Index

Numbers

2D Extractor field solver (Ansoft), 166, 170, 215, 229, 234, 278, 280, 297–305, 315, 389, 391

2D field solvers, 40

capacitance per length, calculating, 160, 164, 165–168

characteristic impedance, calculating, 300–306

differential impedance, calculating, 258–259

LaPlace’s Equation, 471

Maxwell capacitance matrix, 471–477

odd and even modes, determining, 269, 311

3D field solvers, 29, 32, 40, 190–192, 212–213

3-dB bandwidth of an interconnect, 85

3M C-Ply, 16, 158

50-Ohm transmission line

magnitude of S₂₁ for, 644–649

phase of S₂₁ for, 641–644

75-Ohm transmission line, 640

AN-905 National Semiconductor application note, 552

86100 DCA (Agilent), 339–340, 362, 365–367, 371

86100 DCA TDR, 45, 582

A

A_cond, 427, 646

A_dB, 419, 439

A_diel, 646

A_n, 65, 418

AC resistance. See impedance

AC simulation, 118

acceptance mask, 384

active CTLE (continuous-time linear equalizer), 451

active net, 457. See also cross talk

adjacent traces, coupling to, 386

ADS (Advanced System Designer), 101, 543, 544, 562, 591–594

Advanced System Designer (ADS), 543, 544, 562, 591–594

aggressor net, 457. See also cross talk

Agilent

86100 DCA TDR, 45, 339–340, 362, 365–367, 371, 582

ADS (Advanced System Designer), 543, 544, 562, 591–594

DCA86100, 45

N5230 VNA, 627–629, 637, 647, 649, 651–654, 667, 675

PLTS, 629, 644, 667, 675, 678–680

Alloy 42, 179, 229–231

alloys, 179, 229

Altera Stratix II GX FPGA, 697, 784

aluminum, 179

American wire gauge (AWG), 138

amplitude, 59

analytical approximations, 39–40

angular frequency, 109

anomalous dispersion, 417

anomalous phase shift, 417

Ansoft

2D Extractor field solver, 166, 170, 215, 229, 234, 278, 280, 297–305, 315, 389, 391

High Frequency Structure Simulator (HFSS), 31

Q3D field solver, 190, 213, 215

SI2D field solver, 167, 428, 469, 475, 479, 495, 500, 504, 518–519, 546–551, 554, 555–570

antipad clearance holes, 448–449, 690

anti-symmetric waveforms, 64

approximations, 37, 39–40

analytical, 39–40

attenuation, 423–433

characteristic impedance, 297–300

FEXT (far-end cross talk), 498–503

loop inductance, 202–204, 724–733

lossy transmission line modeling, 405–413

number of capacitors, 754–756

numerical-simulation tools, 41

parallel plate approximation, 152–153

resistance of interconnect, 133–136

rules of thumb, 37–38

Archambeault, Bruce, 37

asymmetry in differential pairs, 539, 584, 590–595, 599, 600, 673–674

attenuation, 645

approximations, 423–433

attenuation per length, 432

coax cables, 264

decibels and, 417–423

definition of, 431–432

equalization, 450–452

high-frequency components, 70–71

AVX data sheets, 743–744, 773

AWG (American wire gauge), 138

axial lead, 125–126

B

backward cross-talk coefficient, 494, 579

backward noise. See NEXT (near-end cross talk)

backward-moving current, 486–489, 491

balanced lines, 244

balanced S-parameters, 663–668

ball grid arrays (BGAs). See BGAs (ball grid arrays)

