MOS AK

Noise in RF Circuits and RF Noise DeviceCharacterizationDate 20.4.2007

Peter Baumgartner

RF Circuit Noise Characterization : Outline

Overview:– Typical wireless architectures

– Importance of noise for wireless communication

– Semiconductor Noise Sources

Noise in Linear Amplifiers– Noise Figure, Noise Temperature,

Noise Measure

– NF Measurement

– Noise of Two-Ports

– Characterization of 4 Noise Parameters

– MOS model/characterization examples

– LNA Example

Noise in Mixer Circuits– Mixer Introduction

– Cyclostationary Noise

– Gilbert Mixer

Noise in Oscillators– Basics and Requirements

– Hajimiri and LeesonTheory

– Typical VCO Circuit

– Characterization

Acknowledgment:T. BenetikG. CalabreseM. EttlingerC. HankeU. HodelP. RiessD. SiprakJ. VeledarA. WerthofN. Zanolla

Cellular System

1

2

3

4

5

6

7

1

2

3

4

5

6

7

1

2

3

4

5

6

7

1

2 4

1

3

4

4

7

2

3

4

5

6

7 CCell NBB /=

Re-use distance

)//( __ ChannelperUserUserCelllUserChanne NNBB

Cellular Structure

=

B: Bandwidth of standard(e.g. 2X35MHz for GSM-900)

Channel Capacity in the Presence of Noise

⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅=

BSBPBC

N

02 1log

Shannon (Communication in the Presence of Noise 1948):

( )NSBC /1log2 +⋅= C: Channel Capacity (bit/s)B: Bandwidth of channelS/N: Signal to NoiseP0: Signal Spectral DensitySN: Noise Spectral Density

⇒Noise has direct impact on:Channel capacityTransmit Power (battery power)Channel BandwidthNumber of users per BandwidthNumber of necessary BasestationsMaximum cell size

Increased Noise=> Increased Cost

The Radio Frequency Spectrum

Complete Radio Spectrum3kHz-30GHz is essentially used and occupied

Ultra Wide Band (UWB) to reuse frequency in short range applications:Very wide bandwidth, but signal power below background noise.

Typical RF Receiver Architecture and some Requirements

ADC

equalizer

ADC

0/90°complex LO

Input Signal(from Antenna)

complex outputspectrum

RF Low NoiseAmplifier

VoltageControlledOscillator

Mixer Filter Amplifier

RF Domain Base Band/Analog Domain

RF Receiver BB Processor

Input Signal:~ µV~ fW~ 1E9 dynamic range

(power)Strong interferers

GSM Channels:200kHz seperation(@0.9 and 1.8 GHz)

⇒RF Requirements:High Speed AnalogLow NoiseHigh LinearityLow Power

Some Noise Basics

)()()( tntutun +=

∫−

∞→>=<

T

TT

dttnT

tn 22 )(21lim)(

∫−

∞→=>=<

T

TT

dttnT

tn 0)(21lim)(

Ampl

itude

u

time

Signal (u(t)) Noise (n(t)) Noisy Signal

Noisy Signal is composed of ideal signal and additive noise

Time average of noise is zero

Mean square of noise

Noise is assumed to be small perturbation of signal⇒ Noise propagation in circuit can be described by linear small signal analysisBut Signal can be large⇒ Time varying noise sources or noise propagation (Cyclostationary Noise)

Some Noise Basics

( ) ∫−

∞→+⋅=

T

TT

dttntnT

)()(21lim 2112 ττρ

( ) ∫−

∞→+⋅=

T

TT

dttntnT

)()(21lim ττρ

∫∞

∞−

−⋅= ττπτρ diffS )2exp()()(

Fourier Transform of Autocorrelation => Spectral Power Density of Noise (Wiener-Khinchin Theorem)

