AC coupling

constant capacitors, 490

direct-conversion receivers, 183–184, 187

transformers, 470

Acceptable quality, 59

Accumulation-mode MOS varactors, 486

Accuracy

DAC, 739

I/Q calibration, 232

inductor equations, 438–439

input matching, 72

integer-N frequency synthesizers, 656

output matching, 73

ACPR in power amplifiers, 756–758

Acquisition range of PLLs, 611, 614

with current-source helpers, 393–394

downconversion, 368–369

conversion gain, 370–377

double-balanced, 369–370

linearity, 387–392

noise, 377–387

with enhanced transconductance, 394–397

with high IP_{2}, 397–405

with low flicker noise, 405–408

upconversion, 416–420

design procedure, 421–424

mixer carrier feedthrough, 420–421

ADCs (analog-to-digital converters) in receivers

AGC range, 836

baseband, 858–859

direct-conversion, 186

resolution, 837

Additive noise

AM, 94

conversion to phase noise, 550–552, 554

I/Q mismatches, 198

Adjacent-channel interference

GSM, 135

IEEE802.11, 149

low-IF receivers, 214

ADS simulator, 439

AGC in receivers

design, 856–861

range, 836–837

Aliasing

passive downconversion mixers, 360–361

power amplifiers, 798

Aligned resultants in AM signals, 97

Alignment of VCO phase, 600–601

AM (amplitude modulation), 93–94

direct-conversion receivers, 189–190

heterodyne receivers, 172–173

AM/AM conversion, 757–758

AM/PM conversion (APC)

concepts, 33–35

polar modulation, 794–795, 799–801

power amplifiers, 757–758

Ampere’s law, 452

Amplitude

direct-conversion receivers, 196

in modulation, 92

oscillators, 505–507

power amplifiers, 757–758

VCO variation, 532

Amplitude modulation (AM), 93–94

direct-conversion receivers, 189–190

heterodyne receivers, 172–173

Amplitude shift keying (ASK), 100, 105

Analog modulation, 93

amplitude, 93–94

phase and frequency, 95–99

Analog-to-digital converters (ADCs) in receivers

AGC range, 836

baseband, 858–859

direct-conversion, 186

resolution, 837

Analysis and Simulation of Spiral Inductors and Transformers (ASITIC) simulator, 437–439

Analytic signals, 202

AND gates

current-steering circuits, 683

dual-modulus dividers, 677, 880

phase/frequency detectors, 613–614

Antennas

cellular systems, 122

duplexing method, 130

LNA interface, 258–259

Anti-phase coupling, 582, 584–586, 592

APC (AM/PM conversion)

concepts, 33–35

polar modulation, 794–795, 799–801

power amplifiers, 757–758

ASITIC (Analysis and Simulation of Spiral Inductors and Transformers) simulator, 437–439

ASK (amplitude shift keying), 100, 105

Asymmetries

cascode power amplifiers, 817

direct-conversion receivers, 179, 181, 187–189

heterodyne receivers, 172–174

I/Q mismatches, 194

LO self-mixing, 357

sequence-asymmetric polyphase filters, 221

single-balanced mixers, 398–399

Attenuation

channel, 92

image, 224–225

Auxiliary amplifiers in PLLs, 634–635

Available noise power, 42

Available power gain, 54

Average power in noise, 36

Axis of symmetry, inductors along, 465

Balance systems, 12

Baluns

differential LNAs, 315–324

outphasing, 810

power amplifiers, 758–760, 764, 767

Band-pass filters

differential LNAs, 315

FDD, 123–124

heterodyne transmitters, 244–245

Q, 157

transceivers, 158–159

transmitter overview, 156

Band selection in transceivers, 157–159

Band switching LNAs, 262, 312–314

divide-by-2 circuits, 693–696

efficiency, 93

fractional, 176

frequency synthesizers, 663, 842–843, 883

offset PLLs, 672

outphasing, 805

passive upconversion mixers, 410–411

PLL-based modulation, 667–668

polar modulation, 794, 801–802

QPSK, 107

VCO phase noise, 645–646

Barkhausen’s criteria, 503–505, 512, 544, 583

Baseband

ADC resolution, 858–859

AGC gain, 859

DACs, 409

description, 91–92

offset, 414

outphasing, 804

polar modulation, 796–797

QPSK signals, 108–109

Basic design concepts, 7

dynamic range, 60–62

noise. *See* Noise and noise figure (NF)

nonlinear dynamic systems, 75–77

nonlinearity. *See* Nonlinearity

passive impedance transformation, 62–63

matching networks, 65–71

quality factor, 63

series-to-parallel conversions, 63–65

scattering parameters, 71–75

time variance, 9–12

units, 7–9

Volterra series, 77–85

Basis functions, 105

BER. *See* Bit error rate (BER)

Bias

LNA common-gate stage, 280–281

LNA nonlinearity calculations, 325–326

phase noise current source, 565–570

Bipolar transistor noise, 46

GSM, 132

I/Q mismatch, 198

power amplifiers, 756

receiver noise, 834

transmitters, 838

wireless standards, 131

Blind zones with VCOs, 535–536, 846, 869

Blocking

Bluetooth tests, 145–146

GSM requirements, 133–134

with interferers, 19

wideband CDMA, 140–142

Bluetooth standard

frequency channels, 655

GFSK for, 113

ISM band, 130

LOs, 660

overview, 143–147

receivers, 22–24

Bode plots

charge pumps, 619–620

PLLs, 608–609

cascode CS stage, 284–285

coupling between, 430–431

MOS capacitors, 491

outphasing, 810

power amplifiers, 755, 758–759, 815

Bootstrapping, cascode power amplifiers with, 816–817

Bottom-biased PMOS oscillators, 573

Bottom-plate capacitance

inductors, 440

parallel-plate capacitors, 494

Brickwall spectrum, 103

Broadband model of inductors, 457

Broadband noise, 670–671

Buffers

LOs, 380–381, 413, 499, 576–577

Bypass, LNA, 312

Calibration of image-reject receivers, 213

Capacitance and capacitors

constant, 490–495

divide-by-2 circuits, 690, 692, 694–696

inductors, 437, 439–444, 461–463, 466–469

input impedance, 9

integer-N synthesizer loop design, 883–885

large-signal impedance matching, 780–781

LNAs

band switching, 312–313

common-gate stage, 280–282

common-source stage, 269–271, 286–287, 291–293

differential, 321

gain switching, 308–309

input, 851

matching networks, 65–69

metal-plate, 493–495

Miller dividers, 703

mixers

downconversion, 352, 376–377, 382–383, 500

with enhanced transconductance, 395–397

with high IP_{2}, 398, 403–404

port-to-port feedthrough, 339–340

upconversion, 410, 415–416, 422

MOS, 491–493

oscillators, 571

cross-coupled, 514–515

drive capability, 498–499

outphasing, 808–810

parallel-plate, 493–495

phase noise, 555–557

PLL higher-order loops, 625–626

power amplifiers, 754

cascode, 815–817

class B, 765

class E, 772–774

polar modulation, 792, 795–796

positive-feedback, 819–820

predrivers, 864

quality factor, 63

T-lines, 477

transformers, 470–475

varactors, 483–490

VCOs. *See* Voltage-controlled oscillators (VCOs)