bandwidth

clock frequency and, 78–80

definition of, 69

interconnects, 85–88, 438–444

measurements, 80–82

models, 83–84

real signals, 77–78

rise time and, 68–73

barium titanate, 154–155, 158, 179

basis functions, 55

behavioral models, 619. See also S-parameters

Bell, Alexander Graham, 420

Bells (Bels) scale, 420

Bessel functions, 55

beTheSignal.com, 736, 739

BGAs (ball grid arrays), 10, 251, 295–296, 654, 711, 722, 726, 735–738

bismaleimide triazine (BT), 165

bit error rate, 383–384, 447, 673, 681

blind vias, 448–449, 672

BNC connectors, 161, 262

bounce diagrams, 333–335

bound charges, 105

broadside-coupled stripline, 557, 559–560

Brooks, Doug, 366–367

BT (bismaleimide triazine), 165

bulk capacitors, 705–706

bulk decoupling capacitors, 158, 705, 715–716, 749–751, 754, 767, 786

bulk dielectric constant, 169–171

bulk resistivity, 135, 136–137, 388

buried vias, 448–449, 672

bus noise, 504–505, 508, 510–511

BW_clock, 80

BW_model, 311, 312

BW_sig, 312

BW_TL, 439

C

C_0L, 369, 370

C_10, 467

C_11, 545–550, 611

C_12, 467, 519, 545–550, 609, 611

C_24, 467

C_30, 467

C_bulk, 705

C_corner, 364

C_filled, 169

C_L, 159–164, 255, 258, 285, 292–295, 364, 376, 408, 413, 425, 494, 608

C_load, 609, 611

C_max, 359

C_m, 481

C_mL, 481–488, 494, 498

C_odd, 609

C_planes, 751, 762

C_total, 294–295

C_via1, 435–436

C_via2, 435–436

calculation, creating models from, 36–41

capacitance

2D field solvers, 165–168

capacitance per length, 159–165

capacitance-matrix elements, 608–612

capacitive delay adders, 359–361

capacitive end terminations, reflections from, 353–356

capacitive loads in middle of trace, 356–359

coax cable, 160

decoupling, 156–158

definition of, 103–104

dielectric constant, 153–156

displacement current, 149–150

effective dielectric constant, 168–171

effects of corners and vias, 361–367

Maxwell capacitance matrix, 471–477

measurement of, 147–149

mutual capacitance, 461

on-die capacitance, 707–710

parallel plate approximation, 152–153

polarization current, 150

between power and group planes, 156–158

of a sphere, 150–152

SPICE capacitance matrix, 467–471

capacitive delay adders, 359–361

capacitive discontinuities, 356–359

capacitive end terminations, reflections from, 353–356

capacitive loads in middle of trace, reflections from, 356–359

capacitively coupled current, 461–462

capacitors

bulk decoupling capacitors, 158, 705–706, 715–716, 749–751, 754, 767, 786

chip capacitors, 703

combining in parallel, 740–745

controlled resistance capacitors, 743

cost per nH, 756–760

decoupling, 715–717

electrolytic capacitors, 702, 704–705, 749

IDCs (interdigitated capacitors), 774–776

ideal capacitors, 103–107

MLCC (multilayer ceramic chip capacitors), 703, 717–721, 786

mounting, 733–739

number of, 754–756

PRF (parallel resonant frequency), 746–747, 760–762

reverse aspect ratio capacitors, 773

tantalum capacitors, 702, 704–705

values, 748–753

X2Y capacitors, 722, 775–776

carbon, 179

Cartesian plots, 627

causal models, 155

cavity spreading inductance, 724, 738, 769

center-to-center separation, 191–192, 196, 198–199, 203–204, 726

ceramics, 249–250

characteristic impedance, 259–266, 269–270

calculating with 2D field solver, 300–306

calculating with approximations, 297–300

characteristic impedance matrix, 612–615

characteristic impedance of free space, 262–266

definition of, 259–260

frequency variation of, 314–316

lossy transmission lines, 413–415

odd-mode characteristic impedance, 566

characteristic impedance matrix, 612–615

chassis ground, 240

chip capacitors, 703

chip-fabrication factories, 24

chip-package combination, impact of impedance on, 785–789

chip-scale packages (CSPs), 10

chokes, 19, 95, 599–600

circuit ground, 240

circuit model. See models and modeling

circuit simulators, 29–33

circuit theory, 117–121, 408

circuit topology, 115, 121–126

circular magnetic-field lines, 176–181

clearance holes

antipad clearance holes, 448–449, 690

loop inductance and, 214–215

clock cycle, 21–25

clock frequency

bandwidth and, 78–80

trends in, 20–26

clock period, 52–53

coax cable, 261

capacitance per length, 160

unbalanced nature of, 244

cobalt, 179, 229–231

collapse of the eye, 681

combining capacitors in parallel, 740–745

common impedance, 567–570

common signals, 664

chokes, 599

converting differential signals to, 590–595

EMI (electromagnetic interference), 595–600

in LVDS (low-voltage differential signals), 537

odd- and even-mode voltage components, 570–572

pi and tee topologies, 585–589

S-parameters, 663–668

terminating, 583–590

compensation, 375–377

complex dielectric constant, 432

complex impedance of inductor, 114

conductivity, 136–137

conductor loss, 70, 387–392

conductor resistance, skin depth and, 387–392

contacts, loop inductance via, 211–214

continuous-time linear equalizer (CTLE), 451

controlled resistance capacitors, 743

controlled-impedance interconnect, 256

controlled-impedance lines, 243–244, 259–262

converting

differential signals to common signals, 590–595

to mixed-mode S-parameters, 675–676

convolution integral, 679

coplanar, 168, 234, 243–244

copper, 179

capacitance, 158, 167

copper puddle, 764

current distributions, 220–229

loop self-inductance, 39, 203–204

permeability of the conductor, 229–231

resistance, 131–132

analytical approximation for, 133–136

bulk resistivity, 135, 136–137, 388

ideal resistors, impedance of, 102–103

resistance per length, 138–139

resistor elements, 98

sheet resistance, 139–143

volume resistivity, 138

skin depth and, 220–229

speed of electrons in, 245–247

copper puddle, 764

corners, effects of, 361–367

cosine waves, 111–113

Coulombs, 147

coupled currents

capacitively coupled currents, 485–489

inductively coupled currents, 489–493

coupling

to adjacent traces, 386

capacitively coupled currents, 485–489

coupled currents

capacitively coupled currents, 485–489

inductively coupled currents, 489–493

ideal coupled transmission-line model, 579–580

ideal differential pair, 506

impact on differential impedance, 545–551

inductively coupled currents, 489–493

origin of, 460–462

to other transmission lines, 649–656

tightly coupled differential pairs, 607–608

C-Ply, 16, 158

critical nets, 29

cross talk, 11–13, 457–458. See also ground bounce (switching noise)

active net/aggressor net, 457

capacitively coupled currents, 485–489

causes of, 94

coupling, 460–462

dielectric constant and, 519–520

differential pairs, 601–604

equivalent circuit model, 464–466

FEXT (far-end cross talk)

decreasing, 503–505

definition of, 462–464

differential pairs, 573–578

estimating, 498–503

features of, 496–497

ideal differential pairs, 579–580

fringe fields, 460

guard traces, 512–519

inductance matrix, 478

inductively coupled currents, 489–493

Maxwell capacitance matrix, 471–477

minimizing, 13

mutual capacitance, 461

mutual inductance, 461

NEXT (near-end cross talk), 492–495

definition of, 462–464

ideal differential pairs, 579–580

quiet net/victim net, 457

reducing, 528

saturation length, 479–485

simulating, 505–512

SPICE capacitance matrix, 467–471

superposition, 459–460

switching noise, 524–528

timing, 521–524

in uniform transmission lines, 479–485

CSPs (chip-scale packages), 10

CTLE (continuous-time linear equalizer), 451

current distributions

eddy currents, 232–235

image current, 232–233

skin depth and, 220–229

D

damping, 652–653, 752, 785–787

data mining S-parameters, 661–663

dB. See decibels (dB)

DCA86100 (Agilent), 12

decibels (dB)

attenuation and, 417–423

S-parameters, 624–625

decision-feedback equalization (DFE), 452

decoupling capacitance, 156–158, 715–717

decreasing FEXT (far-end cross talk), 503–505

de-emphasis, 451–452

delay

delay adders

capacitive delay adders, 359–361

definition of, 360

time delay (TD), 250, 349

wiring delay, 251

delay adders

capacitive delay adders, 359–361

definition of, 360

delta I noise. See ground bounce (switching noise)

design guidelines for PDN (power distribution network), 690–691, 772–777, 789–792

design guidelines for signal integrity, 797–803

design methodology

components of, 27–29

need for, 26–27

device under test (DUT), 42–43, 623–626

DFE (decision-feedback equalization), 452

DFT (discrete Fourier transform), 60–61

diagrams, bounce, 333–335

dI/dt, 12, 19, 216, 489–490. See also ground bounce (switching noise)

dielectric constant, 153, 249–250, 364, 399

bulk dielectric constant, 169–171

complex dielectric constant, 432

cross talk and, 519–520

definition of, 399, 432

effective dielectric constant, 168–171

imaginary part of, 432

real part of, 432

relative dielectric constant, 153–156

dielectric loss, 70. See also dielectric constant

definition of, 387

leakage current, 392–396

reorientation of permanent electric dipoles, 394–396

dielectric spectroscopy, 398

differential impedance

calculating, 552–554

impact from coupling, 545–551

with no coupling, 541–545

differential insertion loss, 668–672

differential pairs. See also differential signaling

asymmetry in, 539, 584, 590–595, 599, 600, 673–674

characteristic impedance matrix, 612–615

common impedance, 567–570

cross talk, 601–604

definition of, 533–534, 538

differential impedance

calculating, 552–554

impact from coupling, 545–551

with no coupling, 541–545

EMI (electromagnetic interference), 595–600

even-mode impedance

calculating from capacitance- and inductance-matrix elements, 608–612

definition of, 565

measuring, 567–570, 580–582

even-mode state, 561–566

velocity of, 573–578

voltage components, 570–572

features of, 538–541

FEXT (far-end cross talk), 573–578

gaps in return path, 604–607

ideal differential pairs, 506, 579–580

odd-mode impedance

calculating from capacitance- and inductance-matrix elements, 608–612

definition of, 565

measuring, 566–567, 580–582

odd-mode state, 561–566

velocity of, 573–578

voltage components, 570–572

proximity effect, 547

return-current distribution, 555–561

tightly coupled, 607–608

differential signaling, 664

advantages of, 533–534

converting to common signals, 590–595

definition of, 533

disadvantages of, 534

LVDS (low-voltage differential signals), 534–538, 584

odd- and even-mode voltage components, 570–572

peak-to-peak value, 537

S-parameters, 663–668

terminating, 583–590

differential S-parameters, 663–668, 675–676

differential TDR (DTDR), 582

digital multimeters (DMMs), 267

DIP (dual in-line package), 243

dipole moment, 397

dipoles, 394–396

dielectric constant and, 154–155

dipole moment, 397

dissipation factor and, 396–405

reorientation of, 394–396

discontinuity, 321–323. See also reflections

compensation, 375–377

definition of, 8

effects of, 7–11

inductive discontinuities, 370–375

non-monotonicity, 371–372

unintentional discontinuities, 340–342

discrete Fourier transform (DFT), 60–61

dispersion, 250, 416–417

displacement current, 105, 149–150

dissipation factor, 155, 396–405, 432

distributions (current), skin depth and, 220–229

DMMs (digital multimeters), 267

domains. See frequency domains; time domains

double bonding, 198

driving transmission lines, 271–274

DTDR (differential TDR), 582

dual in-line package (DIP), 243

DUT (device under test), 42–43, 337–339, 623–626

dV/dt, 19, 149, 276, 353–357, 470, 472, 475, 480, 482, 485, 497

E

earth ground, 240

eddy currents, 232–235

effective dielectric constant, 168–171

effective inductance, 181, 193–199, 220

efficiency of conductors, 103–104

eigenfunctions, 55

electric dipoles. See dipoles

electrical models. See models and modeling

electrical simulations, 29–33

electrolytic capacitors, 702, 704–705, 749

electromagnetic (EM) simulators, 29–33

electromagnetic compatibility (EMC), 3–6

electromagnetic interference. See EMI (electromagnetic interference)

