[hree phase, 6S5-687 lEC 10m,603-ft04 IEEE/ANSI sianJard 519, 604 Impedance graph pjper, 310 Inductor copper loss (rff Copper Joss) Inductor Current ripple

in at inductor, 527-528

boost example, 25-26

buck esiiniple, 19

calculation of, 19

in converters containing two-pole fillers, 31-33

converter example, 30-31 in fiher inductor, 525-526 magnitude vs DCM, 108-110 Inductor design

ac inductor design

derivation, 580-581

step-by-slep procedure, 582-583 filter indLLCtor design

derivation, 539-544

step-by-slep prucedure, 544-545 Inductor voll-seconJ balance boost example, 24 buck example, 21 Cuk converter example, 28-29 definition, 20

in Jisconliniious conduction mode, 112 Input filters, 377-408, 857-859 cascaded filter sections, 398-404

noninteraction, impedanceinequalities lor, 398-399

two-secdon design example, 400404 conducted EMI, allenuatiun of, 377-378 conducted suscepltbtlily, 378 damping of 391-404

Rf-C), parallel damping, 394, 395-396 parallel damping, 394, 396-397

RfLt series damping, 394 , 398 effect on conlrol-to-outpul transfer function

buck example, 380, 389-392

general result, 381-382

negative resistance oscillations, 382-384

results tor basic converters, 382

right half-plane zeroes, 390 impedance inetjualities for design

construction of, buck example, 385-389

conlrol-lo-oulput transfer funclion, to avoid changing, 384

output impedance, Ui avoid changing, 385 Inpul port, converler ac modeling of, 197

boosl static characlertstics, 643-644, 655-656

modeling of, via slate-space averaging, 222, 225-226

steady-slale modeling of, 50-52 Inrush current, 646, 665, 676 Insulated-gale bipolar transistor (IGBT)

construction and operation of, 86-88

current tailing in, 87-88, 95-96

equivalent circuii, 87

forward voliage drop, modeling of, 88

idealized switch characlerisdcs, 65-66

parallel operation of, 88

switching loss in, 95-96, 768 Inversion of source and load, 132-133 Inverters, 1

high frequency, 705-709, 727-729, 732-739

line conimutated, 619

single phase, 7, 68-69, 138-141

sinusoidal analysis of resonani converters, 709-715,

726-740 three phase, 69-72, 141-143 Iron laminations, 495, 507

fC, dimensionless parameter

criticalvalue :* (D). 110-112, 116-117, 124 and DCM boundary, 110-112, 116-117, 124 in line-commutated rectifier analysis, 612-613 in sleady-stale DCM analysis, 117, 123-124

K, core geometrical constant definition of, 543-544, 863 ferrile core tables of, 864-869 filter inductor design procedure using, 544-545 multiple winding magnetics design using, 545, 552-554

H, ac core geometrical constant

ac induclor design procedure using, 580-583 definition of, 569-570, 863 ferrile core tables of, 864-869 transformer design using, derivation, 565-570 examples, 573-580 step-by-step procedure, 570-573 Kj, rectifier dimensionless parameter, 612-613 window uttliiiation factor,542

LCC resonani converter

dependence of transistor current on load, 732-733

design example, 737-740

introduction lo, 705-707

ZVS/ZCS boundary, 734-737 Lenzs law, 493, 506, 508, 510

Linear ripple approximation {see Small ripple approximation)

Llne-lij-imlpuL Lriinsfer funtlicm (J\,{f)

of lhe buck, boost, and buck-boost converters in

CCM, 300 canonical model, as predicted by. 248 closed-loop, 334-335, 339-340 conlro! system design of, 347-348, 361-362 of Current-programmed converters, 454, 464-466,

469471, 480 of DCM converters, 427

Litz wire, 522

Loop gain {see also Control .-iy.tem de.sign. Negative feedback) deftailton, 335 measurement of, 362-36S Loss-free resistor model

averaged switch model of dtsconltnuous conduction

mode, 413420 ideal rectifier model

stnglepha.se, 638-640

three phase, 685-686 Low harmonic rectifiers [see also Ideal reclifiers) controller schemes

average currenl control, 648-654

current programmed control, 654-656

critical conduction mode, 657-659

feedforward, 650-652

hysteredc control. 65759

nonlinear carrier control, 659-663 modeling of

efficiency and losses, 678-685

low-bandwidth control loop, 668-673

wide-bandwidth average current control loop, 652-654 rms calculations in, 673-678 Low Q approximation, 287-289

Magnetic circuits, 498-501 Magnetic field И, 491-492 Magnetic path length

definition, 497

ferrite core tables, 864-867 Magnetics, 489-586

ac inductor design, 580-583

basic relationships, 491498

copper loss, 42-45. 508, 510-525

core loss, 42, 506-508, 561-562

coupled inductor design, 550-557

ferrite core tables. 864-867

flyback Iransformer design, 557-562

inductor design, 539-562

inductor design, multiple winding, 550-562

magnetic circuits, 498-501

magnetic devices, types of, 525-531 optimizing Ul minimize total los.s, 569-570 optimizing window allocation to minimize copper

loss, 545-550 proximity effeci, 508-525 transformer basics, 146-149, 501-505 Iransformer design, 565-583

