ჴբϖǴInjection-locked Frequency Divider (GaAs HBT 2͔m)…

2.10.1 ࣴز୏ᐒ

೭ԛޑନᓎႝၡόҔ໺಍ޑMaster-SlaveޑDFFǴԶࢂҔVCOբࣁ ਡЈႝၡǶа۳ନᓎᏔӧଯᓎᏹբ܌੃઻ޑф౗эPLLᕴф౗ޑ๊ε

೽ϩǴӢԜ೭ԛ჋၂ҔVCOޑInjection-locked ޑ੝܄Ǵу΢VCOҁ يޑ੃઻ޑф౗൩Кdigital frequency dividerǵregenerative frequency dividerλǴךॺջё೛ी΋ঁଯᓎեф౗੃઻ޑନᓎᏔӧ೛ीVCO

΢ǶӧVCOޑ೛ी΢ճҔEmitter coupled pair with cross feedbackޑࢎ

ᄬǴ٠ճҔ”ጠӝႝགȹբӣ௤ٰගϲVCOޑਁ൯Ƕ 2.10.2 ࢎᄬᙁϟ

Injection-locked frequency dividers (ILFD)ࢂݙΕ΋ᒡΕૻဦډ

౗ К ٯ Ǵ ё ϩ ࣁ Ο ᜪ injection-locked oscillator(ILO) Ǻ (1)first-harmonicǴ ᒡ Ε ૻ ဦ ᓎ ౗ ޑ ୷ ᓎ ᆶ VCO ਁ ᕏ ᓎ ౗ ࣬ ӕ Ƕ (2)subharmonic Ǵ ᒡ Ε ૻ ဦ ᓎ ౗ ࢂ VCO ਁ ᓎ ౗ ޑ ϩ ኧ Ƕ (3) superharmonicǶᒡΕૻဦᓎ౗ࢂVCO᎜ᕏᓎ౗७ኧǶ೭ԛࢂճҔ superharmonicޑILOٰჴ౜ILFDǶ

კ2.52 Free running VCO კ2.53 Injection-locked VCO კ2.52߄Ңfree running LC oscillatorޑኳಔҢཀკǶf(x)ж߄᏾ޑ LC oscillator ޑߚጕ܄ਏᔈǹH(Ȧ)߄Ңᒧᓎ୔༧(LC resonator)ǹԶך ॺ܌ሡޑILFD൩ࢂճҔচӃoscillatorࢎᄬӆݙΕ΋ᒡΕૻဦVi(კ 2.53)Ƕҗܭ٬ҔVCOޑᜢ߯ǴILFDϝள಄ӝunity loop gainکzero phase excessаᆢ࡭᎜ᕏǴӵ݀а΢Һ΋చҹѨਏǴILFDΨคݤၮբǶ

྽ ILFD ၮ բ ӧ ନ Β ޑ π բ చ ҹ Π Ǵ ଷ ೛ f(x) ࢂ Ο ໘ ӭ ໨ Ԅ (f(x)=a0+a1x+a2x²+a3x³)ǴᒡΕૻဦǺvi(t)=Vicos(Ȧit+ĳ)ǴĳࢂᒡΕᆶᒡ рޑphaseৡǹᒡрૻဦǺvo(t)=V_ocos(Ȧot)ǹu(t)=f(x(t))=f(vo(t)+ v_i(t))ǹ

Q r

j H H

Z Z Z Z

2 1 )

( ⁰ ǴRLC tankޑୖኧǺȦrǴresonant frequencyǹQǴ

quality factorǶ

ᙖ җ а ΢ ޑ ଷ ೛ ё а ௢ Ꮴ р phase-limited ޑ ᙹ ᓎ ጄ ൎ ک gain-limitedޑᙹᓎጄൎǺ

(1) phase-limitedǺ

(2) gain-limitedǺ

»¼

ӧphase-limitedޑచҹύёޕǴቚуViΨёቚу܌ᓎጄൎǴόၸ

྽Viቚуډ٬Voᡂ຀ኧਔǴILFDΨ൩คݤҔբǶ

log

Z

კ2.54 ø2ࡕޑnoise transfer function

ILOޑ ᚇ ૻ ᙯ ౽ Б ำ Ԅ ё வ qbqfs ΢ ࢗ ၌ ځ ௢ Ꮴ ่ ݀ Ǻ

)

noise rejection཮΢ϲN७Ƕ

ᗨฅILFDҁ፦΢ࢂઞᓎޑႝၡǴόၸճҔVCOޑVtuneٰׯᡂ᎜ᕏ ᓎ౗Ǵёஒᏹբᓎ౗уቨǶჴሞ΢ၮҔޑ೯ૻس಍εӭࣁઞᓎǴ܌а ILFDޑᓎቨᗋૈ಄ӝس಍ሡ؃Ƕ

კ2.55 ILFDϐႝၡკ

ךॺԜԛ࿼ܭILFDޑVCOࢂҔ”ጠӝႝགᓸ௓ԄਁᕏᏔ”ӵȐკ 2.55ȑ܌ҢǴԜ೛ीӕኬΨ௦ҔEmitter coupled pair with cross feedback

ޑਁᕏᏔࢎᄬǴ࣬ၨа۳όӕޑӦБࢂǴךॺஒճҔጠӝႝགٰբࣁ ӣ௤ޑၡ৩ǶԶচ౛ࢂǴஒךॺ܌ाޑӣ௤ૻဦǴ೸ၸႝགޑጠӝӣ ډᒡΕᆄǶ

Ԝࢎᄬ࣬ၨ”ޔௗӣ௤”ޑӳೀࢂǴᒡрႝᓸޑਁ൯ό཮Ӣ୷ཱུ-໣ཱུௗय़܌ज़ڋǴёᒡрεਁ൯ǶԶ࣬ၨ௦Ҕ”ճҔႝ৒բӣ௤”ϐႝ

ၡޑӳೀࢂǴஒόሡाୃᓸႝߔǴ܌аёаቚу࣬ՏᚇૻǶ

Ԝࢎᄬஒ཮ౢғ-2/gmޑॄႝߔ೷ԋਁᕏǴԶаӣ௤ޑفࡋٰᢀ

࣮Ǵջёаӧځᒡрᆄౢғ҅ӣ௤ǶճҔᒡрᆄޑॄၩǴӆ࿶җ፾྽

ޑ೛ीځӅਁᓎ౗

Z 1 Ǵջёӧགྷाޑᓎ౗ౢғڬය܄ޑᒡрǶ

ՠҗܭHBTᇙำѝૈճҔٿቫߎឦٰᙅጕǴ܌аा೛ीԋࠟޔԄ ޑጠӝႝག࣬྽όܰǴԶ೭ԛךॺஒճҔ੝ਸޑᙅጕБݤǴٰၲԋѝ ճҔٿቫߎឦǴ൩ё೛ी΋ࠟޔጠӝႝགϐႝၡǴӵკ2.56܌Ң(ճҔ IE3DٰኳᔕрSୖኧ)Ƕ

კ2.56 ޔጠӝႝགϐlayoutკ

2.10.3 Ⴃीೕ਱ӈ߄

Item Spec Supply Voltage 5 V

Current of VCO core 4.22 mA Current of Current

Mirror& Output buffer 8.35 mA Supply Power ~ 62.85 mW Operating frequency range 12.2GHz~13.2GHz

Phase Noise of Free running VCO

-105dBc/Hz@1MHz offset

Turning Range 6.37~6.57GHz

KVCO 40MHz/V Die size 1000 um × 1000 um

2.10.4 ჴෳ่݀

(1) Free running VCO

Vtune=5V, output freq.=5GHz, Vtune=0V, output freq.=5.125GHz, Output power = -8.67dBm. Output power = -7.679dBm.

(2) Injection locked frequency divider ៜᔈ

аinput power = -10dBmࣁٯ:

V_tune=5V, V_tune=5V,

Max. locked freq.= 10.09GHz, Min. locked freq.= 9.90GHz, Output power = -7.689dBm. Output power= -7.995dBm.

Vtune=1V, Vtune=1V,

Max. locked freq.=10.25GHz, Min. locked freq.=10.16GHz, Output power=-7.635dBm. Output power=-7.991dBm.

Π კ Ң Vtune=5Vа Ϸ Vtune=1Vӧ Ӛ ᅿ input power Π ޑ locking rangeໆෳ่݀Ƕӧ Vtune=5Vǵ input powerλܭ0dBmࢂ ೀܭphase limited rangeǹԶεܭ0dBm߾ೀܭgain limited rangeǶԶVtune=1VਔǴ

ࣣࣁphase limited rangeǶёૈࢂӢࣁVtune=1Vਔਁᕏᓎ౗ၨଯǴჹᔈ ޑLC-tankϐQॶၨଯǴphase limited൩ԋޑЬाޑlockingज़ڋచҹǶ

-15 -10 -5 0 5 0.05

0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

Locking range (GHz)

Input Power (dBm) Vtune=5V

Vtune=1V

ΠკҢёᙹۓᒡΕᓎ౗܌ሡाޑᒡΕф౗ǶVtune=5VਔᒡΕ0dBm

཮Ԗനεlocking rangeǶҗԜკΨёаளޕǴVtune=5VਔޑLC-tankϐQ ॶКVtune=1VਔեǴ܌аlocking rangeၨεǶ

9.6 9.7 9.8 9.9 10.0 10.1 10.2 10.3

-15 -10 -5 0 5

Input power (dBm)

Incident frequency (GHz) Vtune=5V

Vtune=1V

2.10.5 ่ፕᆶ૸ፕ

(1) Die Photo

(2) Chip performanceΚ

Item Measurement Supply voltage 5 V

Vdd supply current 8.708 mA Vbias supply current 0.168mA Vmirror supply current 3.899mA Total Supply Power 63.203 mW Operational Frequency 10.246GHz ~

9.636GHz Total locked range 610MHz

Die size 1mm × 1mm

೭ԛΠጕޑݙᙹࠠ୏ᄊନᓎᏔዴჴวචځфૈǴ᏾ᡏޑᙹۓጄൎ

ၲ ډ 610MHz Ǵ ځ ੃ ઻ ޑ ф ౗ ( х ֖ output buffer) К ໺ ಍ ࠠ ޑ master-slave DFFନᓎᏔϿΑஒ߈60%ǹVCOޑਁᕏᓎ౗ᆶኳᔕԖৡǴ

ࢂӢࣁӧኳᔕႝၡਔ٬ҔΑ΋ಔfittingрٰޑtransformer modelǴᆶჴ ሞޑႝགॶԖόӕǶӧᙹۓጄൎ΢ᆶኳᔕ่݀Ԗ150MHzޑပৡǴЬ

ाᗋࢂਁᕏᓎ౗۳Πᅆ୏೷ԋޑ่݀Ƕ

2.11 ჴբϤǴRegenerative Frequency Divider (GaAs HBT 2µ n)

2.11.1 ࣴز୏ᐒ

ᒿ๱೯ૻޑሡ؃ǴࣁΑԖ׳ଯޑ໺ᒡᓎቨǴᏹբޑᓎ౗όᘐӦග ϲǴ΋૓ޑନᓎᏔճҔD-Flip-Flopٰ଺ନᓎǴёࢂځύ೷ԋၨӭޑ hbuf!efmbz཮ज़ڋՐനଯᏹբᓎ౗ǴӢԜҁԛჴբаMixerࣁਡЈႝ