∫∞

>=<0

2)( ndffS

Correlation function between different noise sources

Autocorrelation of one noise source

Mean square is equivalent to total noise power

Typical Noise Sources in Devices

Thermal Noise

Shot Noise

Flicker Noise

√ √

√

√ √

√ √

√√

√

kTfS =)(

IefS ⋅= 2)(

β

α

fIfS ∝)(

√

Noise, Autocorrelation, Frequency and Time Domain

0.0 0.2 0.4 0.6 0.8 1.0

-4

-2

0

2

4

Am

plitu

de

Time (s)

10 100 10000.0

0.5

1.0

1.5

Frequency (Hz)

Spe

ctra

l Pow

er D

ensi

ty S

-1.0 -0.5 0.0 0.5 1.0

0

2000

4000

6000

8000

Aut

ocor

rela

tion

Time Lag (s)

0.0 0.2 0.4 0.6 0.8 1.0

-2

0

2

Ampl

itude

Time (s)

-1.0 -0.5 0.0 0.5 1.0

0

100

200

300

400

500

Aut

ocor

rela

tion

Time Lag (s)

10 100 100010-3

10-2

10-1

100

101

Frequency (Hz)

Spe

ctra

l Pow

er D

ensi

ty S

White Noise Flicker Noise

Transient

Autocorrelation

Spectral Power Density= Fourier Transform of Autocorrelation (Wiener Khinchintheorem)

RF Circuit Noise Characterization : Outline

Overview:– Typical wireless architectures

– Importance of noise for wireless communication

– Semiconductor Noise Sources

Noise in Linear Amplifiers– Noise Figure, Noise Temperature, Noise

Measure

– NF Measurement

– Noise of Two-Ports

– Characterization of 4 Noise Pparameters

– LNA Example

Noise in Mixer Circuits– Mixer Introduction

– Cyclostationary Noise

– Gilbert Mixer

Noise in Oscillators– Basics and Requirements

– Hajimiri and Leeson Theory

– Typical VCO Circuit

– Characterization

Matched Amplifiers (e.g.50Ohm): Noise Temperature

BTkN ⋅⋅=

sJkTKTi /104290 21−⋅==>=

)( NiOut TTGT +⋅=

Thermal Noise:

Standard for Ti

Output Noise TemperatureN

S

i

Out

Matched Amplifiers (e.g.50Ohm): Noise Figure

i

O

iiO

O

O

i

NGN

NSSN

NSNSF

⋅===

)/()/()/(

)(log10 10 FNF ⋅=

KTi 290=

F NF1.0 0.01.1 0.41.3 1.02.0 3.010.0 10.0

BTkN ⋅⋅=

i

N

i

Ni

i

o

i

o

TT

TGTTG

TGT

NGNF +=

⋅+⋅

=⋅

=⋅

= 1)(

Cascade of Amplifiers

...321 GGGGTot ⋅⋅=

).../(/ 213121 GGTGTTT NNNNTotal ⋅++=

...211

1

3

1

21 GG

FG

FFFTotal ⋅−

+−

+=

iN TTF /1+=

iN TFT ⋅−= )1(

Formula of Friis

First Amplifier: Low noise figure& high gain preferred

Noise Characterization: Y-Factor Method

)/()(/ MeasOFF

SMeasON

SOFF TTTTNNY ON ++==

ONSTOFF

STNoise Source: Two Noise Levels

Excess Noise Ratio

Y-Factor

Measured Noise

0/)( TTTENR OFFS

ONS −=

ON OFF

Device under Test

1 1 2

)1/()( −⋅−= YTYTT OFFS

ONSMeas

Noise Characterization: Y-Factor Method

OFFON NNY 22 /2

=)1/()( 222 −⋅−= YTYTT OFF

SON

S

)1/()( 121212 −⋅−= YTYTT OFFS

ONS

NoiseSource

TON,TOFF

Device under Test

DUTNF1, G1

NF Instrument(second stage)

NF2

Calibration

Calibration:

Measurementwith DUT:

OFFON NNY 121212 /=

second stagecorrection

)/()( 2212121OFFONOFFON NNNNG −−=

12121 / GTTT −=

Avalanche Diode Noise Source

0/)( TTTENR OFFS

ONS −=

Diode in avalanche break down for high noise temperature⇒ High noise temperature of Diode (e.g. 300kK)⇒ Attenuator to reduce impedance difference TON vs. TOFF

⇒ Fast switch between on/off⇒ Calibration with thermal noise source

Standard ENR values:5.2dB, 15.2dB

Noise Figure Analyzer

Tuned Superhet Receiver:Oscillator sets measurement frequencyIF Filter sets measurement bandwidth

Pre-Amp Mixer IF

Filter

RMSPower

Detector

LocalOscillator

Frequency

Bandwidth

Input

Noise SourceControlVoltage

CPU

Input Noise Source Ctrl.

General Impedance: Linear Two Ports

TwoPort

VBias

Two-port:“Black box“ with 2 RF ports (= 4 Terminals)

Noise=small signal => linear 2-ports

Non RF connections (e.g. biasing, supply)are not considered

Example for In and Out ports of a transistor amplifier

Two Port Basics

0ZUa In=

0

Re

ZU

b fl=a,b: Amplitudes

of incomingand refl. waves

Y Z

Common Y,Z,A,S – Parameter representation of two-ports

S

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

1

2221

1211

2

1

UU

YYYY

II

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

1

2221

1211

2

1

II

ZZZZ

UU

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

1

2221

1211

2

1

aa

SSSS

bb

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

2

2221

1211

1

1

IU

AAAA

IUA

Transistor: Two-port parameters are a function of bias and frequency

Two Port Basics

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

2

2221

1211

1

1

IU

AAAA

IU

Two noise sources are necessaryConvenient: Add noise sources for

dependent quantitiesCombination of two-ports

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

2

2221

1211

1

1

IU

AAAA

IU

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

2

2221

1211

1

1

IU

AAAA

IU

Noise in Two Ports: Correlation of Noise Sources

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

2

2221

1211

1

1

IU

AAAA

IU

11 nCnc uYi ⋅=

1nui1nu

⇒Two-port has4 Noise Parameters

Noise sources can be partially correlated

Uncorrelated part

Noise in Two Ports: Correlation Matrices

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅

⋅⋅=*

22*

12

*21

*11

21

nnnn

nnnnY

iiiiiiii

BC

General approach with correlation matrices:

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅

⋅⋅=*

22*

12

*21

*11

21

nnnn

nnnnZ

uuuuuuuu

BC

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅

⋅⋅=*

21*

11

*11

*11

21

nnnn

nnnnA

iiuiiuuu

BC

Hermitian 2X2 Matrix:4 Parameters:

-2 real diagonal elements => Strength of noise source

-1 complex off diagonal element=> Correlation of noise sources

Passive two-ports:

{ }ZTkCZ Re2 ⋅⋅⋅={ }YTkCY Re2 ⋅⋅⋅=

Noise in Two Ports: Combining Two Ports and Correlation Matrices

U=Z I

U=Z I

21 YYY CCC +=

Combination of two-ports

I=Y U

I=Y U

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

2

2221

1211

1

1

IU

AAAA

IU

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

2

2221

1211

1

1

IU

AAAA

IU

21 ZZZ CCC +=

tZAA ACACC 1211 ⋅⋅+=

Noise in Two Ports: Transforming Correlation Matrices

+⋅⋅=′ TCTC

⎥⎦

⎤⎢⎣

⎡1001

Correlation matrices can be transformed between different representations by matrix transforms

⎥⎦

⎤⎢⎣

⎡

2221

1211

YYYY ⎥

⎦

⎤⎢⎣

⎡−−

01

21

11

YY

⎥⎦

⎤⎢⎣

⎡

2221

1211

ZZZZ

⎥⎦

⎤⎢⎣

⎡

22

12

10

AA

⎥⎦

⎤⎢⎣

⎡−−

21

11

01

AA

⎥⎦

⎤⎢⎣

⎡−−

21

11

01

ZZ

⎥⎦

⎤⎢⎣

⎡1001

⎥⎦

⎤⎢⎣

⎡1001

TransformationMatrices T:

Y Z A

Y

Z

A

From (C)

To (C

‘)

Noise Deembedding with Correlation Matrices

YS ⇒

G

G G

G

S S

Por

t 1

Por

t 2

Device Teststructure

S-Param.C Noiseparam.

