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
50-Ohm transmission line
75-Ohm transmission line, 640
AN-905 National Semiconductor application note, 552
86100 DCA (Agilent), 339–340, 362, 365–367, 371
Adiel, 646
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
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
characteristic impedance, 297–300
FEXT (far-end cross talk), 498–503
loop inductance, 202–204, 724–733
lossy transmission line modeling, 405–413
numerical-simulation tools, 41
parallel plate approximation, 152–153
resistance of interconnect, 133–136
Archambeault, Bruce, 37
asymmetry in differential pairs, 539, 584, 590–595, 599, 600, 673–674
attenuation, 645
attenuation per length, 432
coax cables, 264
high-frequency components, 70–71
AWG (American wire gauge), 138
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
definition of, 69
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
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
bound charges, 105
broadside-coupled stripline, 557, 559–560
BT (bismaleimide triazine), 165
bulk decoupling capacitors, 158, 705, 715–716, 749–751, 754, 767, 786
bulk dielectric constant, 169–171
bulk resistivity, 135, 136–137, 388
bus noise, 504–505, 508, 510–511
BWclock, 80
BWsig, 312
BWTL, 439
C10, 467
C12, 467, 519, 545–550, 609, 611
C24, 467
C30, 467
Cbulk, 705
Ccorner, 364
Cfilled, 169
CL, 159–164, 255, 258, 285, 292–295, 364, 376, 408, 413, 425, 494, 608
Cmax, 359
Cm, 481
Codd, 609
calculation, creating models from, 36–41
capacitance
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
effective dielectric constant, 168–171
effects of corners and vias, 361–367
Maxwell capacitance matrix, 471–477
mutual capacitance, 461
parallel plate approximation, 152–153
polarization current, 150
between power and group planes, 156–158
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
electrolytic capacitors, 702, 704–705, 749
IDCs (interdigitated capacitors), 774–776
MLCC (multilayer ceramic chip capacitors), 703, 717–721, 786
PRF (parallel resonant frequency), 746–747, 760–762
reverse aspect ratio capacitors, 773
tantalum capacitors, 702, 704–705
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
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
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
circuit ground, 240
circuit model. See models and modeling
circuit topology, 115, 121–126
circular magnetic-field lines, 176–181
clearance holes
antipad clearance holes, 448–449, 690
clock frequency
coax cable, 261
capacitance per length, 160
unbalanced nature of, 244
collapse of the eye, 681
combining capacitors in parallel, 740–745
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
complex dielectric constant, 432
complex impedance of inductor, 114
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
copper, 179
copper puddle, 764
current distributions, 220–229
loop self-inductance, 39, 203–204
permeability of the conductor, 229–231
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
volume resistivity, 138
speed of electrons in, 245–247
copper puddle, 764
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
to other transmission lines, 649–656
tightly coupled differential pairs, 607–608
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
dielectric constant and, 519–520
equivalent circuit model, 464–466
FEXT (far-end cross talk)
ideal differential pairs, 579–580
fringe fields, 460
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
ideal differential pairs, 579–580
quiet net/victim net, 457
reducing, 528
SPICE capacitance matrix, 467–471
in uniform transmission lines, 479–485
CSPs (chip-scale packages), 10
CTLE (continuous-time linear equalizer), 451
current distributions
damping, 652–653, 752, 785–787
data mining S-parameters, 661–663
dB. See decibels (dB)
DCA86100 (Agilent), 12
decibels (dB)
decision-feedback equalization (DFE), 452
decoupling capacitance, 156–158, 715–717
decreasing FEXT (far-end cross talk), 503–505
delay
delay adders
capacitive delay adders, 359–361
definition of, 360
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
device under test (DUT), 42–43, 623–626
DFE (decision-feedback equalization), 452
DFT (discrete Fourier transform), 60–61
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
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
reorientation of permanent electric dipoles, 394–396