ၡǴஒ၀ႝၡᔈҔӧଯೲޑ୏ᄊନᓎᏔ΢Ƕ

Regenerative frequency divider(RFD)ޑനଯᏹբᓎ౗ёК໺಍ޑ Master-Slave D-flip-flop (MS D-FF)܌ಔԋdividerז΢ٿ७ǶStatic frequency dividerޑനଯᏹբᓎ౗fmaxǴԖ΋ज़ڋǺ

tpd

f 12

max d Ǵtpd߄

Ңൂ΋ECL gateޑdelayǴԶRDFѝԖ΋ঁtpdکfeedback loopޑdelayǴ

܌аfmaxёε൯ගϲǶԜѦǴMixerࢎᄬޑႝ඲ᡏኧҁٰ൩КMS-D-FF ޑႝ඲ᡏኧϿǴ࣬ჹޑф౗੃઻ΨၨϿǴԖճܭᔈҔӧՉ୏೯ૻޑႝ

ၡ΢Ƕӧଯ७౗ޑନᓎᏔޑ߻ᆄǴӃҔեф౗੃઻ଯᏹբᓎ౗ޑRFD ஒᓎ౗फ़եǴௗΠٰӆҔቨᓎޑMS D-FFֹԋ܌ሡޑନኧǴӵԜ΋ٰ

ё෧եMS D-FFޑф౗੃઻Ξёගϲᏹբᓎ౗Ƕ 2.11.2 ࢎᄬᙁϟ

კ2.57߄ҢRFDޑblock diagramǴკύх֖Mixerǵlow-pass filter аϷamplifierǶMixerޑ΋ᆄᒡΕfᓎ౗ޑᒡΕૻဦǴќ΋ᆄ߾җᒡр ᆄ܎ӣf/2ᓎ౗ޑૻဦբషᓎǶ౛གྷჹᆀޑMixerѝ཮షрf/2ޑodd harmonic໨Ǵӵ3f/2ǵ5f/2…ǴԶ೭٤όाޑૻဦ཮೏low-pass filterᘠ

௞ǴѝԖf/2཮೏amplifierܫεǴᙖԜΨ෧Ͽconversion lossǶ

კ2.57 RFDϐBlock Diagram

Ԝ ႝ ၡ ཷ ۺ Π ޑ ന ଯ ޑ ᏹ բ ᓎ ౗ fmaxࢂ җ loop ޑ upper cutoff frequency،ۓǴԶ၀cutoff frequencyࢂҗmixerکamplifier܌ज़ڋǹ࣬

ჹޑǴstatic dividerޑfmax߾ࢂڙloop delay،ۓǴ܌аRFDёаКstatic divider׳ଯᓎᏹբǶόၸRFDޑനեᏹբጄൎfmin=f_max/3КstaticޑଯǴ Ӣࣁ྽ᒡΕૻဦեܭ၀ᓎ౗ਔǴ3f/2ޑharmonic൩ό཮೏low-pass filter ᘠ ௞ Ǵ ཮ ຾ Ε mixer ᆶ ᒡ Ε ૻ ဦ ష ᓎ Ǵ ౢ ғ ό ा ޑ ᒡ р ᓎ ౗ (fmax/3*3/2=fmax/2)Ƕ

კ2.58 RFDޑեᓎᏹբज़ڋ

RFDޑ ਡ Ј ႝ ၡ ࢂ Ҕ double-balanced mixer(კ 2.59)Ǵ ӧ Clock Buffer೛ीᆶচ౛΢ࢂၟ”2.8ჴբΟ”΋ኬǶᗨฅؒԖ࣬྽ჹᆀޑ differentialᒡΕ཮٬MixerޑRF-to-IF isolationᡂৡǴόၸቹៜRFDޑၮ բ࣬྽Ԗज़Ǵ܌а௦Ԝ฼ౣǶԜѦRF portޑᒡΕᆄѝ໪០୏ٿঁႝࢬ Ϫඤႝ඲ᡏ(Q5,Q6)ǴКଆௗӣLO portϿٿঁ(Q1~Q4)Ǵ܌аॄၩၨեǴ

ࡺஒfeedbackૻဦௗӣRF portǴᒡΕૻဦҗLOᒡΕǶ

! კ2.59 RFDϐinput bufferϷਡЈႝၡკ

კ2.57ύޑblock diagramᡉҢௗܭmixerϐࡕࢂ΋low-pass filterǴ ՠ ӧჴ ሞႝၡ ೛ी ΢٠ όሡा ᚐѦ уΕfilterǴӢ ࣁmixerҁ ي ޑ conversion gainᓎ౗ៜᔈ൩ࢂlow-passޑ׎ԄǴ܌аൂ΋mixer൩х֖

ΑషᓎᆶᘠݢޑфૈǶԜѦǴΠ΋ભޑamplifierΨςϣࡌܭmixerύǴ Ӣࣁךॺ௦Ҕޑactive mixerҁي൩ૈගٮܫεૻဦޑਏ݀Ƕ

კ2.60 Cherry-Hopperϐimpedance mismatch

ό ၸ ӧ ೭ ԛ ೛ ी ΢ ό ޔ ௗ Ҕ ႝ ߔ բ mixer ޑ ॄ ၩ Ǵ Զ ࢂ Ҕ Cherry-Hooper AmplifierǴᙖҗᡣӚௗᗺ೿ೀܭեߔלǴ٬၀ࢎᄬК

ଆҔ ႝߔբॄ ၩε൯ फ़եRFDޑ time constant٬ f-3dBගϲ (෧Ͽ ऊ 1+gm2RC2ޑኧໆભ)ǴԶЪ၀ܫεᏔԖቨᓎޑᏹբᓎࢤǴёаஒRFD

௢۳׳ଯᓎǴ٠ቚуႝၡޑsensitivityᆶᛙۓࡋǶ

ӧ RFD ޑ ӣ ௤ ၡ ৩ ΢ у Ε ΋ ჹ double emitter follower ECL logicǴё٬LO portޑbase-collectorޑϸୃႝᓸቚуǴ຾Զफ़եCµǴ Miller effectΨ෧λǶECLΨૈᡣךॺፓ᏾ᒡрޑDCྗՏǴа಄ӝ feedbackӣmixerޑRF portਔ܌ሡޑDCྗՏǶ

ନݤᏔϐᒡрᆄΨࢂࡐ৒ܰڙ΋ΠભቹៜǴޔࢬྗՏϷߔלϰ ଛΨό৒ܰၲԋǴӢԜाԖ΋ঁؼӳޑᒡр጗ፂભωૈԖਏޑၲԋ

ֹ᏾ޑႝၡǶ೛ीБݤၟϐ߻ޑჴբ΋ኬǶ

ӧ layout Ե ໆ ΢ Ǵ ᅰ ໆ ٬ ႝ ၡ ჹ ᆀ Ǵ ٠ ᅰ ё ૈ ᕭ อ RFD ύ ޑ feedbackၡ৩ǹӧӚDCୃᓸೀ٠ೱ΋bypassǴόՠёа٬ୃᓸᛙۓǴ

׳ёᘠ௞όѸाޑRF couplingǹӧௗጕБय़ǴࣁΑ٬Ӛঁϡҹ಄ӝ lumpedޑଷ೛ǴѸ໪಄ӝLd0.1OgǴLࢂೱௗጕޑჴሞߏࡋǴԶȜg߄Ң guided wavelengthǶ

2.11.3 Ⴃीೕ਱ӈ߄

Item Spec Supply Voltage 5 V

Current of Mixer core 9.26 mA Current of Input Network

& Output buffer 23.94 mA Supply Power ~ 166 mW Operating frequency range 8GHz~24GHz

Die size 1000 um × 1000 um

Sensitivity

6 8 10 12 14 16 18 20 22 24 26

-30 -25 -20 -15 -10 -5 0

Input Power (dBm)

Input Frequency (GHz)

2.11.4 ჴෳ่݀

(1 ) Max. Incident Frequency (2) Min. Incident Frequency

=22GHz =9GHfz

Output freq.=11GHz, -14.45dBm Output freq.=4.5GHz, -2.53dBm (3) Incident freq.=10GHz, (4) Incident freq.=13GHz,

Output freq.=5GHz, -1.627dBm Output freq.=6.5GHz, -10.74dBm

(5) Incident freq.=16GHz, (6) Incident freq.=18GHz,

Output freq.=8GHz, -11.14dBm Output freq.=9GHz, -14.12dBm (7) Phase noise

-125dBc/Hz @ 100KHz offset (8) Sensitivity

8 10 12 14 16 18 20

-20 -15 -10 -5 0 5 10 15 20 25

Input power (dBm)

Incident Frequency (GHz)

Min. input power Max. input power Dynamic range

2.11.5 ่ፕᆶ૸ፕ

(1) Die PhotoǺ

(2)Chip PerformanceǺ

Itemʳ Measurementʳ Core & output buffer Supply Voltageʳ 5 Vʳ Core & output buffer Supply Currentʳ 27.2 mAʳ

Input buffer supply voltage 5V Input buffer supply current 1.9mA

All bias voltage 5V All bias current 3.92mA Total Supply Powerʳ 165.1 mWʳ Functional frequency range 9~ 22GHz

Die size 1000 um Ø 1000 um ೭ԛΠጕ܌٬ҔޑႝၡࢎᄬǴࢂаMixerࣁਡЈႝၡஒᒡрૻဦ

ௗӣRF portǴԜӣ௤ၡ৩ӵ݀ؒԖ೛ीӳ཮٬ႝၡวғԾਁ౜ຝǶҗ ܭҁႝၡаCherry-Hooper amplifier྽բactive loadǴࣁΑlevel shiftډ RF portǴӭҔΑ΋ಔemitter follower٬᏾ঁӣ௤ၡ৩Ѹ໪ӭ࿶ၸΟঁ

gate delayǴу΢amplifierޑܫεਏ݀٬೭ԛޑႝၡӧ҂ௗinputਔ൩Ԗ 5.77GHzޑਁᕏૻဦᒡрǶҗໆෳډޑsensitivityკ߄ё࣮рǴӧᒡр

ૻဦեܭ5.77GHzҁႝၡᗋԖ5dBmޑdynamic rangeǴ྽ຬၸԜᓎ౗ࡕ dynamic range൩ࡐৡǶԜ౜ຝᜪ՟injection lockedޑନᓎᏔǴόၸሡ

ाࡐεޑinput powerωૈԖନᓎޑфૈǴׯᡂVbias_o padޑႝᓸਔΨ

཮ׯᡂᒡрૻဦޑᓎ౗Ƕ

2.12 ჴբΎǴRegenerative Frequency Divider (SiGe HBT 0.35µ n)

ҁჴբޑࣴز୏ᐒᆶࢎᄬᙁϟک”ჴբϤ”΋ኬǴӧᒡр጗ፂભႝ

ၡ೛ीਔᗋ௦Ҕinductor peakingޑמѯǴᡣᒡрભޑᓎቨό཮ज़ڋډ ਡЈႝၡޑៜᔈǶЬाόӕᗺࢂӧSiGeޑᇙำ΢ჴ౜ǴӢԜޔௗ৖Ң Ⴃीೕ਱کໆෳ่݀Ƕ

IF IF

კ2.61 inductor peakingϐᒡр጗ፂભ

2.12.1 Ⴃीೕ਱ӈ߄

Item Spec Supply Voltage 5 V

Current of Mixer core 9.66 mA Current of Input Network&

Output buffer 22.67 mA Supply Power ~ 161.65 mW Operating frequency range 16GHz~30GHz

Die size 860 um × 822 um

2.12.2 ჴෳ่݀

(1) Max. Incident Frequency (2) Min. Incident Frequency

=27GHz =7GHz

Output freq.=13.5GHz, -34.76dBm. Output freq.=3.5GHz, -7.468dBm

(3) Incident freq.=9GHz, (4) Incident freq.=11GHz,

Output freq.=4.5GHz, -7.66dBm. Output freq.=5.5GHz, -8.009dBm.

