Appendix ABehavioral Models

All the behavioral models are written in Matlab language.

MODEL FOR A LOW NOISE AMPLIFIER

The code for the LNA is given below.

function Output_LNA=lna(PowerGain,NoiseFigure,OIP3dbm,Qs,Input_Signal,Fs);

This program represents a RF LNA model:Output_LNA=lna(PowerGain,NoiseFigure,OIP3dbm,Qs,BW);

PowerGain Gain of LNA in dBNoiseFigure NoiseFigure of LNA in dBOIP3dbm Output IP3 in dBmQs Quality factor input LNAInput_Signal (Noisy) Signal at input LNAFs=30e9; sampling frequency of Input_Signal

program written by Leenaerts, de Vreede and SyllaPhilips Research Laboratories‚ 1999

kBoltzmann=1.38e-23;T=290; Temperature in Kelvin

R=50 Matching resistanceFn=Fs/2; Nyquist frequencyBW=Fn; BT bandwidth

NONLINEARITY

Gain=10^(PowerGain/20); voltageIIP3dbm=OIP3dbm-PowerGain;IIP3=10^((IIP3dbm-30)/10); power (Watts)

IIP3=IIP3/(Qs 2);IIP3v=(IIP3*R) 0.5; voltageA2=0;A3=4*Gain/(3*IIP3v*IIP3v);

A1=Gain;nonlin=[A3 A2 A1 0];NonLinearLNA=polyval(nonlin,Input_Signal);

NOISENF=(total output noise power)/(output noise due to input source)The mean square noise voltage due to input source is 4kTR*BW with BW the sampled band.

NoiseFactor=10^(NoiseFigure/10); noise ratio in numbers

InputNoisems=4*kBoltzmann*T*BW*R; impedance is 50 OhmsInputNoiserms=InputNoisems^0.5; rms noise voltage at input

313

UserDefined

Low Noise Amplifier

314 CIRCUIT DESIGN FOR RF TRANSCEIVERS

OutputNoiseDueToInputrms=polyval(nonlin,InputNoiserms); rms output noise voltagedue to input noise

OutputNoisems=NoiseFactor*((OutputNoiseDueToInputrms)^2);OutputNoiserms=OutputNoisems^0.5; Total output noise root mean square voltage

OutputNoiserms represents the root mean square noise voltage at the output.We have to generate normal distributed noise with a root mean square noise voltageequal to OutputNoiserms and add this time signal to NonLinearLNA

SignalSize=size(Input_Signal);

Noise=randn(l,SignalSize(2)); normal distributionNoiseVoltage=OutputNoiserms*Noise; normal distributed noise at output according

to NoiseFactorOutput_LNA=NonLinearLNA+NoiseVoltage;

End of Low Noise Amplifier

MODEL FOR A MIXERThe code for the mixer is given below.

function Output_Mixer=mixer (RFsignal,LOsignal,PowerConversionGain,NoiseFigure,OIP3dbm,Qs,Fs);

This program represents a RF Mixer model:Output_Mixer=mixer(RFsignal,LOsignal,PowerConversionGain,NoiseFigure,OIP3dbm,Fs);RFsignal (Noisy) RF signal at the RF input of the mixer

LOsignal (Noisy) LO signal at the LO input of the mixer

PowerConversionGain PowerConversionGain of Mixer in dBNoiseFigure NoiseFigure of Mixer in dBOIP3dbm SSB (Single Side Band) Output 1P3 in dBmQs Quallity factor matching network at the inputFs sampling frequency of RFsignal

program written by Leenaerts, de Vreede and SyllaPhilips Research Laboratories, 1999

UserDefined

kBoltzmann=1.38e-23;

T=290; Temperature in KelvinR=50; Matching resistanceFn=Fs/2; Nyquist frequencyBW=Fn; BT bandwidth

ldealMixSignal=RFsignal.*LOsignal;

Mixer

'/.NONLINEARITY

Gain=10^(PowerConversionGain/20); voltageIIP3dbm=OIP3dbm-PowerConversionGain;

IIP3=10^((IIP3dbm-30)/10); power (Watts)IIP3=IIP3/(Qs^2);IIP3v=(IIP3*R)^0.5; voltage

A2=0;A3=4*Gain/(3*IIP3v*IIP3v);A1=Gain;

Appendix A: Behavioral Models 315

nonlin=[A3 A2 A1 0];

NonLinearMixer=polyval(nonlin,IdealMixSignal);

NOISENF=(total output noise power)/(output noise due to input source)

The mean square noise voltage due to input source is 4kTR*BW with BW the sampled band.