dielectric spectroscopy, 398
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
differential impedance
EMI (electromagnetic interference), 595–600
even-mode impedance
calculating from capacitance- and inductance-matrix elements, 608–612
definition of, 565
FEXT (far-end cross talk), 573–578
ideal differential pairs, 506, 579–580
odd-mode impedance
calculating from capacitance- and inductance-matrix elements, 608–612
definition of, 565
proximity effect, 547
return-current distribution, 555–561
differential signaling, 664
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
differential S-parameters, 663–668, 675–676
differential TDR (DTDR), 582
digital multimeters (DMMs), 267
DIP (dual in-line package), 243
dipole moment, 397
dielectric constant and, 154–155
dipole moment, 397
dissipation factor and, 396–405
discontinuity, 321–323. See also reflections
definition of, 8
inductive discontinuities, 370–375
unintentional discontinuities, 340–342
discrete Fourier transform (DFT), 60–61
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
earth ground, 240
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
electrolytic capacitors, 702, 704–705, 749
electromagnetic (EM) simulators, 29–33
electromagnetic compatibility (EMC), 3–6
electromagnetic interference. See EMI (electromagnetic interference)
electronic product trends, 20–26
EM (electromagnetic) simulators, 29–33
embedded microstrips, 170
EMC (electromagnetic compatibility), 3–6
EMI (electromagnetic interference), 4, 17–19
sources of, 95
emulation. See simulations
epoxy resin, 155
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
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)
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
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
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
high frequency, 229
Nyquist frequency, 25
PRF (parallel resonant frequency), 746–747, 760–762
SRF (self-resonant frequency), 207
definition of, 720
frequency domains
bandwidth
definition of, 69
bandwidth and rise time, 68–73
current distributions
definition of, 54
FDTIM (Frequency-Domain Target Impedance Method), 766–772
DFT (discrete Fourier transform), 60–61
FFT (fast Fourier transform), 61
FI (Fourier integral), 60
inverse Fourier transform, 66–68
anti-symmetric, 64
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
garbage in, garbage out (GIGO), 35
GigaTest Labs Probe Station, 45, 362, 365–367, 371
GIGO (garbage in, garbage out), 35
Green’s function of the interconnect, 679
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
ground lines. See return paths
ground plane capacitance, 156–158
hacking interconnects, 622–623
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
Ia, 525
Icomm, 598
Ileakage, 393
Ipeak, 696
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
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
frequency variation of, 314–316
of lossy transmission lines, 413–415
odd-mode characteristic impedance, 566
controlled-impedance interconnect, 256
controlled-impedance lines, 243–244, 259–262
differential impedance
discontinuity, 8
equivalent electric circuit model, 115–117
even-mode impedance
calculating from capacitance- and inductance-matrix elements, 608–612
definition of, 565
FDTIM (Frequency-Domain Target Impedance Method), 766–772
in frequency domains, 57, 109–114
impact on chip-package combination, 785–789
impedance profiles, sculpting, 766–772
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
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
SPICE (Simulation Program with Integrated Circuit Emphasis), 706–707
target impedance, 688–689, 691–700, 763–765
in time domains
impedance discontinuities. See discontinuity
inductance
cavity spreading inductance, 724, 738, 769
current distributions, skin depth and, 220–229
definition of, 175–176, 219, 235
effective inductance, 181, 193–199, 220
equivalent inductance, 220
equivalent inductance of multiple inductors, 216–219
ESL (equivalent series inductance), 208, 721–724
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
PDN (power distribution network) and, 204–209
of planes and via contacts, 211–214
of planes with field of clearance holes, 214–215
magnetic-field lines
direction of, 177
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
definition of, 219
partial mutual inductance, 192
partial self-inductance, 187–191, 220