(5) Incident freq.=13GHz, (6) Incident freq.=16GHz,

Output freq.=6.5GHz, -8.933dBm Output freq.=8GHz, -12.31dBm

(7) Incident freq.=19GHz,

Output freq.=9.5GHz, -16.15dBm

(8) Sensitivity

6 8 10 12 14 16 18 20 22 24 26 28 30

-15 -10 -5 0 5 10 15

0 5 10 15 20 Min. Input power 25 Max. input power

Dynamic Range (dBm)

Input Power (dBm)

Input Frequency (GHz)

Dynamic range

2.12.3 ่ፕᆶ૸ፕ (1) Die Photo

(2) Chip performance summary

Itemʳ Measurementʳ Core & output buffer Supply

Voltageʳ 5 Vʳ Core & output buffer Supply

Currentʳ 19 mAʳ Input buffer supply voltage 5V Input buffer supply current 1mA

The Other bias voltage 3V The Other bias current 3.1mA

Total Supply Powerʳ 109.404 mWʳ Functional frequency range 7~ 27GHz

Die size 860 um Ø 822 um

೭ԛΠጕ܌٬ҔޑႝၡࢎᄬǴࢂаMixerࣁਡЈႝၡஒᒡрૻဦௗ

ӣRF portǶҗჴᡍ่݀᛾ჴԜႝၡӧSiGe 0.35µmᇙำ΢ޑᏹբጄൎ ё җ 7~27GHzǴዴჴ ёаၲ ډ1/2 fTѰ ѓ (SiGe HBTӧ Vce=1Vਔ fT=60GHz)Ƕӧ10GHz~22GHzޑᒡΕᓎࢤѝሡ-10dBmޑф౗൩ёၲԋ ନΒфૈǴЪ୏ᄊጄൎΨଯၲ20dBmѰѓǴ᏾ᡏޑႝၡਏૈКኳᔕਔ ᗋӳǶനեᏹբጄൎज़ڋӧ౛ፕ΢ࢂ1/3ޑനଯᏹբᓎࢤǴӵ݀ךॺ ڗӝ౛ޑၮҔᒡΕф౗ጄൎ-8dBmࣁ୷ྗǴ8~24GHzዴჴ಄ӝႣෳǶ ӧᒡрф౗Бय़ڙज़ܭᒡр጗ፂભޑᓎቨǴ܌аջ٬ճҔinductor peakingמѯᓎቨϝฅᙟᇂ᏾ঁᒡрᓎࢤǴ೷ԋᒡрф౗ӧଯᓎ΋ޔΠ

ྖǶ!

2.13 ჴբନΒႝၡϐ੝܄Кၨ

Kinds of

Dividers Technology Operating range (GHz)

Power (mW)

Core current (mA)

Static InGaP/GaAs 2͔m

HBT 2 ~ 7.3 60.6 12.12

Dynamic InGaP/GaAs 2͔m

HBT 2 ~ 11 65.5 13.1

Superdynamic InGaP/GaAs 2͔m

HBT 6 ~ 9.7 29.4 5.88

RFD SiGe 0.35͔m

BiCMOS HBT 7~27 45 9

ILFD InGaP/GaAs 2͔m

HBT 9.636 ~ 10.246 21.11 4.22

߄2.4 ჴբନΒႝၡϐКၨ

ಃΟക

ᓸ௓ਁᕏᏔϐ೛ी

3.1 ߻ق

ਥᏵBarkhausen criteriaǴE⁽^s⁾^A⁽^s⁾Ѹ໪฻ܭ΋ЪE⁽^s⁾^A⁽^s⁾Ѹ໪ࣁ႟Ƕ

ӵ݀аႝၡ౛ፕٰ࣮ǴਁᕏाวғޑӃ،చҹࢂӧፄኧѳय़ޑ຀

ື΢ाӸӧ΋ჹcomplex conjugate pole(კ3.2)Ƕଷ೛(3-1)Ԅӧᎃ߈຀

ືޑѓъѳय़΢Ԗ΋ಔcomplex conjugate poleǴ྽Viр౜΋٤዗ᚇૻ

ᘋ୏ࡕǴӧᒡрᆄ൩཮р౜ਁ൯೴ᅌᡂεޑ۰ݢૻဦǶҗܭܫεᏔё ගٮޑਁ൯ࢂڙज़ڋޑ(аႝ඲ᡏԶقǴਁ൯΢ϲ཮٬gmΠफ़)Ǵӵ݀

ᒡрૻဦεܭԜज़ڋǴܫεᏔ൩཮ॐ٬ѓъѳय़ޑpole۳຀ື౽୏Ǵ ٠ߥ࡭΋ۓޑਁ൯Ƕനಖ၀ಔcomplex conjugate pole཮ပӧ຀ື΢ᛙ ۓਁᕏǴԜਔރᄊωࢂ੿҅ᅈىBarkhausen criteriaǶ

Re Im

1 pole

2 pole

time

Re Im

1 pole

2 pole

time

Re Im

1 pole

2 pole

time

კ3.2 ਁᕏᏔϐཱུᗺӧፄኧѳय़΢ޑᡂ୏

ਁᕏޑଆۈచҹࢂႝၡҁيѸ໪όᛙۓǴёࢂਥᏵBarkhausen criteria٠όૈዴۓԛచҹǴBarkhausenѝૈᇥࢂѸाచҹԶߚкϩచ ҹ(resonate܈latch೿཮಄ӝ၀ۓ౛)Ǵ܌аᜢܭႝၡࢂցόᛙۓѸ໪Ҕ ќ΋ۓ߾ٰ،ۓǺNyquist stability testǶځБݤࢂஒ^E⁽^s⁾^A⁽^s⁾ ¹ӧፄኧ ѳय़΢ჹᓎ౗բკ(კ3.3)Ǵӵ݀ႝၡҁي཮ਁᕏځॉၞ཮໩ਔଞхൎ (1,0)ᗺǴԶхൎޑ୮ኧ൩ࢂӸӧѓъѳय़ύzeroکpoleޑঁኧৡ(ӵ݀

໩ਔଞᙅ(1,0)΋୮Ǵ߄Ңzeroکpoleޑᕴঁኧৡ΋)Ǵӵ݀ႝၡҁيᛙ ۓǴॉၞ൩ό཮໩ਔ੿хൎ(1,0)ᗺǶ

m1freq=

S(1,1)=5.325 / -5.1114.420GHz

-4 -2 0 2 4

-6 6

freq (1.000GHz to 10.00GHz)

S(1,1) m1

კ3.3 ਁᕏᏔϐNyquist Plot

౜ӧRFᑈᡏႝၡύத٬ҔޑਁᕏᏔӭࢂҔЬ୏ϡҹٰౢғॄႝ

ߔǴஒLC tankύޑཞ઻ႝߔ੃ѐǴځ่ፕၟBarkhausen࣮՟คᜢǴՠ

௢Ꮴޑཷۺࢂ΋ठޑǶӃа༾ݢႝၡޑᢀᗺٰ࣮one-portޑس಍ǴҔ ϸ৔߯ኧٰࡌᄬLC-tankᆶЬ୏চҹ໔ௗय़ޑៜᔈ(კ3.4)Ǵ྽ႝၡύ ޑλᚇૻanݙΕډ၀ௗय़ਔǴёаҔflow graph(კ3.5)ٰ߄Ңس಍཮ӵ

ՖϸᔈǴௗ๱ёа௢ளǺ

ǴR_IN⁽A^,Z⁾<0Ǵॄႝߔޑελ཮ᒿਁ൯ᆶᓎ౗ᡂ୏Ƕ

ϲᒡрૻဦޑਁ൯ǴӢԜόሡቚу DC Supply ൩ёуமᒡрф౗Ƕᗨ ฅΨёа٬Ҕ transformer ٰբߔלᙯඤǴՠࢂ transformer Ԗҁ፦΢

ޑલᗺǺ(1)คݤԭϩԭጠӝૻဦ೷ԋᒡΕૈໆཞ઻Ƕ(2)Ьᙅጕᆶԛ ᙅጕ໔཮Ԗ஌ғޑጠӝႝ৒ਏᔈǶ(3)཮ౢғόሡाޑӅਁǶԜѦǴӧ

ႝၡኳᔕਔሡा٬Ҕፄᚇޑႝၡኳٰࠠඔॊ᏾ঁ transformer ޑ੝

܄Ǵ܌аόҔѬբߔלᙯඤǶ

ஒ(3-8)ԄύޑQL LsZǶ

ĺRP2ёᙖԜගϲ ²

1 1) 1 (

p s

L ७

Colpittsک Hartley ਁᕏᏔΨࢂҔԜวБݤቚу LC-tank ޑ Q ॶǶ όၸ೭ٿঁࢎᄬࣁΑ٬ LC-tank ࣮ډ೏ᙯඤၸࡕޑଯႝߔǴሡाᡣ LS1ᆶ LP1(܈ CP1ᆶ CS1)ޑКॶࡐεǴӧ౜Ϟޑ IC ᇙำ΢όჴҔǴӢ ࣁ཮Ԗय़ᑈکᆒዴࡋޑ trade-offǶ

3.2.3 MD.ubol ϐ฻ਏႝၡ!

კ 3.11 LC-tank ϐ฻ਏႝၡᙯඤ

җܭႝགޑ Q ॶ೯தКႝ৒λǴ܌а LC-tank ޑ฻ਏ٠ᖄႝߔ (Rtotal)җႝགޑ RPL،ۓǺRp QL²/RSL (LZr)²/RSLˀˀˀˀˀˀˀˀˀˀˀˀˀˀˀˀˀˀˀˀˀˀˀ(3.9)

3.3 LC ᓸ௓ਁᕏᏔϐ೛ीୖኧന٫ϯ

3.3.1 LCаϷႝ඲ᡏޑᒧҔచҹ

२ӃԵቾ VCO ܌ሡाޑᒡрਁ൯Ƕ൩ԏวᐒԶقǴVCO ཮ௗӧ Mixerޑ LO ᆄǴԶ Mixer ཮׆ఈ VCO ૈගٮႽБݢ૓ِೲޑኩᄊϪ ඤǴ٬ Mixer ύ LO ᆄޑႝ඲ᡏᚇૻᓸڋӧനեॶǶԶၲԋ߈՟Бݢ ޑ LO ᒡрૻဦёаஒኧঁ࣬ӕޑ VCO ᒡруᕴࡕӆឲډ Mixer ޑ LO portёቚε۰ݢޑᒡрਁ൯Ǵӧ zero crossing ߈՟൩ႽБݢǹԜ