divide-by-2 circuits, 692

integer-N synthesizers, 692, 700, 704

LNA feedback paths, 304

LO interface, 576–577

power amplifiers, 865

substrate loss, 450–452, 457–458, 466

transformers, 470–471, 474–475

Capacitively-degenerated differential pairs, 591

Carrier amplifiers, 811

Carrier feedthrough

active mixers, 420–421

passive mixers, 413–416

Carrier frequency, 91

Carrier leakage

direct-conversion transmitters, 232–234

heterodyne transmitters, 244

Carrier power in phase noise, 539

Cartesian feedback, 786–787

Cascade image rejection, 225

Cascaded loops and modulators, 730–732

Cascaded stages

low-IF receivers, 222

noise figure, 52–56

nonlinear, 29–33

transceiver filters, 158

Cascode stages

LNAs, 284–286

common-gate, 277–279

design procedure, 291–296

differential, 318–321

gain switching, 310–311

noise factor, 287–291

pad capacitance, 286–287

power amplifiers, 776–779, 815–819

CCI (co-channel interference), 120

CCK (complementary code keying), 150

CDMA (code-division multiple access), 126

direct-conversion transmitters, 232–233

direct sequence, 126–129

IS-95, 137–139

wideband, 139–143

Cellular systems, 119–120

antenna diversity, 122

co-channel interference, 120

delay spread, 122–123

hand-offs, 120–121

interleaving, 123

path loss and multipath fading, 121–122

transmitters, 91

Center frequency in LC VCOs, 571

CG (common-gate) stage in LNAs, 272–277

cascode stage, 277–279

design procedure, 279–284

gain switching LNAs, 306

variants, 296–300

CG differential LNAs, 315–318

Chang-Park-Kim dividers, 878, 880

Channel charge injection, 631

Channel-length modulation

charge pumps, 633–634

LNA common-gate stage, 275

Channel selection

vs. image rejection, 166–168

transceiver architectures, 157–159

Channelization standards, 130

Channels

attenuation, 92

integer-N synthesizers, 656, 661, 664

mixer bandwidth, 500

mobile RF communications, 119

overlapping frequencies, 150

Characteristic impedance

coplanar lines, 482

microstrips, 479–482

striplines, 483

Charge-and-hold output in charge pumps, 616

Charge equations for varactors, 487

Charge injection, 630–632

Charge pumps, 614–615

channel-length modulation, 633–634

charge injection and clock feedthrough, 630–632

fractional-N synthesizers, 733–738

integer-N synthesizers, 883–884

regulated cascodes, 634–635

Chips, CDMA, 127–128

Chireix’s cancellation technique, 808–809

Circuit simulators

integer-N synthesizers, 884–886

power amplifiers, 757

varactors, 487

Circular inductors, 435

Clapp oscillators, 517

Class A power amplifiers

with harmonic enhancement, 771–772

overview, 760–764

Class-AB latches, 691

Class AB power amplifiers, 767

Class B power amplifiers, 764–767

Class C power amplifiers, 768–770

Class E power amplifiers, 772–775

Class F power amplifiers, 775–776

Clock feedthrough, 630–632

Close-in phase noise, 539–540

Closed-loop control

IS-95 CDMA, 138

polar modulation, 793

Closed-loop transfer functions

integer-N synthesizers, 666

CML (current-mode logic), 683–687

CMOS technology, 2–3

LNA common-gate stage, 275

oscillator frequency range, 498

ring oscillators, 507

Co-channel interference (CCI), 120

Code-division multiple access (CDMA), 126

direct-conversion transmitters, 232–233

direct sequence, 126–129

IS-95, 137–139

wideband, 139–143

Cognitive radios, 199

Coherent detection

IS-95 CDMA, 137

QPSK, 110

Collector efficiency in power amplifiers, 755, 761, 766

Colpitts oscillators, 517

Common-gate (CG) stage in LNAs, 272–277

cascode stage, 277–279

design procedure, 279–284

gain switching LNAs, 306

variants, 296–300

Common-mode current in mixers, 373–374

Common-mode input in LOs, 349

Common-mode noise

active downconversion mixers, 383

active mixers with low flicker noise, 405

Common-mode stability in power amplifiers, 866–867

Common-source stages

LNAs

with inductive degeneration, 284–296

with inductive load, 266–269

with resistive feedback, 269–272

memoryless systems, 12

Communication concepts, 91

analog modulation, 93–99

considerations, 91–93

digital modulation. *See* Digital modulation

DPSK, 151–152

mobile RF, 119–123

multiple access techniques, 123–130

spectral regrowth, 118–119

wireless standards. *See* Wireless standards

Compact inductor model, 458

Comparators in power amplifiers, 824

Compensation in fractional-N synthesizers, 718

Complementary code keying (CCK), 150

Compression

gain, 16–20

LNAs, 851–852

in mixer linearity, 388–392

power amplifiers, 757–758, 863–864

receivers, 856

upconverters, 868–869

wideband CDMA, 140

Concentric cylinders model, 457

Conduction angles, 764, 768–769

Constant capacitors, 490–495

Constant-envelope modulation, 112

Constant-envelope waveforms, 802

Constellations

dense, 114–115

signal, 105–112

Continuous-time (CT) approximation

charge pumps, 616

type-II PLLs, 622–623

Continuous tuning, VCOs with, 524–532

Hartley receivers, 253

Miller dividers, 701–703

mismatches, 226

mixers

current-source helpers, 393

downconversion, 339, 348, 350–356, 368–382

linearity, 388–391

power amplifiers, 790

upconversion, 409–410, 414, 416, 868

Conversions

additive noise to phase noise, 550–552, 554

AM/AM, 757–758

AM/PM

concepts, 33–35

polar modulation, 794–795, 799–801

power amplifiers, 757–758

current and voltage, 368–369

series-to-parallel, 63–65

Convolution in phase noise, 560–561

Coplanar lines, 482–483

Cosine signals in image-reject receivers, 200

Cost trends, 2

Counters in pulse swallow dividers, 674–676

Coupled oscillators, 583–589

between bond wires, 430

capacitance. *See* Capacitive coupling

magnetic. *See* Magnetic coupling

quadrature oscillators, 581, 590

CPPLLs (charge-pump PLLs), 615–620

continuous-time approximation, 622–623

frequency-multiplying, 623–625

Cross-coupled oscillators, 511–517

phase noise computation, 555

power amplifiers, 820

tail noise, 565–566

time-varying resistance, 553

Cross-coupled pairs

active mixers with low flicker noise, 406

Norton noise equivalent, 548–549

VCOs, 530–531

Cross modulation

description, 20–21

wideband CDMA, 140–141

Cross-talk, 229

Crystal oscillators

integer-N synthesizer design, 881

phase noise, 644

CT (continuous-time) approximation

charge pumps, 616

type-II PLLs, 622–623

Current crowding effect, 448–450

Current domain in single-balanced mixers, 356

Current-driven passive mixers, 366–368

Current impulse

oscillators, 509

in phase noise, 557–559

Current mirroring

active mixers, 395–396

DACs, 741

divide-by-2 circuits, 692

VCOs, 874–876

Current-mode DAC implementation, 741

Current-mode logic (CML), 683–687

Current sources

helpers, 393–394

offset cancellation by, 186

power amplifiers, 752

Current-steering

cross-coupled oscillators, 517

divider design, 683–689

mixer linearity, 388

prescalers, 682

Current-to-voltage (I/V) characteristic of charge pumps, 883–884

Current-to-voltage (I/V) conversion, 368–369

Currents, nonlinear, 81–85

Cyclostationary noise, 552–553, 565

D flipflops in phase/frequency detectors, 613

DACs (digital-to-analog converters)

direct-conversion receivers, 185–187

direct-conversion transmitters, 233–234

feedforward, 738–742

upconversion mixer interfaces, 409

Damping factor

class E power amplifiers, 773–774

divide-by-2 circuits, 693

integer-N synthesizers, 665–666, 883

PLL transfer functions, 608

Dangling bonds, 44

dBm, 8–9

DC offsets

active mixers with high IP_{2}, 398–400

AGC, 859

direct-conversion receivers, 181–187

port-to-port feedthrough, 340–341

DCOs (digitally-controlled oscillators), 536

DCRs. *See* Direct-conversion receivers

DCS1800 standard, 132

Decibels (dB), 7–9

Degenerated differential pairs, 332–333

Degenerated LNA common-source stages

inductive degeneration, 284–296

nonlinearity calculations, 325–329

Degeneration capacitors, 403–404, 591

Delay spread in cellular systems, 122–123

Delayed replicas in IS-95 CDMA, 138

Delays

fractional-N synthesizers, 723–724

integer-N synthesizers, 665–667

OFDM, 115–117

PFD/CP, 629

polar modulation, 793–794, 801

Delta modulators (DMs), 824–825

Demodulation, 92

IS-95 CDMA, 137

QPSK, 110

Demultiplexers in QPSK, 107

Dense constellations, 114–115

Desensitization, 19

Design

active upconversion mixers, 421–424

basic concepts. *See* Basic design concepts

dividers. *See* Dividers

LNA cascode CS stage with inductive degeneration, 291–296

LNA common-gate stage, 279–284

oscillators, 571–575

power amplifier. *See* Power amplifiers (PAs)

transceiver example. *See* Transceivers

type-II PLLs, 646–647

Despreading in CDMA, 128

DET (double-edge-triggered) flipflops, 742–743

Detectability, 92

Detection, 92

IS-95 CDMA, 137

PFDs. *See* Phase/frequency detectors (PFDs)

phase detectors, 597–600

polar modulation, 794, 799–800, 826

power amplifier linearization, 789–790

QPSK, 110

Deterministic mismatches

fractional-N synthesizers, 737

up and down current, 637

Device noise

bipolar transistors, 46

MOS transistors, 43–46

resistors, 40–43

Differential circuits, symmetric inductors in, 460–461, 463–464

Differential LNAs, 314–315

common-gate, 315–318

common-source, 318–321

Differential LO phases

oscillators, 501

Differential mixers, 402

Differential oscillators, 518, 585, 589

Differential pairs

charge pumps, 632

current-steering circuits, 683

downconversion mixers, 500

input/output characteristics, 12–13

LNAs, 331–332

Differential power amplifiers, 758–760

Differential PSK (DPSK), 151–152

GMSK and GFSK, 112–113

intersymbol interference, 101–104

OFDM, 115–118

overview, 99–100

QAM, 114–115

quadrature, 107–112

signal constellations, 105–107

Digital-to-analog converters (DACs)