Open Deemb.

S-Param.

Dee

mbe

ddin

gS

teps

YCC ⇒OpenOpen YS ⇒{ }OpenOpenY YkTC Re2 ⋅=−

OpenDeemb YYY −=

OpenYYDeembY CCC −− −=

Mea

sure

men

t

I=Y U

I=Y U

Device

Pad-Cap.

How to Measure the Noise Correlation Matrix?

BRkTu nn ⋅⋅⋅= 42

BGkTi un ⋅⋅⋅= 42

ncnc uYi ⋅=

4 Noise Par. Correlation Matrix

EquivalentC

Noise figure F is a function of source impedance Ys

BGkTi ss ⋅⋅⋅= 42

2

22

1s

nSCn

i

uYYiF

⋅+++=

sss BjGY ⋅+=

( ) ( )[ ]22min OptsOpts

s

n BBGGGRFF −+−+=

Again 4 equivalent noise parameters:

minF nR OptOptOptS BjGY ⋅+=−

Noise Parameter Test System

( ) ( )[ ]22min OptsOpts

s

n BBGGGRFF −+−+=

MNS (mismatch noise source): Tuner for source impedancevariationBasic procedure: Measure F@Y1,2,3,4 Fit F(Y) to esitmate

Fmin,Rn,Gop,Bopt

LWgTkiS mBdid ~42 γ⋅⋅⋅⋅==

322

2 ~5

4 LWgC

TkiSm

gsBgig ⋅⋅

⋅

⋅⋅⋅⋅== δω

395.022

*

⋅=⋅

⋅= i

ii

iic

dg

dgCorrelation Coefficient:

Thermal Channel Noise:

Induced Gate Noise:

Noise Sources in the MOS Transistor

Local noise sources related to channel resistanceAdditional noise sources: parasitic resistances (e.g. RGate)

Transfer of local channel noise sources to terminal noise: Klaassen-Prins equation

Gate and Drain Noise Spectral Density for different model topologies (130nm Technology) in BSIM4.3

Sig Sid

CY

1 10 100 1k 10k 100k 1M 10M 100M 1G 10G 100G10-30

10-29

10-28

10-27

10-26

10-25

10-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

Sig

Sid

Compact model Compact model+gate resistance Compact model+addtl. noise source Full RF model

Spe

ctra

l Den

sity

(A2 /H

z)

frequency (Hz)Full RF model (shown subcircuit is only an example)

Noise Figure for different model topologies (130nm Technology)

1 10 100 1k 10k 100k 1M 10M 100M 1G 10G 100G

10-3

10-2

10-1

100

101 Compact model Compact model+gate resistance Compact model+addtl. noise source Full RF model

NFm

in (d

B)

frequency (Hz)Full RF model (shown subcircuit is only an example)

RF Transistor Characterization / Model Examples (400nm IO Device)

Sig Sid

CY Characterization vs.Model

Associated Gain Gas vs. drain current

NF50 & NFmin vs. drain currentFmin vs. frequency red: raw data, blue: deembeded data

Optimum Impedance vs. gate voltage

R L

RF Transistor Characterization / Model Examples (250nm Node)

Design Example: Narrowband LNA with Inductors

Bias1 Bias2

DD

)/(/ ωω jII TGD =

GIngs

InsT

InIn LjICj

ILjj

IV ωω

ωωω

⋅+⋅+⋅⋅=1

Mos Transistor:

Ggs

STIn LjCj

LZ ωω

ω ++⋅=1

real part img. part

LSLG

Transit frequency: Tω

Problem: Resistance of inductors(especially for on chip conductors)

Technology Trend: RF Performance and Flicker Noise

0

50

100

150

200

250 Transit Freq. Ft Maximum Osc. Freq. Fmax RF Noise Figure NFmin Flicker Noise kF

frequ

ency

(Ghz

)

inverse gate length

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

NFM

in @

2G

Hz

/ Flic

ker N

oise

(nor

mal

ized

)

350nm 180nm 130nm 90nm 65nm

Summary Noise in Linear Amplifiers

Noise measurement is a narrowband power measurement.

Test system is basically a tunable low noise receiver.

Four noise parameters are necessary to model noise sources of a two port, many representations are used (and are equivalent).

Tuning of source impedance is necessary to characterize all noise parameters.

RF Circuit Noise Characterization : Outline

Overview:– Typical wireless architectures

– Importance of noise for wireless communication

– Semiconductor Noise Sources

Noise in Linear Amplifiers– Noise Figure, Noise Temperature, Noise

Measure

– NF Measurement

– Noise of Two-Ports

– Characterization of 4 Noise Pparameters

– LNA Example

Noise in Mixer Circuits– Mixer Introduction

– Cyclostationary Noise

– Gilbert Mixer

Noise in Oscillators– Basics and Requirements

– Hajimiri and Leeson Theory

– Typical VCO Circuit

– Characterization

Mixer Basics: Why is Frequency Conversion Necessary

0/90°complex LO

Input Signal(from Antenna)

complex outputspectrum

Amplifier

Base Band/Analog Domain

RF Low NoiseAmplifier

VoltageControlledOscillator

Mixer Filter

RF Domain

Freq.

Sig

nal

LocalOscillator

Homodyne (Zero IF) receiver:Direct down conversion to Base Band frequency

• Filtering signal in RF domain difficult:• Changing LO-Freq. easier thanchanging filter freq.

• AD/DA at RF difficult (high power)

FFQ Δ= /

Typical Mixer Circuit

Double BalancedGilbert Mixer

LF Timescale

Sig

nal

Time

Mixer Output Current Output after Low Pass Filtering

RF Timescale

Sig

nal

Time

RF Signal Lo Oscillator Mixer Output Current

Noise Contributors in Gilbert Mixer

RF

LO LOx

LO:HighLOx:Low

LO:LowLOx:High

Transition

Contributes moise:Mixed from RF to base freq.

No addtl. Noise(On)

No addtl. Noise(Off)

No addtl. Noise(On)

Additional Noisewithout Freq. Conversion

Noise Contributors in Gilbert Mixer: Frequency and Time

LOx

RF

LO

TransconductanceTransistor

Mixing Transistors

102 103 104 105 106 107 108 109 1010

Noi

se P

ower

(log

arith

mic

sca

le)

Frequency (Hz)

Noise Spectrum of CMOS Transistor

RF Timescale

Sig

nal

Time

RF Signal Lo Oscillator Mixer Output Current

Transient Signals of Mixer

Mixing Transistors:- Large noise levels (flicker noise)- Short noise duration (transition time)⇒Cyclostationary noise!

Cyclostationary Noise

0.00 0.02 0.04 0.06 0.08 0.10

-0.2

-0.1

0.0

0.1

0.2

0.3

Noi

se

Time (s)

-1.0 -0.5 0.0 0.5 1.005

101520253035404550 Stationary Noise

Cylcostationary Noise

Auto

corr

elat

ion

Time Lag (s)

10 100 100010-4

10-3

10-2

10-1

100 Stationary Noise Cyclostationary Noise

Frequency (Hz)

Pow

er S

pect

ral D

ensi

tyConvolution in frequency domainPart of noise power is shifted tomultiples of switch frequency