ѦǴӵ݀ VCO ૈԖ 50%ޑ duty cycle(ᡄᒠ 1 ᆶᡄᒠ 0 ޑਔ໔Ӛэ 1/2

ຼය)Ǵёаᗉխ LO ૻဦᅅډ IF ᆄǴቚம Mixer ޑ isolation ޑਏ݀Ƕ

ा٬ᒡрਁ൯ගϲǴനޔௗޑБݤ൩ࢂуεႝགॶǶL ຫεǴሡ

ाᙅޑ୮ኧຫεǴᙅጕߎឦޑߏࡋΨຫߏǴՍᖄޑΨၟ๱΢ϲ RSLǴ

܌а྽ L ک RSL΢ϲ k ७жΕ(3.9)Ԅёޕ Rp൩ၟ๱΢ϲ k ७Ƕӵ݀

٬Ҕ Off-chip ޑႝགٰуεགॶǴନΑቚуਁ൯ѦᗋёஒѺጕ೷ԋޑ

஌ғႝགਏᔈफ़եǶόၸਁᕏᓎ౗൩཮КၨեǴதҔޑ 5GHz س಍൩ คݤ٬ҔǶ

ቚуႝགॶᗋ཮Ԗځдޑલᗺᆶज़ڋǺ(1)ႝགޑԾਁᓎ౗फ़եǶ (2)ႝགޑ஌ғႝ৒ࡐεǴӵ݀Кᇙำύගٮޑёᡂႝ৒ᗋεǴVCO ޑᒡрᓎ౗ёፓጄൎ൩ᡂޑࡐλǶ

൩ᒧ᏷switch transistorsԶقǴҗܭ၀ႝ඲ᡏჹࢂЬाޑᚇૻྍǴ

ಃ΋Ѹ໪ᒧ᏷emitter areaၨεޑႝ඲ᡏ٬baseႝߔॶफ़եǴ෧Ͽ thermalᚇૻǶಃΒࢂफ़եbiasႝࢬǴᡣcollectorᆄޑshotᚇૻౢғၨλ ޑቹៜǶόၸБݤ΋཮ቚуႝ඲ᡏޑ஌ғႝ৒ǹБݤΒ߾ࢂᡣᒡрਁ

൯ᡂλǶӧ೛ीVCOਔǴа΢ޑୢᚒ೿ሡाуаԵቾ٠؃ள΋䵽ന٫

೛ीୖኧǶ

3.4 Phase Noise

3.4.1 Ֆᒏ Phase Noise

΋૓ޑ۰ݢૻဦёቪԋ^x⁽^t⁾ ^A^cos(Zc^tI⁽^t⁾⁾ǴI^(t⁾ࢂ΋ᅿ༾λޑᒿ ᐒᘋ୏ૻဦǴ൩ࢂ܌ᒏޑ phase noiseǶѬ೯தᇻλܭ 1 radǴ܌аёа

ஒ x(t) ߈՟ࣁ^A^cosZc^t^A^sinZc^tI⁽^t⁾ǴΨ൩ࢂI^(t⁾཮೏΢ၩډ ȦcǴᡣ Ȧc

ӧᓎ᛼΢Ԗဵៅౢғ(კ 3.12)Ƕ

Zc Z_c

ʳ კ 3.12 VCO ᒡрޑ౛གྷϷჴሞᓎ᛼

Phase noise வᓎ᛼΢ޑीᆉБݤࢂஒᚆύЈᓎ౗'Zޑᒡрф౗

(P2)ନѐύЈᓎ౗Zcޑᒡрф౗(P1)ӆନа'Z(კ 3.13)ǴځൂՏ൩ࢂ

dBc/HzǶШ

¸¸

¨¨

§ 'Z

1 2

log 10 P

ːP2,dBm P1,dBm¹⁰^log^'^Z

Z '

კ 3.13 Phase Noise ޑीᆉБݤ

ӧௗԏᐒஒᒡрૻဦϲᓎ܈ஔԏૻဦफ़ᓎਔǴ೿཮٬Ҕډ VCOౢғҁӦᆄޑਁᕏૻဦǶӵ݀Ԝ LO ૻဦԖ phase noiseǴӧԏว ၸำύǴځд channel ޑૻဦ཮೏ phase noise ޑဵៅਏᔈઇᚯǴӵკ 3.14Ǵךॺว৔рଯф౗ޑૻဦਔځဵᘍਏᔈ཮ᇂၸ adjacent channel ޑૻဦǴ٬ adjacent channel ޑ٬ҔޣԏόډѬ܌ሡޑૻဦǶ

Z

Zc Z,₃_dB

) (s H

ʳ კ 3.16 LC-tank ϐ band-pass ਏᔈ

Q ॶᗋԖќ΋ᅿۓကǴ൩ࢂ૸ፕ LC-tank ӧ໒଑ၡ(კ 3.17)ਔޑ

࣬Տᡂϯ(კ 3.18)Ǻ

Z I Z

d Q ^c d

2 ---(3.10) (open loop Q)Ƕ྽ LC VCO ೀܭᛙۓਁᕏਔǴLC-tank ޑߔלѝഭΠ ჴ೽ޑႝߔॶǴ܌а LC ޑ໒଑ၡᙯ౽ڄኧ཮ᆢ࡭ӧ ͠cǴό཮ගٮ ҺՖ࣬ՏޑᡂϯǶӵၸ Q ॶଯ൩߄Ң࣬Տჹᓎ౗ޑᡂϯ௹౗ࡐε(კ 3.18)Ǵӵ݀଑ၡ΢ԖҺՖᚇૻ೷ԋഈ଑ၡޑ࣬Տόࣁ႟ǴLC-tank ѝ ሡᅆ୏΋ᗺᓎ౗൩ёᔆံᚇૻ೷ԋޑ࣬ՏৡǴߥ࡭ഈ଑ၡޑ࣬Տࣁ

႟ǶӢԜǴQ ॶӵ݀ຫଯຫૈլܺᚇૻ೷ԋޑᓎ౗ᘋ୏Ƕӧ RF س಍

ύǴӵ݀ Q ॶૈӧ 20 а΢൩ё፾ҔܭࡐӭᔈҔύǶ

კ 3.17 LC-tank ໒଑ၡϐႝၡკ

1.5 2 2.5 3 3.5

Frequency (Hz)

Phase (degree)

Q=50 Q=10

ʳ კ 3.18 Q=50 ᆶ Q=10 ϐ LC-tank ࣬Տᡂϯკ

3.4.3 Phase Noise ӧ VCO ޑౢғᐒڋ

phase noiseёа٩ྣᚇૻྍޑݙΕᗺϩࣁٿᅿǺ(1)வਁᕏഈ଑

ၡύޑҺ΋࿯ᗺݙΕǹ(2)җ௓ڋᓎ౗ޑ Vtune ᆄݙΕǴ೭ٿᅿ׎Ԅ཮

җܭ VCO ࢎᄬ΢཮Ԗ΋ঁ LC resonator բᒧۓᓎ౗ҔǴ܌аҔ band-pass filterޑ໒଑ၡᙯ౽ڄኧٰ߄ҢǶ

2.3 2.32 2.34 2.36 2.38 2.4 2.42 2.44 2.46 2.48 2.5

ঁ߈՟ޑ໒଑ၡڄኧ(ࢂճҔ Taylor expension)Ǻ

> @

ĺ ⁽ ⁾ ^exp( ⁾ ^exp( I⁾

ǴаΠ൩ࢂҔ MatLab ฝрޑᚇૻᙯ౽ڄኧ( Leeson’s equation )( კ 3.21)Ǻ

კ 3.21 Leeson’s equation ӧᓎ᛼΢ޑៜᔈ

(3.16)Ԅࢂஒ࣬ՏᚇૻϷਁ൯ᚇૻ೯೯Եቾ຾ѐǴ܌аໆෳډޑ

࣬Տᚇૻ೯தѝԖ(3.16)Ԅᆉрޑ΋ъǶӵ݀ाளډӳޑ࣬ՏᚇૻǴ

ܴᡉޑሡाஒ Q ॶගϲǶԜѦǴӧ௢Ꮴ(3.16)Ԅਔ೿ଷ೛ࢂӧጕ܄ޑ

ॄӣ௤س಍Ǵόၸ΋૓ޑ VCO ೿཮Ԗਁ൯ज़ڋޑᐒڋǴ཮ౢғߚጕ

܄ ޑ ਏ ᔈ ٬ ᚇ ૻ ᡂ ε Ǵ ܌ а ሡ ा ஒ (3.16) Ԅ բ অ ҅ Ǻ

² ²

2 2

) 4 (

) (

A Q s

X s

Y _c

Z Z

' ǴA ࢂλૻဦഈ଑ၡቚ੻ǴӢԜ೛ीഈ଑ၡቚ੻ਔ ΨѸ໪ᖿ߈ܭ”1”಄ӝଆਁచҹջёǴց߾཮ஒᚇૻܫεǶ

კ 3.22 Noise җ VtuneᆄݙΕ

ಃ⁽²⁾ᅿǺӧ ^Vtuneᆄޑ^noise܌ౢғޑਏᔈ⁽კ ^3.22)

VCOޑ Vtuneᆄ(௓ڋᓎ౗ᆄ)ӵ݀Ԗ΋۰ݢૻဦᒡΕǴ཮೷ԋ FM ޑਏᔈǺ

Z

c Z

Z Zc

კ 3.23 ۰ݢ Noise җ VtuneᆄݙΕӧᓎ᛼΢ޑਏᔈ

Vtune ჹ VCO ޑ ᒡ р ᓎ ౗ϐ ௓ ڋБ ำ Ԅ ࣁǺZout Z0KVCOVtune Ξ

࣬଑ၡႝၡ(PLL)ύǴVCO ཮ௗܭ Law-pass filter ϐࡕǴӢԜ࿶җ Law-pass filterၸٰޑեᓎᚇૻ཮ᙖҗԜ noise ౢғၡ৩ቹៜ᏾ᡏ PLL ޑᚇૻ੝܄ǶࣁࣁΑׯ๓ԜᚇૻǴёஒ Kvco ޑॶफ़եǴόၸ཮ཞѨ VCOޑ Tunning rangeǶ

ځჴόѝࢂӧ VtuneᆄԖᐒ཮ౢғ Spurious ᚇૻǴҺՖૈׯᡂᓎ

౗ޑᐒڋ೿ё཮ౢғǴႽ BJT ޑ Icႝࢬ཮ׯᡂ base ک emitter ໔ޑ diffusion ႝ৒Ǵ຾Զׯᡂ LC ޑޑਁᕏᓎ౗Ǵ൩཮ౢғ Spurious ᚇૻǶ