sheet inductance, 727
spreading inductance, 212–213, 777–785
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
InfiniBand, 26
input ports, 625
input/output buffer interface (IBIS) models, 34–35
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
capacitance
capacitive delay adders, 359–361
capacitive end terminations, 353–356
capacitive loads in middle of trace, 356–359
coax cable, 160
effective dielectric constant, 168–171
effects of corners and vias, 361–367
Maxwell capacitance matrix, 471–477
mutual capacitance, 461
parallel plate approximation, 152–153
polarization current, 150
between power and group planes, 156–158
SPICE capacitance matrix, 467–471
Green’s function of the interconnect, 679
analytical approximation for, 133–136
bulk resistivity, 135, 136–137, 388
conductor resistance and skin depth, 387–392
resistance per length, 138–139
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
inverse Fourier transform, 66–68
IPDs (integrated passive devices), 125–126
IR drop, 688
ISI (intersymbol interference), 10–11, 381, 382–385
ITRS ( International Technology Roadmap for Semiconductors), 21–22
kb. See backward cross-talk coefficient
kf, 498
Kapton, 398
Keysight PLTS, 33
Keysight Technology ADS (Advanced System Designer), 101
knee frequency, 74
Leven, 611
LL, 292–295, 369, 376, 408, 413, 425, 494, 498, 608
LLoop, 200–203, 210, 478, 724–727
Lmax, 373
Lmutual, 478
Lparallel, 218
Lself, 39
Lself-return, 478
Lself-signal, 478
Lseries, 218
Lstub-max, 352
Lvia, 436
Laguerre polynomials, 55
lead, 179
leading edge, spatial extent of, 251–252
Legendre polynomials, 55
Lenstub, 671
length
Lentz’s Law, 490
line drivers, 274
approximations, 202–204, 724–733
definition of, 219
inductance per square, 210–211
loop mutual inductance, 216, 219
loop self-inductance, 219
PDN (power distribution network) and, 204–209
of planes and via contacts, 211–214
of planes with field of clearance holes, 214–215
loop mutual inductance, 219
loop self-inductance, 219
loop spreading inductance, 729–731
lossy transmission lines, 381–382
acceptance mask, 384
attenuation
attenuation per length, 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
reorientation of permanent electric dipoles, 394–396
dissipation factor, 396–405, 432
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
lossless model, 385
low-loss approximation, 410–413
measured properties of, 433–438
radiative loss, 386
rise-time degradation, 385–387, 442–444
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
magnetic-field lines
direction of, 177
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
measurement-based modeling, 121–126
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
causal models, 155
creating models from calculation, 36–41
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
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
loop mutual inductance, 216
partial mutual inductance, 220
Nunique, 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
ideal differential pairs, 579–580
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
dielectric constant and, 519–520
equivalent circuit model, 464–466
FEXT (far-end cross talk), 462–464, 496–505, 573–578, 579–580
fringe fields, 460
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
SPICE capacitance matrix, 467–471
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
ISI (intersymbol interference), 10–11
signal-integrity generalizations, 19–20
skew
definition of, 11
effects of, 11
non-50-Ohm transmission lines, insertion loss for, 655–661
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
OC (optical carrier) spec, 25
odd waveforms, 64
odd-mode impedance
calculating from capacitance- and inductance-matrix elements, 608–612
definition of, 565
Ohmmeter, 268
Ohm’s Law, 103
on-die core power rail, 4
optical carrier (OC) spec, 25
optimizing mounting of capacitors, 733–739
orthonormal functions, 55
output ports, 625
Pmax, 696
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
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
decoupling capacitors, 715–717
electrolytic capacitors, 702, 704–705, 749
IDCs (interdigitated capacitors), 774–776
MLCC (multilayer ceramic chip capacitors), 703, 717–721, 786
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
design guidelines for, 690–691, 772–777, 789–792
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
target impedance, 688–689, 691–700, 763–765