Cyclostationary Noise: On/Off Dutycycle

0.000 0.002 0.004 0.006 0.008 0.010-505

101520253035404550

Stationary Noise Cylcostationary Noise (50% DC) Cyclostationary Noise (30% DC)

Aut

ocor

rela

tion

Time Lag (s)

10 100 100010-4

10-3

10-2

10-1

100

Stationary Noise Cyclostationary Noise (50% DC) Cyclostationary Noise (30% DC)

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty

Reduced duty cycle (=faster switching of mixer)

⇒Overall noise power decreases

⇒Larger percentage is mixed to higher frequencies

But: small devices, which are necessary for fast switching have higher flicker noise!

How to Optimizer Noise of Gilbert Mixer: Darabi/Abidi Model

Slew

Rat

e SR

(V/s

)

T X ( 1-DutyC)T X DutyC

LO Period = T LO LOx

volta

ge

time

LO LOx

Itail

Vt1 Vt2

FLWCoxeffKFVtVtVDiffNoise

⋅⋅⋅⋅>=<+>>=<< 2

222 21μ

Model: Variation of Duty cycle is responsible for output noise:

Duty cycle variation depends on LO slew rate

TSRVDiffNoiseDutyCNoise

×= KF: Flicker Noise Parameter

CParLWCoxIbufferSR

+××=

And threshold voltage variation of switch transistors

222 DutyCNoiseII tailOut ⋅∝

22

22 )(

TILWCCLWCI

BufferOx

ParOxOut ⋅⋅⋅⋅

+⋅⋅∝

22

22 )(

TILWCCLWCI

BufferOx

ParOxOut ⋅⋅⋅⋅

+⋅⋅∝

0 100 200 300 400 5000

200

400

600

800

1000

1200

1400

1600

1800

2000

CPar=30fF CPar=100fF CPar=200fF

(Cox

X W

X L

+CP

ar)^

2/(C

ox X

W X

L)

Cox X W X L

Some results:• To optimize stationary noise:

Increase transistor size

• To optimize cyclostationary mixer noise:Reduce transistor size (till parasitics appear)

• Minimize parasitics

• Noise scales with=> Advantage for superhet: First mixer to intermediate frequency (IF) Second mixer to baseband frequencyTradeoff: Complexity, power consumption, size

• Maximize gate drive current Tradeoff: power consumption

22 /1 TF =

How to Optimize Noise of Gilbert Mixer:Darabi/ Abidi Model

RF Circuit Noise Characterization : OutlineOverview:

– Typical wireless architectures

– Importance of noise for wireless communication

– Semiconductor Noise Sources

Noise in Linear Amplifiers– Noise Figure, Noise Temperature, Noise

Measure

– NF Measurement

– Noise of Two-Ports

– Characterization of 4 Noise Parameters

– LNA Example

Noise in Mixer Circuits– Mixer Introduction

– Cyclostationary Noise

– Gilbert Mixer

Noise in Oscillators– Basics and Requirements

– Hajimiri and Leeson Theory

– Typical VCO Circuit

– Characterization

Frequency Generation for Local Oscillator

withoutLO Phase Noise

withLO Phase Noise

Freq.

LocalOscillator

Freq.

LocalOscillator

Freq. Freq.

MixerOutput

Reciprocal Mixing

Requirements:- Frequency Stability:

Crystal Oscillator- Low Phase Noise:

VCO (far off carrier)Loop Filter, Divider, Phase Detector

(near carrier)

Signal

Interferer

Phase Noise Basics

PhaseNoise

AMNoise

( ) ( )( )ttftAAtA ϕω +⋅⋅Δ+⋅= 00 )(1)(

Am

plitu

de

Time

Phase Variation

ttt

∂∂

=Δ)()( ϕω

Phase Noise is equivalent to frequency Noise

AM-Noise typically unimportant (e.g. Gilbert Mixer works at LO=LOx) and can be reduced with an amplitude regulation

Phase Noise Basics

( ) ( )

