
`
`a typical medium as shown in Figure 2.13 will reverse only half the magnetizatio
`
`Due to the nonsquare nature of these loops, a field equal to two or three times
`
`is applied to reverse all the magnetization. A factor of 2.5 is commonly used
`will be used in illustrative examples. The stray magnetic field near the gap of-
`inductive head looks like that shown in Figure 3.4. This figure gives a more deta
`
`(and inverted) picture of the head stray field previously illustrated in Figure 3.
`
`The arrows indicate field direction with the length representing the magni
`of the field strength. Notice that arrow directions are effectively horizontal at t
`.-
`-
`~
`\
`x
`.
`k
`..
`~
`~
`
`4
`
`r
`
`a
`
`.
`
`
`
` 3.3 FIELD FROM THE HEAD
`
`v
`
`-
`
`.v
`
`u
`
`'0
`
`~
`
`..
`
`~
`
`\
`
`x
`
`x
`
`igure 3.4 Head field and contours of equal fields.
`
`
`
`
`
`
`
`
`
`\ F
`
`
`Page 16 of 80
`
`

`

`
`Sec. 3.3 I Field from the Head
`
`rap. 3 I Disk Drive Magnetic Recordin
`
`
`mg of information in the disk driv
`ents——on the order of a few tens
`;k medium is high enough to writ
`ages in the range 0.1 to 1 millivol
`amplification to extract usable da
`
`this technology lies in its ability
`ve it inexpensively and reliably.
`
`
`
`
`
`
`
`cture of how data are written to aria
`eral design principles as well as
`
`me needs to have a quantitative
`
`ng and reading processes.
`
`to the disk medium to write magn
`
`:d by the head at the medium mus
`
`vever, applying a field equal to H
`reverse only half the magnetizat
`
`field equal to two or three times
`
`factor of 2.5 is commonly used
`
`ay magnetic field near the gap 0
`
`3.4. This figure gives a more deta
`
`)reviously illustrated in Figure 3‘.-
`
`he length representing the magni
`
`tions are effectively horizontal a
`
`
`
`
`
`center of the gap above the gap center. Everywhere else, they are at various angles
`with respect to the horizontal or x axis. First, we obtain a simple equation of the
`head field based on an intuitive argument and later we discuss a more accurate
`one. In Figure 3.4, it seems that the field contours are circular; that is, equal fields
`are located on the circumference of a circle. Recalling Ampere’s law (refer to Sec.
`2.7), the magnetic field surrounding a straight conductor with current is radially
`distributed, and the field is given by 1/21'rr, where r is the radius of the circular
`path. In the limiting case for the head where the gap becomes very small, the field
`contours become circular and the value of the field at radius r approaches ni/qrr
`amperes/meter. Here, i is the current in the coil, 11 is the number of coil turns, and
`m' is the ampere turns or approximately the magnetomotive force at the gap. The
`denominator has 1rr instead of 211'r because the field is integrated over a semicircle
`instead of a full circle as is done in the definition of Ampere’s law (refer to Sec. 2.7).
`For longitudinal recording, our main interest is the magnetic field in the x direction.
`Converting the foregoing field from cylindrical (r; 9) coordinates to cartesian (x, y)
`coordinates, x and y components of the field are given by
`m
`y
`m
`x
`w‘wm+fl’ m—ww+fl
`The x field equation will be used several times in the text since it allows usable
`voltage signal equations and simplifies the understanding of recording concepts.
`Strictly speaking, the validity of the equation requires that the gap is negligible
`or very small compared to the distance y. In many cases, the equation is usable
`even when y is only slightly larger than gap g. However, as relatively smaller fly-
`ing heights are used, there is a need for an accurate field equation including gap
`parameter for design.
`More general equations for the x and y fields of a ring head of infinite poles
`have been derived [1] and are
`H
`
`+ /2
`
`—
`
`
`
`47
`
`(3.1)
`
`(3.2)
`(3 3)
`
`.
`
`
`
`
`
`
`Hx(x, y) = —g (arctan 1—5; ~ arctan w)
`y“ y)
`2n n[(x — g/z)2 + y2
`
`1T
`
`y
`
`H ,
`
`=
`
`
`—H
`
`(x + g/2)2 + y2
`1 ——————
`
`y
`
`.
`
`In these equations g is the gap and Hg is the magnetic field strength inside the head
`gap due to current in the coil (Fig. 3.2). The units of~Hx and Hy are the same as
`
`the units of Hg. Since equation (3.2) plays a major role in longitudinal recording,
`
`let us examine it more closely. There is a simple way of visualizing equation (3.2).
`
`The difference of the two arctangent functions in the parentheses is nothing more
`
`than the angle 6 subtended by the gap at a location x, y, where the value of field is
`
`required. The geometric construction is illustrated in Figure 3.5.
`
`Accordingly, equation (3.2) can be simply written as
`
`
`Hx(x,y) = fife
`
`:ontours of equal fields.
`
`(3.4)
`
`
`
`
`Page 17 of 80
`
`

