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Thread: Eectrical engineering ebook by John Bird

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    Pdf 32 Eectrical engineering ebook by John Bird

    book on electrical engineering by john bird

    Part 1 Basic Electrical Engineering Principles.................................... 1
    1 Units associated with basic electrical quantities........................................ 1
    SI units .......................................................................................................................... 1
    Charge........................................................................................................................... 4
    Force ............................................................................................................................. 4
    Work .............................................................................................................................. 5
    Power ............................................................................................................................ 5
    Electrical potential and e. m. f. ...................................................................................... 6
    Resistance and conductance ........................................................................................ 6
    Electrical power and energy .......................................................................................... 7
    Summary of terms, units and their symbols .................................................................. 8
    Further problems on units associated with basic electrical quantities........................... 9
    2 An introduction to electric circuits .............................................................. 10
    Standard symbols for electrical components................................................................. 10
    Electric current and quantity of electricity ...................................................................... 11
    Potential difference and resistance ............................................................................... 13
    Basic electrical measuring instruments ......................................................................... 13
    Linear and non- linear devices ...................................................................................... 13
    Ohms law ..................................................................................................................... 14
    Multiples and sub- multiples .......................................................................................... 14
    Conductors and insulators............................................................................................. 16
    Electrical power and energy .......................................................................................... 16
    Main effects of electric current ...................................................................................... 20
    Fuses............................................................................................................................. 20
    Further problems ........................................................................................................... 13
    3 Resistance variation .................................................................................. 23
    Resistance and resistivity.............................................................................................. 23
    Temperature coefficient of resistance ........................................................................... 26
    Further problems on resistance variation ...................................................................... 29
    4 Chemical effects of electricity .................................................................... 31
    Introduction.................................................................................................................... 31
    Electrolysis .................................................................................................................... 31
    Electroplating................................................................................................................. 32
    The simple cell .............................................................................................................. 32
    Corrosion ....................................................................................................................... 33
    E.m.f. and internal resistance of a cell .......................................................................... 34
    Primary cells .................................................................................................................. 36
    Secondary cells ............................................................................................................. 37
    Cell capacity .................................................................................................................. 39
    Further problems on the chemical effects of electricity ................................................. 39
    Assignment 1................................................................................................ 41
    5 Series and parallel networks ..................................................................... 42
    Series circuits ................................................................................................................ 42
    Potential divider............................................................................................................. 44
    Parallel networks ........................................................................................................... 45
    Current division ............................................................................................................. 48
    Wiring lamps in series and in parallel ............................................................................ 52
    Further problems on series and parallel networks ........................................................ 53
    6 Capacitors and capacitance ...................................................................... 55
    Electrostatic field ........................................................................................................... 57
    Electric field strength ..................................................................................................... 57
    Capacitance .................................................................................................................. 57
    Capacitors ..................................................................................................................... 57
    Electric flux density........................................................................................................ 59
    Permittivity..................................................................................................................... 59
    The parallel plate capacitor ........................................................................................... 61
    Capacitors connected in parallel and series.................................................................. 63
    Dielectric strength.......................................................................................................... 67
    Energy stored ................................................................................................................ 68
    Practical types of capacitor ........................................................................................... 69
    Discharging capacitors .................................................................................................. 70
    Further problems on capacitors and capacitance ......................................................... 70
    7 Magnetic circuits........................................................................................ 74
    Magnetic fields .............................................................................................................. 74
    Magnetic flux and flux density ....................................................................................... 75
    Magnetomotive force and magnetic field strength......................................................... 76
    Permeability and B Ò H curves ....................................................................................... 77
    Reluctance .................................................................................................................... 80
    Composite series magnetic circuits ............................................................................... 81
    Comparison between electrical and magnetic quantities .............................................. 84
    Hysteresis and hysteresis loss ...................................................................................... 84
    Further problems on magnetic circuits .......................................................................... 85
    Assignment 2................................................................................................ 87
    8 Electromagnetism...................................................................................... 89
    Magnetic field due to an electric current........................................................................ 89
    Electromagnets ............................................................................................................. 91
    Force on a current- carrying conductor ......................................................................... 92
    Principle of operation of a simple d. c. motor ................................................................ 96