3.4.4 VCO ޑୃᓸႝࢬჹ Phase Noise ޑቹៜ

җ Leeson’s modelǺ ₂ ₂

2 Z

Z ' Q P F kT

S ^c

sig

SSB ёޕǴࣁΑගϲ࣬Տᚇૻ

όѝाஒᚇૻ࣬Տᙯ౽ڄኧᓸեǴᗋाஒ VCO ᒡрޑф౗уεǶࣁ Αቚуᒡрф౗Ѹ໪ஒ bias ႝࢬуεǴёࢂ BJT ޑᚇૻႝࢬྍ฻ܭ

c f qI

i²/' 2 ǴIc ΢ϲ K ७཮٬ᚇૻႝࢬྍޑᒡрф౗уε K ७Ƕό ၸ൩ᒡрф౗ԶقǴIc ΢ϲ K ७ᒡрф౗ᡂࣁgmRPL² vIc²ǴගϲΑ K²७Ǵ܌а᏾ᡏᒡрф౗ᗋࢂёаගϲ K ७ǴӢԜуε bias ႝࢬё аׯ๓࣬ՏᚇૻǶҗܭᇙำόᘐޑ຾؁Ǵૈ٬Ҕޑႝᓸᡂޑຫٰຫ եǴVCO ޑᒡрਁ൯ΨᡂλǴჹ phase noise ޑቹៜࡐεǶ

ךॺᗋёаஒ K ঁ࣬ӕ VCO ޑᒡрӄ೽уӧ΋ଆ(კ 3.24)Ǵᒡ рૻဦޑਁ൯ёаቚу K ७Ǵඤᆉԋф౗ёаගϲ K²७Ǵᗨฅᚇૻ

Ψ཮ܫε K ७Ǵՠ᏾ᡏ࣬ՏᚇૻᗋࢂΠफ़ K ७ǶԜࢎᄬޑ trade-off

ၟ΢΋ࢤගډޑ bias ႝࢬཷۺ࣬үǴᗨฅׯ๓࣬Տᚇૻޑ੝܄όၸႝ

ၡޑӄ೽੃઻ф౗ΨቚуΑ࣬ӕޑКٯǶ

კ 3.24 ஒኧঁ VCO ޑᒡруᕴ

ӵ݀Ԗӳޑ Q ॶǴVCO ൩όሡाуε bias ႝࢬٰၲډس಍ा؃

ޑ࣬Տᚇૻೕ਱Ǵόՠ VCO ޑ੃઻ф౗ёаफ़եǴவႝ඲ᡏౢғޑ

ᚇૻႝࢬΨ཮ᡂλǶ

3.5 Pulling Ϸ Pushing ౜ຝ

ϐ߻܌૸ፕޑᚇૻਏᔈǴ೿ࢂӃଷ೛ᚇૻޑૻဦ࣬ჹܭ VCO ޑ ᒡрૻဦλࡐӭǶӵ݀Ԗᚇૻᚆ VCO ޑᓎ౗ࡐ߈Ъф౗ελၟ VCO ৡόӭε(კ 3.25)ǴVCO ޑᓎ౗൩཮೏܎୏ǴࣗԿᓎ౗൩೏ᚇૻᓎ౗

ᙹՐǴᆀϐ”Injection Pulling”Ƕ

Z0 Z_n

კ 3.25 VCO ϐ Injection Pulling ౜ຝ

೭ᅿ౜ຝதـܭௗԏᐒࢎᄬύǴႽࢂ Power Amplifier ൩཮วଌ ଯф౗Ъᓎ౗ᚆ VCO όᇻޑૻဦǴ VCO ޑᓎ౗൩཮೏ Power Amplifierޑว৔ૻဦ܎୏ǹԜѦǴӧךॺགྷௗԏ channel ޑᎃ߈ channel Ԗଯф౗ޑૻဦӧว৔(კ 3.26)ǴԜଯф౗ૻဦΨ཮ᙖҗ Mixer ቹៜ ډ VCO ޑᓎ౗ǴӢӢԜ VCO ሡा΋ಔଯ reverse isolation ޑ Buffer

ٰᗉխᚇૻݙΕ VCO Զቹៜᒡрᓎ౗ǴόၸԜ Buffer ཮೷ԋ Mixer ޑ Noise Figure ᡂεǶ

VCO LNA Mixer Signal

Desirede

Interferer

྽ VCO ᏹբӧ open-loop ਔჹܭ Loading ޑᡂϯΨ੝ձ௵གǴႽ

ࢂ DECT س಍ύǴPower Amplifier ཮όਔޑ໒ᜢٰ࿯࣪ႝྍǴ೷ԋ VCO ޑ Loading ΋ޔӧᡂϯǴځᒡрᓎ౗Ψ൩คݤᛙۓǴᆀϐ”load pulling”ǶࣁΑׯ๓ԜਏᔈǴሡӧ VCO Ϸ PA ໔࿼Ε΋ঁ high-isolaiton ޑ BufferǶ

VCO ჹܭ DC ٮᔈႝྍޑᡂ୏Ψࡐ௵གǶ྽ VddౢғᡂϯǴӧ varactor ٿᆄޑᓸৡ൩཮ၟ๱ᡂϯǴਁᕏᓎ౗Ψ൩ၟ๱ᅆ୏Ǵᆀ ϐ”supply pushing”ǶӧЋᐒύ PA ᗋࢂ೷ԋԜ౜ຝޑЬӢǴҗܭႝԣ Ԗᒡрႝߔу΢ PA ໒໒ᜢᜢ೷ԋ Loading ޑᡂ୏Ǵ٬ VddԖኧԭ mV ޑᡂ୏Ƕ

3.6 ৡ୏ Bipolar LC Oscillator

Ԑයޑ RF ਁᕏᏔӭ٬Ҕൂ΋ transistor ٰჴ౜Ǵҗܭ٬ҔനϿޑ Ь୏ϡҹ Phase Noise ёаԖӳޑ੝܄ǴЪԜႝၡޑሽ਱ΨёаᓸեǶ όၸᒿ๱ᇙำόᘐ຾؁ǴIC ޑሽ਱ςε൯फ़եǴ܌аҞ߻ςόӆ٬

Ҕൂ transistor ࢎᄬǴόၸᗋࢂёаᙖҗځচ౛௢ቶډৡ୏ VCO ޑၮ բኳԄǶ

ൂ΋ transistor ޑ VCO ௗጕБԄӵკ 3.27Ǵӣ௤ၡ৩Ѹ໪ᒧ᏷ᡣ ӄ೽ၡ৩ޑᕴ࣬Տৡࣁ႟(Barkhausen criteria)ǴЪ LC-tank ӧਁᕏਔ ό཮ගٮ࣬ՏᡂϯǴӢԜѸ໪ᒧ᏷ஒ collector ޑૻဦӣ௤ډ emitter аගٮ႟࣬Տᡂϯ(კ 3.27)ǶԜѦ LC-tank ޑӣ௤ၡ৩Ѹ໪ௗܭଯߔ לᆄаᗉխ LC-tank ޑ Q ॶΠफ़(

L R C L

p o p

)

( Z )Ǵ܌аஒځௗܭ Collector ᆄ(Emitter ᆄޑߔלѝԖ 1/gm)Ξ٬ Q ॶӆԛΠफ़ǴӢࣁ LC-tank Ξ࣮ډ emitter ᆄޑեႝߔǶׯ๓Бݤ൩ࢂճҔ 3.2.2 ࿯ύ܌

ගޑ passive impedance transformation(კ 3.28)Ǵᡣ LC-tank ᆄ࣮ډଯ ߔלǶԜБԄ൩ࢂ Colpttis Ϸ Hartly ਁᕏᏔ(კ 3.29)Ƕ

LC

Q1 ^feedback^path

კ 3.27 ൂ΋ transistor ϐ VCO ௗጕკ

tion transforma impedence

კ 3.28 კ 3.27 ϐׯ຾ VCO ႝၡ

Colpitts Hartley

ӵ ݀ ࣁ Α ᡣ LC-tank ࣮ ډ ၨ ଯ ޑ ߔ ל ٠ ό ΋ ۓ ा passive impedance transformationޑБݤǴёаճҔ΋ঁ active buffer ٰၲԋ

࣬ӕ ਏ݀(კ 3.30)ǴӢ ࣁѬёаගٮࡐ εޑᒡΕߔלǴcommon collectorܫεᏔ൩ૈᙁൂޑ಄ӝ΢ॊा؃Ƕӵ݀ӆஒ Q2ஒޑ Collector ᆄӧௗ΢΋䵽 LC-tank ٠ௗӣ Q1 ޑ emitterǴ൩׎ԋΑதـޑৡ୏

VCO(კ 3.31)ǶԜࢎᄬόѝёаҔ Barkhausen criteria ٰᇥܴځਁᕏচ

౛Ǵҭё࿶җλૻဦኳࠠ௢ᏤрǺவ Q1ک Q2ޑ Collector ᆄ࣮Εёа

࣮ډ฻ਏޑॄႝߔ(-2/gm)(კ 3.32)Ǵ܌аԜࢎᄬΞᆀࣁ Negative-Gm

ਁᕏᏔǶ

Q1 Q1

კ 3.30 ճҔ active buffer ౢғߔלᙯඤ

Q1 Q₂

Rin

კ 3.31 ৡ୏ LC ਁᕏᏔ კ 3.32 ճҔ cross-coupled pair ౢғॄႝߔ

3.7 ჴբ΋ǴVoltage-Controlled Oscillator with

Differential Excitation Trifilar ( SiGe HBT 0.35 ͔m)

3.7.1 ࣴز୏ᐒ

ਁᕏᏔႝၡӧคጕ೯ૻس಍ႝၡύǴתᄽΑ΋ঁ࣬྽ख़ाޑف ՅǴ߈ԃٰ΋ޔԖӚԄӚኬޑ᎜ᕏځ่ᄬӧ paper ΢ว߄ǴႽࢂճҔ όӕޑႝགᙅጕБݤஒ Q ޔගϲǴ٬ phase noise ளаׯ๓ǹ׭܈ࢂ

ׯᡂ᏾ঁႝၡޑࢎᄬǴ෧λႝ඲ᡏޑᚇૻჹᒡрૻဦޑυᘋǶӧᇙำ Бय़ǴSiGe BiCMOS ᇙำ࣬྽፾ӝҔٰჴ౜ SOC ႝၡǴӧኧՏ܈ᜪ КႝၡБय़ёаҔ CMOS ٰ࿯࣪य़ᑈǹӧଯᓎႝၡБय़൩ёճҔଯ ᄒЗᓎ౗ޑ HBT ٰჴ౜Ƕᗨฅ SiGe ޑ୷݈ཞ઻КځдΟϖ௼ϯӝ୷

ٰ݈ޑεǴՠࣁΑ࿯࣪ԋҁǴӵ݀೯ૻس಍ڙԜલᗺޑቹៜόεǴᗋ

ࢂ໼ӛ٬Ҕ SiGe BiCMOS ٰჴ౜ႝၡǶ

ҁԛჴբޑႝၡࢎᄬࢂճҔཥԄޑ TransformerǴёаӕਔჴ౜

Hartleyࢎᄬޑ VCO аϷ inductive coupling ޑӣ௤БݤǴ٬ VCO ޑ Phase NoiseᡂեǵᒡрႝᓸጄൎᡂεǶԜࢎᄬӧ IEEE ޑ paper ΢ᗋ

҂ـว߄Ƕ

3.7.2 ࢎᄬᙁϟ

Part1. VCOϐӣ௤Бݤ೛ीǺ

ࣁΑ٬ VCO ޑ phase noise ᡂλǴനᙁൂޑБݤ൩ࢂᙖҗуεӅ

ਁ๚ޑਁᕏႝᓸٰቚமӅਁ๚ύޑૈໆᓯӸǶ΋૓ޑ VCO ࢎᄬࢂճ Ҕ΋ჹ emitter-coupled ႝ඲ᡏу΢ cross feedback ٰౢғॄႝߔǴӧ Ԝࢎᄬ΢ᒡрႝᓸޑελ൩ڙډ feedback Бݤޑज़ڋǴԶதـޑӣڙ