`

`Chap. 3 I Disk Drive Magnetic Recordi
`
`Sec.
`
`X)"
`
`61: aman (x + g/2)/y
`92 = arctan (x - gl2)/y
`9:91—92
`
`
`
`
`
`
`
`
`
`
`Figure 3.5 Karlqvist head field in terms of an angle.
`where 6 is as defined in the last paragraph and is in radians. Hx(x, y) is the large
`where 6 is the largest; that is, from Figure 3.5 where the point of interest x, y
`
`closest to the gap and directly over the gap (6 = 11' and Hx = H8). Using the ang
`6, one can qualitatively plot the contours of equal fields surrounding the gap of
`
`ring head.
`and Hy along the x and y axes. The x-axis v:
`Figure 3.6 shows plots of Hx
`are divided by Hg to make these u ,
`ues are divided by g, and head fields HI and Hy
`
`
`
`
`
`
`Figure 3.6 Normalized x and y components of head field.
`
`
`
`
`
`
`
`
`
`
`
`Page 18 of 80
`
`

`

`.113 I Disk Drive Magnetic Record“!
`
`sec. 3.3 I Field from the Head
`
`
`
`49
`
`
`
`n terms of an angle.
`
`is in radians. Hz“! 3") is the lar
`g
`5 where the pomt Of interest x,
`= TI and Hx = Hg)-.U31“g the aug
`qual fields surroundlng the gap
`.
`vng the x and y axes. The x—axrs
`are divided by Hg to make these
`
`~
`
`‘
`
`,
`
`versal plots, that is, independent of particular g and Hg values. Three field contours
`are shown for ylg values of 0.05, 0.25, and 0.5. As illustrated earlier in Figure
`3.4, the Hx component of the field (solid lines in Fig. 3.6) is maximtim along the
`vertical axis. Hx also is shown growing larger as y becomes smaller, that is, nearer
`the head. Hy, on the other hand (dashed lines), is zero at the gap center; there is no
`vertical component of the field along the vertical center line (see Fig. 3 .4). However,
`this field peaks at some distance from the center line. It turns out that the locations
`on the x axis, where the Hy field is a maximum or a minimum in Figure 3.6, are
`the points where the Hx field is 50% of the maximum value of Hx. The values of x,
`where Hy has a maximum and a minimum, are obtained by differentiating it with
`respect to x on the right—hand side of equation (3.2) and equating the result to zero.
`We define the distance between these two x values, where HI is 50% of its peak
`value as the half width (Ax) of Hx. The value of Ax can be obtained in equation
`form by manipulating equations (3.2) and (3.3).
`‘
`2
`
`1/2
`
`Ax = 2
`
`5 + y2
`2
`
`(3.5)
`
`The equation gives the half width of the x component of the head field. In Section
`3.7, it will be seen that under certain conditions, the shape of the read voltage pulse
`becomes identical to that of the head field, and the same equation (3.5) gives a pulse
`half width of the read voltage. Note that in the close vicinity of the gap (y = 0), Ax
`becomes equal to the gap size g. Putting x = 0 in equation (3.2), we get the (peak)
`horizontal field along the y axis. This equation is plotted in Figure 3.7.
`2H
`11,.(0, y) = —£ arctan fi—
`’lT
`2y
`
`(3.6)
`
`(H1ME) . ‘ ‘
`
`
`RelativeFieldStrength
`
`0.25 y/g
`0.5
`
`l 0
`i
`------ - —
`g _ _ .
`’ g 2 : g ’
`\\ \‘__,, I”I
`I
`1’
`I
`I
`\J
`
`_
`
`.
`
`_
`
`.
`
`0
`
`0.2
`
`0.6
`0.4
`Spacing /Head gap (ylg)
`
`0.8
`
`l
`
`components of head field.
`
`Figure 3.7 Peak head field as a function of the ratio of spacing and gap.
`
`
`
`
`Page 19 of 80
`
`