    Principle of operation of a moving coil instrument ......................................................... 97
    Force on a charge ......................................................................................................... 98
    Further problems on electromagnetism......................................................................... 98
    9 Electromagnetic induction ......................................................................... 100
    Introduction to electromagnetic induction ...................................................................... 100
    Laws of electromagnetic induction ................................................................................ 101
    Inductance..................................................................................................................... 104
    Inductors........................................................................................................................ 106
    Energy stored ................................................................................................................ 107
    Inductance of a coil ....................................................................................................... 107
    Mutual inductance ......................................................................................................... 108
    Further problems on electromagnetic induction ............................................................ 109
    10 Electrical measuring instruments and measurements............................. 113
    Introduction.................................................................................................................... 113
    Analogue instruments.................................................................................................... 113
    Moving-iron instrument .................................................................................................. 113
    The moving-coil rectifier instrument .............................................................................. 114
    Comparison of moving- coil, moving- iron and moving- coil rectifier instruments ......... 114
    Shunts and multipliers ................................................................................................... 115
    Electronic instruments ................................................................................................... 117
    The ohmmeter ............................................................................................................... 117
    Multimeters .................................................................................................................... 118
    Wattmeters .................................................................................................................... 118
    Instrument ˛ loadingÌ effect ............................................................................................ 118
    The cathode ray oscilloscope ........................................................................................ 121
    Waveform harmonics .................................................................................................... 124
    Logarithmic ratios .......................................................................................................... 126
    Null method of measurement ........................................................................................ 129
    Wheatstone bridge ........................................................................................................ 129
    D.c. potentiometer ......................................................................................................... 130
    A.c. bridges ................................................................................................................... 130
    Measurement errors ...................................................................................................... 131
    Further problems on electrical measuring instruments and measurements.................. 133
    11 Semiconductor diodes ............................................................................. 137
    Types of materials ......................................................................................................... 137
    Silicon and germanium.................................................................................................. 138
    n-type and p-type materials ........................................................................................... 138
    The p-n junction............................................................................................................. 139
    Forward and reverse bias.............................................................................................. 140
    Semiconductor diodes................................................................................................... 140
    Rectification ................................................................................................................... 143
    Further problems on semiconductor diodes .................................................................. 143
    12 Transistors............................................................................................... 145
    The bipolar junction transistor ....................................................................................... 145
    Transistor action............................................................................................................ 147
    Transistor symbols ........................................................................................................ 149
    Transistor connections .................................................................................................. 149
    Transistor characteristics .............................................................................................. 150
    The transistor as an amplifier ........................................................................................ 152
    The load line .................................................................................................................. 154
    Current and voltage gains ............................................................................................. 155
    Thermal runaway........................................................................................................... 158
    Further problems on transistors .................................................................................... 159
    Assignment 3................................................................................................ 162
    Main formulae for Part 1............................................................................... 164
    General.......................................................................................................................... 164
    Capacitors and capacitance .......................................................................................... 164
    Magnetic circuits............................................................................................................ 164
    Electromagnetism.......................................................................................................... 164
    Electromagnetic induction ............................................................................................. 164
    Measurements............................................................................................................... 164
    Part 2 Electrical Principles and Technology ....................................... 165
    13 D.c. circuit theory..................................................................................... 167
    Introduction.................................................................................................................... 167
    Kirchhoffs laws ............................................................................................................. 167
    The superposition theorem............................................................................................ 171
    General d.c. circuit theory ............................................................................................. 174
    Th · evenins theorem.................................................................................................... 176
    Constant-current source ................................................................................................ 181
    Nortons theorem........................................................................................................... 181
    Th · evenin and Norton equivalent networks ................................................................. 184
    Maximum power transfer theorem................................................................................. 187
    Further problems on d. c. circuit theory ......................................................................... 189
    14 Alternating voltages and currents............................................................ 193
    Introduction.................................................................................................................... 193
    The a.c. generator ......................................................................................................... 194
    Waveforms .................................................................................................................... 194
    A.c. values..................................................................................................................... 195
    The equation of a sinusoidal waveform......................................................................... 200