direct-conversion receivers, 185–187

direct-conversion transmitters, 233–234

feedforward, 738–742

upconversion mixer interfaces, 409

Digitally-controlled oscillators (DCOs), 536

Dimensions of inductors, 433–434

Diode-connected devices

active mixers with low flicker noise, 405–406

power amplifiers, 816–817

VCOs, 525–526

Direct-conversion mixers, 344

Direct-conversion receivers, 179

DC offsets, 181–187

even-order distortion, 187–191

flicker noise, 191–194

I/Q mismatch, 194–199

LO leakage, 179–184

mixing spurs, 199

noise figure, 346–348

Direct-conversion transmitters, 227–229

carrier leakage, 232–234

I/Q mismatch, 229–232

mixer linearity, 234–235

mixers, 339–342

modern, 238–243

noise, 238

oscillator pulling, 237–238

TX linearity, 235–236

Direct sequence CDMA, 126–129

Direct sequence SS (DS-SS) communication, 127

Discrete-time (DT) systems, 622–623

Discrete tuning in VCOs, 532–536

Distortion

direct-conversion receivers, 187–191

duty-cycle, 398

harmonic. *See* Harmonics and harmonic distortion

intersymbol interference, 101–104

outphasing, 808

power amplifier linearization, 787–788

Distributed capacitance

dividers, 694

inductors, 440

LNA common-source stage, 293

varactors, 488–489

Distributed inductor model, 458

Distributed resistance in varactors, 487–489

Dithering in fractional-N synthesizers, 728

Diversity

antenna, 122

IS-95 CDMA, 138

Divide-by-1.25 circuits, 746

Divide-by-1.5 circuits, 743

Divide-by-2 circuits, 878–880

designing, 689–697

direct-conversion transmitters, 239–240

dual-modulus dividers, 677

heterodyne receivers, 175

Miller dividers, 706–707

pulse swallow dividers, 675–676

true single-phase clocking, 697–698

Divide-by-2/3 circuits

dual-modulus dividers, 679

pulse swallow dividers, 676–677

Divide-by-3 circuits

dual-modulus dividers, 677–678

Miller dividers, 706–707

Divide-by-3/4 circuit, 680, 881–882

Divide-by-4 circuits, 177–178

Divide-by-8/9 circuit, 680

Divide-by-15/16 circuit, 681–682

Dividers, 673–674

divide-by-2 circuit, 878–880

divider delay and phase noise, 709–712

dual-modulus, 677–682, 880–881

frequency multiplication, 609–611

injection-locked, 707–709

LO path, 499

logic styles, 683

current-steering circuits, 683–689

divide-by-2 circuits, 689–697

true single-phase clocking, 697–699

Miller, 699–707

prescaler modulus, 682–683

pulse swallow, 673–677

DMs (delta modulators), 824–825

Doherty power amplifiers, 811–813, 818–819

Double-balanced mixers, 348–350

active downconverters, 369–370

active upconverters, 416

capacitive degeneration, 403–404

input offset, 399–400

Miller dividers, 700

passive downconverters, 351–352

passive upconverters, 411, 414

polar modulation power amplifiers, 826

sampling, 356

voltage conversion gain, 377

Double-edge-triggered (DET) flipflops, 742–743

Double-quadrature downconversion

low-IF receivers, 224–226

Weaver architecture, 213

Double-sideband (DSB) mixers, 867

Double-sideband (DSB) noise figure, 344, 853

Double-transformer topology, 822

Down currents and pulses

charge pumps, 614–615, 630–633, 635–637

fractional-N synthesizers, 733–734

integer-N synthesizers, 883

PLL higher-order loops, 625, 627

quantization noise, 739

Down skew in PFD/CP, 627–630

Downbonds, 285

Downconversion and downconversion mixers, 339

active, 368–369

conversion gain, 370–377

double-balanced, 369–370

linearity, 387–392

noise, 377–387

design, 851–856

heterodyne receivers, 160–164, 168–170

image-reject receivers, 206, 210

LO ports, 500

low-IF receivers, 219–221, 224–226

noise figures, 343

passive, 350

current-driven, 366–368

gain, 350–357

input impedance, 364–367

LO self-mixing, 357

noise, 357–364

phase noise, 540–541

and self-corruption of asymmetric signals, 173–175

Weaver architecture, 213

Downlinks, 119

DPSK (differential PSK), 151–152

DR (dynamic range), 60–62

Drain capacitance in large-signal impedance matching, 780

Drain current

LNA common-gate stage, 280

power amplifiers, 768, 771, 773, 776

Drain efficiency in power amplifiers, 755

Drive capability of oscillators, 498–499

DS-CDMA power control, 128–129

DSB (double-sideband) mixers, 867

DSB (double-sideband) noise figure, 344, 853

DT (discrete-time) systems, 622–623

Dual downconversion, 168–170

Dual-gate mixers, 374

Dual-modulus dividers, 677–682, 880

Dual-modulus prescalers, 674–675

Dummy switches for charge pumps, 631

Duplexer filters

FDD systems, 124

offset PLLs, 671

Duplexers and duplexing methods

antennas, 130

time and frequency division duplexing, 123–124

transceivers, 158–159

Duty cycle distortion, 398

Dynamic dividers, 699–702

with inductive load, 702–705

moduli with, 705–707

Dynamic logic in divide-by-2 circuit, 878

Dynamic nonlinearities, 28

Dynamic range (DR), 60–62

Dynamic systems, 14

Eddy currents in inductors, 448–449, 452–455, 466

EDGE (Enhanced Data Rates for GSM Evolution) systems

description, 136–137

polar modulation, 801–802

Edge-triggered devices

DET flipflops, 742–743

phase/frequency detectors, 612–613

EER (envelope elimination and restoration), 790–793

Efficiency

modulation, 93

power amplifiers, 755–756

class AB, 767

class B, 764–767

class C, 768–771

class E, 772–775

class F, 775–776

8-PSK waveforms, 136–137

Electrostatic discharge (ESD) protection devices, 280

Embedded spirals

high-IP_{2} LNAs, 323–324

transformers, 471

Encoding operations in DS-CDMA, 127

End points in fractional-N synthesizers, 736

Enhanced Data Rates for GSM Evolution (EDGE)

description, 136–137

polar modulation, 801–802

Enhanced transconductance, active mixers with, 394–397

Envelope-controlled loads, 793

Envelope detection

polar modulation, 794, 799–800, 826

power amplifier linearization, 789–790

Envelope elimination and restoration (EER), 790–793

Envelopes

polar modulation, 793, 795, 825–826

power amplifier linearization, 788–790

QPSK, 110

Error cancellation loops, 783

Error vector magnitude (EVM)

description, 106–107

receivers, 838

ESD (electrostatic discharge) protection devices, 280

Even-order harmonics, 15, 187–191

EVM (error vector magnitude)

description, 106–107

receivers, 838

Excess frequency, 95

Excess phase in VCOs, 581

Excessive noise coefficient, 43

Exclusive-NOR (XNOR) gates, 152

Exclusive-OR (XOR) gates

current-steering circuits, 685–686

phase detectors, 598–599

PLLs, 603

reference doubling, 743

Expansive characteristic, 17

Extrapolation, intermodulation, 27

Fading, multipath, 121–123

Far-out phase noise

description, 539–540

offset PLLs, 672

Faraday’s law

inductors, 448

magnetic coupling to substrate, 452

Fast Fourier Transform (FFT), 391

FDD (frequency-division duplexing), 123–124

FDMA (frequency-division multiple access), 125

Feedback

direct-conversion transmitters, 232–233

dividers. *See* Dividers

fractional-N synthesizers, 716, 718–720, 722–723, 725

integer-N synthesizers, 661

LNAs

common-gate, 296–297

gain switching, 311

noise-cancelling, 300–301

resistance, 851

offset cancellation by, 185

oscillators, 502–508, 513, 582–584

polar modulation, 793, 798–800

power amplifiers, 759, 783, 786–787

VCO phases, 601

Feedforward

common-gate LNAs, 298–300

gain switching LNAs, 311

power amplifier linearization, 783–786

quantization noise, 738–742

Feedthrough, mixer

active upconversion, 420–421

passive upconversion, 413–416

port-to-port, 339–343

FFT (Fast Fourier Transform), 391

FH (frequency hopping) in CDMA, 129–130

Field simulations for inductors, 439

Figure of merit (FOM) of VCOs, 570–571

Filters, 101

active mixers with high IP_{2}, 402

Bluetooth, 143–144

differential LNAs, 315

direct-conversion receivers, 179, 184

duplexer, 124

FDD, 123–124

fractional-N synthesizers, 716, 738

front-end band-pass, 124

heterodyne transmitters, 244–245

integer-N synthesizers, 665

LNAs with high-IP_{2}, 323–324

low-IF receivers, 217–224

low-pass, 101

polar modulation, 824–826

power amplifier linearization, 790

Q, 157

transceivers, 157–159

transmitter overview, 156

First-order dependence in AM/PM conversion, 34

First-order *Σ Δ* modulators, 726

Flat fading, 123

Flat phase noise profiles, 644

Flicker noise, 44–45

active mixers

with current-source helpers, 394

downconversion, 385–387

low, 405–408

direct-conversion receivers, 191–194

low-IF receivers, 215

passive downconversion mixers, 366

quadrature oscillators, 591–592

receiver design, 853–854

VCOs, 642

Floating resonators in VCOs, 531

Floating switches in VCOs, 535, 870

FM (frequency modulation), 95–96

frequency synthesizer spurs, 843–844

heterodyne receivers, 173

narrowband approximation, 96–98

FNSs. *See* Fractional-N synthesizers (FNSs)

FOM (figure of merit) in VCOs, 570–571

Forward channels, 119

Four-level modulation schemes, 92

Fourier coefficients

cascode output stages, 776

power amplifiers, 770

Fourier series

flicker noise, 563–564

LO waveforms, 368

reference doubling, 743–744

VCOs, 580

Fourier transforms

fractional-N synthesizers, 716–717

mixer gain, 352–353

mixer impedance, 364

power spectral density, 37

quantization noise, 748–749

VCO sidebands, 628

Volterra series, 77–81

Fractional bandwidth

IF, 176

LNA systems, 262

Fractional dividers, 742–743

Fractional-N synthesizers (FNSs), 715

basic concepts, 715–718

basic noise shaping, 722–728

charge pump mismatch, 733–738

higher-order noise shaping, 728–732

modulus randomization, 718–721

out-of-band noise, 732–733

quantization noise, 738–749

Fractional spurs, 716

Free-running VCOs, 655

Frequencies. *See also* Bandwidth

cellular system reuse, 119–120

divide-by-2 circuits, 693–694

injection-locked dividers, 709

integer-N synthesizers, 664, 881

LNAs, 259

bandwidth, 261–263

cascode stage, 294–296

common-gate stage, 278–279

Miller dividers, 704

mixers. *See* Mixers

oscillators, 497–498, 503–507, 514, 517

PLLs, 605–606

polar modulation, 794

system-level considerations, 844–848

VCOs, 519–520, 526, 532, 571, 600

wireless standards, 130

Frequency-dependent phase shift, 504, 507

Frequency-dependent values, 73

Frequency detectors (FDs) in PLLs, 602

Frequency deviation, 95

Frequency diversity

cellular systems, 122

IS-95 CDMA, 138

Frequency division, multiphase, 745–748

Frequency-division duplexing (FDD), 123–124

Frequency-division multiple access (FDMA), 125

Frequency hopping (FH), 129–130

Frequency-locked loops (FLLs), 602

Frequency modulation (FM), 95–96

frequency synthesizer spurs, 843–844

heterodyne receivers, 173

narrowband approximation, 96–98

Frequency multiplication, 609–611, 623–625

Frequency noise, 732

Frequency responses

LNA systems, 262

oscillators, 512

VCO phase noise, 645

Frequency-selective fading, 123

Frequency shift keying (FSK), 100

direct-conversion receivers, 184, 197–198

noise, 105–106

PLLs, 605–606

Frequency synthesizers, 498

fractional-N. *See* Fractional-N synthesizers (FNSs)

integer-N. *See* Integer-N synthesizers

system-level considerations, 840–844

Friis’ equation

LNAs, 264

Fringe capacitance in inductors, 439–440, 461, 463

Fringe capacitors

parallel-plate capacitors, 495

VCOs, 529–530

Front-end band-pass filters, 124

Front-end band-select filters, 158

FSK (frequency shift keying), 100

direct-conversion receivers, 184, 197–198

noise, 105–106

PLLs, 605–606

Full-duplex LNA systems, 260–261

Full scale in dynamic range, 60

Fully-integrated power amplifiers, 770

Fundamentals in harmonic distortion, 15, 34

Gain

AGC

design, 856–861

range, 836–837

conversion. *See* Conversion gain

current-steering circuits, 686

Miller dividers, 703

oscillators, 504–507

transmitter, 838–839

Gain compression, 16–20, 388–392

Gain error in DACs, 741

Gain mismatch

direct-conversion receivers, 196

direct-conversion transmitters, 231–232, 241

image-reject receivers, 209

Gain switching

LNAs, 305–312

receivers, 837

Gap capacitance, 466–467

Gate capacitance

divide-by-2 circuits, 692

power amplifiers, 815

Gate-induced noise current, 43–44

Gate-referred noise voltage, 256

Gate switching in PLLs, 636

Gaussian distribution, 122

Gaussian filters

Bluetooth, 143–144

impulse response, 112

Gaussian frequency shift keying (GFSK)