electron velocity, 245–247

electronic product trends, 20–26

EM (electromagnetic) simulators, 29–33

embedded microstrips, 170

EMC (electromagnetic compatibility), 3–6

EMI (electromagnetic interference), 4, 17–19

common signals and, 595–600

sources of, 95

emulation. See simulations

epoxy resin, 155

equalization, 450–452

equivalent circuit models, 115–117, 408, 464–466

equivalent inductance, 216–219, 220

equivalent series inductance (ESL), 208, 721–724

ESL (equivalent series inductance), 208, 721–724

ether, 105

even-mode impedance

calculating from capacitance- and inductance-matrix elements, 608–612

definition of, 565

measuring, 567–570, 580–582

even-mode state, 561–566

velocity of, 573–578

voltage components, 570–572

eye diagrams, 448–450, 680

F

F_clock, 52, 80

F_max, 760–763, 769, 782, 791

f_max, 713, 754

f_res, 308, 652–653

fabs, 24

Farads, 147

far-end cross talk. See FEXT (far-end cross talk)

fast Fourier transform (FFT), 61

FCC (Federal Communications Commission) certification tests, 24–25

FDTIM (Frequency-Domain Target Impedance Method), 766–772

Federal Communications Commission (FCC) certification tests, 24–25

feed-forward equalization (FFE), 451–452

ferrite chokes, 19, 95, 599–600

ferromagnetic metals, 179, 229

FEXT (far-end cross talk)

decreasing, 503–505

definition of, 462–464

differential pairs, 573–578

estimating, 498–503

features of, 496–497

ideal differential pairs, 579–580

FFE (feed-forward equalization), 451–452

FFT (fast Fourier transform), 61

FI (Fourier integral), 60

field solvers

2D field solvers, 40

capacitance per length, calculating, 160, 164, 165–168

characteristic impedance, calculating, 300–306

differential impedance, calculating, 258–259

LaPlace’s Equation, 471

Maxwell capacitance matrix, 471–477

odd and even modes, determining, 269, 311

3D field solvers, 29, 32, 40, 190–192, 212–213

fields, fringe, 460

filters, “windowing,” 62–63

first harmonic, 63

first-order models

definition of, 116

of transmission lines, 291–297, 406

forward noise. See FEXT (far-end cross talk)

