Preface ....................................................... vii
Acknowledgements ............................................... ix
Resources for Readers ........................................... x
1 Introduction ............................................... 1
1.1 What is an NMR Probe? ...................................... 1
1.1.1 The basic pulsed NMR experiment ..................... 5
1.1.2 The head probe from a theoretical point of view ..... 9
1.1.2.1 The principle of reciprocity and the
calculation of the induced emf .................. 9
1.1.2.2 Losses ......................................... 13
1.1.2.3 The sensitivity ................................ 16
1.2 What Probes for a Specific NMR Experiment? ................ 18
1.2.1 High resolution NMR in solution ..................... 19
1.2.2 Solid state NMR .................................... 20
1.2.3 Biomedical and biophysical applications ............ 21
2 Radio Frequency Components ................................ 23
2.1 The RF Parts of NMR Spectrometers and Scanners ............ 23
2.2 Characterization of RF Components ......................... 26
2.2.1 Frequency range .................................... 26
2.2.2 Complex impedance and admittance ................... 28
2.2.3 Impedance measurements and reflection coefficient .. 30
2.2.4 S-parameters ....................................... 36
2.2.5 The Smith Chart .................................... 40
2.3 Electrical Properties of Materials ........................ 44
2.3.1 Resistance of metal conductors ..................... 44
2.3.2 Losses in dielectric substrate ..................... 48
2.4 Passive Linear Components at RF ........................... 51
2.4.1 Conductors ......................................... 51
2.4.1.1 Round wire ..................................... 52
2.4.1.2 Ribbon conductor ............................... 53
2.4.1.3 Litz wire ...................................... 55
2.4.2 Cables and transmission lines ...................... 58
2.4.2.1 Wave propagation and characteristic impedance ... 59
2.4.2.2 Low-loss transmission lines .................... 63
2.4.2.3 Attenuation in low-loss lines terminated by
ZC ............................................. 65
2.4.2.4 Attenuation when the line is not terminated
by its characteristic impedance ................ 70
2.4.2.5 Impedance transformation ....................... 75
2.4.3 Discrete passive components ........................ 81
2.4.3.1 Resistors ...................................... 81
2.4.3.2 Inductors (generalities) ....................... 82
2.4.3.3 The air-solenoid (high frequency model, Q
optimization) .................................. 83
2.4.3.4 High frequency model of the air-solenoid ....... 90
2.4.3.5 Toroidal inductors ............................. 91
2.4.3.6 Other inductors (single loop, printed spiral
coil) .......................................... 93
2.4.3.7 Choke inductor ................................. 98
2.4.3.8 Adjustable inductor ........................... 103
2.4.3.9 Capacitors (generalities) ..................... 104
2.4.3.10 Capacitors (high frequency model) ............. 105
2.4.3.11 Fixed capacitor ............................... 107
2.4.3.12 Variable capacitor ............................ 108
2.4.3.13 Resonators .................................... 109
2.4.4 Distributed components made by transmission
lines ............................................. 116
2.5 Non-linear Devices (Diodes) .............................. 124
2.5.1 Silicon and Schottky P-N diodes ................... 125
2.5.2 PIN diodes ........................................ 127
2.5.3 Varactors ......................................... 127
2.6 Active Devices (Low Noise Amplifier or LNA) .............. 128
2.6.1 Noise factor (F) and noise figure (NF) ............ 128
2.6.2 LNA designs for NMR frequencies ................... 131
2.7 Metamaterials (Flux Guides) .............................. 137
2.7.1 Magnetic metamaterials at RF ...................... 138
2.7.2 Components of a magnetic metamaterial ............. 143
2.7.2.1 "Swiss-Rolls" ................................. 144
2.7.2.2 Ring planar resonators ........................ 145
2.7.2.3 Transmission line network ..................... 148
2.7.3 RF metamaterial designs ........................... 150
2.7.3.1 Flux compressors and flux guides .............. 151
2.7.3.2 Lenses ........................................ 151
2.7.4 Dielectric resonators ............................. 152
3 Introduction to Linear Network Analysis .................. 155
3.1 Introduction to Network Theory ........................... 156
3.1.1 Impedance and admittance matrices .................. 160
