Introduction ................................................. xiii
Symbols and Acronyms .......................................... xix
1 Analysis of Nonhomogeneous Helical Systems Using
Electrodynamical Methods ..................................... 1
1.1 Modeling of Nonhomogeneous Helical Systems .............. 1
1.2 Simulation of Axially Symmetrical Helical System ........ 5
1.3 Simulation of Complex Helical Systems without
Internal Shields ....................................... 14
1.3.1 Modeling and Properties of the Helix
Asymmetrically Mounted inside the External
Shield .......................................... 15
1.3.2 Generalized Model of Helical Systems without
Internal Shields ................................ 19
1.4 Summary ................................................ 24
References .................................................. 24
2 Multiconductor Line Method .................................. 27
2.1 Electromagnetic Waves in Multiconductor Lines .......... 28
2.1.1 Wave Equation ................................... 28
2.1.2 Space Harmonics in Periodic Structures .......... 29
2.1.3 Waves in Multiconductor Lines with Homogeneous
Dielectric ...................................... 31
2.1.4 Space Harmonics in Multiconductor Lines ......... 33
2.2 Voltages and Currents in Multiconductor Lines .......... 34
2.2.1 Multiconductor Lines with Homogeneous
Dielectric ...................................... 34
2.2.2 Multiconductor Lines with Nonhomogeneous
Dielectric ...................................... 37
2.3 Normal Waves in Multiconductor Lines ................... 38
2.3.1 Telegraph Equations and Their Solutions ......... 39
2.3.2 Relationships for Voltages and Currents in
Normal Waves .................................... 42
2.3.3 Parameters of Multiconductor Lines in Normal
Waves ........................................... 43
2.4 Dependence of Wave Admittances and Effective
Dielectric Permittivities on Phase Angle ............... 46
2.5 Calculation of Capacitances ............................ 50
2.6 Principles of Modeling of Slow-Wave Structures ......... 53
2.7 Application of the Multiconductor Line Method for
Analysis of Nonhomogeneous Systems ..................... 55
2.7.1 Model of the System ............................. 57
2.7.2 Dispersion Equation, Retardation Factor, and
Input Impedance ................................. 59
2.7.3 Calculation Results ............................. 60
2.7.1 Contents
2.8 Calculations of Frequency Characteristics Using
Numerical Iterations ................................... 62
2.8.1 Calculation of Characteristics Avoiding
Derivation of Dispersion Equations .............. 62
2.8.2 Simulation of an Axially Symmetrical Helical
System .......................................... 67
2.9 Application of Scattering Transmission Line Matrices ... 72
2.9.1 Two-Port Circuits in Models of Periodic
Systems ......................................... 72
2.9.2 Composition of Scattering Matrix for
Multiconductor Lines ............................ 75
2.9.3 Meander Slow-Wave System Model Based on
Scattering Parameters ........................... 80
2.9.4 Results of Calculations ......................... 85
2.10 Summary ................................................ 86
References .................................................. 88
3 Calculation of Characteristic Impedances of Multiconductor
Lines ....................................................... 91
3.1 Finite Difference Method ............................... 91
3.1.1 General Information ............................. 91
3.1.2 Calculation of Potential Distribution ........... 93
3.1.3 Calculation of Distributed Capacitances ......... 96
3.1.4 Calculations of Characteristic Impedances of
Multiconductor Lines ............................ 97
3.1.5 Duration and Errors of Calculations ............. 99
3.1.6 Software for Calculations of Characteristic
Impedances ...................................... 99
3.2 Finite Element Method ................................. 102
3.2.1 General Information ............................ 102
3.2.2 Finite Elements ................................ 104
3.2.3 Conjunction of Cells ........................... 107
3.2.4 Computation of Potentials of Nodes ............. 108
3.2.5 Software Based on the Finite Element Method .... 109
3.3 Integral Equation Method .............................. 112
3.3.1 Integral Equations ............................. 112
3.3.2 The Principles of the Method of Moments ........ 113
3.3.3 Calculation of Charges ......................... 114
3.3.4 Calculation of Characteristic Impedance ........ 117
3.3.5 Software Based on Integral Equation Method ..... 120
3.4 Application of the Method of Integral Equations ....... 120
3.4.1 Characteristic Impedance of the Microstrip
Line ........................................... 121
3.4.1.1 Partial Images in the Space
Containing a Dielectric Plate ......... 124
3.4.1.2 The Mathematical Model of the
Microstrip Line ....................... 125
3.4.1.3 Results of Calculations ............... 128
3.4.2 Characteristic Impedances of Coupled
Microstrip Lines ............................... 130
3.4.2.1 Model of Coupled Microstrip Lines ..... 131
3.4.2.2 Model of Coupled Microstrip Lines
with a Homogeneous Dielectric ......... 132
3.4.2.3 Model of Coupled Microstrip Lines
with a Nonhomogeneous Dielectric ...... 133
3.4.2.4 Results of Calculations ............... 135
3.4.3 Calculation of Characteristic Impedances of