IR drop, 688
loop inductance, 204–209, 724–733
parallel resonant peak, 741, 746–747
PRF (parallel resonant frequency), 746–747, 760–762
product PDN requirements, 700–701
SRF (self-resonant frequency)
definition of, 720
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
loop inductance
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
Polyimide, 398
port-labeling convention, 650
ports
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)
PQFP (plastic quad flat pack), 30–31, 135
PRBS (pseudorandom bit sequence), 680
PRF (parallel resonant frequency), 746–747, 760–762
processors
single-chip microprocessor-based systems, 21
product-design methodology
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
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
RAC, 406
rb, 151
RHF, 227
Rleakage, 393
RL, 142, 406, 408, 411, 413, 425–427
Rseries, 407
Rshunt, 407
Rsource, 273
Rs, 333
Rterm, 543
Rt, 333
radians, 109
radiative loss, 386
rail collapse
definition of, 205
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
best design practices, 8
capacitive delay adders, 359–361
from capacitive end terminations, 353–356
from capacitive loads in middle of trace, 356–359
definition of, 7
effects of corners and vias, 361–367
from inductive discontinuities, 370–375
reflected waveforms, simulating, 335–337
reflection coefficient, 323–324, 328–331
from short series transmission lines, 348–351
from short-stub transmission lines, 351–353
transmission line termination
strategy for point-to-point topology, 345–348
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
resistance per length, 138–139
resistor elements, 98
volume resistivity, 138
resistive loads, reflections from, 328–331
resistor elements, 98, 102–103
resonance
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
switches of reference planes, 278–291
return-current distribution, 555–561
reverse aspect ratio capacitors, 773
review questions and answers, 819
ripple, 205–207, 640, 647, 658, 669, 688–700
rise time
capacitive loads in middle of trace, 356–359
impedance and, 94
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
round-trip time of flight, 270–271
RT. See rise time
RTinterconnect, 87
RTsignal, 444
s. See center-to-center separation
S12, 631
S32, 663
S33, 662
S42, 662
SdB, 624
Smag, 624
Ss, 676
scalar-network analyzers, 622
scattering parameters. See S-parameters
SCSI (small computer system interface), 268
sculpting impedance profiles, 766–772
second harmonic, 63
second-order models, 116
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
Semiconductor Industry Association (SIA), 20–26
sheet inductance, 210–211, 727
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 effects, rules to estimate, 805
lossy transmission lines, 415–417
signal-to-noise ratio (SNR), 57
silicone, 398
Simulation Program with Integrated Circuit Emphasis. See SPICE (Simulation Program with Integrated Circuit Emphasis)
AC simulations, 118
numerical-simulation tools, 41
QUCS (Quite Universal Circuit Simulator), 118
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
definition of, 69
first harmonic, 63
inverse Fourier transform, 66–68
second harmonic, 63
waveforms
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 mask, 170, 300, 503, 569–570
source-series termination, 345–348
balanced S-parameters, 663–668
Cartesian plots, 627
coupling to other transmission lines, 649–656
differential S-parameters, 663–668
eye diagrams, 680
frequency behavior of, 627
differential insertion loss, 668–672
for non-50-Ohm transmission lines, 655–661
transparent interconnect, 636–639
uniform transmission lines, 644–649
mixed-mode S-parameters, 663–668, 675–676
mode conversion terms, 672–674
polar plots, 627
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
transmission coefficient, 631
transparent interconnect, 636–638
uniform 50-Ohn transmission line, 641–644
spatial extent of leading edge, 251–252
spectrum of waveform
spheres, capacitance of, 150–152
SPICE (Simulation Program with Integrated Circuit Emphasis), 32–33, 117–121, 706–707
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
SSC (spread spectrum clocking), 4
SSN (simultaneous switching noise). See ground bounce (switching noise)
SSO (simultaneous switching output), 12
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
surface-mount technology (SMT), 123–126
switching noise. See ground bounce (switching noise)