БݤԖΟᅿǺ(1)ޔௗӣ௤ (კ 3.33)ǵ(2) ճҔႝ৒բጠӝӣ௤ (კ 3.34)ǵ(3)ճҔႝགբጠӝӣ௤ (კ 3.35)Ƕ

კ 3.33 ޔௗӣ௤ࢎᄬ კ 3.34 ႝ৒ጠӝӣ௤

നᙁൂޑӣ௤Бݤ൩ࢂ௦Ҕ”ޔௗӣ௤”ࢎᄬǴѬόҔᚐѦޑୃᓸ

ႝၡ܌а෧Ͽф౗ޑ੃઻Ǵόၸႝ඲ᡏޑ base-collector junction ཮ԋ

ࣁᒡрႝᓸޑज़ڋӢનǴ೭ࢂӢࣁ྽ᒡрਁ൯ၸεਔǴ཮೷ԋ୷ཱུ-໣ཱུ໩ୃǴԶߚךॺགྷाޑ଍ୃރᄊȐ೛ीਁᕏᏔሡᏹբӧЬ୏୔ȑǴ ځ໔ޑ diode ൩཮ჹႝၡౢғᚇૻྍ٬ phase nosie ᡂৡǴ܌аځᒡр

ႝᓸਁ൯ஒ཮೏Ԝௗय़ޑႝᓸ܌ज़ڋՐǶऩ௦Ҕ”ႝ৒ጠӝӣ௤”ϐႝ

ၡǴᗨёаׯ๓΢ॊޑਁ൯લᗺǴՠѸ໪ӧ୷ཱུගٮୃᓸǴԶගٮୃ

ᓸਔǴሡ٬Ҕଯߔॶႝߔ܈ࢂଯགॶႝགǴՠ཮೷ԋ࣬Տᚇૻᡂৡ܈

ࢂሡा՞Ᏽεໆ඲Тय़ᑈ(p.s ୃᓸႝߔѸ໪Кҗႝ඲ᡏ base ᆄ࣮рѐ ޑႝߔ R1(х֖ጠӝႝ৒ک LC tank ӧਁᕏਔޑߔॶ)ଯ 10 ७Ѱѓωё ۹ౣځᚇૻྍ)Ƕ

კ 3.35 ႝགጠӝӣ௤

ࣁΑᗉխ΢ॊٿᅿࢎᄬޑલᗺǴԜԛ೛ीޑӣ௤ࢎᄬǴஒճҔ”

ႝགጠӝӣ௤”ٰ೛ी೭ԛޑᓸ௓ਁᕏᏔǶեᒡрߔॶޑୃᓸႝၡё аޔௗௗ΢ႝၡǴӢࣁԖႝགௗܭႝᓸྍ߻ǴόҔᏼЈ VCO ૻဦ཮

ᅅрѐǶԜѦό٬ҔႝߔٰୃᓸǴёٛЗౢғ white noise Զ٬ Phase NoiseΠफ़ޑ౜ຝǶԜѦǴ၀ࢎᄬёаፓ᏾ base ᆄޑႝᓸǴӅਁ๚ޑ നεਁ൯൩όӆڙ base-collector ޑ໩ୃज़ڋǴѝाԵቾ base-emitter diodeک current source ޑᓸफ़Ƕ

നεᒡрႝᓸޑज़ڋచҹҞ߻ѝഭ varactorǴӵ݀ᒡрਁ൯ຬၸ

΋ঁ diode ޑ໒௴ႝᓸ཮٬ varactor ޑ pn-junction Ꮴ೯Ǵౢғཥޑᚇ

ૻྍǶׯ๓Бݤ൩ࢂӧ varactor ߻Սᖄ΋ႝ৒Ǵᗨฅ཮෧Ͽ VCO ޑ ᓎ౗ёచጄൎόၸёаᡣᓎ౗ፓ᏾ޑ੝܄ၨࣁጕ܄Ƕӵკ 3.36 ճҔ fC1ஒ varactor ᆶ output signal ႖໒ǴӧҔ R1Ϸ R2ჹ varactor բୃᓸǶ

კ 3.36 Varactor ୃᓸႝၡϷӣ௤ႝၡϐ่ӝ Part2. Hartley VCOճҔtransformerբӣ௤Ǻ

ਥᏵ paper ޑࣴزว߄ࡰрǴColpitts VCO (კ 3.37) ࣬ჹܭځд

ࢎᄬޑ VCO Ԗၨӳ ISF(impulse sensitivity function)Ǵ൩ࢂӧ΋ঁ VCO ᒡрຼයϣѝԖ΋λࢤਔ໔ collector ཮ԖႝࢬݙΕǴЪ၀λࢤਔ໔ว ғӧ VCO ᒡрനεਁ൯ߕ߈Ǵ٬ளႝ඲ᡏᚇૻྍჹ phase noise ޑଅ

᝘നλǴ܌аӵ݀ाၲډե Phase Noise ޑा؃ǴColpitts ࢎᄬࢂΜϩ

፾ӝޑǶόၸჴሞ΢ךॺ٬Ҕޑࢎᄬკ 3.39 ӵ݀฻ਏԋკ 3.40 ཮К

ၨႽ Hartley (კ 3.38)Ǵѝৡӣ௤ၡ৩όҔႝ৒ԶࢂҔ transformerǶό ޔௗ٬Ҕ Colpitts ޑচӢࢂӧ٬Ҕႝ৒բӣ௤ਔ཮࿘ډ LC-tank impedanceаϷ Q ॶޑ trade-offǺࣁΑቚу LC-tank ޑ Q ॶѸ໪ஒ

C L

ॶᡂεǴ܌а C ॶѸ໪λǴёࢂӵ݀ाஒ tank ޑ impedance ᡂεѸ

໪ගଯ

2 1

C Ǵՠ tank ޑ C ॶς࿶όεǴӧჴሞ layout rules ΢൩όܰჴ

౜Ƕ

კ 3.37 Colpitts VCO კ 3.38 Hartley VCO

ךॺ٬Ҕޑࢎᄬځӣ௤Бݤᆶ Colpitts ࣬՟Ъ ISF Ψک Colpitts

࣬үǴ܌а٩ฅ཮Ԗե Phase Noise ޑ੝܄Ƕ

1 / :

2 2 1

k L L

კ 3.39 ճҔ transformer բߔלᙯඤ კ 3.40 კ 3.39 ϐ฻ਏႝၡ Single-ended Colpitts VCOӧჴሞၮҔ΢٠όቶݱᗋԖ΋ঁЬा

ޑচӢǴ൩ࢂሡाၨଯޑ open-loop gain ٰዴߥႝၡ཮ԾวਁᕏǴЪ single-endedჹܭ substrate ک power supply ޑ noise ၨ௵གǴ܌а೭ԛ

೛ीޑႝၡճҔ cross-coupled ႝ඲ᡏჹ(Part1.ύගډޑ transformer coupling)ٰၲԋ differential ࢎᄬ (კ 3.41) Ǵ෧ᇸଆਁ߻܌ሡޑ open-loop gainǶ

კ 3.41 ҁჴբϐֹ᏾ VCO ႝၡკ Part3. ཥԄ Transformer (Trifilar)Ǻ

ךॺགྷჴ౜ޑཥ VCO ࢎᄬύ(კ 3.41)ሡा΋ჹΒޑ transformer (კ 3.42)Ǵӧ paper ύමр౜ԖԜфૈޑ transformer ћ଺ TrifilarǴࢂ

ௗ ӧ Single-ended LNA ࡕ ౢ ғ ΋ ಔ differential ޑ ૻ ဦ ٰ ០ ୏ Double-balanced Mixer (კ 3.43)ǶTrifilar ޑ Layout ่ᄬ(კ 3.44)ࢂᙖ җΟঁ transformer ϕᙅǴёаගϲӚႝགҁيޑ Q ॶǴ຾Զׯ๓ Phase NoiseǶ

კ 3.42 1-to-2 transformer Ңཀკ კ 3.43 Trifilar ӧჴሞႝၡ٬Ҕϐጄ ٯ

კ 3.45 ճҔ Center-tape ٰჴ౜ Differential Trifilar

җܭҁ VCO ࢂ differential ࢎᄬǴךॺёஒൂ΋ Trifilar բ differential excitationǴԶ DC ޑᒡΕ൩җ center-tape(c.t)ௗᗺᒡΕ(კ 3.45)ǴӵԜ΋ٰ൩ёаҔ΋ঁ Trifilar ၲԋკ 3.41 ܌ሡޑ transformer couplingਏ݀Ǵ඲Тय़ᑈёаε൯ᕭ෧Ƕ

(1)ጠӝᡂᓸᏔϐኳᔕ

ճҔEM ኳᔕ೬ᡏ՗ᆉᡂᓸᏔޑୖኧϷጠӝ߯ኧǺ

m5freq=

K_sim2=0.5614.000GHz

2 3 4 5 6

freq, GHz

K_sim2

K_sim1

Primary inductorډٿঁSecondary inductorଽӝ߯ኧǺ ĺ K=0.561 Transmission Coefficient= -9.242dB @4GHzǶ

m6freq=

dB(S(2,1))=-9.2424.000GHz

2 3 4 5 6

freq, GHz

dB(S(1,1))dB(S(2,1)) m6

dB(S(3,1))

Primary inductorᆶٿঁSecondary inductorޑႝག QॶǶ

m3freq=

Q11=11.5024.000GHz m4freq=

Q12=6.2624.000GHz

2 3 4 5 6

freq, GHz

Q11

Q12 m4

Q13

3.7.3 Ⴃीೕ਱ӈ߄

Item Spec Supply Voltage 3 V

Current of QVCO core 4.18 mA Current of Output buffer 21.8 mA Power Consumption of core ~ 12.54 mW

Tuning frequency range 4.170GHz~4.381GHz

KVCO 263MHz/V

Phase Noise -115.6dBc/Hz @ 1MHz offset

FOM -176.7 dBc/Hz

Die size 1.040 × 0.880 mm Layout Photo

3.8 ჴբΒǴTrifilar Based Voltage-Controlled Oscillator ( SiGe HBT 0.35 ͔m)

ҁ ჴ բ ޑ ࣴز ୏ᐒ ᆶ ࢎ ᄬ ᙁϟ ࣣᆶ ȹ ჴ բ ΋ȹ ࣬ӕ Ǵ ୤ ӧ usjgjmbs ޑ٬Ҕ΢ӧȹჴբ΋ȹࢂҔൂ΋ঁٰբ ejggfsfoujbm!

fydjubujpoǴԶӧҁჴբ΢ࢂ٬Ҕٿޑൂᐱޑ usjgjmbsǶ!