3.1.2 The transmission (ABCD) matrix .................... 162
3.1.3 The scattering matrix ............................. 167
3.2 Linear Network Simulation of Probe Coil Circuits ......... 168
3.2.1 NMRP: a simple tool for probe evaluation .......... 169
3.2.1.1 Simprobe: a linear probe network analyzer ..... 169
3.2.1.2 Building the Zmatrix .......................... 176
3.2.1.3 Analysis of simprobe outputs .................. 179
3.2.1.4 Calculating inductances ....................... 185
3.2.1.5 Calculating current densities ................. 186
3.2.1.6 Calculating resonant spectrum ................. 188
3.2.1.7 Mutual inductance and current distribution .... 190
3.2.2 Other dedicated linear circuit analyzers .......... 194
4 Interfacing the NMR Probehead ............................ 197
4.1 Impedance Matching ....................................... 199
4.1.1 The Bode-Fano limit ............................... 199
4.1.2 Connected matching circuits ....................... 201
4.1.2.1 Basic L-matching circuits ..................... 201
4.1.2.2 Series tuned/parallel matched ................. 203
4.1.2.3 Parallel tuned/series matched ................. 207
4.1.2.4 Efficiency of the capacitive matching
circuits ...................................... 212
4.1.2.5 Transmission line matching (remote matching) .. 214
4.1.2.6 Efficiency of transmission line matching
networks ...................................... 221
4.1.3 Flux coupled matching circuits .................... 225
4.1.3.1 Theory of inductive matching .................. 228
4.1.3.2 Inductive matching with tuned coupling loop ... 230
4.1.3.3 Inductive matching with a non-tuned coupling
loop .......................................... 231
4.1.3.4 Inductive matching with fixed mutual and
variable capacitor ............................ 233
4.1.3.5 Efficiency of the inductive coupling .......... 235
4.1.3.6 Coupled resonators ............................ 236
4.1.3.7 Flux concentrators ............................ 238
4.2 Balancing the Probehead .................................. 243
4.2.1 Evidencing the electric losses effect ............. 244
4.2.1.1 Experimental setup ............................ 245
4.2.1.2 Expected sensitivity .......................... 246
4.2.1.3 Frequency shifts .............................. 248
4.2.1.4 g factors ..................................... 250
4.2.2 Evidencing the electric losses: the antenna
effect ............................................ 251
4.2.3 Symmetrical capacitive coupling networks .......... 254
4.2.3.1 Splitting the matching capacitor .............. 254
4.2.3.2 A versatile capacitive balanced matching
network ....................................... 256
4.2.3.3 Capacitive bridge ............................. 264
4.3 Summary of useful matching circuits ...................... 265
4.4 Accessories .............................................. 268
4.4.1 Transmit/Receive (TR) switches .................... 268
4.4.2 Damping circuits .................................. 270
4.4.3 Baluns and cable traps ............................ 275
4.4.3.1 LC-balun ...................................... 277
4.4.3.2 The 4:1 λ/2 balun transformer ................. 278
4.4.3.3 Broadband balun transformers .................. 279
4.4.3.4 Tuned cable traps ............................. 281
4.5 Interfacing the Probe to a Low Noise Amplifier (LNA) ..... 284
4.6 Ultra-broadband and Ultrafast Recovery Probes ............ 289
4.6.1 Delay line ultra-broadband NMR probe .............. 290
4.6.2 Transmission line ultra-broadband NMR probe ....... 292
4.6.3 Non-resonant probe circuit ........................ 293
5 Quadrature Driving ....................................... 295
5.1 Interfacing the Quadrature Probehead to the Console ...... 297
5.2 Quadrature Hybrids ....................................... 302
5.2.1 λ/4 transmission line hybrid ...................... 302
5.2.2 λ/8 transmission line hybrid ...................... 309
5.2.3 Lumped element quadrature hybrids ................. 315
5.2.3.1 Quarter-wave hybrid equivalent ................ 316
5.2.3.2 λ/8 hybrid equivalent ......................... 319
5.2.4 Frequency response of the quad hybrids ............ 320
5.3 180° Hybrid .............................................. 325
5.3.1 The 180° rat-race hybrid .......................... 326
5.3.2 Using the rat-race hybrid 180° in quadrature NMR .. 334
5.3.3 Lumped element equivalent of the 180° hybrid ...... 336
5.3.4 Frequency response of the 180° ring hybrids ....... 338
5.4 Other 90° Hybrids ........................................ 341
6 Multiple Frequency Tuning ................................ 345