    Combination of waveforms ............................................................................................ 204
    Rectification ................................................................................................................... 208
    Further problems on alternating voltages and currents................................................. 209
    Assignment 4................................................................................................ 212
    15 Single-phase series a.c. circuits .............................................................. 213
    Purely resistive a.c. circuit ............................................................................................. 214
    Purely inductive a.c. circuit ............................................................................................ 214
    Purely capacitive a. c. circuit ......................................................................................... 214
    R … L series a.c. circuit ................................................................................................... 215
    R … C series a.c. circuit .................................................................................................. 220
    R … L … C series a.c. circuit ............................................................................................. 221
    Series resonance .......................................................................................................... 225
    Q-factor ......................................................................................................................... 227
    Bandwidth and selectivity .............................................................................................. 229
    Power in a.c. circuits ..................................................................................................... 230
    Power triangle and power factor.................................................................................... 232
    Further problems on single- phase series a. c. circuits ................................................. 234
    16 Single-phase parallel a. c. circuits ........................................................... 238
    Introduction.................................................................................................................... 238
    R … L parallel a.c. circuit ................................................................................................. 238
    R … C parallel a.c. circuit ................................................................................................ 240
    L … C parallel a.c. circuit ................................................................................................. 241
    LR … C parallel a.c. circuit .............................................................................................. 243
    Parallel resonance and Q- factor ................................................................................... 247
    Power factor improvement ............................................................................................ 252
    Further problems on single- phase parallel a. c. circuits ............................................... 256
    17 D.c. transients ......................................................................................... 259
    Introduction.................................................................................................................... 259
    Charging a capacitor ..................................................................................................... 260
    Time constant for a C … R circuit .................................................................................... 260
    Transient curves for a C … R circuit ................................................................................ 261
    Discharging a capacitor ................................................................................................. 266
    Current growth in an L … R circuit ................................................................................... 268
    Time constant for an L … R circuit ................................................................................... 269
    Transient curves for an L … R circuit............................................................................... 269
    Current decay in an L … R circuit .................................................................................... 272
    Switching inductive circuits............................................................................................ 275
    The effects of time constant on a rectangular waveform............................................... 275
    Further problems on d. c. transients.............................................................................. 276
    18 Operational amplifiers ............................................................................. 278
    Introduction to operational amplifiers ............................................................................ 278
    Some op amp parameters ............................................................................................. 280
    Op amp inverting amplifier ............................................................................................ 282
    Op amp non- inverting amplifier .................................................................................... 285
    Op amp voltage- follower .............................................................................................. 286
    Op amp summing amplifier ........................................................................................... 286
    Op amp voltage comparator .......................................................................................... 288
    Op amp integrator ......................................................................................................... 288
    Op amp differential amplifier ......................................................................................... 289
    Digital to analogue ( D/ A) conversion........................................................................... 291
    Analogue to digital ( A/ D) conversion ........................................................................... 293
    Further problems on operational amplifiers................................................................... 294
    Assignment 5................................................................................................ 296
    19 Three phase systems .............................................................................. 297
    Introduction.................................................................................................................... 297
    Three-phase supply....................................................................................................... 298
    Star connection ............................................................................................................. 298
    Delta connection............................................................................................................ 302
    Power in three- phase systems ..................................................................................... 303
    Measurement of power in three- phase systems .......................................................... 306
    Comparison of star and delta connections .................................................................... 312
    Advantages of three- phase systems ............................................................................ 312
    Further problems on three- phase systems................................................................... 312
    20 Transformers ........................................................................................... 315
    Introduction.................................................................................................................... 315
    Transformer principle of operation ................................................................................ 316
    Transformer no- load phasor diagram........................................................................... 319
    E.m.f. equation of a transformer .................................................................................... 320
    Transformer on- load phasor diagram........................................................................... 324
    Transformer construction .............................................................................................. 325
    Equivalent circuit of a transformer ................................................................................. 326
    Regulation of a transformer ........................................................................................... 329
    Transformer losses and efficiency................................................................................. 330
    Resistance matching ..................................................................................................... 334
    Auto transformers .......................................................................................................... 337
    Isolating transformers.................................................................................................... 340
    Three-phase transformers ............................................................................................. 340
    Current transformers ..................................................................................................... 342
    Voltage transformers ..................................................................................................... 343