Bluetooth, 143

description, 112–113

direct-conversion transmitters, 234–235

Gaussian minimum shift keying (GMSK)

Bluetooth, 143

description, 112–113

direct-conversion transmitters, 234–235

Generic transmitter upconversion requirements, 408

Gilbert cell in upconversion mixers, 418

Global System for Mobile Communication (GSM)

adjacent-channel interference, 135

blocking requirements, 133–134

description, 132–133

EDGE, 136–137

intermodulation requirements, 134–135

G_{m} oscillators, 516–517

GMSK (Gaussian minimum shift keying)

Bluetooth, 143

description, 112–113

direct-conversion transmitters, 234–235

Ground inductances in LNAs, 260, 281

Grounded shield inductors, 435, 466–467

GSM. *See* Global System for Mobile Communication (GSM)

GSM/EDGE mask margins, 801

Hand-offs

cellular systems, 120–121

IS-95 CDMA, 139

Handheld units, 119

Hard transistors, 776

Harmonics and harmonic distortion, 14–16

AM/PM conversion, 34

class A power amplifiers, 771–772

class E power amplifiers, 775

class F power amplifiers, 775–776

direct-conversion transmitters, 241

heterodyne transmitters, 244–246

narrowband systems, 25

phase noise, 564–565

Hartley architecture

calibration, 213

image-reject receivers, 205–210

low-IF receivers, 215–216

Heterodyne receivers, 160–161

dual downconversion, 168–170

high-side and low-side injection, 164–166

image problem, 161–164

image rejection, 166–168

mixers, 342

sliding-IF, 174–178

zero second IFs, 171–174

Heterodyne transmitters, 244

carrier leakage, 244

mixing spurs, 245–248

HFSS simulator for inductors, 439

High currents in power amplifiers, 754–755

High-efficiency power amplifiers, 770

class A, 771–772

class E, 772–775

class F, 775–776

High IP_{2}, mixers with, 397–405

High-IP_{2} LNAs, 313–314

differential, 314–315

common-gate, 315–318

common-source, 318–321

improvement methods, 323–324

direct-conversion receivers, 184

image-reject receivers, 203, 206

LNAs with high-IP_{2}, 323–324

mixers with high IP_{2}, 402

High-side injection, 164–166

Higher harmonics in phase noise, 564–565

Higher-order noise shaping, 728–732

Higher-order PLL loops, 625–627

Hilbert transform

image-reject receivers, 201, 203–206

low-IF receivers, 215–217

Hold-mode noise, 359–362

Homodyne architecture, 179

HPFs. *See* High-pass filters (HPFs)

HSPICE simulator for varactors, 487

I/Q mismatches

frequency planning, 848

transmitters, 229–232, 241, 244, 839–840

I/V (current-to-voltage) characteristic of charge pumps, 883–884

I/V (current-to-voltage) conversion, 368–369

IEEE802.11a/b/g standard, 147–151

IF (intermediate frequency)

heterodyne receivers, 160–162, 168–169

low-IF receivers, 214–217

zero second, 171–178

IF ports, 337

IIP3 (input third intercept points), 26

ILDs (injection-locked dividers), 707–709

IM. *See* Intermodulation (IM)

Image issues

heterodyne receivers, 161–164, 166–168

low-IF receivers, 224–225

Image-reject receivers (IRRs), 200, 838

90° phase shift, 200–205

calibration, 213

Hartley architecture, 205–210

low-IF, 215–217

Weaver receivers, 210–213

Image-to-signal ratio, 208

Impedance, 9

charge pumps, 634–635

coplanar lines, 482

current sources, 634–635

divide-by-2 circuits, 692–693

downconversion mixers, 500

large signals, 780–781

matching networks, 69

microstrips, 479–482

power amplifiers, 780–782, 809, 812–813, 821

T-lines, 478

Impedance transformation

passive, 62–63

matching networks, 65–71

quality factor, 63

series-to-parallel conversions, 63–65

power amplifiers, 753

Impulse sensitivity function in phase noise, 559, 563

IMT-2000 air interface, 139–143

In-band blockers in GSM, 133

In-band interferers, 158

In-band loss, 158

In-band noise in fractional-N synthesizers, 728

In-channel IP_{3}, 835

In-loop PLL modulation, 667–669

In-phase coupling, 582, 585, 588, 592

Incident waves, 71–73

basic structure, 431–434

capacitive coupling to substrate, 450–452, 457–458

cross-coupled oscillators, 514

divide-by-2 circuits, 692–696

equations, 436–439

geometries, 435

with ground shields, 466–467

LNAs

common-gate, 281

common-source, 266–269, 291, 294

differential, 320–322

parasitic, 260

loss mechanisms, 444–455

magnetic coupling to substrate, 452–455, 457–458

metal resistance, 444–448

Miller dividers, 702–705

mixers

enhanced transconductance, 396–397

passive upconversion, 412–413

modeling, 455–460

off-chip, 430–431

one-port oscillators, 511

outphasing, 808–810

parasitic capacitances, 439

power amplifiers, 752–755, 765–767, 815, 817

skin effect, 448–450

stacked, 467–470

symmetric, 460–466

T-lines, 477

Inductive degeneration in LNAs, 284–296, 310

Industrial-scientific-medical (ISM) band, 130

Infradyne system, 164

Injected noise, 562–563

Injection-locked dividers (ILDs), 707–709

Injection-locked power amplifiers, 820–821

Injection locking in quadrature oscillators, 592–593

Injection pulling between oscillators, 237, 589

Input capacitance

cross-coupled oscillators, 514

power amplifiers, 754, 819, 864

Input impedance, 9

one-port oscillators, 510

PLL-based modulation, 668

Input level range in wireless standards, 131

Input matching

LNAs, 263–266

common-gate, 299

noise-cancelling, 304

power amplifiers, 814

Input/output characteristics of Doherty power amplifiers, 811

Input-referred noise

active downconversion mixers, 381–384, 390

LNAs, 256–257

Input reflection coefficient, 74

Input resistance in LNAs, 308, 851

Input return loss in LNAs, 258–259

Input third intercept points (IIP_{3}), 26

Instantaneous frequency, 95

Integer-N synthesizers, 655, 869

basic, 659–661

considerations, 655–659

dividers. *See* Dividers

loop design, 882–886

PLL-based modulation, 667–673

settling behavior, 661–664

spur reduction techniques, 664–667

VCO design, 869–877

Integration trends, 2

Integrators

DAC, 739–740

fractional-N synthesizers, 723–724, 728

VCOs, 581

Inter-spiral capacitance in inductors, 468–469

Interference

adjacent-channel, 135

co-channel, 120

with compression, 18–19

with cross modulation, 20–21

direct-conversion receivers, 187

high-IP_{2} LNAs, 324

integer-N frequency synthesizers, 657

with intermodulation, 21–23

mixers, 341

transceivers, 156–158

Interleaving in cellular systems, 123

Intermediate frequency (IF)

heterodyne receivers, 160–162, 168–169

low-IF receivers, 214–217

zero second, 171–178

in cascades, 30–33

GSM requirements, 134–135

integer-N frequency synthesizers, 658

overview, 21–25

power amplifiers, 757

between receiver blockers, 835

Intermodulation tests

Bluetooth, 146

wideband CDMA, 142

wireless standards, 131–132

Intersymbol interference (ISI), 101–104, 115–116

Interwinding capacitance in inductors, 440–442, 461–463

Inverse Laplace transform, 621

IP_{2} (second intercept points), 188

IP_{3} (third intercept points), 25–27

IRR (image rejection ratio), 208–209, 212

IRRs. *See* Image-reject receivers (IRRs)

IS-95 CDMA, 137–139

ISI (intersymbol interference), 101–104, 115–116

ISM (industrial-scientific-medical) band, 130

Isolation

LNAs, 260

outphasing, 809

reverse, 72

Jitter in divider design, 711

L-section topologies, 67–68

Laplace transform

charge pumps, 615–617

PLL transient response, 621

Large-signal impedance matching, 780–782

Latches

current-steering circuits, 686–689

divide-by-2 circuits, 878–879

Latchup in mixers, 406–407

Lateral-field capacitors, 529

Lateral substrate currents, 452

Layout parasitics in divide-by-2 circuit, 879

LC oscillators

cross-coupled, 511–517

LO swings, 366

open-loop Q, 545–546

phase noise, 501

Leakage

direct-conversion receivers, 179–184

direct-conversion transmitters, 232–234

heterodyne transmitters, 244

LNA systems, 261

polar modulation, 802

Least mean square (LMS) algorithm, 234

Leeson’s Equation, 547

Lenz’s law, 452

L’Hopital’s rule, 769

Limit cycles in fractional-N synthesizers, 728

Limiting stage in polar modulation, 794–795

Line-to-line inductor spacing, 463

Linear amplification with nonlinear components (LINC), 802–803

Linear drain capacitance, 780

Linear model of oscillators, 548–549

Linear power amplifiers, 110

Linear systems, 9

LNAs, 260–261

nonlinearity. *See* Nonlinearity

power amplifiers, 756–758, 782–783

Cartesian feedback, 786–787

Class A, 761–762

envelope detector, 794

envelope feedback, 788–790

feedforward, 783–786

predistortion, 787–788

LMS (least mean square) algorithm, 234

LNAs. *See* Low-noise amplifiers (LNAs)

LO. *See* Local oscillator (LO)

