Acknowledgements .............................................. xvi
Section I Foundations ........................................... 1
1. The big picture ............................................. 3
1.1. Importance of ultra-low-power electronics ............. 5
1.2. The power-efficient subthreshold regime of
transistor operation .................................. 7
1.3. Information, energy, and power ........................ 9
1.4. The optimum point for digitization in a mixed-signal
system ............................................... 10
1.5. Examples of biomedical application contexts .......... 14
1.6. Principles for ultra-low-power design ................ 17
1.7. Ultra-low-power information processing in biology .... 18
1.8. Neuromorphic system example: the RF cochlea .......... 19
1.9. Cytomorphic electronics .............................. 22
1.10. Energy sources ....................................... 23
1.11. An overview of the book's chapters and
organization ......................................... 24
1.12. Some final notes ..................................... 26
2. Feedback systems: fundamentals, benefits, and root-locus
analysis ................................................... 28
2.1. Feedback is universal ................................ 29
2.2. The basic linear feedback loop ....................... 32
2.3. Connections between feedback loops and circuits ...... 35
2.4. The seven benefits of feedback ....................... 36
2.5. Root-locus techniques ................................ 44
2.6. Eight root-locus rules ............................... 46
2.7. Example of a root-locus plot ......................... 53
2.8. The zeros of a closed-loop system .................... 55
2.9. Farewell to feedback systems ......................... 55
3. MOS device physics: general treatment ...................... 57
3.1. Intuitive description of MOS transistor operation .... 60
3.2. Intuitive model of MOS transistor operation .......... 63
3.3. Intuitive energy viewpoint for MOS transistor
operation ............................................ 65
3.4. The MOS capacitor (MOSCAP) ........................... 68
3.5. Quantitative discussion of the MOSCAP ................ 71
3.6. Determining (Q1 + Qdep) in a MOSCAP for a given
ΨS ................................................... 73
3.7. Equating the gate charge and bulk charge ............. 76
3.8. Quantitative discussion of the MOSFET ................ 79
3.9. Summary of physical insights ......................... 82
4. MOS device physics: practical treatment .................... 84
4.1. The к approximation .................................. 85
4.2. Charge-based current models with the к
approximation ........................................ 92
4.3. Derivation of current in weak inversion .............. 93
4.4. Derivation of current in strong inversion ............ 95
4.5. Source-referenced model for strong inversion ......... 97
4.6. Moderate inversion .................................. 101
5. MOS device physics: small-signal operation ................ 103
5.1. Weak-inversion small-signal models .................. 104
5.2. Strong-inversion small-signal models ................ 108
5.3. Small-signal capacitance models in strong
inversion ........................................... 113
5.4. Extrinsic or parasitic capacitances ................. 120
5.5. Small-signal capacitance models in weak inversion ... 122
5.6. The transit time .................................... 123
5.7. The'beta'of an MOS transistor ....................... 125
6. Deep. submicron effects in MOS transistors ............... 129
6.1. The dimensionless EKV model ......................... 130
6.2. Velocity saturation ................................. 133
6.3. Drain induced barrier lowering (DIBL) ............... 140
6.4. Vertical-field effects .............................. 143
6.5. Effect on the intuitive model ....................... 145
6.6. High-frequency transistor models .................... 146
6.7. Ballistic transport ................................. 147
6.8. Transport in nanoscale MOSFETs ...................... 149
6.9. Tunneling ........................................... 151
6.10. Scaling of transistors in the future ................ 152
7. Noise in devices .......................................... 155
7.1. The mathematics of noise ............................ 155
7.2. Noise in subthreshold MOS transistors ............... 161
7.3. Noise in resistors .................................. 165
7.4. Unity between thermal noise and shot noise .......... 167
7.5. Noise in above-threshold MOS transistors ............ 168
7.6. Input-referred gate noise ........................... 169
7.7. l/ƒ or flicker noise in MOS transistors ............. 170
7.8. Some notes on 1/ƒ noise ............................ 173
7.9. Thermal noise in short-channel devices .............. 176
7.10. Thermal noise in moderate inversion ................. 179
7.11. Induced gate noise .................................. 181
7.12. Some caveats about noise ............................ 182
8. Noise in electrical and non-electrical circuits ........... 184
8.1. Noise in an RC lowpass-filter circuit ............... 185
8.2. A subthreshold photoreceptor circuit ................ 187