Multiconductor Microstrip Lines ................ 137
3.4.4 Results of Calculations ........................ 139
3.5 Summary ............................................... 143
References ............................................ 143
4 Models and Properties of Slow-Wave Systems ................. 147
4.1 Models and Properties of Special Types of Helical
Systems ............................................... 147
4.1.1 Twined Helical System .......................... 147
4.1.1.1 Model of the Twined Helical System .... 147
4.1.1.2 Properties of the Twined Helical
System ................................ 151
4.1.1.3 Additionally Shielded Twined Helical
System ................................ 152
4.1.2 Quasi-Symmetrical Helical System ............... 160
4.1.2.1 Simplified Model of the Quasi-
Symmetrical Helical System ............ 161
4.1.2.2 Properties of the Quasi-Symmetrical
Helical System ........................ 165
4.1.2.3 Analysis of the Quasi-Symmetrical
Helical System Using the Advanced
Model ................................. 166
4.2 Gutter-Type Helical and Meander Systems ............... 175
4.2.1 Models and Properties of Homogeneous Gutter-
Type Systems ................................... 176
4.2.2 Models and Properties of Nonhomogeneous
Gutter-Type Helical Systems .................... 177
4.2.3 Models and Properties of Nonhomogeneous
Meander Systems ................................ 181
4.3 Influence of Periodical Inhomogeneities on
Properties of Slow-Wave Systems ....................... 186
4.4 Simulation of Meander Systems with Finite Length ...... 192
4.4.1 Model of the Microstrip Delay Line with
Limited Length ................................. 192
4.4.2 Results of Simulation and Measurements ......... 193
4.5 Summary ............................................... 196
References ................................................. 197
5 Investigation of Slow-Wave Systems Applying Versatile
Electromagnetic Simulation and Design Tools ................ 199
5.1 Model of a Helical Slow-Wave System ................... 200
5.1.1 Calculation of Amplitude and Phase-Frequency
Responses of a Helical Slow-Wave System ........ 203
5.1.2 Calculation of Phase Delay Time and
Characteristic Impedance ....................... 205
5.2 Investigation of the Twined Helical Slow-Wave System .. 210
5.2.1 Models of the Twined Helical System ............ 210
5.2.2 Properties of the Twined System at Varying
Widths of Helical Conductors ................... 215
5.3 Input Impedance of Helical Systems .................... 216
5.4 Resonances in the System of Shields and
Possibilities of Avoiding Them ........................ 221
5.4.1 Model and Methodology of Investigation of the
System ......................................... 221
5.4.2 Application of Microwave Office for
Investigation of Resonant Effects .............. 223
5.4.3 Possibilities for Avoiding Resonant Effects .... 224
5.5 Application of Software for Three-Dimensional
Modeling .............................................. 228
5.5.1 Brief Information about MicroWave Studio
Tools .......................................... 228
5.5.2 Investigation of the Influence of Internal
Anisotropic Shields on Properties of Helical
Systems ........................................ 229
5.5.3 Investigation of the Influence of Periodical
Inhomogeneities ................................ 231
5.5.4 Investigation of the Meander Slow-Wave System .. 234
5.5.4.1 Simulation of an Asymmetrical
Meander System ........................ 235
5.5.4.2 Simulation of a Symmetrical Meander
System ................................ 237
5.5.4.3 Simulation of an Axially Symmetrical
Meander System ........................ 238
5.6 Summary ............................................... 241
References ................................................. 242
6 Investigation of Slow-Wave Structures Using Synergy of
Various Methods ............................................ 245
6.1 Simulation of an Inhomogeneous Meander Line ........... 245
6.1.1 Simulation of Asymmetrical Inhomogeneities ..... 246
6.1.2 Simulation of Inhomogeneities at the Sides of
the Meander Electrode .......................... 249
6.1.3 Simulation of Terminals ........................ 250
6.2 Simulation and Properties of the H-Profile Meander
System ................................................ 251
6.2.1 Simulation Using the Multiconductor Line
Method ......................................... 252
6.2.2 Simulation Using the MicroWave Studio Software
Package ........................................ 254
6.3 Simulation of Symmetrically and Asymmetrically
ShidSed Helical Lines ................................. 258
6.3.1 Simulation Using the Multiconductor Line
Method ......................................... 258
6.3.2 Simulation Using the MicroWave Studio Package .. 261
6.4 Simulation of the Axially Symmetrical Helical Line .... 264
6.4.1 Simulation Using the Multiconductor Line
Method ......................................... 265
6.4.2 Simulation Using the MicroWave Studio Package .. 268
6.5 Summary ............................................... 270
References ................................................. 271
7 Application of Slow-Wave Structures for Deflection of
Electron Beams ............................................. 273
7.1 Correction of Phase Distortions in Traveling-Wave
Deflecting Systems .................................... 274
7.2 Electrical Field in the Deflecting System ............. 278