Load capacitance

divide-by-2 circuits, 696

Load design for class E power amplifiers, 772

Load inductors in divide-by-2 circuits, 696

Load-pull tests, 781–782

Load switching in LNAs, 311

Local envelope feedback, 793

Cartesian feedback, 787

coupling in power amplifiers, 760

direct-conversion receivers, 179–184

direct-conversion transmitters, 237–240

drive capability, 499

frequency synthesizers, 656–657, 660, 840

heterodyne receivers, 160–164, 170–172, 176–177

heterodyne transmitters, 244–246

ideal waveforms, 349–350

interface, 575–577

leakage, 179–184, 341–342, 357

LO-IF feedthrough, 340

mixers

buffers, 413

with high IP_{2}, 398

with low flicker noise, 407–408

single-balanced and double-balanced, 348–350

upconversion, 413–416

off-chip inductors, 430–431

offset PLLs, 673

on-off keying transceivers, 248–249

outphasing mismatches, 805

output waveforms, 501

phase noise, 540–542

polar modulation, 798

ports

pulling, 846

swings, 366

VCO phases, 746

Lock range in injection-locked dividers, 707–709

Lock time in integer-N synthesizers, 658–659, 885–886

Logic styles in divider design

current-steering circuits, 683–689

divide-by-2 circuits, 689–697

true single-phase clocking, 697–699

Loops

integer-N synthesizers, 663, 881–886

oscillator gain, 504–507

phase-locked. *See* Phase-locked loops (PLLs)

VCO phase noise, 645–646

Losses

inductors, 444–455

matching networks, 69–71

microstrips, 480–482

Lossy circuits, noise in, 42, 56–58

Lossy oscillatory systems, Q in, 459

Lossy tanks in one-port oscillators, 509–510

Low-frequency beat in active mixers, 402–403

Low-frequency components in phase noise, 569

Low-IF receivers, 214–217

double-quadrature downconversion, 224–226

polyphase filters, 217–224

Low-noise amplifiers (LNAs), 255

common-gate stage. *See* Common-gate (CG) stage in LNAs

common-source stage

with inductive degeneration, 284–296

with inductive load, 266–269

with resistive feedback, 269–272

design, 849–852

gain switching, 305–312

heterodyne receivers, 166, 169, 174–175

high-IP_{2}. *See* High-IP_{2} LNAs

input matching, 263–266

input return loss, 258–259

linearity, 260–261

noise-cancelling, 300–303

noise computations, 49–51

noise figure, 255–257

nonlinearity calculations, 325

degenerated common-source stage, 325–329

degenerated differential pairs, 332–333

differential and quasi-differential pairs, 331–332

undegenerated common-source stage, 329–330

power dissipation, 263

reactance-cancelling, 303–305

stability, 259–260

Low-noise VCOs, 573–575

Low-pass filters, 101

direct-conversion receivers, 179

fractional-N synthesizers, 716

image-reject receivers, 203, 206

noise, 40

polar modulation, 824–826

power amplifier linearization, 790

Low-pass signals in direct-conversion receivers, 189–190

Low-side injection

heterodyne receivers, 164–166

image-reject receivers, 211–212

Lumped capacitance

interwinding, 462

substrate, 453

transformers, 472

MOS capacitors, 491

MOS varactors, 487–489

MOSFETs, 44

Lumped resistance of varactors, 487–488

along axis of symmetry, 465

and coupling capacitance, 475

eddy currents, 466

plots, 433–434

to substrate, 452–455, 457–459

Make-before-break operations, 139

MASH architecture, 732

Matching networks, 62–63. *See also* Mismatches

losses, 69–71

passive impedance transformation, 65–69, 752–753

power amplifiers, 752–753, 814

high currents, 755

large-signal, 780–782

power combining, 821

Mathematical model for VCOs, 577–581

MATLAB for power amplifiers, 757

Memoryless systems, 12

Metal losses in inductor modeling, 455

Metal-plate capacitors, 493–495

Metal resistance in inductor Q, 444–448

Metastability in divider design, 711

Microstrips, 479–482

Microwave theory, 71

Miller dividers, 699–702

with inductive load, 702–705

moduli with, 705–707

Miller multiplication, 291–292

Mirror symmetry in inductors, 464

active mixers with high IP_{2}, 400

antenna/LNA interface, 258–259

fractional-N synthesizers, 733–738

I/Q

frequency planning, 848

transmitters, 229–232, 241, 244, 839–840

image-reject receivers, 209

integer-N synthesizers, 883

LNAs, 263–266

multiphase frequency division, 746–747

outphasing, 805

passive upconversion mixers, 414

PFD/CP, 627–630

PLL higher-order loops, 625

polar modulation, 793–794

quadrature oscillators, 588–590

receivers, 837–838

up and down current, 632–633, 637, 733–734

active. *See* Active mixers

considerations, 337–338

design, 851–856

direct-conversion receivers, 187–189

direct-conversion transmitters, 234–235, 240–243

double-balanced. *See* Double-balanced mixers

downconversion. *See* Downconversion and downconversion mixers

as envelope detector, 789–790

gain. *See* Conversion gain

harmonic distortion, 15–16

heterodyne receivers, 160–164, 168–170

high-IP_{2} LNAs, 324

injection-locked dividers, 708

and LNA noise, 257

noise and linearity, 338–339

noise figures, 343–348

oscillators. *See* Local oscillator (LO)

passive. *See* Passive mixers

performance parameters, 338–343

phase noise, 566

PLLs, 672–673

polar modulation, 826

port-to-port feedthrough, 339–343

single-balanced. *See* Single-balanced mixers

upconversion. *See* Upconversion and upconversion mixers

Mixing spurs, 338

direct-conversion receivers, 179, 199

heterodyne receivers, 170–171

heterodyne transmitters, 245–248

Mobile RF communications, 119

antenna diversity, 122

cellular systems, 119–120

co-channel interference, 120

delay spread, 122–123

hand-offs, 120–121

interleaving, 123

path loss and multipath fading, 121–122

Mobile stations, 131

Mobile telephone switching offices (MTSOs), 120–121

Modeling

inductors, 455–460

transformers, 475–476

Modems, 92

Modulation, 92–93

AM. *See* Amplitude modulation (AM)

analog, 93–99

digital. *See* Digital modulation

direct-conversion receivers, 184

FM, 95–96

frequency synthesizer spurs, 843–844

heterodyne receivers, 173

narrowband approximation, 96–98

image-reject receivers, 200

intermodulation, 21–29

phase, 95–99

PLL-based, 667–673

polar. *See* Polar modulation power amplifiers

wireless standards, 130

Modulation index, 93

Modulus

dual-modulus, 677–682, 880–881

multi-modulus, 732

prescaler, 682–683

fractional-N synthesizers, 718–721

frequency multiplication, 610–611

MOS capacitors, 491–493

MOS switches, 600

MOS transistors, 43–46

MOS varactors, 485–490, 519–520

MTSOs (mobile telephone switching offices), 120–121

Multi-carrier spectrum in OFDM, 117

Multi-modulus dividers, 732

Multipath fading, 121–123

Multipath propagation, 115–116

Multiphase frequency division, 745–748

Multiple access techniques

CDMA, 126–130

FDMA, 125

TDMA, 125–126

time and frequency division duplexing, 123–124

Multiplexers (MUX)

fractional dividers, 742

frequency planning, 846–847

multiphase frequency division, 745–746

VCOs, 877

Mutual injection pulling between oscillators, 589

NAND gates

current-steering circuits, 683–684

divide-by-2 circuits, 676

divide-by-2/3 circuits, 680

phase/frequency detectors, 614

single-phase clocking, 698

Narrowband FM approximation, 96–98

Narrowband noise, 551

Natural frequency

divide-by-2 circuits, 693

oscillator mismatches, 588

PLLs, 608

Near/far effect in CDMA, 129

Negative feedback systems

noise-cancelling LNAs, 303

oscillators, 502–503

power amplifier linearization, 783

VCO phase in PLLs, 601

Negative-Gm oscillators, 516

Negative resistance

cross-coupled oscillators, 516

LNA systems, 268

one-port oscillators, 509–510

Nested feedforward architecture, 785

90° phase shift

image-reject receivers, 200–205

low-IF receivers, 215–216

NMOS devices

transconductance, 282

transit frequency, 3

VCO cross-coupled pairs, 530

Noise and noise figure (NF), 35–36

AGC, 859

bipolar transistors, 46

cascaded stages, 52–56

CDMA, 127

direct-conversion receivers, 190–191, 346

direct-conversion transmitters, 238

flicker. *See* Flicker noise

fractional-N synthesizers. *See* Fractional-N synthesizers (FNSs)

frequency planning, 846

frequency synthesizers, 840–843

FSK signals, 105–106

IEEE802.11, 149

input-referred, 46–48

LNAs. *See* Low-noise amplifiers (LNAs)

lossy circuits, 56–58

mixers

with current-source helpers, 393–394

in design, 853–854

linearity, 387–392

noise figures, 343–348

overview, 338–339

qualitative analysis, 377–381

quantitative analysis, 381–387

RZ, 357–359

sampling, 359–364

upconversion vs. downconversion, 409

modulus randomization, 718–721

MOS transistors, 43–46

offset PLLs, 670–671

oscillators, 501, 503, 546–548

overview, 48–52

phase. *See* Phase noise

polar modulation, 802

PSK signals, 105

quadrature oscillators, 591–592

quantization. *See* Quantization noise

as random process, 36–37

direct-conversion, 191–194

heterodyne, 169

low-IF, 215

representation in circuits, 46–58

resistors, 40–43

and sensitivity, 59–60

spectrum, 37–39

transfer function, 39–40

Noise-cancelling LNAs, 300–303

Noise floor, 59

Non-delaying integrators, 728

Non-return-to-zero (NRZ) mixers, 352

Nonlinear power amplifiers, 93

AM/PM conversion, 33–35

cascaded stages, 29–33

cross modulation, 20–21

drain capacitance in impedance matching, 780

gain compression, 16–20

harmonic distortion, 14–16

intermodulation, 21–29

degenerated common-source stage, 325–329

degenerated differential pairs, 332–333

differential and quasi-differential pairs, 331–332

undegenerated common-source stage, 329–330

noise relationship to, 387–388

overview, 12–14

PFD/CP, 735–736

receivers, 834–835

Volterra series currents, 81–85

Nonmonotonic error, 736

NOR gates

current-steering circuits, 683–684, 689

dual-modulus dividers, 677–679

synthesizer design, 883

Norton noise equivalent, 40, 548–549

NRZ (non-return-to-zero) mixers, 352

Number of turns factor

metal resistance inductors, 445–446

spiral inductors, 432–434, 436–437, 441–442

Octagonal inductors, 435

OFDM. *See* Orthogonal frequency division multiplexing (OFDM)