8.3. The equipartition theorem ........................... 190
8.4. Noise in a subthreshold transconductance
amplifier ........................................... 193
8.5. Noise in general circuits ........................... 200
8.6. An ultra-low-noise MEMS capacitance sensor .......... 201
9. Feedback systems .......................................... 212
9.1. The Nyquist criterion for stability ................. 212
9.2. Nyquist-based criteria for robustness: Gain margin
and phase margin .................................... 216
9.3. Compensation techniques ............................. 219
9.4. The closed-loop two-pole τ-and-Q rules for
feedback systems .................................... 228
9.5. Conditional stability ............................... 229
9.6. Describing-function analysis of nonlinear feedback
systems ............................................. 231
9.7. Positive feedback ................................... 232
9.8. Feedback in small-signal circuits ................... 233
9.9. The 'fake label' circuit-analysis trick ............. 235
9.10. A circuit example ................................... 235
10. Return-ratio analysis ..................................... 240
10.1. Return ratio for a dependent generator .............. 241
10.2. Return ratio for a passive impedance ................ 243
10.3. Transfer function modification with the return
ratio ............................................... 244
10.4. Robustness analysis with the return ratio ........... 249
10.5. Examples of return-ratio analysis ................... 250
10.6. Blackman's impedance formula ........................ 256
10.7. Driving-point transistor impedances with
Blackman's formula .................................. 258
10.8. Middlebrook's extra-element theorem ................. 261
10.9. Thevenin's theorem as a special case of return-
ratio analysis ...................................... 264
10.10.Two final examples of return-ratio analysis ......... 265
10.11.Summary of key results .............................. 270
Section II Low-power analog and biomedical circuits ........... 273
11. Low-power transimpedance amplifiers and photoreceptors .... 275
11.1. Transimpedance amplifiers ........................... 275
11.2. Phototransduction in silicon ........................ 278
11.3. A transimpedance-amplifier-based photoreceptor ...... 283
11.4. Feedback analysis of photoreceptor .................. 286
11.5. Noise analysis of photoreceptor ..................... 292
11.6. The adaptation resistor RA .......................... 294
11.7. Experimental measurements of the photoreceptor ...... 296
11.8. Adaptive biasing of IA for energy efficiency ........ 297
11.9. Zeros in the feedback path .......................... 298
12. Low-power transconductance amplifiers and scaling laws
for power in analog circuits .............................. 301
12.1. A simple ordinary transconductance amplifier
(OTA) ............................................... 302
12.2. A low-power wide-linear-range transconductance
amplifier: the big picture .......................... 303
12.3. WLR small-signal and linear-range analysis .......... 305
12.4. WLR dc characteristics .............................. 310
12.5. Dynamic characteristics of the WLR .................. 317
12.6. Noise analysis ...................................... 317
12.7. Distortion analysis ................................. 322
12.8. Signal-to-noise ratio and power analysis ............ 323
12.9. Scaling laws for power in analog circuits ........... 325
12.10.Low-voltage transconductance amplifiers and low-
voltage analog design ............................... 326
12.11.Robust operation of subthreshold circuits ........... 329
13. Low-power filters and resonators .......................... 330
13.1. Gm-С filter synthesis ............................... 331
13.2. Gyrators ............................................ 333
13.3. Introduction to second-order systems ................ 334
13.4. Synthesis of a second-order Gm-C filter ............. 337
13.5. Analysis of a second-order Gm-C filter .............. 339
13.6. Synthesis and analysis of an alternative Gm-C
filter .............................................. 342
13.7. Higher-order Gm-C filter design ..................... 347
13.8. A-s2-plane geometry for analyzing the frequency
response of linear systems .......................... 347
14. Low-power current-mode circuits ........................... 354
14.1. Voltage versus current .............................. 355
14.2. Static translinear circuits ......................... 356
14.3. Dynamic translinear lowpass filters ................. 359
14.4. Dynamic translinear integrators and high-order
filters ............................................. 365
14.5. Biasing of current-mode filters ..................... 367
14.6. Noise, SNR, and dynamic range of log-domain
filters ............................................. 370
14.7. Log-domain vs. Gm-C filters ......................... 372
14.8. Winner-take-all circuits ............................ 373
14.9. Large-signal operation of the winner-take-all
circuit ............................................. 379
14.10.Distributed-feedback circuits ....................... 380