Fourier integral (FI), 60

Fourier transforms, 60–62

DFT (discrete Fourier transform), 60–61

FFT (fast Fourier transform), 61

FI (Fourier integral), 60

inverse Fourier transform, 66–68

free space, characteristic impedance of, 264

frequency

angular frequency, 109

definition of, 58–59

high frequency, 229

Nyquist frequency, 25

PRF (parallel resonant frequency), 746–747, 760–762

SRF (self-resonant frequency), 207

definition of, 720

optimizing, 746–747

frequency domains

bandwidth

clock frequency and, 78–80

definition of, 69

of interconnects, 85–88

of measurements, 80–82

of models, 83–84

of real signals, 77–78

bandwidth and rise time, 68–73

current distributions

eddy currents, 232–235

image current, 232–233

skin depth and, 220–229

definition of, 54

FDTIM (Frequency-Domain Target Impedance Method), 766–772

Fourier transforms, 60–62

DFT (discrete Fourier transform), 60–61

FFT (fast Fourier transform), 61

FI (Fourier integral), 60

inverse Fourier transform, 66–68

impedance in, 109–114

S-parameters, 676–681

time to solution in, 56–57

waveforms

anti-symmetric, 64

significant components, 73–77

sine wave features, 54–56, 58–60

spectrum of ideal square wave, 64–66

spectrum of repetitive signal, 62–63

wavelets, 54

frequency variation of characteristic impedance, 314–316

frequency-dependent losses, 10–11

Frequency-Domain Target Impedance Method (FDTIM), 766–772

fringe fields, 460

fully embedded microstrips, 170, 499–504

functions, orthonormal, 55

G

G_L, 408, 413, 427

gaps in return path, 604–607

garbage in, garbage out (GIGO), 35

Gigabit Ethernet, 25, 26

GigaTest Labs Probe Station, 45, 362, 365–367, 371

GIGO (garbage in, garbage out), 35

glass, 155, 249–250

gold, 134–135, 138, 179

Grasso, Charles, 213, 215

Green’s function of the interconnect, 679

ground, 240–242

chassis ground, 240

circuit ground, 240

earth ground, 240

ground lines. See return paths

ground bounce (switching noise), 12, 216, 462, 524–528, 686–687

causes of, 94

definition of, 283

inductance, 193–199

ground lines. See return paths

ground plane capacitance, 156–158

guard traces, 512–519

H

habits, 27–28

hacking interconnects, 622–623

Hamming filters, 62–63

Hanning filters, 62–63

HDIs (high-density interconnects), 13

Henry, 180

Hermite polynomials, 55

HFSS ( High Frequency Structure Simulator), 31

high frequency, 229

High Frequency Structure Simulator (HFSS), 31

high-density interconnects (HDIs), 13

high-frequency regime, 3

high-permeability materials, 229–231

high-speed regime, 3

high-speed serial links, 26

humidity, 398

I

I_a, 525

I_C, 481–488

I_comm, 598

I_inc, 326–327

I_leakage, 393

I_max, 695–696

I_one, 541–542, 549

I_peak, 696

I_refl, 326–327

I_transient, 694–698

I_trans, 326–327

IBIS (input/output buffer interface) models, 34–35

IC (integrated circuit), 270

IDCs (interdigitated capacitors), 288, 774–776

ideal capacitors, impedance of, 103–107

ideal circuit elements, 99–102

ideal coupled transmission-line model, 579–580

ideal differential pairs, 506, 579–580

ideal inductors, impedance of, 107–109

ideal resistors, impedance of, 102–103

ideal square wave, spectrum of, 64–66

image current, 232–233

imaginary part of dielectric constant, 432

impedance. See also discontinuity; reflections

best design practices, 8

characteristic impedance, 259–266, 269–270

calculating with 2D field solver, 300–306

calculating with approximations, 297–300

characteristic impedance matrix, 612–615

characteristic impedance of free space, 262–266

definition of, 259–260

frequency variation of, 314–316

of lossy transmission lines, 413–415

odd-mode characteristic impedance, 566

circuit theory, 117–121

common impedance, 567–570

controlled-impedance interconnect, 256

controlled-impedance lines, 243–244, 259–262

definition of, 93, 97–98

differential impedance

calculating, 552–554

impact from coupling, 545–551

with no coupling, 541–545

discontinuity, 8

equivalent electric circuit model, 115–117

even-mode impedance

calculating from capacitance- and inductance-matrix elements, 608–612

definition of, 565

measuring, 567–570, 580–582

FDTIM (Frequency-Domain Target Impedance Method), 766–772

in frequency domains, 57, 109–114

impact on chip-package combination, 785–789

impedance analyzers, 42–43

impedance profiles, sculpting, 766–772

input impedance, 266–271

instantaneous impedance, 252–259, 269

magnitude of, 111, 414–415, 644–649

measurement-based modeling, 121–126

odd-mode impedance

calculating from capacitance- and inductance-matrix elements, 608–612

definition of, 565

measuring, 566–567, 580–582

port impedance, 639–640

insertion loss for non-50-Ohm transmission line, 655–661

magnitude of S₂₁ for 50-Ohm transmission line, 644–649

phase of S₂₁ for 50-Ohm transmission line, 641–644

real versus ideal circuit elements, 99–102

signal-integrity generalizations, 19–20

signal-integrity solutions and, 94–97

source impedance, 331–333

SPICE (Simulation Program with Integrated Circuit Emphasis), 706–707

target impedance, 688–689, 691–700, 763–765

in time domains

ideal capacitors, 103–107

ideal inductors, 107–109

ideal resistors, 102–103

impedance analyzers, 42–43

impedance discontinuities. See discontinuity

impulse response, 677–679

induced voltage, 184–186

inductance

cavity spreading inductance, 724, 738, 769

current distributions, skin depth and, 220–229

definition of, 175–176, 219, 235

eddy currents, 232–235

effective inductance, 181, 193–199, 220

equivalent inductance, 220

equivalent inductance of multiple inductors, 216–219

ESL (equivalent series inductance), 208, 721–724

ground bounce, 193–199

high-permeability materials, 229–231

inductance matrix, 478

inductance-matrix elements, calculating odd and even modes from, 608–612

inductively coupled currents, 489–493

loop inductance, 181

approximations, 202–204, 724–733

definition of, 219

inductance per square, 210–211

loop mutual inductance, 216, 219

loop self-inductance, 219

loop spreading inductance, 729–731

measurement of, 199–204

PDN (power distribution network) and, 204–209

per square of planes, 210–211

of planes and via contacts, 211–214

of planes with field of clearance holes, 214–215

sheet inductance, 210–211

magnetic-field lines

changes in number of, 184–186

direction of, 177

explained, 176–179

number of, 179–181

mutual inductance, 181–184

definition of, 219, 461

partial mutual inductance, 220

net inductance, 181, 193–199, 220

partial inductance, 181, 187–192

definition of, 219

partial mutual inductance, 192, 220

partial self-inductance, 187–191, 220

principles of, 176–186

self-inductance, 181–184

definition of, 219

partial mutual inductance, 192

partial self-inductance, 187–191, 220

sheet inductance, 727

spreading inductance, 212–213, 777–785

summary of, 219–220

total inductance, 181, 193–199, 220

inductance matrix, 478

inductance per square, 210–211

inductive discontinuities, reflections from, 370–375

inductively coupled current, 461–462

inductors, ideal, 107–109

InfiniBand, 26

input impedance, 266–271

input ports, 625

input/output buffer interface (IBIS) models, 34–35

insertion loss, 433, 645

definition of, 631–635

differential insertion loss, 668–672

for non-50-Ohm transmission lines, 655–661

transparent interconnect, 636–639

uniform transmission lines, 644–649

instantaneous impedance, 252–259, 269

integrated circuit (IC), 270

integrated passive devices (IPDs), 125–126

interconnects, 175–176. See also impedance; inductance

bandwidth of, 85–88, 438–444

capacitance

2D field solvers, 165–168

capacitive delay adders, 359–361

capacitive end terminations, 353–356

capacitive loads in middle of trace, 356–359

coax cable, 160

decoupling, 156–158

dielectric constant, 153–156

displacement current, 149–150

effective dielectric constant, 168–171

effects of corners and vias, 361–367

Maxwell capacitance matrix, 471–477

measurement of, 147–149

mutual capacitance, 461

parallel plate approximation, 152–153

per length, 159–165

polarization current, 150

between power and group planes, 156–158

of a sphere, 150–152

SPICE capacitance matrix, 467–471

Green’s function of the interconnect, 679

hacking, 622–623

Maxwell’s Equations, 131–132

resistance, 131–132

analytical approximation for, 133–136

bulk resistivity, 135, 136–137, 388

conductor resistance and skin depth, 387–392

resistance per length, 138–139

sheet resistance, 139–143

volume resistivity, 138

transparent interconnect, 636–638

interdigitated capacitors (IDCs), 288, 774–776

International Technology Roadmap for Semiconductors (ITRS), 21–22

intersymbol interference (ISI), 10–11, 381, 382–385

intrinsic rise time, 86–87

inverse Fourier transform, 66–68

IPDs (integrated passive devices), 125–126

IR drop, 688

iron, 179, 229–231

ISI (intersymbol interference), 10–11, 381, 382–385

ITRS ( International Technology Roadmap for Semiconductors), 21–22

J-K

jitter, 14, 382–385, 681

k_b. See backward cross-talk coefficient

k_f, 498

Kapton, 398

Keysight PLTS, 33

Keysight Technology ADS (Advanced System Designer), 101

kink of field, 247, 248–249

knee frequency, 74

Kovar, 179, 229–231

L

L_ab, 195, 200

L_b, 194, 195, 200

L_even, 611

L_L, 292–295, 369, 376, 408, 413, 425, 494, 498, 608

L_Loop, 200–203, 210, 478, 724–727

L_max, 373

L_mL, 482, 494, 498

L_m, 216, 525–526