OFDM channelization in IEEE802.11, 147–148

Off-chip devices

image-reject filters, 166

inductors, 429–431

Offset frequency

mixers, 853–855

Offset PLLs, 670–673

Offset QPSK (OQPSK), 110

Offsets

active mixers with high IP_{2}, 398–400

AGC, 859

direct-conversion receivers, 181–187

passive upconversion mixers, 414–415

port-to-port feedthrough, 340–341

On-chip devices

ac coupling, 183

high-pass filters, 214

inductors, 179, 320–322, 694, 770

low-pass filters, 179

passive. *See* Passive devices

transformers, 299–300, 821, 826

transmission lines, 829

On-off keying (OOK), 100, 248–249

1–1 cascades, 731

1-dB compression point, 17–18

1/f noise, 44–46

One-port view of oscillators, 508–511, 584

One-sided spectra, 38

OOK (on-off keying), 100, 248–249

Open-loop control

IS-95 CDMA, 138

polar modulation, 793

Open-loop model of cross-coupled oscillators, 545, 547–548

Open-loop modulation, 667

Opposite signs in sidebands, 97–98

OQPSK (offset QPSK), 110

OR gates

current-steering circuits, 684, 689

divide-by-2/3 circuits, 679

divide-by-15/16 circuits, 681

dual-modulus divider, 880

Orthogonal frequency division multiplexing (OFDM)

average power, 235

for delay spread, 147–148

flicker noise, 854

I/Q mismatch, 198

overview, 115–118

in transceiver design, 835, 837–838, 854

Orthogonal messages, 126

Orthogonal phasors, 585

Oscillators, 497

cross-coupled. *See* Cross-coupled oscillators

design procedure, 571–575

drive capability, 498–499

feedback view, 502–508

frequency range, 497–498

integer-N synthesizer design, 881

linear model, 548–549

LO. *See* Local oscillator (LO)

output voltage swing, 498

performance parameters, 497–501

phase/frequency detectors, 613

phase noise. *See* Phase noise

pulling in direct-conversion transmitters, 237–238

quadrature. *See* Quadrature oscillators

three-point, 517–518

VCOs. *See* Voltage-controlled oscillators (VCOs)

Out-of-band blocking

Bluetooth, 146

GSM, 133

transceivers, 157–158

wideband CDMA, 140

Out-of-band noise, 732–733

Out-of-channel IP_{3}, 835

Outphasing power amplifiers

basics, 802–804

design, 826–829

issues, 805–810

Output capacitance

divide-by-2 circuits, 696

mixers, 376

power amplifiers, 819

Output impedance

common-gate LNAs, 298

current sources, 634–635

large signals, 780–781

matching networks, 69

PLLs, 634

power amplifiers, 809

Output matching networks, 69, 814

Output power control, 820

Output voltage swing, 9

flicker noise, 566

oscillators, 498

power amplifiers, 756, 762, 778, 792, 816, 861–863

Output waveforms for RF oscillators, 501

Overdrive voltage, 413

Overlap for blind zones, 536

Overlapping spectra

CDMA, 127–128

IEEE802.11, 150

Packages

coupling between pins, 430

power amplifier parasitics, 755

Pad capacitance, 281, 286–287, 291–293

PAE (power-added efficiency), 756

Parallel inductors, 435

Parallel-plate capacitors, 493–495, 529

Parallel resistance

ideal capacitors, 63

inductor modeling, 455–456

Parameters, scattering, 71–75

Parasitics

active mixers, 396–397

class E power amplifiers, 772

cross-coupled oscillators, 514

divide-by-2 circuits, 694, 879

parallel-plate capacitors, 494

PARs (peak-to-average ratio) in OFDM, 117–118

Partial channel selection, 168

PAs. *See* Power amplifiers (PAs)

Passband signals, 91–92

Passive devices, 429

considerations, 429–431

constant capacitors, 490–495

inductors. *See* Inductance and inductors

modeling issues, 431

transformers. *See* Transformers

transmission lines. *See* Transmission lines (T-lines)

varactors, 483–490

Passive filters, 158

Passive impedance transformation, 62–63

matching networks, 65–71

quality factor, 63

series-to-parallel conversions, 63–65

carrier feedthrough, 413–416

current-driven, 366–368

gain, 350–357

input impedance, 364–367

LO self-mixing, 357

Miller dividers, 704–705

noise, 357–364

upconversion, 409–413

Path loss, 121–122

Patterned ground shields, 466

PCS1900, 132

PDs (phase detectors) in phase-locked loops, 597–600

Peak detection, 790

Peak-to-average ratio (PARs) in OFDM, 117–118

Peak-to-peak voltage swing, 8–9

Peak value, 18

Peaking amplifiers, 811

Performance

high-speed dividers, 690

oscillators, 497–501

power amplifier linearization, 787

trends, 2

Periodic impulse response, 559

Periodic waveforms, low-pass filters with, 101

Periods in phase noise, 536

Perpendicular resultants in FM signals, 97

PFDs. *See* Phase/frequency detectors (PFDs)

Phase detectors (PDs) in PLLs, 597–600

Phase-domain models for PLLs, 607

Phase errors

GSM, 135

PLLs, 600–601, 603–606, 608, 611, 615

QPSK, 108

Phase feedback in polar modulation, 798–799

Phase/frequency detectors (PFDs)

charge pump capacitive cascades, 615–618

fractional-N synthesizers, 718, 734–737

nonidealities, 627

channel-length modulation, 633–634

charge injection and clock feedthrough, 630–632

circuit techniques, 634–638

up and down current mismatches, 632–633

up and down skew and width mismatch, 627–630

voltage compliance, 630

reset pulses, 737

Phase-locked loops (PLLs), 597

charge-pump, 615–620

continuous-time approximation, 622–623

design, 646–647

frequency multiplying CPPLLs, 623–625

higher-order loops, 625–627

in-loop modulation, 667–669

loop bandwidth, 645–646

offset, 670–673

PFD/CP nonidealities. *See* Phase/frequency detectors (PFDs)

phase detectors, 597–600

phase noise, 638–644

polar modulation, 798, 800, 802, 825

transient response, 620–622

type-I. *See* Type-I PLLs

type-II. *See* Type-II PLLs

Phase-locked phase noise profiles, 841

Phase margin of PLLs, 625, 647–651

Phase mismatches

direct-conversion receivers, 196

direct-conversion transmitters, 241

multiphase frequency division, 746–747

Phase modulation (PM)

AM/PM conversion, 33–35

overview, 95–99

power amplifiers, 757

Phase modulation index, 95

divider design, 709–712

frequency planning, 846

frequency synthesizers, 720–723, 732–733, 840–843

offset PLLs, 672

additive noise conversions to, 550–552, 554

basic concepts, 536–539

bias current source, 565–570

computation, 554–555

current impulse, 557–558

effects, 539–543

flicker, 563–564

higher harmonics, 564–565

injected, 562–563

linear model, 548–549

noise shaping, 546–548

Q, 544–546

tail capacitance, 555–557

time-variant systems, 559–561

time-varying resistance, 553–554

reference, 643–644

type-II PLLs, 638–644

VCOs, 570–572, 638–643, 871–875

Phase shift

Miller dividers, 702

offset PLLs, 673

oscillators, 504–505, 507, 512, 591

polar modulation, 794

power amplifier linearization, 787

Phase shift keying (PSK)

quadrature PSK, 107–112

signal constellation, 105–106

spectrum, 103

waveforms, 100

Phases

charge pumps, 616

phase/frequency detectors, 612

polar modulation, 791, 802, 826

QPSK, 109–110

Phasor diagrams, 550

anti-phase coupling, 585–586

in-phase coupling, 585

quadrature oscillators, 587

Piecewise-linear waveforms, 383

Planar transformers, 470, 473–474

PLL-based modulation

in-loop modulation, 667–669

offset PLLs, 670–673

PLLs. *See* Phase-locked loops (PLLs)

PM (phase modulation)

AM/PM conversion, 33–35

overview, 95–99

power amplifiers, 757

PMOS devices

channel-length modulation, 633

charge pumps, 629

cross-coupled pairs, 530–531

dividers, 878

PLLs, 636

surface states, 44

*PN*-junction varactors, 484–486

Polar modulation power amplifiers, 790

basic idea, 790–793

design, 824–826

improved, 796–802

issues, 793–796

Polyphase filters, 217–224

Port-to-port feedthrough, 339–343

Ports, mixer, 337–338

Positive feedback in oscillators, 504

Positive-feedback power amplifiers, 819–821

Power-added efficiency (PAE), 756

Power amplifiers (PAs), 93, 755–756

cascode output stages, 751, 776–779

class AB, 767

class B, 764–767

class C, 768–770

class E, 772–775

class F, 775–776

considerations, 751–754

cascode examples, 815–819

common-mode stability, 866–867

outphasing, 826–829

polar modulation, 824–826

positive-feedback, 819–821

power combining, 821–824

predrivers, 864–865

Doherty, 811–813

efficiency, 755–756

high currents, 754–755

large-signal impedance matching, 780–782

linearity. *See* Linearity and linearization

OFDM, 117

outphasing

basic idea, 802–804

design, 826–829

issues, 805–810

polar modulation. *See* Polar modulation power amplifiers

single-ended and differential, 758–760

Power combining in power amplifiers, 821–824

Power consumption trends, 2

Power control

direct-conversion transmitters, 232–233

DS-CDMA, 128–129

IS-95 CDMA, 138

polar modulation, 801

power amplifiers, 820

Power conversion gain in mixers, 339

Power dissipation

LNAs, 263

oscillators, 501

VCOs, 571

Power efficiency, 93

Power gain, 7–9

Power spectral density (PSD) noise, 37, 44–45

Predistortion, 787–788

Prescaler modulus, 674–675, 682–683

Primary inductances in power amplifiers, 765–767

Primary turns in transformers, 473–474

Program counters in pulse swallow dividers, 674–675

Programmable AGC gain, 859

Propagation

mismatches, 625

multipath, 115–116

PSD (power spectral density) noise, 37, 44–45

Pseudo-random noise, 127

PSK (phase shift keying)