Carrier

HzbandSingleSide

PP

L 1,0 ωωω Δ+=Δ

Unit used for phase noise:dBc/Hz (dB relativ to carrier)

ωΔ

-1.0M -500.0k 0.0 500.0k 1.0M

L(Δω

)

Δω

dBc

Phase noise is characterizedby spectral power density:

LC Oscillators for Good Phase Noise Performance

LC1

=ω

Typical VCO Circuit:

- LC tank

- Tuning with varactor- Differential circuit- Cross coupled transistors:Negative resistance around Vout=Voutxto compensate LC tank losses

Vout-Voutx

Iout-Ioutx

Phase Noise: Hajimiri Model

8.0x10-10 1.0x10-9 1.2x10-9 1.4x10-9 1.6x10-9

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Ampl

itude

time (s)

undisturbed charge injection at zero crossing charge injection at maximum

8.0x10-10 1.0x10-9 1.2x10-9 1.4x10-9 1.6x10-9

ISF

time (s)

Phase Noise Response to Noise Current depends on Injection Time Impulse Sensitivity Function:

∫∞−

⋅⋅=t

n diISFq

t τττϕ )()(max1)(

qmax: maximum charge on capacitor

Phase Noise: Leesons Heuristic Model

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ+⋅

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛Δ⋅⋅

+⋅⋅⋅⋅

⋅=Δω

ω

ωωω

3/12

0 12

12log10 f

Carrier QPTkFL

103 104 105 106 107 108 109 1010

Leeson‘s Heuristic Formula (1966)

L(Δω

) dB

c/H

z

Δω (Hz)

Flicker NoiseCorner Frequency Oscillator Optimization:

Q

PCarrier

B. Razavi, „RF Microelectronics“, Prentice Hall 1998

M. Golio, „Microwave and RF Product Applications“, CRC Press 2003

S.A. Maas, „Noise in Linear and Nonlinear Circuits“, Artech House 2005

H.T. Friis, „Noise figures of radio receivers“, Proc. IRE, vol 32, 1944, pp. 419-422

Agilent Application Notes: 95-1,57-1,57-2,57-3

V. Adamian, A. Uhlir Jr., „A novel procedure for receiver noise characterization“, IEEE Trans. on Instr. Meas.,1973 ,pp 181-182

L. F. Tiemeijer, R.J. Havens, R. de Kort, A. J. Scholten, „Improved Y-Factor Method for Wide-Band On-Wafer Noise Parameter Measurements“, IEEE Trans. on Microwave Theory and Techniques, Vol. 53, No.9, 2005, pp. 2917-2925

H. Hillbrand, P. Russer, „An Efficient Method for Computer Aided Noise Analysis of Linear Amplifier Networks“, IEEE Trans. on Circuits and Systems, Vol. Cas. 23, No. 4, 1976, pp 235-238

J. Engberg, T. Larsen, „Noise Theory of Linear and Nonlinear Circuits“, Wiley 1995

T.H. Lee, „The Design of CMOS Radio-Frequency Integrated Circuits“, Cambridge 2004 (second edition)

http://www.designers-guide.org/Theory/cyclo-pub.ppt

H. Darabi, A. Abidi, „Noise in RF-CMOS Mixers: A Simple Physical Model“, IEEE Trans. Solid State Circuits, vol. 35, no.1, 2000, pp. 15-25

E. Hegarzi, J. Rael, A. Abidi, „High-Purity Oscillators“, Kluwer Academic Publishers 2005

M. Tiebout, „Low Power VCO Design in CMOS Low Power VCO Design in CMOS“, Springer 2005

A. Hajimiri, T.H. Lee, A General Theory of Phase Noise in Electrical Oscillators, IEEE Journal of Solid-State Circuits, Vol. 33, No. 2, 1988, pp 179-194

D.B. Leeson, “A simple model of feedback oscillator noise spectrum”, Proc. IEEE, vol. 54, 1966, pp.329-330

Literature