6.1 Shunting Methods ......................................... 350
6.1.1 Dual frequency switching circuits ................. 350
6.1.2 Practical double tuned circuits ................... 355
6.1.3 Multiple tuning of a single coil .................. 361
6.1.4 Balancing the shunting configurations ............. 367
6.1.4.1 Approximate balanced circuit .................. 368
6.2 Multiple-pole Circuits ................................... 374
6.2.1 Approximate double-pole network component values ... 378
6.2.2 Exact solutions ................................... 382
6.2.3 Multiple-pole tuning for more than two
frequencies ....................................... 383
6.2.4 Balancing the multiple-pole circuits .............. 384
6.2.4.1 Inductive coupling ............................ 384
6.2.4.2 The null-point method ......................... 386
6.3 Coupling Tank Circuits ................................... 388
6.3.1 Coupled identical resonators ...................... 392
6.3.2 Coupled resonators having the same resonance
frequency but different L/C ratio ................. 395
6.3.3 General case (different coupled resonators) ....... 396
6.3.4 Fluxed coupled resonators ......................... 398
6.3.5 Special case of a short circuited coil ............ 402
6.3.6 П-network configuration ........................... 403
6.3.7 Summary of coupled resonator properties ........... 407
6.4 Efficiency of Multiple Tuned NMR Probe ................... 411
6.4.1 Efficiency of shunting methods .................... 411
6.4.2 Efficiency of multiple pole circuits .............. 415
6.4.3 Efficiency of coupled resonant circuits ........... 421
6.5 Interfacing the Multiple Frequency Resonator to the
Spectrometer ............................................. 422
6.6 Is the Q Factor Representative of the Sensitivity? ....... 424
7 Magnetic Field Amplitude Estimation ...................... 427
7.1 The Biot-Savart Approximation ............................ 427
7.1.1 Magnetic field produced by straight wires ......... 429
7.1.2 Magnetic field produced by a loop ................. 432
7.2 Effective Field for NMR Experiments ...................... 436
7.3 Estimation of the Current Distribution ................... 441
7.3.1 Limits and usefulness of the thin wire
approximation ..................................... 441
7.3.2 Current distribution in the isolated flat strip ... 443
7.3.3 Proximity effects ................................. 452
7.3.3.1 Two coplanar strips ........................... 452
7.3.3.2 Three or more strips .......................... 455
7.3.3.3 Wire in proximity of a conductive plane ....... 456
7.3.4 Current density in round wires .................... 459
7.3.5 Concluding remarks ................................ 461
7.4 Survey of Modern Electromagnetic Simulation Methods ...... 462
8 Homogeneous Resonators ................................... 467
8.1 Axial Resonators ......................................... 469
8.1.1 Magnetic field amplitude .......................... 469
8.1.2 Approximations of the spherical uniform current
density ........................................... 473
8.1.2.1 Helmholtz coil ................................ 473
8.1.2.2 Four coil configuration ....................... 475
8.1.2.3 Guidelines for a practical design of
Helmholtz probes and four coil probes ......... 478
8.1.3 Solenoid types .................................... 480
8.1.3.1 The solenoid coil ............................. 480
8.1.3.2 The loop gap .................................. 485
8.1.4 Practical designs of solenoid type coils .......... 490
8.1.4.1 A microcoil for static magnetic field
mapping ....................................... 490
8.1.4.2 A 0.4 ml high sensitivity phosphorous coil
(162 MHz) ..................................... 491
8.1.4.3 A 150 ml double tuned (1H/31P)coil operating
at 4.7 T ...................................... 493
8.2 Transverse Resonators .................................... 498
8.2.1 Magnetic field amplitude .......................... 498
8.2.2 The saddle-shaped coil ............................ 501
8.2.2.1 The optimum geometry and RF magnetic field .... 501
8.2.2.2 A practical design ............................ 505
8.2.3 UHF saddle coil-like resonators ................... 509
8.2.3.1 The Alderman-Grant coil; a version of the
slotted cylinder .............................. 511
8.2.3.2 Coupling the Alderman-Grant resonator to the
spectrometer; a practical design .............. 515
8.2.3.3 Shielding the UHF saddle coil-like
resonators .................................... 520
8.2.4 The birdcage resonator ............................ 527