15. Ultra-low-power and neuron-inspired analog-to-digital
conversion for biomedical systems ......................... 385
15.1. Review of ADC topologies ............................ 389
15.2. A neuron-inspired ADC for biomedical applications ... 395
15.3. Computational ADCs and time-to-digital ADCs ......... 408
15.4. A time-based ΣΔ ADC ................................. 410
15.5. Pipelined ADCs with comparators ..................... 411
15.6. Adiabatic charging and energy-efficient
comparators in ADCs ................................. 412
15.7. Digital correction of analog errors ................. 415
15.8. Neurons and ADCs .................................... 416
Section III Low-power RF and energy-harvesting circuits
for biomedical systems ............................ 419
16. Wireless inductive power links for medical implants ....... 421
16.1. Theory of linear inductive links .................... 422
16.2. Experimental system design .......................... 441
16.3. Experimental measurements ........................... 448
17. Energy-harvesting RF antenna power links .................. 454
17.1. Intuitive understanding of Maxwell's equations ...... 455
17.2. The non-lossy, one-dimensional transmission line .... 456
17.3. The impedance of free space ......................... 459
17.4. Thevenin-equivalent circuit models of antennas ...... 459
17.5. Near-field coupling ................................. 463
17.6. Far-field coupling: the 'monopole' antenna .......... 463
17.7. Far-field coupling: basics of dipole antennas ....... 465
17.8. Directional radiation and antenna gain .............. 467
17.9. Derivation of far-field transfer impedance or Z12 ... 469
17.10.Impedance matching: the Bode-Fano criterion ......... 471
17.11.Making the antenna and the load part of the
matching network .................................... 474
17.12.Rectifier basics .................................... 477
17.13.Rectifier analysis and optimization ................. 481
17.14.Output voltage ripple in rectifiers ................. 482
17.15.Latchup in CMOS rectifiers .......................... 483
17.16.Rectifier modeling .................................. 483
17.17.Experimental measurements ........................... 486
17.18.Summary ............................................. 488
18. Low-power RF telemetry in biomedical implants ............. 489
18.1. Impedance modulation in coupled parallel
resonators .......................................... 493
18.2. Impedance-modulation transceiver .................... 495
18.3. Pulse-width modulation receiver ..................... 503
18.4. Dynamic effects in impedance modulation ............. 505
18.5. Experimental results for a complete transceiver ..... 508
18.6. Energy efficiency of the uplink and downlink ........ 511
18.7. Scaling laws for power consumption in impedance-
modulation links .................................... 511
18.8. The energy per bit in impedance-modulation links .... 518
18.9. Incoherent versus coherent RF receivers ............. 522
18.10.Radiated emissions and FCC regulations .............. 523
18.11.Seven considerations in choosing a carrier
frequency ........................................... 524
18.12.RF antenna links for implants ....................... 525
18.13.The skin depth of biological tissue ................. 525
Section IV Biomedical electronic systems ...................... 529
19. Ultra-low-power implantable medical electronics ........... 531
19.1. Cochlear implants or bionic ears .................... 534
19.2. An ultra-low-power programmable analog bionic ear
processor ........................................... 537
19.3. Low-power electrode stimulation ..................... 558
19.4. Highly miniature electrode-stimulation circuits ..... 562
19.5. Brain-machine interfaces for the blind .............. 565
19.6. Brain-machine interfaces for paralysis, speech,
and other disorders ................................. 572
19.7. Summary ............................................. 575
20. Ultra-low-power noninvasive medical electronics ........... 579
20.1. Analog integrated-circuit switched-capacitor model
of the heart ........................................ 581
20.2. The electrocardiogram ............................... 585
20.3. A micropower electrocardiogram amplifier ............ 590
20.4. Low-power pulse oximetry ............................ 595
20.5. Battery-free tags for body sensor networks .......... 601
20.6. Intra-body galvanic communication networks .......... 604
20.7. Biomolecular sensing ................................ 605
Section V Principles for ultra-low-power analog and digital
design .............................................. 615
21. Principles for ultra-low-power digital design ............. 617
21.1. Subthreshold CMOS-inverter basics ................... 618
21.2. Sizing and topologies for robust subthreshold
operation ........................................... 622
21.3. Types of power dissipation in digital circuits ...... 623
21.4. Energy efficiency in digital systems ................ 630
21.5. Optimization of energy efficiency in the
subthreshold regime ................................. 632
21.6. Optimization of energy efficiency in all regimes
of operation ........................................ 635