NoiseFactor=10ˆ(NoiseFigure/10); noise ratio in numbers

InputNoisems=4*kBoltzmann*T*BW*R; impedance is 50 Ohms

InputNoiserms=InputNoisemsˆ0.5; rms noise voltage at input

OutputNoiseDueToInputrms=polyval(nonlin,InputNoiserms); rms output noise voltage

due to input noiseOutputNoisems=NoiseFactor*((OutputNoiseDueToInputrms)^2);

OutputNoiserms=OutputNoisems^0.5; Total output noise root mean square voltage

OutputNoiserms represents the root mean square noise voltage at the output.

We have to generate normal distributed noise with a root mean square noise voltage

equal to OutputNoiserms and add this time signal to NonLinearLNA

SignalSize=size(IdealMixSignal);

according to NoiseFactorOutput_Mixer=NonLinearMixer+NoiseVoltage;

End of Mixer

MODEL FOR A POWER AMPLIFIER

The code for the PA is given below.

function Output_PA=pa(PowerGain,NoiseFigure,OIP3dbm,Qs,Input_Signal,Powsupp,PAE,Fs);

This program represents a RF Linear PA model:

Output_PA=pa(PowerGain,NoiseFigure,OIP3dbm,Qs,BW,Powsupp,PAE);

PAE Power Added Efficiency of the PA

Powsupp Supply Voltage

NoiseFigure NoiseFigure of PA in dB

OIP3dbm Output IP3 in dBm

Qs Quality factor input PAInput_Signal (Noisy) Signal at input PA

Fs=30e9; sampling frequency of Input_Signal

program written by Leenaerts, de Vreede and SyllaPhilips Research Laboratories, 1999

UserDefined

kBoltzmann=1.38e-23;T=290; Temperature in Kelvin

R=50; Matching resistanceFn=Fs/2; Nyquist frequency

BW=Fn; BT bandwidth

Power Amplifier

we first have to compute the averaged input power. This can be find by integration

over the input signal over the full time period;

LocalPower=(Input_signal.^2)/R; power in Watts per time unit

[n,m]=size(LocalPower);

Noise=randn(1,SignalSize(2)) ; normal distributionNoiseVoltage=OutputNoiserms*Noise; normal distributed noise at output

316 CIRCUIT DESIGN FOR RF TRANSCEIVERS

powervector=reshape(LocalPower,1,n*m); generate vector

Pin_PA=cumsum(powervector); cumulative powerPin_PA=Pin_PA(n*m)/(n*m); averaged power in Watts

NONLINEARITY

Pin_PAdbm= 10*log10(Pin_PA/1e-3);

Pout_PA= ((Powsupp*PAE))+Pin_PA;Pout_PAdbm=10*log10(Pout_PA/1e-3);Gain=((Powsupp*PAE)/Pin_PA)+1;PowerGain=10*log10(Gain);

IIP3dbm=OIP3dbm-PowerGain;IIP3=10 ((IIP3dbm-30)/10);IIP3=IIP3/(Qs 2);IIP3v=(IIP3*R) 0.5;A2=0; 0.01;

Gain in db

power (Watts)

voltage

NF=(total output noise power)/(output noise due to input source)The mean square noise voltage due to input source is 4kTR*BW with BW the sampled band.

NoiseFactor=10^(NoiseFigure/10); noise ratio in numbersInputNoisems=4*kBoltzmann*T*BW*R; impedance is 50 OhmsInputNoiserms=InputNoisems^0.5; rms noise voltage at inputOutputNoiseDueToInputrms=polyval(nonlin,InputNoiserms); rms output noise voltage

due to input noiseOutputNoisems=NoiseFactor*((OutputNoiseDueToInputrms)^2);OutputNoiserms=OutputNoisems^0.5; Total output noise root mean square voltage

OutputNoiserms represents the root mean square noise voltage at the output.We have to generate normal distributed noise with a root mean square noise voltageequal to OutputNoiserms and add this time signal to NonLinearPA