L_mutual, 478

L_{parallel, 218}

L_pkg, 713, 791

L_self, 39

L_self-return, 478

L_self-signal, 478

L_series, 218

L_spread, 729, 782

L_stub-max, 352

L_total, 195, 294–295

L_via, 436

L_via-via, 731, 758

Laguerre polynomials, 55

LaPlace’s Equation, 165, 471

lattice diagrams, 333–335

lead, 179

leading edge, spatial extent of, 251–252

leakage current, 392–396

Legendre polynomials, 55

Len_max, 344, 350

Len_sat, 484, 578

Len_stub, 671

length

capacitance per, 159–165

resistance per, 138–139

Lentz’s Law, 490

line drivers, 274

line parameters, 292, 408

loaded lines, 367–370

loop inductance, 181, 729–731

approximations, 202–204, 724–733

definition of, 219

inductance per square, 210–211

loop mutual inductance, 216, 219

loop self-inductance, 219

measurement of, 199–204

PDN (power distribution network) and, 204–209

per square of planes, 210–211

of planes and via contacts, 211–214

of planes with field of clearance holes, 214–215

sheet inductance, 210–211

loop mutual inductance, 219

loop self-inductance, 219

loop spreading inductance, 729–731

loss angle, 402–403, 432

lossless models, 385, 406

lossy transmission lines, 381–382

acceptance mask, 384

attenuation

approximations, 423–433

attenuation per length, 432

dB and, 417–423

decibels and, 417–423

definition of, 431–432

bandwidth of interconnect, 438–444

characteristic impedance of, 413–415

conductor loss, 70

conductor resistance and skin depth, 387–392

coupling to adjacent traces, 386

definition of, 431

dielectric loss, 70

definition of, 387

leakage current, 392–396

reorientation of permanent electric dipoles, 394–396

dissipation factor, 396–405, 432

equalization, 450–452

eye diagrams, 448–450

insertion loss, 433, 645

definition of, 631–635

differential, 668–672

differential insertion loss, 668–672

for non-50-Ohm transmission lines, 655–661

transparent interconnect, 636–639

uniform transmission lines, 644–649

ISI (intersymbol interference), 381, 382–385

loss angle, 402–403, 432

lossless model, 385

low-loss approximation, 410–413

measured properties of, 433–438

models and modeling, 405–413

radiative loss, 386

return loss, 433, 631–635

rise-time degradation, 385–387, 442–444

signal velocity, 415–417

time-domain behavior, 445–448

low-loss approximation, 410–413

low-voltage differential signals (LVDS), 534–538, 584

lumped-circuit models, 306–314

LVDS (low-voltage differential signals), 534–538, 584

M

magnetic-field lines

changes in number of, 184–186

direction of, 177

explained, 176–179

number of, 179–181

magnetics, 600

magnitude of impedance, 111, 414–415, 644–649

MATLAB, 33

matrices

characteristic impedance matrix, 612–615

inductance matrix, 478

Maxwell capacitance matrix, 471–477

S-parameter matrix elements, 627

SPICE capacitance matrix, 467–471

Maxwell, James Clerk, 105

Maxwell capacitance matrix, 471–477

Maxwell’s Equations, 30–31, 132, 150–151, 165, 490

Mears, James, 552

measured properties of lossy transmission lines, 433–438

measurement-based modeling, 121–126

measurements

bandwidth of, 80–82

measurement-based modeling, 121–126

role of, 45–47

types of, 42–45

impedance analyzers, 42–43

TDR (time-domain reflectometer) plug-in, 44–45

VNAs (vector-network analyzers), 43–44

Mentor Graphics HyperLynx, 2

microstrips. See also differential pairs

capacitance per length, 163

definition of, 261

embedded microstrips, 170

fully embedded microstrips, 170, 499–504

partially embedded microstrips, 170

unbalanced nature of, 244

microvias, 672

mixed-mode S-parameters, 663–668, 675–676

MLCC (multilayer ceramic chip capacitors), 703, 717–721, 786

mode conversion quadrants, 672

mode conversion terms, 672–674

models and modeling, 34–36

bandwidth of, 83–84

causal models, 155

creating models from calculation, 36–41

definition of, 32, 96

equivalent circuit model, 464–466

equivalent circuit models, 408

equivalent electric circuit model, 115–117

first-order models

definition of, 116

of transmission lines, 291–297, 406

ideal coupled transmission-line model, 579–580

lossless models, 406

lossy transmission lines, 405–413

measurement-based modeling, 121–126

n-section lumped-circuit models, 306–314, 385, 406

second-order models, 116

third-order models, 116

translating physical design into electrical performance, 132–133

zeroth-order models, 256

modes of the pair, 561–566

Moore’s Law, 24–25

mounting capacitors, 733–739

multilayer ball grid arrays. See BGAs (ball grid arrays)

multilayer ceramic chip capacitors (MLCC), 703, 717–721, 786

multiple inductors, equivalent inductance of, 216–219

mutual capacitance, 461

mutual inductance, 12, 181–184

definition of, 219, 461

loop mutual inductance, 216

partial mutual inductance, 220

N

N_unique, 630

N5230 VNA (Agilent), 627–629, 637, 647, 649, 651–654, 667, 675

nanoHenry, 180

napers, 418

Napier, John, 418

napiers, 418

near-end cross talk (NEXT). See NEXT (near-end cross talk)

nepers, 418

net inductance, 181, 193–199, 220

nets, signal integrity effects on, 7–11

NEXT (near-end cross talk), 492–495

definition of, 462–464

ideal differential pairs, 579–580

nH, cost of, 756–760

nickel, 179, 229–231

noise, 49. See also cross talk; discontinuity; reflections

bus noise, 504–505, 508, 510–511

cross talk, 11–13, 457–458. See also ground bounce (switching noise)

active net/aggressor net, 457

capacitively coupled currents, 485–489

causes of, 94

coupling, 460–462

dielectric constant and, 519–520

differential pairs, 601–604

equivalent circuit model, 464–466

FEXT (far-end cross talk), 462–464, 496–505, 573–578, 579–580

fringe fields, 460

guard traces, 512–519

inductance matrix, 478

inductively coupled currents, 489–493

Maxwell capacitance matrix, 471–477

minimizing, 13

mutual capacitance, 461

mutual inductance, 461

NEXT (near-end cross talk), 462–464, 492–495, 579–580

quiet net/victim net, 457

reducing, 528

saturation length, 479–485

simulating, 505–512

SPICE capacitance matrix, 467–471

superposition, 459–460

switching noise, 524–528

timing, 521–524

in uniform transmission lines, 479–485

EMI (electromagnetic interference), 4, 17–19

ground bounce, 12, 216, 462, 524–528, 686–687

causes of, 94

definition of, 283

inductance, 193–199

ISI (intersymbol interference), 10–11

rail collapse, 14–17

“ringing,” 322, 334–335

signal-integrity generalizations, 19–20

skew

definition of, 11

effects of, 11

undershoot, 321, 356–359

non-50-Ohm transmission lines, insertion loss for, 655–661

non-monotonicity, 371–372

non-return-to-zero (NRZ), 25

nonuniform transmission lines, 243

NRZ (non-return-to-zero), 25

n-section lumped-circuit models, 306–314, 385, 406

numerical-simulation tools, 29–33, 41

Nyquist frequency, 25, 671

O

OC (optical carrier) spec, 25

odd waveforms, 64

odd-mode impedance

calculating from capacitance- and inductance-matrix elements, 608–612

definition of, 565

measuring, 566–567, 580–582

odd-mode state, 561–566

velocity of, 573–578

voltage components, 570–572

Ohmmeter, 268

Ohm’s Law, 103

on-die capacitance, 707–710

on-die core power rail, 4

optical carrier (OC) spec, 25

optimizing mounting of capacitors, 733–739

orthonormal functions, 55

output ports, 625

P

P_max, 696

package barrier, 710–715

PAM (pulse amplitude modulation), 25–26

parallel, combining capacitors in, 740–745

parallel plate approximation, 152–153

parallel resonant frequency (PRF), 746–747, 760–762

parallel resonant peak, 741, 746–747

parallel rods, capacitance per length, 161

parameter values, 115

parameters of transmission lines, 408

parasitic extraction, 40, 115, 132–133

parasitic values, 115

partial inductance, 181, 187–192

definition of, 219

partial mutual inductance, 192, 220

partial self-inductance, 187–191, 220

partial mutual inductance, 192, 220

partial self-inductance, 187–191, 220

partially embedded microstrips, 170

paths

return paths, 239, 241

current flow, 274–278

gaps in, 604–607

switches of reference planes, 278–291

signal paths, 239

PCI Express, 26

PCIe, 25

PDN (power distribution network), 4, 94–95, 685

capacitors

bulk decoupling capacitors, 158, 705–706, 715–716, 749–751, 754, 767, 786

chip capacitors, 703

combining in parallel, 740–745

controlled resistance capacitors, 743

cost per nH, 756–760

decoupling capacitors, 715–717

electrolytic capacitors, 702, 704–705, 749

IDCs (interdigitated capacitors), 774–776

MLCC (multilayer ceramic chip capacitors), 703, 717–721, 786

mounting, 733–739

number of, 754–756

PRF (parallel resonant frequency), 746–747, 760–762

reverse aspect ratio capacitors, 773

SRF (self-resonant frequency), 720, 746–747

tantalum capacitors, 702, 704–705

values, 748–753

X2Y capacitors, 722, 775–776

design guidelines for, 690–691, 772–777, 789–792

engineering, 701–703

ESL (equivalent series inductance), 721–724

impedance

FDTIM (Frequency-Domain Target Impedance Method), 766–772

impact on chip-package combination, 785–789

impedance profiles, sculpting, 766–772

SPICE simulations, 706–707

target impedance, 688–689, 691–700, 763–765

IR drop, 688

loop inductance, 204–209, 724–733

on-die capacitance, 707–710

package barrier, 710–715

parallel resonant peak, 741, 746–747

PRF (parallel resonant frequency), 746–747, 760–762

product PDN requirements, 700–701

purpose of, 686–689

spreading inductance, 777–785

SRF (self-resonant frequency)