`

`
`
`50
`
`The following example is given to demonstrate the use of this equation and increase
`familiarity with the nomenclature. The example also points out the importance 0
`parameters that lead to head and medium technology enhancements.
`
`3.4 EXAMPLE: HEAD FIELD CALCULATION
`
`
`
`
`
`
`3.5 HEAD EFFICIENCY AND FIELD IN THE GAP
`
`The Objectives are, first, to calculate the head gap field, which allows writing mag
`netic transitions on the medium and second, to calculate the current required in th
`head coil to produce this field. The following parameters are assumed:
`
`1. The medium has a coercivity of 1600 Oe (127 kA/m).
`
`2. A field Hx equal to 2.5 times the coercivity of the medium is required f
`proper writing.
`
`3. Head gap g = 400 nm.
`4. Flying height (magnetic distance between head and medium, Fig. 3 .2) y
`100 nm.
`
`5. Medium thickness is considered negligibly small compared to the flyin
`height.
`Solving equation (3.6) for Hg results in Hg = 5666 Oe (451 kA/m).
`
`More easily and less accurately, Figure 3.7 may be used to calculate the sam
`quantity. For y/g = 100 urn/400 mm = 0.25, HJEIHg = 0.7. For a field at th
`medium of 1600 0e (127 kA/m) X 2.5 = 4000 0e (318 kA/rn), a gap field
`4000 Oe/0.7 = 5700 0e (454 kA/rn) is required.
`
`This field in the gap is generated by the head coil current. It is assumed th
`all the ampere turns (current multiplied by number of turns) are utilized to produ
`a head gap field. This happens if the permeability of the head material is very hig
`
`The magnetomotive force (refer to Sec. 2.10) required to produce a gap field is giv
`by Hg X g = (451 X 103) X (400 X 10—9) = 180.4 ma for a single-tum head. F
`a 20-turn head a current of 9 ma would be required. In practice, the permeability
`
`the material is finite, and not all the field generated by the coil reaches the head ga
`To account for the geometry of the head and permeability of the head core, the te
`
`“head efficiency” is introduced. The next section describes a formula to calcula
`head efficiency for a ring head structure.
`
`
`
`The magnetic circuit of the ring head can be approximated by two reluctances
`series: that of the head gap and that of the head core (see Sec. 2.10 for a discussi
`of magnetic circuits). These reluctances are given by 9R8 and gic as
`
`
`3
`lg
`I-I'OAg
`ILAC
`
`9R =
`g
`
`,
`
`9R =
`c
`
`where
`
`g and lo
`Ag and Ac
`p.
`
`II
`II
`
`the lengths of the gap and head core
`the gap and head core areas, respectively
`the permeability of the head core material.
`
`
`
`
`
`
`
`
`(3
`
`
`
`
`
`
`
`
`
`
`
`h-I-h—u-‘AH,.
`want—om".A
`
`3.6 REA
`
`On‘z-rnnnI-hj
`
`’2‘
`
`
`Page 20 of 80
`
`

`

`
`
`3 I Disk Drive Magnetic Recordin
`
`
`
`
`se of this equation and increas
`
`
`;0 points out the importance o
`
`;y enhancements.
`
`
`
`leld, which allows writing mag f
`ulate the current required in th
`
`neters are assumed:
`
`
`
`
`
`head and medium, Fig. 3.2) y
`
`
`)ly small compared to the flyi
`
`66 0e (451 kA/m).
`nay be used to calc