3.8.1 Ⴃीೕ਱ӈ߄

Item Spec Supply Voltage 3 V

Current of QVCO core 2.95 mA Current of Output buffer 21.6 mA Power Consumption of core ~ 8.85 mW

Tuning frequency range 4.010GHz ~ 4.131GHz

KVCO 153MHz/V

Phase Noise -117dBc/Hz @ 1MHz offset Die size 1222 um × 784 um Layout Photo

ಃѤക

҅Ҭ࣬Տᓸ௓ਁᕏᏔ

4.1 ߻ق

Zero-IFک Low-IF ࢂҞ߻೏ቶݱၮҔޑௗԏᐒࢎᄬǴҗܭԜࢎᄬ όሡ٬ҔѦௗޑ೏୏ϡҹǴёаֹӄҔൂ΋ᑈᡏႝၡٰჴ౜Ǵ܌аӧ คጕԏวᐒ೛ीਔத཮٬Ҕ၀ࢎᄬǶࣁΑᗉխ໺ԏૻဦόֹӄǴԜࢎ

ᄬሡाӕ࣬Տ(in-phase)ک҅Ҭ࣬Տ(quadrature)ޑҁӦਁᕏᏔ(LO)ૻ

ဦٰ໺ԏૻဦǶԜѦǴimage-reject ޑௗԏᐒΨाҔ҅Ҭ࣬Տޑ LO ע

᜔Ⴝૻဦ੃௞Ǵനதـޑٯη൩ࢂ Hartley ک Weaver ࢎᄬǶӧ΋٤ፄ ᚇޑኧՏፓᡂس಍ύ(GSMǵDECT)ࣁΑᕭλᓎቨޑ٬ҔǴ҅Ҭ࣬Տ ޑ LO ૻဦ׳ࢂόёϿǶౢғ҅Ҭ࣬Տޑ LO Ԗ೚ӭБݤǴႽࢂ٬Ҕ

೏୏ϡҹޑ poly-phase filterǵᕉࠠਁᕏᏔ(Ring Oscillator)ǵ܈ࢂಔӝ

΋٤Ь୏ႝၡֹٰԋǴόၸа΢Бݤ೿཮Ԗ΋٤લᗺ٬ѬॺޑჴҔ܄

फ़եǴӢԜҁക࿯ஒϟಏኧᅿёՉ܄ଯޑႝၡࢎᄬ٠৖Ңჴբ่݀Ǵ ჹܭதҔޑ໺ԏᐒࢎᄬΨբ૸ፕǶ

4.2 Homodyne Receivers

4.2.1 Homodyne ௗԏᐒޑ੝܄ᙁϟ

Homodyne ک Heterodyne Receiver ޑനεόӕᗺǴ൩ࢂӧಃ΋ԛ ޑ फ़ ᓎ ਔ ޔௗ ע RF ޑ ᓎ ᛼ फ़ ډ ୷ᓎ Ǵ ܌ а Ξ೏ ᆀࣁ ”Zero-IF”

܈”Direct-conversion”Ƕკ 4.1 ࢂ΋ঁᙁൂޑ Homodyne ௗԏᐒǴLO ޑᓎ౗کᒡΕၩݢޑᓎ౗΋ኬǴ࿶ၸ LNA ܫεϷ Mixer फ़ᓎϐࡕௗ

΋ঁե೯ᘠݢᏔջёᕇளགྷाௗԏޑૻဦǴόၸ၀ࢎᄬѝёҔܭ double-sidebandޑ AM ૻဦǴӢࣁ AM ҅ॄٿୁޑᓎ᛼ࢂ΋ኬޑǴӧ फ़ᓎࡕᓎ᛼ֹӄख़᠄٠ό཮วғୢᚒ(კ 4.2)Ƕӵ݀ा໺ଌ FM ܈ࢂ

QPSKޑૻဦǴѸ໪٬Ҕ҅Ҭ࣬Տޑࢎᄬ(კ 4.4)Ǵҗܭፓᡂࡕޑߞဦ

ӧ҅ॄᓎ᛼΢٠όჹᆀǴӵ݀Ҕკ 4.1 ޑБݤӧफ़ᓎਔ҅ॄᓎ᛼཮࣬

Ҭ᠄Ǵ೷ԋૻဦޑཞᚯ(კ 4.3)Ƕ

LNA

0t cosZ

LPF

Zc Z ₀ Z

კ 4.1 Homodyne Receiver

0 Zc Z

კ 4.2 AM ૻဦ࿶ Homodyne ௗԏᐒϐफ़ᓎៜᔈ

0 Zc Z

კ 4.3 FM ૻဦ࿶ Homodyne ௗԏᐒϐफ़ᓎៜᔈ

LNA

0t cosZ

LPF

0t sinZ

LPF

I

Q

კ 4.4 ҅Ҭ࣬Տௗԏᐒ

0 Zc Z Zc

კ 4.5 FM ૻဦ࿶҅Ҭ࣬Տௗԏᐒϐफ़ᓎៜᔈ

Homodyne ௗԏᐒޑࢎᄬၨ Heterdyne ࢎᄬᙁܰǴගٮΑٿ໨ᓬ ᗺǺ(1)җܭύᓎૻဦ(IF)ࣁ႟Ǵό཮Ԗ᜔Ⴝ(Image)ૻဦౢғ൩όሡा

уΕ Image FilterǴLNA ൩όҔ០୏ 50 ኻۅޑॄၩǶ(2)IF SAW Filter کΠ΋ભޑफ़ᓎႝၡӧԜࢎᄬύόӧሡाǴѝाե೯ޑᘠݢᏔک୷ᓎ ޑܫεᏔջёǴᡣௗԏᐒёӧൂ΋ᇙำ΢ֹӄჴ౜Ǵаճܭ SoC ᏾ ӝ Ƕ ό ၸ Ԝ ࢎ ᄬ ᗋ ࢂ Ԗ ΋ ٤ Heterdyne ό ཮ ၶ ډ ޑ ୢ ᚒ Ǵ ೷ ԋ Direct-conversionؒԖᐱэ᏾ޑௗԏᐒѱ൑ǶаΠբᇥܴǺ

(1) DC Offsets

Homodyne ࢂஒૻဦޔௗफ़ᓎډ DCǴ܌аҺՖѦٰޑ DC ୃ౽೿

཮٬ૻဦᎁڙઇᚯǴҗკ 4.6 ک 4.7 ٰ૸ፕӧௗԏᐒύԜୢᚒӵՖว ғǺ

LNA

0t cosZ

LPF

Leakage LO

A B C

კ 4.6 LO ૻဦ೷ԋޑ Self-mixing

LNA

0t cosZ

LPF

Leakage Interferer

კ 4.7 RF ૻဦ೷ԋޑ Self-mixing

२ӃǴMixer ύ LO port ډ RF port аϷ LNA ᒡΕᆄޑ႖๊ਏ݀

(Isolation)٠ߚԭϩϐԭǴLO ૻဦ൩཮ᅅډ A Ϸ B ᗺǴӵ݀Քᒿ୷݈

ޑጠӝਏᔈǴԜ”LO leakage”׳ࣁᝄख़ǶԜᅅૻဦਏᔈനಖ཮ӧ Mixer

ၟ LO բషݢǴӧ C ᗺౢғ΋ঁ DC ॶǴԜ౜ຝᆀϐࣁ”self-mixing”(კ 4.6)Ƕӕኬޑӵ݀Ԗଯф౗ޑυᘋૻဦҗ LNA ᆄௗԏΠٰǴᗋࢂҗܭ Mixer ޑ RF-to-LO Isolation Ԗज़ǴυᘋૻဦΨ཮ᅅډ LO portǴ self-mixingΞӆౢғ(კ 4.7)Ƕ

(2) I/Q mismatch

ӧ Homodyne ࢎᄬ΢ाჴ౜ PM ܈ FM Ѹ໪٬Ҕ҅Ҭ࣬Տޑࢎ

ᄬǴ܌аाஒ LO բ 90 ࡋޑ࣬Տѳ౽Ƕӵ݀ IǵQ ໔ؒԖྗዴޑ 90 ࡋৡ܈ࢂԖਁ൯ޑό΋ԿǴӧբफ़ᓎਔૻဦޑ০኱კ཮ౢғᇤৡ٬

bit error rateϲଯ(კ 4.8)

LNA

Error Phase and Gain Induced

კ 4.8 I/Q mismatch ӧԏวᐒ΢ޑቹៜ

ࣁΑ׳၁ᅰޑΑှ IǵQ όჹᆀჹௗԏૻဦޑቹៜǴբаΠޑ௢

Gain PhaseError

Q Q

კ 4.9 I/Q mismatch ჹૻဦ০኱კౢғޑቹៜ (3) Even-Order Distortion

೯ த ך ॺ ѝ ཮ ຎ Odd-order distortion ࣁ υ ᘋ ૻ ဦ Ǵ ё ࢂ ӧ HomodyneޑௗԏᐒΠ Even-order ޑߚጕ܄੝܄Ψჹௗԏૻဦ೷ԋυ ᘋǶаკ 4.10 ٰᇥܴǺٿঁᎃ߈ޑଯф౗ૻဦ(^x(^t) ^A1cosZ1^t^A2cosZ2^t)

t A

A₁ ₂cos( ₁ ₂)

2 Z Z

D Ǵҗܭٿᓎ౗ᚆࡐ߈ǴԜ Even-order distortion ӧ཮

ӧ DC ߕ߈р౜ǶӵၸௗΠٰޑ Mixer ࢂ idealǴ΢ॊޑ distortion ൩

კ 4.10 Even-order distortion

ځჴόѝ LNA ཮Ԗ Even-order distortion ޑ౜ຝǴMixer ޑ RF port ΨԖ࣬ӕޑୢᚒวғǴӢࣁௗԏૻဦ࿶ၸ LNA ࡕޑਁ൯ς࿶ᡂεǴ

܌ а ׎ ԋ distortion ޑ ៜ ᔈ ཮ ׳ ᝄ ख़ Ƕ ኳ ᔕ Mixer ਔ ൩ ा Ե ቾ ډ”IP2”(second-order intercept point)ǴኳᔕޑБݤၟ IP3 ΋ኬǴѝࢂஒ Odd-orderޑբკඤԋ Even-order ޑբკǶ

(4)Flicker Noise

೯தௗԏૻဦ࿶ၸ LNA ک Mixer ࡕεऊԖ 10mV ޑਁ൯Ǵ܌а

ௗΠٰӚભႝၡޑᒡΕᚇૻᡂޑߚதख़ाǴЀځ Homodyne ࢂޔௗஒ

ૻဦ໺ډ DCǴ܌аЬ୏ϡҹޑ¹^/ ^f noise ൩཮೷ԋᝄख़ቹៜǴׯ๓Б ݤ൩ࢂӧ RF ૻဦᆄஒቚ੻ӧගଯǴႽࢂ٬Ҕ active ޑ Mixer ڗж passiveޑ MixerǶ

4.2.2 а Homodyne ࣁ୷ᘵޑ image-reject ௗԏᐒ

җܭ Heterodyne ޑௗԏᐒѸ໪٬Ҕ image-filter ٰ੃ѐ᜔ႽૻဦǴ

ޣޑࣴزБӛϐ΋ǶҞ߻ቶݱ٬Ҕޑ image-reject ࢎᄬࣁǺ(1)Hartley

ࢎᄬǹ(2)Weaver ࢎᄬǶ (1) HartleyǺ

Ԝ่ᄬѝሡ΋䵽҅Ҭ࣬Տޑ LOǴӧሽ਱΢ёаᙖ๱෧Ͽ඲Тय़ ᑈԶफ़եǹځԛǴࢂ೛ी΢ΨКၨᙁൂѝሡу΋䵽 90⁰ޑ phase shifterǶ

ӧઞᓎޑచҹΠǴphase shifter ӧᓎ᛼΢ёҔG⁽Z⁾ j^sgn(Z⁾(კ 4.12)ٰ߄ҢǴჴኧૻဦ࿶ၸ phase shifter ࡕϝ཮ࢂჴኧǴѝ཮ᡣ҅ॄ