definition of, 720

optimizing, 746–747

VRMs (voltage regulator modules), 701, 703–706

peak-to-peak value, 537

permanent electric dipoles. See dipoles

permeability

of the conductor, 229

of dielectrics, 249

of free space, 249

high-permeability materials, 229–231

phase (sine waves), 59

phase locked loop (PLL), 701

photolithography, 20

physical design, translating into electrical performance, 132–133

pi termination strategy, 583–590

planes

capacitance, 156–158

loop inductance

per square of planes, 210–211

of planes and via contacts, 211–214

of planes with field of clearance holes, 214–215

resonances in the planes, 290

returns paths switching, 278–291

plastic quad flat pack (PQFP), 30–31, 135

PLL (phase locked loop), 701

PLTS (Agilent), 629, 644, 667, 675, 678–680

point-to-point topology, termination strategy for, 345–348

polar plots, 627

polarization, 105, 150

polyethylene, 161, 398

Polyimide, 398

port-labeling convention, 650

ports

port assignments, 623–626

port impedance, 639–640

insertion loss for non-50-Ohm transmission line, 655–661

magnitude of S₂₁ for 50-Ohm transmission line, 644–649

phase of S₂₁ for 50-Ohm transmission line, 641–644

port-labeling convention, 650

power distribution network. See PDN (power distribution network)

power integrity defined, 3–6

PQFP (plastic quad flat pack), 30–31, 135

PRBS (pseudorandom bit sequence), 680

pre-emphasis, 451–452

PRF (parallel resonant frequency), 746–747, 760–762

processors

clock frequency, 20–26

single-chip microprocessor-based systems, 21

product-design methodology

components of, 27–29

need for, 26–27

profiles (impedance), sculpting, 766–772

properties of lossy transmission lines, 433–438

proximity effect, 547

pseudorandom bit sequence (PRBS), 680

pulse amplitude modulation (PAM), 25–26

Python, 33

Q

Q3D field solver (Ansoft), 190, 213, 215

QFP (quad flat pack), 243

quad flat pack (QFP), 243

quarter wave stub resonance, 669–671

QUCS (Quite Universal Circuit Simulator), 33, 118

questions and answers review, 819

quiet net, 457. See also cross talk

Quite Universal Circuit Simulator (QUCS), 33, 118

R

R_AC, 406

r_b, 151

R_DC, 226, 406

R_equiv, 586–587

R_HF, 227

R_leakage, 393

R_L, 142, 406, 408, 411, 413, 425–427

R_series, 407

R_shunt, 407

R_source, 273

R_sq, 140, 142

R_s, 333

R_term, 543

R_t, 333

radians, 109

radiative loss, 386

rail collapse

definition of, 205

impedance and, 94–95

noise, 14–17

rail droop. See rail collapse

real part of dielectric constant, 432

real versus ideal circuit elements, 99–102

reference planes

resonances in the planes, 290

returns paths switching, 278–291

reflected waves, 622

reflection coefficient, 323–324, 328–331. See also S₁₁

reflections, 321–322

best design practices, 8

bounce diagrams, 333–335

capacitive delay adders, 359–361

from capacitive end terminations, 353–356

from capacitive loads in middle of trace, 356–359

causes of, 324–328

compensation, 375–377

definition of, 7

effects of corners and vias, 361–367

at impedance changes, 323–324

from inductive discontinuities, 370–375

loaded lines, 367–370

measuring with TDR, 337–340

reflected waveforms, simulating, 335–337

reflection coefficient, 323–324, 328–331

from resistive loads, 328–331

from short series transmission lines, 348–351

from short-stub transmission lines, 351–353

source impedance, 331–333

transmission line termination

strategy for point-to-point topology, 345–348

when to terminate, 343–345

unintentional discontinuities, 340–342

relative dielectric constant. See dielectric constant

reorientation of permanent electric dipoles, 394–396

repetitive signal, spectrum of, 62–63

resistance, 131–132. See also impedance

analytical approximation for, 133–136

bulk resistivity, 135, 136–137, 388

conductor resistance and skin depth, 387–392

ideal resistors, 102–103

resistance per length, 138–139

resistor elements, 98

sheet resistance, 139–143

volume resistivity, 138

resistive loads, reflections from, 328–331

resistor elements, 98, 102–103

resonance

definition of, 30–31

in the planes, 290

PRF (parallel resonant frequency), 746–747, 760–762

quarter wave stub resonance, 669–671

SRF (self-resonant frequency)

definition of, 720

optimizing, 746–747

return loss, 433, 631–635

return paths, 160, 239, 241

current flow, 274–278

gaps in, 604–607

switches of reference planes, 278–291

return-current distribution, 555–561

reverse aspect ratio capacitors, 773

review questions and answers, 819

“ringing” noise, 322, 334–335

ripple, 205–207, 640, 647, 658, 669, 688–700

rise time

bandwidth and, 68–73

capacitive loads in middle of trace, 356–359

definition of, 52–54

impedance and, 94

intrinsic rise time, 86–87

rise-time degradation, 385–387, 442–444

rule of thumb for, 441

from short series transmission lines, 348–351

from short-stub transmission lines, 351–353

unterminated lines and, 343–345

rise-time degradation, 385–387, 442–444

rods. See also center-to-center separation

parallel rods, 161

rod over plane, 162

rotation of dipoles, 394–396

round-trip time of flight, 270–271

RT. See rise time

RT_in, 87, 442

RT_{interconnect,} 87

RT_out, 87, 442

RT_signal, 444

RT_TL, 440–442

S

s. See center-to-center separation

S_11, 43, 433, 627, 631

S_12, 631

S_21, 433, 631

magnitude of, 644–649

phase of, 641–644

S_31, 442–444, 650, 663

S_32, 663

S_33, 662

S_41, 650, 663

S_42, 662

S_43, 650, 662, 681

S_dB, 624

S_d, 675–676

S_mag, 624

S_s, 676

SATA (Serial ATA), 25, 26

saturation length, 479–485

scalar-network analyzers, 622

scattering parameters. See S-parameters

SCD11, 673, 682

SCD12, 666, 673, 675, 682

schematics, 32, 115

SCSI (small computer system interface), 268

sculpting impedance profiles, 766–772

second harmonic, 63

second-order models, 116

self-inductance, 181–184

definition of, 219

loop self-inductance, 219

partial mutual inductance, 192

partial self-inductance, 187–191, 220

self-resonant frequency (SRF), 207

definition of, 720

optimizing, 746–747

Semiconductor Industry Association (SIA), 20–26

Serial ATA (SATA), 25, 26

sheet inductance, 210–211, 727

sheet resistance, 139–143

short series transmission lines, reflections from, 348–351

shorting vias, 209, 214, 516–517

short-stub transmission lines, reflections from, 351–353

SI2D field solver (Ansoft), 167, 428, 469, 475, 479, 495, 500, 504, 518–519, 546–551, 554, 555–570