21.7. Varying the power-supply voltage and threshold
voltage ............................................. 641
21.8. Gated clocks ........................................ 641
21.9. Basics of adiabatic computing ....................... 642
21.10.Adiabatic clocks .................................... 645
21.11.Architectures and algorithms for improving energy
efficiency .......................................... 647
22. Principles for ultra-low-power analog and mixed-signal
design .................................................... 651
22.1. Power consumption in analog and digital systems ..... 653
22.2. The low-power hand .................................. 661
22.3. The optimum point for digitization in a mixed-
signal system ....................................... 663
22.4. Common themes in low-power analog and digital
design .............................................. 669
22.5. The Shannon limit for energy efficiency ............. 671
22.6. Collective analog or hybrid computation ............. 674
22.7. HSMs: general-purpose mixed-signal systems with
feedback ............................................ 679
22.8. General principles for low-power mixed-signal
system design ....................................... 683
22.9. The evolution of low-power design ................... 691
22.10.Sensors and actuators ............................... 692
Section VI Bio-inspired systems ............................... 695
23. Neuromorphic electronics .................................. 697
23.1. Transmission-line theory ............................ 705
23.2. The cochlea: biology, motivations, theory, and RF-
cochlea design ...................................... 706
23.3. Integra ted-circuit unidirectional and
bidirectional RF cochleas ........................... 721
23.4. Audio cochleas and bio-inspired noise-robust
spectral analysis ................................... 725
23.5. A bio-inspired analog vocal tract ................... 728
23.6. Bio-inspired vision architectures ................... 733
23.7. Hybrid analog-digital computation in the brain ...... 739
23.8. Spike-based hybrid computers ........................ 741
23.9. Collective analog or hybrid systems ................. 743
23.10.Energy efficiency in neurobiological systems ........ 743
23.11.Other work .......................................... 747
23.12.Appendix: Power and computation in the brain, eye,
ear, and body ....................................... 747
24. Cytomorphic electronics: cell-inspired electronics for
systems and synthetic biology ............................. 753
24.1. Electronic analogies of chemical reactions .......... 755
24.2. Log-domain current-mode models of chemical
reactions and protein-protein networks .............. 759
24.3. Analog circuit models of gene-protein dynamics ...... 766
24.4. Logic-like operations in gene-protein circuits ...... 769
24.5. Stochastics in DNA-protein circuits ................. 772
24.6. An example of a simple DNA-protein circuit .......... 774
24.7. Circuits-and-feedback techniques for systems and
synthetic biology ................................... 776
24.8. Hybrid analog-digital computation in cells and
neurons ............................................. 783
Section VII Energy sources .................................... 787
25. Batteries and electrochemistry ............................ 789
25.1. Basic operation of a battery ........................ 789
25.2. Example mechanism for battery operation ............. 791
25.3. Chemical reaction kinetics and electrode current .... 793
25.4. Mass-transport limitations .......................... 796
25.5. Large-signal equivalent circuit of a battery ........ 799
25.6. Battery voltage degradation with decreasing state
of charge ........................................... 802
25.7. Small-signal equivalent circuit of a battery and
of electrodes ....................................... 806
25.8. Operation of a lithium-ion battery .................. 812
25.9. Operation of a zinc-air battery ..................... 815
25.10.Basic operation of fuel cells ....................... 816
25.11.Energy density, power density, and system cost ...... 817
26. Energy harvesting and the future of energy ................ 822
26.1. Sources of energy ................................... 824
26.2. Electrical circuit models of mechanical systems ..... 825
26.3. Energy harvesting of body motion .................... 827
26.4. Energy harvesting of body heat ...................... 831
26.5. Power consumption of the world ...................... 835
26.6. A circuit model for car power consumption ........... 836
26.7. Electric cars versus gasoline cars .................. 841
26.8. Cars versus animals ................................. 844
26.9. Principles of low-power design in transportation .... 846
26.10.Solar electricity generation ........................ 848
26.11.Biofuels ............................................ 854
26.12.Energy use and energy generation .................... 855
Epilogue ...................................................... 859
Bibliography .................................................. 860
Index ......................................................... 879
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