SignalSize=size(Input_Signal);Noise=randn(1,SignalSize(2)); normal distribution

NoiseVoltage=OutputNoiserms*Noise; normal distributed noise at output accordingto NoiseFactor

Output_PA=NonLinearPA; +NoiseVoltage;

End of Power Amplifier

A3=0; 4*Gain/(3*IIP3v*IIP3v);A1=Gain;nonlin=[A3 A2 A1 0];

NonLinearPA=polyval(nonlin,Input_Signal);

NOISE

Input power in dBmoutput power of the PA in wattOutput power in dbm

About the Authors

Dr. Domine Leenaerts studied electrical engineering at Eindhoven Universityof Technology. He gained his degree in 1987 and his Ph.D. in 1992. Between1992 and 1999 he worked at this university as assistant and associate profes-sor in the micro-electronic circuit design group. In 1995, he was a VisitingScholar at the Department of Electrical Engineering and Computer Science atthe University of California, Berkeley, and at the Electronic Research Labo-ratory of the same department. In 1997, he was a visiting professor at theTechnical University of Lausanne (EPFL). He has been a senior research sci-entist at Philips Research Laboratories Eindhoven since 1999. Currently, he isa principal research scientist, responsible for the RF Telecom circuit activitiesin the Integrated Transceivers department.

Ir. Johan van der Tang received his Ing. degree in electrical engineering fromthe Technical College in Leeuwarden in 1992. He received his Ir. degree in thesame field from the University of Twente in Enschede in 1995. From 1995 until2000 he was a research scientist in the field of integrated transceivers at PhilipsResearch Laboratories Eindhoven. In this function he worked on analog inte-grated HF key building blocks for satellite, radio and optical front-ends. Since2000, he is an assistant professor in the Mixed-signal Microelectronics groupat Eindhoven University of Technology and responsible for the RF transceiveractivities. His research interests are design methodology for High-Frequencyintegrated oscillators and in general, design of integrated transceivers.

Dr. Cicero Vaucher graduated in electrical engineering from the Federal Uni-versity of Rio Grande do Sul, Porto Alegre, Brazil, in 1989. He received thePh.D. degree from the University of Twente, Enschede, The Netherlands, in2001. Since 1990 he is with Philips Research Laboratories Eindhoven, wherehe is a senior research scientist in the Integrated Transceivers department. Hisresearch activities have been mainly focused on PLL frequency synthesizers,with emphasis on low-power high-speed PLL building blocks and on low phasenoise, fast settling time PLL architectures. At the moment, he is responsiblefor activities on analogue IC design for microwave applications.

317

Index

Active inductors, 234Adjacent channel power ratio, 150, 156AM-modulation, 218AM-PM conversion, 218Amplitude noise, 187, 201Antenna, 43

dipole, 44effective area, 45monopole, 45radiation resistance, 45

Automatic Gain Control (AGC), 198set-level, 198

Available power, 3

Balanced design, 204, 231Barkhausen conditions, see Oscillation, Barkhausen

conditionsBehavioral model

LC oscillator, 206multi-phase oscillator, 215RC oscillators, 223ring oscillator, 223two-integrator oscillator, 198, 223

Bipolarcurrent gain, 18cut-off frequency, 17double poly, 24input limited frequency, 22maximum available bandwidth, 23maximum oscillation frequency, 21model, 15output limited frequency, 22

Blocking, 11Bond pad, 59Bond wire, 46, 161

Capacitor, 35double poly, 35fringe, 35, 162MiM, 37MOS capacitor, 37

Cartesian feedback, 180CCO, see Oscillator, CCOCharge-pump, see PFD/CP combinationClosed-loop transfer function, see PLL, closed-

loop transfer functionColpitts oscillator, 193

oscillation frequency, 194phase noise calculations, 220

Compression point, 11Coplanar strip line, 58

Dead-zone, see PFD/CP combination, dead-zoneDelivered power, 3DRO, see Oscillator, DRODual-modulus prescaler, 286Dynamic range, 14

spurious-free, 14

EER, 178ESD, 60, 93

crowbar, 64ggNMOST, 61HBM, 60leakage current, 65np-diode, 64pn-diode, 64reverse voltage, 66