SIA (Semiconductor Industry Association), 21–22

Siemens, 137

signal integrity defined, 3–6

signal integrity effects, rules to estimate, 805

signal paths, 160, 239

signal velocity, 416–417

even-mode state, 573–578

lossy transmission lines, 415–417

odd-mode state, 573–578

transmission lines, 247–251

signal-to-noise ratio (SNR), 57

significant components, 73–77

silicone, 398

silver, 179, 231

Simulation Program with Integrated Circuit Emphasis. See SPICE (Simulation Program with Integrated Circuit Emphasis)

simulations, 29–33

AC simulations, 118

cross talk, 505–512

definition of, 96, 622

numerical-simulation tools, 41

QUCS (Quite Universal Circuit Simulator), 118

reflected waveforms, 335–337

SPICE (Simulation Program with Integrated Circuit Emphasis), 117–121, 706–707

transient simulations, 118

simultaneous switching noise (SSN). See ground bounce (switching noise)

simultaneous switching output (SSO), 12

sine waves. See also S-parameters

bandwidth

clock frequency and, 78–80

definition of, 69

of interconnects, 85–88

of measurements, 80–82

of models, 83–84

of real signals, 77–78

rise time and, 68–73

features of, 54–56, 58–60

first harmonic, 63

Fourier transforms, 60–62

impedance, 109–114

inverse Fourier transform, 66–68

second harmonic, 63

significant components, 73–77

waveforms

significant components, 73–77

sine wave features, 54–56, 58–60

spectrum of ideal square wave, 64–66

spectrum of repetitive signal, 62–63

wavelets, 54

single-chip microprocessor-based systems, 21

single-ended S-parameters, 663–668

single-ended transmission-line signal, 534–535

skew, 11

skin depth

conductor resistance and, 387–392

current distributions and, 220–229

small computer system interface (SCSI), 268

SMT (surface-mount technology), 123–126

SNR (signal-to-noise ratio), 57

solder balls, 685, 711, 723

solder mask, 170, 300, 503, 569–570

source impedance, 331–333

source-series termination, 345–348

S-parameters, 99, 433

balanced S-parameters, 663–668

behavioral model, 619–620

Cartesian plots, 627

coupling to other transmission lines, 649–656

data mining, 661–663

dB and magnitude, 624–625

definition of, 43, 621–623

differential S-parameters, 663–668

eye diagrams, 680

frequency behavior of, 627

frequency domains, 676–681

importance of, 619–620

insertion loss, 631–635, 645

definition of, 631–635

differential, 668–672

differential insertion loss, 668–672

for non-50-Ohm transmission lines, 655–661

transparent interconnect, 636–639

uniform transmission lines, 644–649

magnitude of, 624, 644–649

matrix elements, 627–631

mixed-mode S-parameters, 663–668, 675–676

mode conversion terms, 672–674

phase of, 641–644

polar plots, 627

port assignments, 623–626

port impedance, 639–640

insertion loss for non-50-Ohm transmission line, 655–661

magnitude of S₂₁ for 50-Ohm transmission line, 644–649

phase of S₂₁ for 50-Ohm transmission line, 641–644

port-labeling convention, 650

reflected signals, 43

reflection coefficient, 631

return loss, 631–635

single-ended, 663–668

time domains, 676–681

transmission coefficient, 631

transparent interconnect, 636–638

uniform 50-Ohn transmission line, 641–644

spatial extent of leading edge, 251–252

spectrum of waveform

definition of, 61, 63

of ideal square wave, 64–66

of repetitive signal, 62–63

spheres, capacitance of, 150–152

SPICE (Simulation Program with Integrated Circuit Emphasis), 32–33, 117–121, 706–707

capacitance matrix, 467–471

QUCS (Quite Universal Circuit Simulator), 118

spread spectrum clocking (SSC), 4

spreading inductance, 212–213, 777–785

square of planes, loop inductance per, 210–211

SRF (self-resonant frequency)

definition of, 720

optimizing, 746–747

SSC (spread spectrum clocking), 4

SSN (simultaneous switching noise). See ground bounce (switching noise)

SSO (simultaneous switching output), 12

step edge, 677–679

Stratix II GX FPGA (Altera), 697, 784

striplines. See also differential pairs

broadside-coupled stripline, 557, 559–560

capacitance per length, 164

definition of, 261

unbalanced nature of, 244

superposition, 459–460

surface-mount technology (SMT), 123–126

switching noise. See ground bounce (switching noise)