Magnetizing current, 147-148, 502-504

Magnett>motive force (MMF) definition, 491-492 magnetic circuit, in, 498499 MMF diagrams, 512-514

Majority carrier devices (see also MOSFET, Schottky diode), 74-75

Matrix converter, 72-73

Meal length per turn [MLT] definition, 543 ferrile core tables, 864-867

Measurement of transfer functions and loop gains [see Experimental techniques)

Middlebrooks extra element theorem (see Extra element theorem)

Minority carrier devices {see also Bipolar junclion transistor. Diode, Gale lurn-off thyristor, Insulated-gale bipolar transistor, MOS-conlrolled thyristor, Silicon controlled rectifier), 74-75

Modulation index, 689-690

MOS-controlled thyristor (MCT), 91-92

MOSFET

body diode, 67-68, 78-79

conduction loss, modeling of, 52-56, 204-213 , 816-819

con.struttion and operation of. 78-81

on resistance, 52-56, 78-81

swilching loss owing lo С , 98-99, 765-768

as synchronous rectifier, 73-74

terminal capacitances, 80-81

lypical characteristics, 80-81

zero-vollage and zero-current swilching of, 721-726,

765-768 Motor drive system, 8-9

Multiplying contfoller (see also Average currenl control, Current programmed control), 648-659

Multi-resonant switch, 784-786

Negative feedback [see also Control system design) effects of, on network transfer functions. 334-337 objectives of. 187,331-334 reduction of disturbances by, 335-337 reduction of sensidvily lo variations in forward gain by, 337

Nonlinear carrier control, 659-663

Nonrainimura-phase zero {лее Right half-plane zero)

Oulpul charatLerislios

oflhe parallel resonani oonverler. 750

of resonani inverters, 727-729

of Ihe Series resonani eonvener, 747-748

Overshoot, 346-347, 348

Parallel resonani eonverler

analysis via sinusoidal approjiiraalion, 7)8-72) dependence of Iransislttr current on load, 730-731 es.ael characlerislics

continuous conduction mode, 748-751

control plane, 751

discontinuous conduction mode, 749-751 ouiput plane, 750

introduction to, 705-706 Permeability Ц

definition, 494495

of free space, Ц, 494

relative, p 495 Phase asymptotes

ol complex poles, 284-285

inverted forms, 278

of real pole, 272-274

of real /еп), 275

of RHP zero, 276 Phase control

of resonant converters, 705

of Ihree-phase rectifiers, 6)7-622

of zero-voltage transition dc-dc converter, 791-794 Phase margin

vs. closed-loop damping facior, 342-346

inpul filler, undamped, effecl on, 390-391

stability (est, 341-342 Poles

complex. Bode plots of, 282-286

the low Q approximation, 287-289

real. Bode plots of, 269-274 Pol core data, 864 Powdered iron, 495, 507

Power facior [see also Total harmonic distortion. Displacement factor. Distortion facior) definition of, 594-598

of bridge recdfier, single phase, 597, 6)0-6)3 of peak deteclton rectifier, 597 of phase-conlro)led reclifier, three phase, 616, 619-620

Power sink elemeni Isee Power source element) Power source elemeni

in averaged switch models

current programmed mode, CCM, 454-457

current programmed mode, DCM, 475-477 discontinuous conduction mode, 414-430 definidon of, 415-416

in ideal reclilier mode), 638-640, 646-647, 650, 666,

668-670, 686 linearization of, 383-384,423424, 457, 668-671 in loss-free resistor model, 416-417, 639-640 properties of, 415-416

in switched-mode regulators, 383-384,455, 665-666 PQ core data, 867 Proximity effecl

Conductor spacing facUjr Г], 5l5

interleaving, effect on, 520-522

layer copper loss, 515-517

Litz wire, effect of, 522

MMF diagrams, 512-514

PWM waveform harmonics, 522-525

simple explanation, 5Q8-512

trans former design procedure, accounting for, 572

winding loss, lolal, 518-520 PSpice {see Simulation) Pulse width modulation (PWM), 4-6

modulator ac model, 253-255

operation of modulator, 253-255

spectrum of PWM waveform, 188-189 Push-pull isolated converters

based on boost converler, 167-168

based on buck converter, 159-160, 441

Walkins-Johnson converler, 167-168

Q facior, 283-286

canonical model, predicted by, 300 closed-loop, vs. phase margin, 342-346 oflhe CCM buck, boost, and buck-boost converters, 300

graphical determination of, 307, 310, 312, 3)4

the low Q approximation, 287-289

vs. overshoot, 346-347

of parallel resonant circuii, 309-3)0

of series resonani circuit, 305-307 Quasi-re.sonanl converters {see also Mu)[i-resonant

switch, Quasi-st]uare-wave switch)

zero-current switching dc-dc full wave, 779-781 half wave, 768-779

zero-voltage .switching dc-Jc, 783-784 Quasi-square-wave converters, 787-790 Quasi-static approximation, 653-654 Quiesceni operaiing point, 190-191, 198,2205

Reactance graph paper {xee Impedance graph paper) Reactive power