Feedback correction, 167Feedforward correction, 167FM modulation

signal-to-noise ratio reduction, 203Frequency

cut-off, 17, 19, 26input limited, 21maximum available, 23maximum oscillation, 20, 28output limited, 22

Frequency dividerarchitectures, 285CMOS technology, 290–300dual-modulus prescaler, 286input amplifier, 295input sensitivity, 297–300logic implementation, 291power dis. optimization, 293programmable prescaler, 287–290transfer function, 252

Frequency synthesizer, see PLLFriis’ formula, 8

Gain, 2antenna, 44maximum, 4

319

320 CIRCUIT DESIGN FOR RF TRANSCEIVERS

power, 3, 80transducer, 4voltage, 80voltage gain, 2

GSMphase noise specification, 202

Hartley oscillator, 193oscillation frequency, 194

Hartley receiver architecture, 204

I/Q mismatch, 204I/Q signals, see Quadrature signal generationImpedance

antenna, 44characteristic, 5, 50load, 2normalized, 10optimal source, 10source, 2

Impulse sensitivity function (ISF), 220Inductor, 37

bond wire, 47model, 38planar, 37substrate, 39

Intercept pointinput, 12n-th order, 12output, 12, 92third order, 12

Jitter, 187time domain analysis, 229

LC oscillator, see Oscillator, LCLC Tank, see ResonatorLeeson’s formula, 209, 211LNA, 79

bipolar, 84CE-CB stage, 85CMOS, 94model, 79

Local oscillator, see Oscillator, local

Matchingconjugate, 3impedance, 3, 79, 100noise, 9, 10optimal source, 85power, 4,10

Microstrip line, 54Mixer, 113

double-balanced, 117, 125Gilbert, 116

noise, 121, 123, 127passive, 117power conversion gain, 114, 120single-balanced, 117voltage conversion gain, 114, 120

Modulationcross, 11inter, 12

MOS, 31bulk model, 16cut-off frequency, 19, 30finger layout, 32, 161gate resistance, 15input limited frequency, 22maximum oscillation frequency, 21, 31model, 17, 19, 98NQS effect, 16output limited frequency, 23parallel layout, 31

MOS-varactor, see Varactor, MOS-type

Narrow range system, 199Negative resistance oscillator, see Oscillator

topology, cross-coupled pairNoise

1/f-noise, 124, 209DSB, 118factor, 6, 14, 106figure, 6, 123floor, 14, 209, 213in-band, 14input referred, 7,9minimum noise factor, 9phase noise, 209spectral density, 6, 128spot noise factor, 8SSB, 118

Open-loop bandwidth, see PLL, open-loop band-width

Open-loop transfer function, see PLL, open-looptransfer function

Orthogonalamplitude control, 198frequency control, 198

Oscillationamplitude stabilization, 196Barkhausen conditions, 191current limited region, 197gain condition, 191multi-oscillation, 195oscillation conditions, 191phase condition, 191saturation effects, 219start-up condition, 192

Index 321

voltage limited region, 197Oscillation frequency

Colpitts oscillator, 194Hartley oscillator, 194large signal, 224LC oscillator, 207maximum, 207, 225practical resonator, 208RC oscillators, 224ring oscillator, 225two-integrator oscillator, 225

Oscillatoramplitude stabilization, 197applications, 188bipolar differential pair, 212classification, 188crystal, 189current controlled (CCO), 186design examples, 231–236dielectric resonator (DRO), 189efficiency, 213feedback model, 191, 209Figure of Merit, 238harmonics, 187ideal, 185LC, 188, 206–223local (LO), 188MOS differential pair, 212multi-phase LC, 214open loop gain, 192optimal LC oscillator coupling, 216power spectrum, 233, 236RC, 189, 223–231RC oscillator benchmarking, 238relaxation, 191ring oscillator, 223three terminal, 193tuning constant, 186, 200two-integrator, 190, 223van der Pol, 197voltage controlled (VCO), 186

Oscillator specification, 199–205carrier to noise ratio (CNR), 201chip area, 205frequency, 199harmonics, 204I/Q mismatch, 204phase noise to carrier ratio, 201power budget, 200process spread, 199technology, 205tuning, 199tuning constant, 200tuning linearity, 200

Oscillator topology

AC-coupling, 222complementary differential topology, 221cross-coupled pair, 212LC, 221–223quadrature LC oscillator, 223RC, 229–231two-integrator oscillator, 229