T

T_clock, 52

tangent of loss angle. See dissipation factor

tantalum capacitors, 702, 704–705

target impedance, 688–689, 691–700, 763–765

TDA Systems IConnect software, 45, 339

TD_adder, 374

TD_Load, 370

TDR ( time-domain reflection) response, 622, 677

TDRs (time-domain reflectometers), 12, 44–45, 57, 337–340, 580–582, 622

TDT (time-domain transmitted) waves, 622

tee termination strategy, 583–590

Teflon, 179, 398

Teledyne LeCroy SI Studio, 33

Teraspeed Consulting Group, 765

termination

common signals, 583–590

differential signaling, 583–590

reflections from capacitive end terminations, 353–356

source-series termination, 345–348

strategy for point-to-point topology, 345–348

when to terminate, 343–345

third-order models, 116

tightly coupled differential pairs, 607–608

time delay (TD), 250, 349, 521–524

time domains, 52–54

bandwidth

clock frequency and, 78–80

definition of, 69

of interconnects, 85–88

of measurements, 80–82

of models, 83–84

of real signals, 77–78

rise time and, 68–73

Fourier transforms, 60–62

DFT (discrete Fourier transform), 60–61

FFT (fast Fourier transform), 61

FI (Fourier integral), 60

inverse Fourier transform, 66–68

impedance

of ideal capacitors, 103–107

of ideal inductors, 107–109

of ideal resistors, 102–103

inverse Fourier transforms, 66–68

lossy transmission line behavior, 445–448

S-parameters, 676–681

waveforms

anti-symmetric, 64

significant components, 73–77

spectrum of ideal square wave, 64–66

spectrum of repetitive signal, 62–63

wavelets, 54

time-domain reflection (TDR) response, 622, 677

time-domain reflectometers (TDRs), 12, 44–45, 57, 337–340, 580–582, 622

time-domain transmitted (TDT) waves, 622

timing, cross talk and, 521–524

tin, 179

topology, point-to-point, 345–348

total inductance, 181, 193–199, 220

traces

capacitive loads in middle of trace, 356–359

guard traces, 512–519

transforms

Fourier transforms, 60–62

inverse Fourier transform, 66–68

transient simulations, 118

transistor-transistor logic (TTL) gates, 331

transmission coefficient, 324, 328

transmission lines, 102. See also ground bounce (switching noise); S-parameters

50-Ohm transmission lines

magnitude of S₂₁ for, 644–649

phase of S₂₁ for, 641–644

75-Ohm transmission lines, 640

balanced lines, 244

characteristic impedance, 259–266, 269–270

calculating with 2D field solver, 300–306

calculating with approximations, 297–300

characteristic impedance of free space, 264

definition of, 259–260

famous characteristic impedances, 262–266

frequency variation of, 314–316

chassis ground, 240

circuit ground, 240

controlled-impedance lines, 243–244, 259–262

coupling to other transmission lines, 649–656

cross talk, 11–13, 457–458

active net/aggressor net, 457

capacitively coupled currents, 485–489

causes of, 94

coupling, 460–462

dielectric constant and, 519–520

differential pairs, 601–604

equivalent circuit model, 464–466

FEXT (far-end cross talk), 462–464, 496–505, 573–578, 579–580

fringe fields, 460

guard traces, 512–519

inductance matrix, 478

inductively coupled currents, 489–493

Maxwell capacitance matrix, 471–477

minimizing, 13

mutual capacitance, 461

mutual inductance, 461

NEXT (near-end cross talk), 462–464, 492–495, 579–580

quiet net/victim net, 457

reducing, 528

saturation length, 479–485

simulating, 505–512

SPICE capacitance matrix, 467–471

superposition, 459–460

switching noise, 524–528

timing, 521–524

in uniform transmission lines, 479–485

definition of, 239–240

differential pairs

asymmetry in, 539, 584, 590–595, 599, 600, 673–674

characteristic impedance matrix, 612–615

common impedance, 567–570

cross talk, 601–604

definition of, 533–534, 538

differential impedance, 541–554

EMI (electromagnetic interference), 595–600

even-mode impedance, 565, 567–570, 580–582, 608–612

even-mode state, 561–566, 570–578

features of, 538–541

FEXT (far-end cross talk), 573–578

gaps in return path, 604–607

ideal differential pair, 506

ideal differential pairs, 579–580

odd-mode impedance, 565, 566–567, 580–582

odd-mode state, 561–566, 570–578

proximity effect, 547

return-current distribution, 555–561

tightly coupled, 607–608

differential signaling, 533–537

converting to common signals, 590–595

peak-to-peak value, 537

terminating, 583–590

driving, 271–274

earth ground, 240

first-order models, 291–297

ideal coupled transmission-line model, 579–580

input impedance, 266–271

instantaneous impedance, 252–259, 269

kink of field, 247, 248–249

line parameters, 292, 408

lossless model, 385

lossy transmission lines, 381–382

acceptance mask, 384

attenuation and dB, 417–423

attenuation and decibels, 417–423

attenuation approximations, 423–433

bandwidth of interconnect, 438–444

characteristic impedance, 413–415

conductor resistance and skin depth, 387–392

coupling to adjacent traces, 386

dielectric loss, 387, 392–396

dissipation factor, 396–405, 432

equalization, 450–452

eye diagrams, 448–450

insertion loss, 433, 631–635, 636–639, 644–649, 655–661, 668–672

ISI (intersymbol interference), 381, 382–385

loss angle, 402–403, 432

low-loss approximation, 410–413

measured properties of, 433–438

modeling, 405–413

radiative loss, 386

return loss, 433

rise-time degradation, 385–387, 442–444

signal velocity, 415–417

time-domain behavior, 445–448

nonuniform transmission lines, 243

n-section lumped-circuit models, 306–314, 385, 406

reflections, 321–322

bounce diagrams, 333–335

capacitive delay adders, 359–361

from capacitive end terminations, 353–356

from capacitive loads in middle of trace, 356–359

causes of, 324–328

compensation, 375–377

effects of corners and vias, 361–367

at impedance changes, 323–324

from inductive discontinuities, 370–375

loaded lines, 367–370

measuring with TDR, 337–340

reflected waveforms, simulating, 335–337

reflection coefficient, 323–324, 328–331

from resistive loads, 328–331

from short series transmission lines, 348–351

from short-stub transmission lines, 351–353

source impedance, 331–333

unintentional discontinuities, 340–342

return paths, 239, 241

current flow, 274–278

switches of reference planes, 278–291

round-trip time of flight, 270–271

signal paths, 239

single-ended transmission-line signal, 534–535

spatial extent of leading edge, 251–252

speed of electrons in copper, 245–247

termination

reflections from capacitive end terminations, 353–356

strategy for point-to-point topology, 345–348

when to terminate, 343–345

transmission coefficient, 328

uniform transmission lines, 243–244

voltage on signal line, 242–243

zeroth-order model, 256

transmitted waves, 622

transparent interconnect, 636–638

trends in electronic products, 20–26

TTL (transistor-transistor logic) gates, 331

twisted pair, 261, 599–600

U

UL (Underwriters Laboratory) specifications, 240

undershoot, 321, 356–359

uniform 50-Ohm transmission line, 243–244

cross talk, 479–485

magnitude of S₂₁ for, 644–649

phase of S₂₁ for, 641–644

unintentional discontinuities, 340–342

V

V_a, 494, 498, 525, 579

V_b, 494, 579

V_cc, 698

V_comm. See common signals

V_dd, 694

V_diff. See differential signaling

V_even, 571, 577–578

V_f, 498, 577, 579

V_gb, 195

V_incident, 43, 323, 581

V_inc, 326

V_in, 418–419

V_launched, 273

V_L, 481–482

V_noise, 186, 216, 694

V_n, 525–526

V_odd, 571, 577–578

V_one, 541–542, 549–550

V_output, 273

V_PDN, 689

V_reflected, 43, 323, 581

V_ripple, 689

V_t, 333

V_trans, 326

values, capacitor, 748–753

Vdd rail, 4

vector-network analyzers (VNAs), 43–44, 57, 433, 622

velocity

dispersion, 416–417

of electrons in copper, 245–247

of signals

even-mode state, 573–578

in lossy transmission lines, 415–417

odd-mode state, 573–578

in transmission lines, 247–251

vias. See also center-to-center separation

blind vias, 448–449, 672

buried vias, 448–449, 672

effects of, 361–367

loop inductance of via contacts, 211–214

microvias, 672

multiple, 198–199

shorting vias, 209, 214, 516–517

victim net, 457. See also cross talk

VNAs (vector-network analyzers), 43–44, 57, 433, 622

voltage components

even-mode, 570–572

odd-mode, 570–572

voltage on signal line, 242–243

voltage regulator modules (VRMs), 4, 701, 703–706

volume resistivity, 138

VRMs (voltage regulator modules), 4, 701, 703–706

W

waveforms. See also S-parameters

anti-symmetric, 64

bandwidth

clock frequency and, 78–80

definition of, 69

of interconnects, 85–88

of measurements, 80–82

of models, 83–84

of real signals, 77–78

rise time and, 68–73

clock period, 52–53

Fourier transforms, 60–62

DFT (discrete Fourier transform), 60–61

FFT (fast Fourier transform), 61

FI (Fourier integral), 60

inverse Fourier transform, 66–68

impulse response, 677–679

reflected waveforms, simulating, 335–337

reflected waves, 622

rise time, 52–54

significant components, 68–73

spectrum of ideal square wave, 64–66

spectrum of repetitive signal, 62–63

step edge, 677–679

TDT (time-domain transmitted) waves, 622

transmitted waves, 622

wavelets, 54

wavelets, 54

Webers, 178–181

“windowing” filters, 62–63

wiring delay, 251

X

X2Y Attenuators, 775

X2Y capacitors, 722, 775–776

XAUI, 26

Y

Youngman, Henny, 28

Youngman Principle, 28

Z

Z₀. See characteristic impedance

Z_capacitors, 754

Z_cap, 357

Z_comm, 568, 586, 598

Z_diff, 542–545, 552, 566

Z_DUT, 43

Z_even, 568, 586

Z_inductor, 373

Z_odd, 566

Z_PDN, 689, 694

Z_target, 689, 694, 705, 713, 754, 757, 759, 760, 763, 782, 791

zeroth harmonic, 65

zeroth-order models, 256