7.2.1 Analytical Methods and Approximations .......... 278
7.2.2 Distribution of Potential and Deflecting
Field .......................................... 281
7.2.3 Results of Calculations ........................ 284
7.2.4 Electric Field in a Twined Helical Deflecting
System ......................................... 286
7.3 Nonlinear Distortions in Traveling-Wave Cathode-Ray
Tubes ................................................. 292
7.3.1 Distortions of Harmonic Oscillations in
Asymmetrical Helical Systems ................... 293
7.3.2 Reduction of Nonlinear Frequency-Dependent
Distortions .................................... 297
7.3.3 Distortions of Electrical Pulses ............... 298
7.4 Simulation of Transitions to Traveling-Wave
Deflecting Systems .................................... 304
7.4.1 Model of the Deflection Path ................... 305
7.4.2 Calculation Results ............................ 309
7.4.3 Reduction of Frequency Distortions ............. 313
7.5 Opportunities for Improvement of Dynamic
Characteristics of Traveling-Wave Cathode-Ray Tubes
and Their Signal Paths ................................ 314
7.5.1 Influence of Dispersion ........................ 314
7.5.2 Influence of Attenuation ....................... 316
7.5.3 Influence of Characteristic Impedance
Variation ...................................... 318
7.5.4 Influence of Peculiarities of a Deflecting
Field .......................................... 319
7.5.5 The Conjoint Influence of Various Factors ...... 321
7.6 Conclusions ........................................... 322
References ............................................ 323
8 Application of Slow-Wave Systems for Delay ................. 327
8.1 Simulation of Meander Systems Containing
Periodical Inhomogeneities ............................ 327
8.1.1 Analysis of Multiconductor Line at Irregular
Step of Conductors ............................. 329
8.1.1.1 Model of Microstrip Multiconductor
Line .................................. 329
8.1.1.2 Simulation of Multiconductor Line ..... 331
8.1.2 Properties of Microstrip Meander Lines
Containing Periodical Inhomogeneities .......... 337
8.1.2.1 Dispersion Properties ................. 338
8.1.2.2 Input Impedance ....................... 340
8.2 Properties of Packaged Microstrip Meander Systems ..... 342
8.2.1 Dispersion Properties of Packaged Microstrip
Meander Delay Lines ............................ 343
8.2.2 Dispersion Properties of Packaged Microstrip
Meander Delay Lines Containing Periodical
Inhomogeneities ................................ 345
8.2.3 Input Impedance of Packaged Microstrip Meander
Delay Lines .................................... 348
8.2.4 Input Impedance of Packaged Microstrip
Meander Delay Lines Containing Periodical
Inhomogeneities ................................ 351
8.3 Characteristic Impedance of Meander Systems ........... 352
8.4 Models of Meander Systems Containing Additional
Shields ............................................... 357
8.4.1 General Principles for Composing Models ........ 359
8.4.2 Simplified Model of Microstrip Meander
Systems Containing Digital Additional Shields .. 363
8.4.3 Simplified Model of Meander System Containing
Interdigital Additional Shields ................ 368
8.4.4 Calculation Results ............................ 372
8.5 Analysis of Wide-Band Meander Slow-Wave Systems
Using an Advanced Model ............................... 375
8.5.1 Advanced Model of Wide Pass-Band Meander
Systems ........................................ 375
8.5.2 Properties of Microstrip Meander Systems
Containing Digital Additional Shields .......... 381
8.5.2.1 Influence of Digital Additional
Shields on Dispersion Properties ...... 383
8.5.2.2 Influence of Digital Additional
Shields on Input Impedance ............ 386
8.5.2.3 Dependence of Properties of
Microstrip Meander Systems on Length
of Digital Additional Shields ......... 386
8.6 Wide-Band Modified Gutter-Type Delay Lines ............ 387
8.7 Summary ............................................... 390
References ................................................. 392
9 Computer-Aided Design of Electrodynamical Delay Lines ...... 395
9.1 General Information ................................... 395
9.2 Methodology of Computer-Aided Design of Wide-Band
Meander Systems ....................................... 397
9.2.1 Algorithm of Computer-Aided Design ............. 397
9.2.2 Input Data ..................................... 400
9.2.3 Synthesis and Analysis of the Initial
Structure ...................................... 401
9.2.4 Improvement of the Structure ................... 402
9.3 Principles of Synthesis of Initial Structure of
Microstrip Meander Delay Line Containing Additional
Shields ............................................... 402
9.4 Algorithm for Synthesis of Microstrip Meander Delay
Lines ................................................. 404
9.5 Methodology and Algorithm for Design of Helical
Delay Lines ........................................... 407
9.5.1 Modeling of Helical Delay Lines ................ 407
9.5.2 Algorithm for Synthesis of Helical Delay
Lines .......................................... 409
9.6 Summary ............................................... 410
References ................................................. 411
Index ......................................................... 413
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