PFD/CP combinationcharge-pump implementation, 303dead-zone, 300dynamic transfer function, 306high frequency operation, 257high-frequency architecture, 302implementation, 253operation, 254spectral components of output signal, 258static transfer function, 306transfer function, 255

Phase correction, 172Phase noise

1/f noise corner, 220AM-PM conversion, 218baseband representation, 250cyclo-stationary, 219definition, 201dependency on Q, 214down-conversion, 219extrapolation, 213improvement by power scaling, 214, 228impulse sensitivity function (ISF), 220LC oscillators, 209–221linear modeling, 209–217, 228–229measurement, 202multi-phase LC oscillators, 214–217noise folding, 221nonlinear modeling, 217–221, 229offset frequency, 201optimum number of stages, 229prediction, 217RC oscillators, 228–229regions, 209saturation effects, 219sidebands, 187single-sideband (SSB), 201tail current noise filtering, 219time domain analysis, 229up-conversion, 218

Phase-frequency detector, see PFD/CP combina-tion

Phase-locked loop, see PLLPhase-margin, see PLL, phase marginPierce oscillator, 195PLL

322 CIRCUIT DESIGN FOR RF TRANSCEIVERS

closed-loop transfer function, 263equivalent phase noise floor, 274, 278fractional-N architecture, 245input amplifier, 295integer-N architecture, 244latch-up condition, 254loop filter, 258

active, 261passive, 260

loop filter designintegration capacitance, 283phase noise contribution, 281spurious ref. breakthrough, 280

minimum step size, 245open-loop bandwidth, 263, 268open-loop transfer function, 262phase margin, 263, 268phase noise model, 273phase noise performance, 272, 278settling time, 246spectral purity, 268spurious ref. breakthrough, 268

charge-pump mismatch, 271leakage currents, 269

PLL building blocks, see Frequency divider andPFD/CP combination

PN-junction varactor, see Varactor, PN-junctiontype

Power amplifier, 145class A, 146class AB, 152, 161class B, 147class C, 147class D, 147class E, 147class F, 147efficiency, 146heating, 149hot carrier, 165PAE, 146

Predistortion, 168modulation, 169

Q, see Quality factorQuadrature signal generation, 214

correct-by-construction, 205device matching, 205layout symmetry, 205

Quadrature signals, 186Quality factor (Q), 189

capacitor, 206definition, 210high-ohmic substrates, 205inductor, 206loaded, 214

multi-phase LC oscillator, 215optimum phase shift, 215, 216RC oscillator, 228unloaded, 214

RC oscillator, see Oscillator, RCReciprocal Mixing, 202Reflection coefficient, 5, 51Resistor, 34

double poly, 34model, 34

Resonatorcapacitive tapping, 221lumped losses, 206practical, 206SAW, 190

Ring oscillator, see Oscillator, ringRuggedness, 151

Scatter parameters, 5Self-limiting, 197Sensitivity, 14Signal-to-noise ratio, 6Signal-to-noise-ratio (SNR), 202Spectral purity

phase noise sidebands, 249spurious signals, 247

Spurious emission, 203Spurious oscillation, see Oscillation, multi-modeStability

bode plot, 192root locus, 193

Substrate, 39, 67bounces, 60, 69high-ohmic, 76low-ohmic, 73noise, 69

Tank circuit, see ResonatorTechnology

CMOS, 30SiGe, 30silicon bipolar, 24Silicon-on-Anything, 26

Telecom standardstuning range, 199

Transceivereffects of phase noise, 202

Transceiver architecture, xvTransmission line, 49, 100

attenuation factor, 51dispersion, 51model, 49propagation constant, 50

Trench

Index 323

deep, 24swallow, 25

Tuningcapacitive, 208, 226capacitor switching, 209coarse range, 229delay interpolation, 227fine range, 229inductor switching, 208LC oscillator range, 209LC oscillators, 208parasitic reduction, 209RC oscillators, 225resistive, 226

varactor requirements, 208Tuning constant, 186Tuning system, see PLLTwo-integrator oscillator, see Oscillator, two-

integrator

Van der Pol Oscillator, 197Varactor

MOS-type, 200, 209PN-junction type, 209

VCO, see Oscillator, VCOVCO gain constant, see tuning constant

Wide range system, 199