    Further problems on transformers................................................................................. 344
    Assignment 6................................................................................................ 349
    21 D.c. machines.......................................................................................... 350
    Introduction.................................................................................................................... 350
    The action of a commutator ........................................................................................... 351
    D.c. machine construction ............................................................................................. 352
    Shunt, series and compound windings.......................................................................... 353
    E.m.f. generated in an armature winding ...................................................................... 353
    D.c. generators .............................................................................................................. 356
    Types of d.c. generator and their characteristics .......................................................... 356
    D.c. machine losses ...................................................................................................... 362
    Efficiency of a d.c. generator ......................................................................................... 363
    D.c. motors .................................................................................................................... 364
    Torque of a d.c. machine............................................................................................... 365
    Types of d.c. motor and their characteristics................................................................. 368
    The efficiency of a d. c. motor ....................................................................................... 373
    D.c. motor starter........................................................................................................... 376
    Speed control of d. c. motors ........................................................................................ 377
    Motor cooling................................................................................................................. 381
    Further problems on d. c. machines .............................................................................. 381
    22 Three-phase induction motors................................................................. 386
    Introduction.................................................................................................................... 386
    Production of a rotating magnetic field .......................................................................... 387
    Synchronous speed....................................................................................................... 388
    Construction of a three- phase induction motor ............................................................ 390
    Principle of operation of a three- phase induction motor ............................................... 390
    Slip ................................................................................................................................ 391
    Rotor e.m.f. and frequency ............................................................................................ 393
    Rotor impedance and current ........................................................................................ 394
    Rotor copper loss .......................................................................................................... 395
    Induction motor losses and efficiency ........................................................................... 395
    Torque equation for an induction motor ........................................................................ 397
    Induction motor torque - speed characteristics ............................................................. 401
    Starting methods for induction motors........................................................................... 403
    Advantages of squirrel- cage induction motors ............................................................. 404
    Advantages of wound rotor induction motor .................................................................. 405
    Double cage induction motor......................................................................................... 405
    Uses of three-phase induction motors........................................................................... 405
    Further problems on three- phase induction motors ..................................................... 406
    Assignment 7................................................................................................ 408
    Main formulae for Part 2............................................................................... 409
    A.c. theory: .................................................................................................................... 409
    Single-phase circuits: .................................................................................................... 410
    D.c. transients: .............................................................................................................. 410
    Operational amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
    Three-phase systems: ................................................................................................... 411
    Transformers: ................................................................................................................ 411
    D.c. machines:............................................................................................................... 411
    Three-phase induction motors:...................................................................................... 411
    Part 3 Advanced Circuit Theory and Technology ............................... 413
    23 Revision of complex numbers ................................................................. 415
    Introduction.................................................................................................................... 415
    Operations involving Cartesian complex numbers ........................................................ 417
    Complex equations........................................................................................................ 419
    The polar form of a complex number ............................................................................ 421
    Multiplication and division using complex numbers in polar form.................................. 421
    De Moivres theorem „ powers and roots of complex numbers ..................................... 423
    Further problems on complex numbers ......................................................................... 424
    24 Application of complex numbers to series a. c. circuits........................... 429
    Introduction.................................................................................................................... 429
    Series a.c. circuits ......................................................................................................... 429
    Further problems on series a. c. circuits ....................................................................... 440
    25 Application of complex numbers to parallel a. c. networks...................... 25
    Introduction.................................................................................................................... 25
    Admittance, conductance and susceptance.................................................................. 25
    Parallel a.c. networks .................................................................................................... 448
    Further problems on parallel a. c. networks .................................................................. 454
    26 Power in a.c. circuits ............................................................................... 459
    Introduction.................................................................................................................... 459
    Determination of power in a. c. circuits ......................................................................... 459
    Power triangle and power factor.................................................................................... 464
    Use of complex numbers for determination of power .................................................... 465
    Power factor improvement ............................................................................................ 470
    Further problems on power in a. c. circuits ................................................................... 472
    Assignment 8................................................................................................ 475
    27 A.c. bridges ............................................................................................. 476
    Introduction.................................................................................................................... 476
    Balance conditions for an a. c. bridge ........................................................................... 476
    Types of a.c. bridge circuit ............................................................................................ 478
    Further problems on a. c. bridges ................................................................................. 488
    28 Series resonance and Q- factor .............................................................. 491
    Introduction.................................................................................................................... 491