quadrature PSK, 107–112

signal constellation, 105–106

spectrum, 103

waveforms, 100

Pulse-swallow counters, 880, 881

Pulse-swallow dividers, 673–677

Pulsewidth modulation, 386

Q. *See* Quality factor (Q)

QPSK (quadrature PSK) modulation, 107–112

EDGE, 136

phase noise, 542–543

Quadrature amplitude modulation (QAM), 114–115

Quadrature downconversion

heterodyne receivers, 174–175

low-IF receivers, 219–221

Weaver architecture, 213

Quadrature LO phases, 746

Quadrature mismatches, 195

Quadrature oscillators, 581

basic concepts, 581–584

coupled oscillators, 584–589

feedback model, 582–584

improved, 589–592

one-port model, 584

simulation, 592–593

Quadrature phase separation, 216

Quadrature PSK (QPSK) modulation, 107–112

EDGE, 136

phase noise, 542–543

Quadrature upconverters, 227

GMSK, 113

heterodyne transmitters, 247–248

I/Q mismatch, 230–231

passive mixers in, 411

polar modulation, 797–798

Qualitative analysis of mixer noise, 377–381

definitions, 459–460

and frequency, 454

inductors

differential, 463

ground shields, 466–467

metal resistance, 444–447

passive impedance transformation, 63

phase noise, 544–546

polar modulation, 796

quadrature oscillators, 588

varactors, 484, 487, 489, 522–524

VCOs, 534–535

Quantitative analysis of mixer noise, 381–387

Quantization noise, 719–721

basic noise shaping, 722–728

charge pump mismatch, 736–737

DAC feedforward for, 738–742

fractional dividers, 742–743

higher-order noise shaping, 728–732

multiphase frequency division, 745–748

out-of-band, 732–733

reference doubling, 743–745

spectrum, 748–749

Quasi-differential pairs

active mixers with high IP_{2}, 401–402

active upconversion mixers, 416–417

LNAs, 331–332

Quasi-static approximation, 757

Radiation resistance, 42, 49–50

Rail-to-rail operation

LO, 366, 577, 852–853, 867–868

PLLs, 636

VCOs, 877–878

Raised-cosine spectrum, 104

Rake receivers, 138

Random bit streams in low-pass filters, 101

Random mismatches

fractional-N synthesizers, 737

up and down current, 637

Random process, noise as, 36–37

Randomization, modulus, 718–721

Ratioed logic, 878

Rayleigh distribution, 122

RC-CR networks

image-reject receivers, 203, 209–210

low-IF receivers, 215–217

Reactance-cancelling LNAs, 303–305

Receive bands, 157

Receiver/demodulators, 92

Receivers (RX), 848

AGC design, 856–861

AGC range, 836–837

Bluetooth characteristics, 145–147

direct-conversion. *See* Direct-conversion receivers

front ends, 156

heterodyne. *See* Heterodyne receivers

image-reject. *See* Image-reject receivers (IRRs)

input level range, 131

LNA design, 849–852

LNA leakage, 261

low-IF, 214–217

double-quadrature downconversion, 224–226

polyphase filters, 217–224

mixer design, 851–856

nonlinearity, 834–835

sensitivity, 131

simple view, 4–5

system-level considerations, 834–838

tolerance to blockers, 131

wideband CDMA requirements, 140–143

Receiving antenna thermal noise, 42

Reciprocal mixing

frequency synthesizers, 657–658, 840

phase noise, 540

Reconstructed error in quantization noise, 738–739

Reference cycles in fractional-N synthesizers, 716–718

Reference doubling in quantization noise, 743–745

Reference frequency in integer-N synthesizers, 656, 660, 664

Reference phase noise in PLLs, 643–644

Reference sidebands in integer-N synthesizers, 663

Reflected waves, 71–73

Regeneration mode current-steering circuits, 686–688

Regulated cascodes, 634–635

Regulator noise in oscillators, 501

Replicas, IS-95 CDMA, 138

Representation of noise, 46–58

Reset pulses in phase/frequency detectors, 613

Resettable D flipflops, 613

Resistance and resistors

cross-coupled oscillators, 516

ideal capacitors, 63

inductor modeling, 455–456

inductor Q, 444–448

microstrips, 482

one-port oscillators, 509–511

power amplifier loads, 752–753

skin effect, 448–450

T-lines, 477

time-varying, 553–554

varactors, 487–489

Resistance-free coupling with inductors, 470

Resistive-feedback LNAs, 269–272, 849–851

Resistive termination for LNAs, 264

Resolution of ADCs, 837, 858–859

Resonance frequency

inductor equations, 438

VCOs, 519

Response decays in PLLs, 621

Restoration force in phase noise, 544

Retiming flipflops in integer-N synthesizers, 667

Return paths in T-lines, 478

Return-to-zero (RZ) mixers

noise, 357–359

passive downconversion, 350

passive upconversion, 410

Reverse channels, 119

RF chokes (RFC), 752

RF design hexagon, 3

RF-LO feedthrough, 341–343

Ring oscillators

divide-by-2 circuits as, 690–691

injection-locked, 709

waveforms, 507

Ripple

fractional-N synthesizers, 738

integer-N synthesizers, 665, 883, 885–886

power amplifiers, 759

Roaming in cellular systems, 120–121

Roll-off factor, 104

RZ (return-to-zero) mixers

noise, 357–359

passive downconversion, 350

passive upconversion, 410

S (scattering) parameters, 71–75

S/P (serial-to-parallel) converters, 107

Sampling filters in fractional-N synthesizers, 665, 738

Sampling mixers, 352–354

noise, 359–364

passive upconversion, 409–410

Scattering (S) parameters, 71–75

Second intercept points (IP_{2}), 188

Second-order 1-bit *Σ Δ* modulators, 729

Second-order nonlinearity, 29

Second-order parallel tanks, Q in, 460

Secondary images in image-reject receivers, 212

Secondary inductances in power amplifiers, 765–767

Secondary turns in transformers, 473–474

asymmetric signals, 173–175

direct-conversion receivers, 179, 190

Self-oscillation in divide-by-2 circuits, 691

Self-resonance frequency of inductor capacitance, 442

Sense mode for current-steering circuits, 686–687

Sensitivity

overview, 59–60

VCOs, 518

wireless standards, 131

Sequence-asymmetric polyphase filters, 221

Serial-to-parallel (S/P) converters, 107

Series inductance in LNA common-source stage, 291

Series inductors, 435

Series peaking in divide-by-2 circuits, 694–696

Series resistance

ideal capacitors, 63

inductor modeling, 455–456

Series-to-parallel conversions, 63–65

Servo amplifiers in PLLs, 636

Settling behavior in integer-N synthesizers, 661–664

7-cell reuse pattern, 120

SFDR (spurious-free dynamic range), 60–62

Shannon’s theorem, 155

Shift-by-90° operation in image-reject receivers, 200–205

Shot noise, 46

Shunt peaking in divide-by-2 circuits, 694–695

Shunt tail noise in low-noise VCOs, 573

Sidebands

direct-conversion transmitters, 240–243

fractional-N synthesizers, 716

frequency-multiplying PLLs, 624

heterodyne transmitters, 245

integer-N synthesizers, 657, 663

opposite signs in, 97–98

VCO, 628

*Σ Δ* modulators

fractional-N synthesizers, 726–730, 733, 736–738

VCO phases, 748

Signal cancellation loops, 783

Signal constellations, 105–112

Signal-to-noise ratio (SNR). *See* Noise and noise figure (NF)

Signs in sidebands, 97–98

Simulators

integer-N synthesizers, 884–886

power amplifiers, 757

varactors, 487

Sinc pulses, 103–104

Single-balanced mixers, 348–350

input impedance, 365

passive, 351

sampling, 355–356

voltage conversion gain, 377

Single-ended power amplifiers, 758–760

Single-ended stage in differential LNAs, 315–317

Single-ended to differential LNA conversion, 320

Single-sideband (SSB) mixing

direct-conversion transmitters, 240–243

heterodyne transmitters, 247–248

Miller dividers, 706

noise figure, 344

Single-sideband (SSB) transmitters in image-reject receivers, 206

16QAM constellation

description, 114

phase noise, 543

spectral regrowth, 118

64QAM constellation, 115

Skin effect in inductors, 448–450, 457

Sliding-IF receivers, 174–178

Slope of I/O characteristic, 17

SNR (signal-to-noise ratio). *See* Noise and noise figure (NF)

Soft hand-offs in IS-95 CDMA, 139

Software-defined radios, 199

Sonnet simulator, 439

Source-bulk capacitance in LNA common-source stage, 293

Source impedance in noise figure, 50

Source switching in charge pumps, 631

Space diversity in cellular systems, 122

Spectra

amplitude modulation, 94

noise, 37–39

Spectral masks, 130–131

Spectral regrowth, 118–119

Spiral inductors

equations, 436–439

geometries, 435

high-IP_{2} LNAs, 323–324

number of turns factor, 432–434, 436–437, 441–442

overview, 431–434

stacking, 467

transformers, 471

VCOs, 520–521

Split reset pulses, 737

Spread spectrum (SS) communications, 127

Spreading sequence code, 127

Spurious-free dynamic range (SFDR), 60–62

Spurs, 338

direct-conversion receivers, 179, 199

fractional, 716

frequency synthesizers, 843–844

heterodyne receivers, 170–171

heterodyne transmitters, 245–248

integer-N synthesizers, 664–667

Square-wave LOs, 170

SS (spread spectrum) communications, 127

SSB (single-sideband) mixing

direct-conversion transmitters, 240–243

heterodyne transmitters, 247–248

Miller dividers, 706

noise figure, 344

SSB (Single-sideband) transmitters in image-reject receivers, 206

Stability

LNAs, 259–260

power amplifiers, 866–867

Stacked inductors, 467–470

Stacked metal layers in microstrips, 482

Stacked spirals

high-IP_{2} LNAs, 323–324

transformers, 473–474

Stacked transformers

description, 474–475

power amplifiers, 821

Standards, wireless, 130–132

Bluetooth, 143–147

GSM, 132–137

IEEE802.11a/b/g, 147–151

IS-95 CDMA, 137–139

wideband CDMA, 139–143

State diagrams for phase/frequency detectors, 612

Static phase errors in PLLs, 603, 605

Static systems, 12

Step symmetry of inductors, 464

Stern stability factor, 259

Striplines, 483

Subcarriers in OFDM, 117

Substrate

capacitive coupling to, 439–440, 450–452, 457–458

magnetic coupling to, 452–455, 457–459

Superdyne system, 164

Supply sensitivity of oscillators, 501

Surface states, 44

Swallow counters, 674–676, 682, 880, 881

Switch on-resistance of VCOs, 535

Switch parasitics in band switching LNAs, 313

Switch transistors

class E power amplifiers, 772–773

phase noise, 538

VCOs, 534

Switchable stages in polar modulation, 824

Switched capacitors for VCOs, 533, 872

Switching pair current in active mixers, 405, 407

Switching power amplifiers, 772–773

Symbols in QPSK, 107

Symmetric inductors, 435, 460–466, 520–521

Symmetrically-modulated signals, 172

Synchronous AM detectors, 790

Synchronous operation of dual-modulus dividers, 680

Synthesizers

fractional-N. *See* Fractional-N synthesizers (FNSs)