8.2.4.1 RF field map of the k = 1 mode ................ 528
8.2.4.2 Network analysis of the birdcage circuit ...... 534
8.2.4.3 Estimation of the current in a birdcage coil .. 541
8.2.4.4 Estimation of the tuning capacitance .......... 548
8.2.5 Practical use of the birdcage ..................... 552
8.2.5.1 Tuning the birdcage resonator ................. 552
8.2.5.2 Asymmetry effects ............................. 556
8.2.5.3 Interfacing the birdcage to the spectrometer .. 560
8.2.5.4 A practical design ............................ 562
8.2.6 Practical design of a quadrature birdcage ......... 570
8.2.6.1 Designing and adjusting the birdcage
resonator for quadrature operation ............ 572
8.2.6.2 Interfacing the resonator to the console ...... 575
8.2.6.3 Design of the shield .......................... 577
8.2.6.4 Evaluation of the probe ....................... 578
8.2.7 Double tuning the birdcage resonator .............. 579
8.2.7.1 Pole insertion methods ........................ 580
8.2.7.2 Alternate rang method ......................... 581
8.2.7.3 Four ring double resonant birdcage ............ 583
8.2.7.4 Crossed-coil resonators ....................... 585
8.2.7.5 A practical design ............................ 587
8.3 Transmission lines resonator ............................. 592
8.3.1 ТЕМ resonators .................................... 592
8.3.2 Split transmission line resonators ................ 597
9 Heterogeneous Resonators ................................. 601
9.1 The Basic Surface Coil ................................... 601
9.1.1 The simple loop magnetic field distribution ....... 603
9.1.1.1 "Ideal" case .................................. 603
9.1.1.2 Effect of inductive coupling .................. 606
9.1.2 Practical design guidelines ....................... 611
9.1.2.1 How many turns? ............................... 611
9.1.2.2 Spiral windings ............................... 611
9.1.2.3 Non-circular winding shapes ................... 616
9.1.2.4 Wiring shape .................................. 618
9.1.2.5 Opened resonators ............................. 622
9.1.3 Surface coils for ultra high frequency ............ 623
9.1.3.1 Segmented loop ................................ 623
9.1.3.2 The crossover coil ............................ 625
9.1.3.3 Split ring resonator (common mode) ............ 626
9.1.3.4 Microstrip coils (differential mode) .......... 628
9.1.4 Superconducting surface coils ..................... 630
9.1.5 Interfacing the coil to the spectrometer .......... 632
9.2 Extending the Observed Volume (Multi-Ring Coils) ......... 634
9.2.1 Coaxial rings ..................................... 634
9.2.1.1 RF field profiling ............................ 634
9.2.1.2 X-observed, proton decoupled system ........... 637
9.2.2 Array coils ....................................... 640
9.3 The Surface Coil as Receive-Only Probe ................... 643
9.3.1 Passive decoupling ................................ 644
9.3.2 Active decoupling ................................. 651
10 Probe Evaluation and Debugging ........................... 655
10.1 Instrumentation .......................................... 656
10.1.1 The pick-up coil .................................. 656
10.1.2 Impedance bridge .................................. 657
10.1.3 Power divider, hybrid, and directional coupler .... 660
10.1.4 Sweep generator, crystal detector, and spectrum
analyzer .......................................... 662
10.1.5 Scalar and vector network analyzer ................ 665
10.1.5.1 Transmission/reflection and S-parameters
test sets ..................................... 666
10.1.5.2 Calibration ................................... 667
10.1.6 Other impedance measuring instruments ............. 670
10.2 Characterization of a Transmission Line .................. 670
10.2.1 Velocity coefficient .............................. 671
10.2.2 Evaluation of the characteristic impedance ........ 672
10.2.3 Estimation of the loss parameters ................. 674
10.3 Noise Figure Measurement ................................. 674
10.4 Evaluating the Probe on the RF Workbench ................. 678
10.4.1 Matching the probe input impedance to 50 Ω ........ 678
10.4.2 Evaluation of the Q factor ........................ 680
10.4.3 B1/√Р evaluation methods .......................... 684
10.5 Evaluating the Probe on the NMR Instrument ............... 686
Appendix A. Physical Constants and Useful Formulae ............ 691
Bibliography .................................................. 709
Index ......................................................... 733
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