    Series resonance .......................................................................................................... 491
    Q-factor ......................................................................................................................... 495
    Voltage magnification .................................................................................................... 498
    Q-factors in series ......................................................................................................... 502
    Bandwidth...................................................................................................................... 504
    Small deviations from the resonant frequency .............................................................. 509
    Further problems on series resonance and Q- factor.................................................... 512
    29 Parallel resonance and Q- factor............................................................. 515
    Introduction.................................................................................................................... 516
    The LR … C parallel network ........................................................................................... 516
    Dynamic resistance ....................................................................................................... 517
    The LR … CR parallel network ........................................................................................ 517
    Q-factor in a parallel network ........................................................................................ 519
    Further problems on parallel resonance and Q- factor.................................................. 527
    Assignment 9................................................................................................ 530
    30 Introduction to network analysis .............................................................. 531
    Introduction.................................................................................................................... 531
    Solution of simultaneous equations using determinants ............................................... 532
    Network analysis using Kirchhoffs laws ....................................................................... 535
    Further problems on Kirchhoffs laws............................................................................ 542
    31 Mesh-current and nodal analysis ............................................................ 545
    Mesh-current analysis ................................................................................................... 545
    Nodal analysis ............................................................................................................... 550
    Further problems on mesh- current and nodal analysis ................................................ 559
    32 The superposition theorem...................................................................... 562
    Introduction.................................................................................................................... 562
    Using the superposition theorem................................................................................... 562
    Further problems on the superposition theorem ........................................................... 573
    33 Thevenins and Nortons theorems ......................................................... 5755
    Introduction.................................................................................................................... 575
    Thevenins theorem....................................................................................................... 575
    Nortons theorem........................................................................................................... 587
    Thevenin and Norton equivalent networks .................................................................... 593
    Further problems on Thevenins and Nortons theorem................................................ 598
    Assignment 10.............................................................................................. 602
    34 Delta-star and star-delta transformations ................................................ 603
    Introduction.................................................................................................................... 603
    Delta and star connections ............................................................................................ 603
    Delta-star transformation............................................................................................... 603
    Star-delta transformation............................................................................................... 611
    Further problems on delta-star and star-delta transformations ..................................... 614
    35 Maximum power transfer theorems and impedance matching................ 617
    Maximum power transfer theorems ............................................................................... 617
    Impedance matching ..................................................................................................... 623
    Further problems on maximum power transfer theorems and impedance matching .... 626
    Assignment 11.............................................................................................. 629
    36 Complex Waveforms ............................................................................... 631
    Introduction.................................................................................................................... 631
    The general equation for a complex waveform ............................................................. 632
    Harmonic synthesis ....................................................................................................... 633
    Rms value, mean value and the form factor of a complex wave................................... 645
    Power associated with complex waves ......................................................................... 650
    Harmonics in single- phase circuits ............................................................................... 653
    Resonance due to harmonics........................................................................................ 664
    Sources of harmonics.................................................................................................... 666
    Further problems on complex waveforms ..................................................................... 671
    37 A numerical method of harmonic analysis............................................... 678
    Introduction.................................................................................................................... 678
    Harmonic analysis on data given in tabular or graphical form....................................... 683
    Complex waveform considerations ............................................................................... 683
    Further problems on a numerical method of harmonic analysis.................................... 685
    38 Magnetic materials .................................................................................. 688
    Revision of terms and units used with magnetic circuits ............................................... 688
    Magnetic properties of materials ................................................................................... 690
    Hysteresis and hysteresis loss ...................................................................................... 692
    Eddy current loss........................................................................................................... 696
    Separation of hysteresis and eddy current losses......................................................... 701
    Nonpermanent magnetic materials ............................................................................... 704
    Permanent magnetic materials...................................................................................... 706
    Further problems on magnetic materials ....................................................................... 707
    Assignment 12.............................................................................................. 710
    39 Dielectrics and dielectric loss .................................................................. 711
    Electric fields, capacitance and permittivity................................................................... 711
    Polarization.................................................................................................................... 711
    Dielectric strength.......................................................................................................... 712
    Thermal effects.............................................................................................................. 714
    Mechanical properties ................................................................................................... 714
    Types of practical capacitor ........................................................................................... 715
    Liquid dielectrics and gas insulation .............................................................................. 715
    Dielectric loss and loss angle ........................................................................................ 715
    Further problems on dielectric loss and loss angle ....................................................... 719
    40 Field theory.............................................................................................. 720
    Field plotting by curvilinear squares .............................................................................. 720