integer-N. *See* Integer-N synthesizers

PLLs, 611

System-level design considerations, 833

frequency planning, 844–848

frequency synthesizers, 840–844

receivers, 834–838

transmitters, 838–840

System specifications for oscillators, 497

T-lines (transmission lines), 476–478

coplanar, 482–483

microstrips, 479–482

striplines, 483

Tail capacitance

phase noise, 555–557

Tail current

cross-coupled oscillators, 513–515

passive upconversion mixers, 412

phase noise, 556

time-varying resistance, 554

VCOs, 525–526, 531–532, 874–875

Tail noise

cross-coupled oscillators, 513, 565–566

Tails coupling in quadrature oscillators, 589

Tapered stages in power amplifiers, 754

TDD (time division duplexing), 123–124

TDMA (time-division multiple access), 125–126

Temperature. *See* Thermal noise

Terminals in mobile RF communications, 119

Terminating resistors in LNAs, 264

Thermal noise, 36

direct-conversion receivers, 191

MOS transistors, 43–46

resistors, 40–43

Thevenin equivalent of divide-by-2 circuits, 695

Thevenin model of resistor thermal noise, 40, 57

Third intercept points (IP_{3}), 25–27

Third-order characteristic, 13

Third-order intermodulation, 22, 31

Three-point oscillators, 517–518

Time constants in PLL transient response, 621

Time-contracted simulation of integer-N synthesizer loops, 884

Time diversity

cellular systems, 122

IS-95 CDMA, 138

Time division duplexing (TDD), 123–124

Time-division multiple access (TDMA), 125–126

overview, 9–12

passive downconversion mixers, 366

phase noise, 559–561

Time-varying resistance in phase noise, 553–554

Time-varying voltage division in outphasing, 808

Timing errors in class E power amplifiers, 773

Tones

fractional-N synthesizers, 727–728

power amplifiers, 756–757

Top-biased VCOs, 525–526

Top current in phase noise, 568–569

Total frequency, 95

Total noise power in phase noise, 541

Total phase

modulation, 95

VCOs, 579

Total stored energy in inductor capacitance, 441

Track-mode noise, 359–361

Tradeoffs in design, 3

channel selection and band selection, 157–159

considerations, 155–157

design example, 833

integer-N synthesizers, 869–886

receivers, 848–861

system-level design. *See* System-level design considerations

transmitters, 861–869

on-off keying, 248–249

receivers. *See* Receivers (RX)

transmitters. *See* Transmitters (TX)

TX-RX feedthrough, 159–160

Transconductance

LNAs

common-gate stage, 279–280, 282

common-source stage, 288–291

differential, 319

gain switching, 306

oscillators, 511

quadrature oscillators, 591

time-varying resistance, 554

VCOs, 875

Transfer functions

fractional-N synthesizers, 722, 724, 728, 732–733

integer-N synthesizers, 661–662, 665–666, 669, 693–696, 709

integrators, 506

noise, 39–41, 544, 569, 638–641, 643

oscillators, 544, 547–548, 562

PLLs, 606–608, 615, 617–620, 622–623, 649

RC-CR networks, 203

Transformation, passive impedance, 62–63

matching networks, 65–71

quality factor, 63

series-to-parallel conversions, 63–65

Transformers, 470

coupling capacitance, 474–475

impedance transforms, 69

modeling, 475–476

outphasing, 806–807

power amplifiers, 753, 767, 821–824

structures, 470–475

Transient response in type-II PLLs, 620–622

Transistors

class E power amplifiers, 772–773

cross-coupled oscillators, 514

phase noise, 538

thermal noise, 43–46

VCOs, 534

Transmission lines (T-lines), 476–478

coplanar, 482–483

microstrips, 479–482

striplines, 483

Transmission masks in IEEE802.11, 147–148

Transmit bands, 158–159

Transmit spectrum masks, 144–145

Transmitted noise in offset PLLs, 670–671

Transmitter antenna thermal noise, 42

Transmitters (TX), 861

Bluetooth characteristics, 143–145

cell phones, 91

considerations, 226–227

direct-conversion. *See* Direct-conversion transmitters

GSM specifications, 135–136

harmonic distortion, 16

heterodyne, 244–248

LNA leakage, 261

outphasing, 804

power amplifiers, 861–867

in simple view, 4–5

system-level considerations, 838–840

upconverters, 867–869

wideband CDMA, 139–140

wireless standards, 130–131

wireless systems, 156

Trends, 2–3

True single-phase clocking (TSPC), 697–699

Tuning VCOs, 521–522

amplitude variation with frequency tuning, 532

continuous, 524–532

discrete, 532–536

range limitations, 521–522

Turn-to-turn capacitances in inductors, 441–442

Two-level modulation schemes, 92

Two-pole oscillators, 504–505

Two-sided spectra, 38

Two-tone tests

active downconversion mixers, 392

intermodulation, 22, 24–25, 28

power amplifiers, 756–757

sensitivity, 61–62

TX-RX feedthrough, 159–160

drawbacks, 611

frequency multiplication, 609–611

loop dynamics, 606–609

simple circuit, 601–606

VCO phase alignment, 600–601

Type-II PLLs, 611–612

charge pumps, 614–620

continuous-time approximation limitations, 622–623

design procedure, 646–647

frequency-multiplying CPPLLs, 623–625

higher-order loops, 625–627

loop bandwidth, 645–646

PFD/CP nonidealities. *See* Phase/frequency detectors (PFDs)

phase/frequency detectors, 612–614

phase margin, 647–651

phase noise, 638–644

transient response, 620–622

Undegenerated common-source stages, LNA nonlinearity calculations for, 329–330

Uniformly-distributed model of inductor capacitance, 441–442

Unilateral coupling in quadrature oscillators, 581

Units, 7–9

Unity-gain voltage buffers, 602, 607

Up currents and pulses

charge pumps, 614–615, 630–633, 645–647

fractional-N synthesizers, 733–734

integer-N synthesizers, 883

PLL higher-order loops, 625, 627

quantization noise, 739

Up skew in PFD/CP, 627–630

Upconversion and upconversion mixers, 339, 408

active, 416–424

design, 867–869

heterodyne transmitters, 244–248

I/Q mismatch, 229–232

linearity, 234–235

offset PLLs, 671

output spectrum, 844

passive, 409–416

performance requirements, 408–409

polar modulation, 797–798

power amplifiers, 758

scaling up, 230–231

Uplinks, 119

V/I (voltage-to-current) conversion

downconversion, 368–369

upconversion, 867–868

Varactors

overview, 483–490

Q, 522–524

Variable coding rates in IS-95 CDMA, 139

Variable-delay stages in integer-N synthesizers, 665–667

Variable-envelope signals in QPSK, 110

Variable-gain amplifiers (VGAs), 860

Variance, time. *See* Time-variant systems

VCOs. *See* Voltage-controlled oscillators (VCOs)

Vector modulators, 227

VGAs (variable-gain amplifiers), 860

Vn_{1} and Vn_{2} spectrum in mixers, 360–364

Voice signals, 91

Voltage compliance issues in PFD/CP, 630

Voltage-controlled oscillators (VCOs), 485

Bluetooth, 144

figure of merit, 570–571

fractional-N synthesizers, 716, 723

free-running, 655

frequency multiplication, 610

FSK, 112

integer-N synthesizers, 656, 666, 869–877

low-noise, 573–575

mathematical model, 577–581

multiphase frequency division, 745–748

overview, 518–521

PLLs, 603–606

offset, 672–673

phase alignment, 600–601

PLL-based modulation, 667–668

polar modulation, 797–798

transceiver design, 842, 845–847

tuning, 521–522

amplitude variation with frequency tuning, 532

continuous, 524–532

discrete, 532–536

range limitations, 521–522

varactor Q, 522–524

Voltage-dependent capacitors, 483–490

Voltage gain, 7–9

conversion. *See* Conversion gain

LNA common-gate stage, 276

Voltage swings, 9

flicker noise, 566

power amplifiers, 756, 762, 778, 792, 816, 861–863

Voltage-to-current (V/I) conversion

downconversion, 368–369

upconversion, 867–868

Voltage-voltage feedback in common-gate LNAs, 296

Volterra series

nonlinear currents, 81–85

overview, 77–81

Walsh code, 127

Weaver receivers, 210–213

Wideband CDMA, 139–143

Width mismatches in PFD/CP, 627–630

Wilkinson combiners, 827–829

Wilkinson dividers, 828

Wire capacitance and inductors, 441

Wire resistance and inductors, 444–448

Wireless communication overview, 1–3

big picture, 4–5

RF challenges, 3–4

Wireless standards, 130–132

Bluetooth, 143–147

GSM, 132–137

IEEE802.11a/b/g, 147–151

IS-95 CDMA, 137–139

wideband CDMA, 139–143

Wires

bond. *See* Bond wires

transmission lines. *See* Transmission lines (T-lines)

XNOR (exclusive-NOR) gates, 152

XOR (exclusive-OR) gates

current-steering circuits, 685–686

phase detectors, 598–599

PLLs, 603

reference doubling, 743

Zero crossings

Miller dividers, 701–702

mixer flicker noise, 385–386, 407–408

phase-modulated signals, 95

Zero-IF architecture, 179

Zero second IFs in heterodyne receivers, 171–174

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