Tclock, 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
TDadder, 374
TDLoad, 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
Teledyne LeCroy SI Studio, 33
Teraspeed Consulting Group, 765
termination
differential signaling, 583–590
reflections from capacitive end terminations, 353–356
source-series termination, 345–348
strategy for point-to-point topology, 345–348
third-order models, 116
tightly coupled differential pairs, 607–608
time delay (TD), 250, 349, 521–524
bandwidth
definition of, 69
DFT (discrete Fourier transform), 60–61
FFT (fast Fourier transform), 61
FI (Fourier integral), 60
inverse Fourier transform, 66–68
impedance
inverse Fourier transforms, 66–68
lossy transmission line behavior, 445–448
waveforms
anti-symmetric, 64
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
transforms
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
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
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
active net/aggressor net, 457
capacitively coupled currents, 485–489
causes of, 94
dielectric constant and, 519–520
equivalent circuit model, 464–466
FEXT (far-end cross talk), 462–464, 496–505, 573–578, 579–580
fringe fields, 460
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
SPICE capacitance matrix, 467–471
in uniform transmission lines, 479–485
differential pairs
asymmetry in, 539, 584, 590–595, 599, 600, 673–674
characteristic impedance matrix, 612–615
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
FEXT (far-end cross talk), 573–578
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
differential signaling, 533–537
converting to common signals, 590–595
peak-to-peak value, 537
earth ground, 240
ideal coupled transmission-line model, 579–580
instantaneous impedance, 252–259, 269
lossless model, 385
lossy transmission lines, 381–382
acceptance mask, 384
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
dissipation factor, 396–405, 432
insertion loss, 433, 631–635, 636–639, 644–649, 655–661, 668–672
ISI (intersymbol interference), 381, 382–385
low-loss approximation, 410–413
measured properties of, 433–438
radiative loss, 386
return loss, 433
rise-time degradation, 385–387, 442–444
nonuniform transmission lines, 243
n-section lumped-circuit models, 306–314, 385, 406
capacitive delay adders, 359–361
from capacitive end terminations, 353–356
from capacitive loads in middle of trace, 356–359
effects of corners and vias, 361–367
from inductive discontinuities, 370–375
reflected waveforms, simulating, 335–337
reflection coefficient, 323–324, 328–331
from short series transmission lines, 348–351
from short-stub transmission lines, 351–353
unintentional discontinuities, 340–342
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
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
UL (Underwriters Laboratory) specifications, 240
uniform 50-Ohm transmission line, 243–244
unintentional discontinuities, 340–342
Vcc, 698
Vcomm. See common signals
Vdd, 694
Vdiff. See differential signaling
Vgb, 195
Vinc, 326
Vlaunched, 273
Voutput, 273
VPDN, 689
Vripple, 689
Vt, 333
Vtrans, 326
Vdd rail, 4
vector-network analyzers (VNAs), 43–44, 57, 433, 622
velocity
of electrons in copper, 245–247
of signals
in lossy transmission lines, 415–417
in transmission lines, 247–251
vias. See also center-to-center separation
loop inductance of via contacts, 211–214
microvias, 672
shorting vias, 209, 214, 516–517
victim net, 457. See also cross talk
VNAs (vector-network analyzers), 43–44, 57, 433, 622
voltage components
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
waveforms. See also S-parameters
anti-symmetric, 64
bandwidth
definition of, 69
DFT (discrete Fourier transform), 60–61
FFT (fast Fourier transform), 61
FI (Fourier integral), 60
inverse Fourier transform, 66–68
reflected waveforms, simulating, 335–337
reflected waves, 622
spectrum of ideal square wave, 64–66
spectrum of repetitive signal, 62–63
TDT (time-domain transmitted) waves, 622
transmitted waves, 622
wavelets, 54
wavelets, 54
wiring delay, 251
X2Y Attenuators, 775
XAUI, 26
Youngman, Henny, 28
Youngman Principle, 28
Z0. See characteristic impedance
Zcapacitors, 754
Zcap, 357
ZDUT, 43
Zinductor, 373
Zodd, 566
Ztarget, 689, 694, 705, 713, 754, 757, 759, 760, 763, 782, 791
zeroth harmonic, 65
zeroth-order models, 256
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