    Capacitance between concentric cylinders ................................................................... 725
    Capacitance of an isolated twin line .............................................................................. 733
    Energy stored in an electric field ................................................................................... 737
    Induced e.m.f. and inductance ...................................................................................... 741
    Inductance of a concentric cylinder ( or coaxial cable).................................................. 741
    Inductance of an isolated twin line ................................................................................ 746
    Energy stored in an electromagnetic field ..................................................................... 750
    Further problems on field theory ................................................................................... 753
    41 Attenuators .............................................................................................. 758
    Introduction.................................................................................................................... 758
    Characteristic impedance.............................................................................................. 759
    Logarithmic ratios .......................................................................................................... 761
    Symmetrical T-and p- attenuators ................................................................................. 764
    Insertion loss ................................................................................................................. 772
    Asymmetrical Tand p- sections ..................................................................................... 775
    The L-section attenuator ............................................................................................... 779
    Two-port networks in cascade....................................................................................... 782
    Further problems on attenuators ................................................................................... 785
    Assignment 13.............................................................................................. 789
    42 Filter networks ......................................................................................... 790
    Introduction.................................................................................................................... 791
    Basic types of filter sections .......................................................................................... 791
    The characteristic impedance and the attenuation of filter sections.............................. 792
    Ladder networks............................................................................................................ 795
    Low-pass filter sections ................................................................................................. 797
    High-pass filter sections ................................................................................................ 807
    Propagation coefficient and time delay in filter sections................................................ 815
    ˛m-derivedÌ filter sections .............................................................................................. 825
    Practical composite filters.............................................................................................. 833
    Further problems on filter networks ............................................................................... 837
    43 Magnetically coupled circuits................................................................... 841
    Introduction.................................................................................................................... 841
    Self-inductance.............................................................................................................. 841
    Mutual inductance ......................................................................................................... 842
    Coupling coefficient ....................................................................................................... 843
    Coils connected in series .............................................................................................. 845
    Coupled circuits............................................................................................................. 849
    Dot rule for coupled circuits ........................................................................................... 857
    Further problems on magnetically coupled circuits ....................................................... 864
    44 Transmission lines................................................................................... 869
    Introduction.................................................................................................................... 869
    Transmission line primary constants ............................................................................. 869
    Phase delay, wavelength and velocity of propagation .................................................. 871
    Current and voltage relationships .................................................................................. 873
    Characteristic impedance and propagation coefficient in terms of the primary
    constants ....................................................................................................................... 875
    Distortion on transmission lines..................................................................................... 882
    Wave reflection and the reflection coefficient ................................................................ 885
    Standing waves and the standing wave ratio ................................................................ 890
    Further problems on transmission lines ........................................................................ 897
    45 Transients and Laplace transforms ......................................................... 901
    Introduction.................................................................................................................... 901
    Response of R … C series circuit to a step input ............................................................ 901
    Response of R … L series circuit to a step input ............................................................. 906
    L … R … C series circuit response .................................................................................... 910
    Introduction to Laplace transforms ................................................................................ 914
    Inverse Laplace transforms and the solution of differential equations .......................... 921
    Laplace transform analysis directly from the circuit diagram......................................... 930
    L … R … C series circuit using Laplace transforms ........................................................... 944
    Initial conditions............................................................................................................. 949
    Further problems on transients and Laplace transforms ............................................... 952
    Assignment 14.............................................................................................. 958
    Main formulae for part 3 advanced circuit theory and technology................ 960
    Complex numbers: ........................................................................................................ 960
    General:......................................................................................................................... 960
    R … L … C series circuit: ................................................................................................... 9600
    LR … C network: .............................................................................................................. 961
    LR … CR network: ........................................................................................................... 961
    Determinants: ................................................................................................................ 961
    Delta-star:...................................................................................................................... 961
    Star-delta:...................................................................................................................... 961
    Impedance matching: .................................................................................................... 961
    Complex waveforms: ..................................................................................................... 961
    Harmonic analysis: ........................................................................................................ 961
    Hysteresis and Eddy current: ........................................................................................ 961


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  2. #2
    Fuchcha FaaDoO Engineer
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    Re: Eectrical engineering ebook by John Bird

    this book is great

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    Re: Eectrical engineering ebook by John Bird

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  4. #4
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    Re: Eectrical engineering ebook by John Bird

    i want this book pls tell wherte i could find this
    Grewal, B. S., Higher Engineering Mathematics, Khanna Publishers, New Delhi.