ᓎޑૻဦ࣬ՏวғᡂϯǶ90 ࡋޑ࣬Տѳ౽ёаճҔᙁൂޑ೏୏ϡҹ

ٰჴ౜Ǵკ 4.13Ǵ^Vin^(t⁾࿶ၸ phase shifter ࡕV_out1⁽t⁾ǵV_out2⁽t⁾ᆶ^Vin^(t⁾ޑ࣬

Տৡ฻ܭS^/²^tan¹⁽^RCZ⁾Ϸ^tan¹⁽^RCZ⁾Ǵ܌аӧV_out1⁽t⁾ǵV_out2⁽t⁾໔൩ౢ

ғΑ 90 ࡋޑ࣬ՏৡǶόၸԜ phase shifter ႝၡѝૈ፾ҔܭઞᓎǴ܌а HartleyࢎᄬόૈҔܭቨᓎޑ೯ૻس಍ࢎᄬύǶ

90^oshift

Channel

Desired Image

კ 4.12 Phase shifter ӧᓎ᛼΢ޑៜᔈ

Vin

܌аVout1ᆶVout2ޑ࣬Տৡ90ࡋǶᗨฅவ࣬Տ΢࣮ଆٰόፕӧবঁᓎ౗

ޑ࣬Տৡ೿཮Ԗ90ࡋǴόၸਁ൯΢൩ό࣬ӕΑǴѝӧZ ^{1 RC}^/( ⁾཮΋

ኬǴӢԜ၀ phase shifter ࢎᄬ٠όૈቨᓎ٬ҔǶ

(2) Weaver Ǻ

ࣁΑׯ๓ Hartly ޑઞᓎલᗺǴஒ೷ԋႝၡઞᓎޑಔҹҔځдБݤ ڗжǴ܌аҔಃΒಔޑ Mixer ٰඹඤ 90 ࡋޑ phase shifterǴёᆢ࡭

Image-reject ޑ੝܄ǴόၸΨӢࣁӭ٬Ҕ΋ಔ Mixer ٬ԋҁ΢ϲǴ೛

ीਔΨၨࣁፄᚇǶ

Channel

Desired Image

΋ठ೿཮ቹៜډ᏾ঁࢎᄬޑ Image-rejection ਏ݀Ƕ೯த Image rejection ratio ၲ 30~40dBǴLO εཷԖ 0.2~0.6dB ޑਁ൯ᇤৡϷ 1~5 ࡋޑ࣬Տ

ݱ٬ҔޑБݤࢂஒ LC-tank ޑ VCO ᏹբӧךॺሡाᓎ౗ޑٿ७ᓎǴ ӆ࿶ၸନᓎႝၡࡕளډ҅Ҭ࣬Տޑૻဦ(კ 4.15)ǶԜБݤёаᗉխ VCOڙډ PA ౢғமεૻဦޑ௢܎ਏᔈ(pushing/pulling effect)ǴӢࣁ VCO ᏹբӧ PA ޑٿ७ᓎǴՠࢂ཮ԖаΠޑલᗺǺ(1)ٿ७ᓎޑ VCO ӧ೛ीၨ֚ᜤǴЪ҅Ҭ࣬Տޑྗዴ܄཮೏ VCO ࢂցԖ 50%ޑ duty cycleज़ڋՐǶ(2)ௗܭ VCO ϐࡕޑନᓎᏔѸ໪ଯᓎᏹբǴ܌аႝ඲ᡏ ޑ current density Ѹ໪ගଯډᡣ fTၲཱུॶǴӢԜቚуႝၡޑф౗੃઻Ƕ

Latch D

Latch D Clk

Clk

Clk

I I

Q Q

კ 4.15 ճҔø2 ႝၡౢғ I/Q ૻဦ

ӵ݀Ҕ RC ಔԋޑ poly-phase filter ࢎᄬ൩׳઻ф౗Α(კ 4.16)Ǵ Ѹ໪ӧ VCO ک poly-phase filter ໔уΕ bufferǴ΋Бय़ёᗉխ VCO ύ LC-tankޑ Q ॶ෧ϿǴ΋Бय़Ҕٰံᓭ RC ႝၡ೷ԋޑૻဦ૰෧Ǵω

ૈ௢୏ௗΠٰޑ MixerǶԜѦǴpoly-phase filter ཮઻຤࣬྽εޑ඲Т य़ᑈǴԋҁӢԶගଯǶ

კ 4.16 ճҔ Poly-phase Filter ౢғ I/Q ૻဦ

ऩགྷҔ ring oscillator ޑࢎᄬǴѬޑ phase noise Ξϼৡό፾Ҕܭ౜

ϞޑԏวᐒǴ܌аന֎ЇΓޑБݤᗋࢂճҔٿঁჹᆀࠠ(ৡ୏ࠠ)ޑ VCOᡣѬॺ࣬ጠӝǴౢғե࣬Տᚇૻޑ҅ҬૻဦǶკ 4.17 ࢂٿ VCO ጠӝၡ৩ޑௗݤǴӧၡ৩΢཮Ԗ΋ԛޑҬᒱጠӝ(cross-coupling)ගٮ 180ࡋޑ࣬ՏৡǴࣁΑᅈى Barkhausen criteria ޑᕴӣ௤ၡ৩࣬Տৡ฻

ܭ႟ǴഭΠޑ 180 Ѹ໪җٿ VCO ޑ LC-tank ගٮǴ܌аӧ VCO_A ᆶ VCO_B ޑᒡрӚගٮ 90 ࡋޑ࣬Տୃ౽Ǵ҅Ҭ࣬Տޑ੝܄җԜౢ

ғǶԜཷۺၟ Differential Ring Oscillator ࣬՟(კ 4.18)Ǵӵ݀Ԗ N ભ InvertorsՍௗǴ؂ભޑёளޑ࣬Տৡ฻ܭǺ

N ) 180 360

( ⁰ ⁰

T Ƕ

კ 4.17 ҅Ҭ࣬ՏਁᕏᏔϐௗጕБԄ

კ 4.18 N ભޑ Ring Oscillator

4.3.2 ճҔ VCO ጠӝౢғ҅Ҭ࣬Տޑ LO

ӧ IC ΢ౢғଯᓎ҅Ҭ࣬ՏޑႝၡמѯӵΠǺ(1) Parallel quadrature VCOǵ(2) Parallel with phase shift quadrature VCOǵ(3) Bottom-series quadrature VCOǵ(4) Top-series quadrature VCOǵ(5) Superharmonic quadrature VCOǶനӃ೏೛ीрޑႝၡࢎᄬࢂ Parallel quadrature VCO(PQVCO)ǴௗΠٰޑӚঁ่ᄬ೿ࢂࣁΑׯ๓ PQVCO ϐ੝܄Զ़

ғрٰޑǴѬॺԖᐱԾޑ౛ፕ୷ᘵکόӕᓬલᗺǴௗΠٰஒჹӚࢎᄬ բుΕ௖૸Ƕ

(1) Parallel QVCO Ǻ

კ 4.19 Parallel QVCO

Ԝࢎᄬх֖ٿಔֹӄ࣬ӕޑ LC-tank VCOǴନΑҔٰౢғॄႝߔ ޑ cross-coupling ႝ඲ᡏჹ(Qsw)ǴQsw਒ӆ௠΢Qcplаගٮٿ VCO ࣬ϕ ጠӝޑၡ৩Ƕёаᙖҗׯᡂ IswϷ Icplޑελٰׯᡂٿಔ VCO ޑጠӝ மࡋǴ࣬ჹޑ཮೷ԋ࣬Տᇤৡᆶ࣬Տᚇૻٿޣ໔ޑ trade-offǺӵ݀ Isw

ၨ IcplεǴ࣬Տᚇૻ཮ၨ࣬ՏᇤৡӳǹϸϐǴ࣬ՏᚇૻၨৡǶځচӢ

ࢂҗܭ Isw ᆶ Icpl ޑᕴӝႝࢬ(Itot)ޑ࣬Տᆶᒡрႝᓸ࣬Տόӕ(კ 4.20)Ǵ೷ԋ LC tank Ѹ໪ගٮ࣬Տୃ౽ٰᔆံ၀࣬Տৡ(Ires)ǴவಃΟ കύ܌ۓကޑ Q ॶٰ࣮ӧ ^f ¹^/ ^LCਔԖനεॶЪ LC-tank ό཮ගٮ

ҺՖ࣬Տត౽Ǵ΋ՠࣁΑံᓭIresਁᕏᓎ౗༈Ѹᅆ୏ǴQ ॶ൩คݤᆢ

࡭ӧനεॶǴ࣬ՏᚇૻΨӢԜ΢ϲǶ

Ires

კ 4.20 PQVCO ϐႝࢬᆶႝᓸ࣬Տკ

ਥᏵࢗ၌Ӛ Paper ࡕǴԜࢎᄬޑ Phase Noise ᆶ Phase Error ޑന

٫ϯॶεऊࢂஒ Iswᆶ IcplޑКॶ೛ۓࣁ 3Ǻ1Ƕ

კ 4.21 PQvco ޑጕ܄ኳࠠ

კ 4.21 ࢂ Parallel ࢎᄬ Qvco ޑጕ܄ኳࠠǴҗܭу΢ parallel ႝ඲

ᡏჹࡕ཮٬ਁᕏᓎ౗ᅆᚆ LC-tank ޑਁᕏᓎ౗(Z0 ¹^/ ^LC )ऊ ǻȦǴё ᙖ Ԝ ኳ ࠠ ඔ ॊ ǻȦ ǵ GMCǵ GMǶ GM ߄ Ң ॄ ႝ ಔ ჹ ( Qsw )ޑ transconductanceǹGMC߄Ңጠӝჹ(Qcpl)ޑ transconductanceǹIswࢂ GM

ౢғޑ in-phase ޑႝࢬǴҔٰံᓭ LC-tank ౢғޑ஌ғႝߔ RpǺ

G_M { I^sw (effective transconductance)---(4-2)ǹ

࣬ӕޑǴۓကǺ

0 1 ,

G_MC { I^cpl (effective coupling transconductance)---(4-3)ǹ

I_cpl,1ࢂᆶ Vxԋ҅Ҭޑ΋໘ᒋݢႝࢬǶ

source

კ 4.22 Parallel QVCO ϐѤᅿᏹբރᄊ

კ 4.23 ࢬ຾ LC-tank ޑႝࢬໆ߄

p sourceR I

(2) Parallel with phase shift QVCO

җ΢ॊޑ parallel quadrature VCO ޑচ౛ύёаΑှǴ೷ԋ Phase Noiseό٫ޑচӢ൩ࢂ LC-tank Ѹ໪ගٮ೽ϩޑ࣬Տୃ౽ςၲԋ 90 ࡋ

კ 4.24 PQVCO with Phase Shifter ϐጕ܄ኳࠠ

ӧႝၡჴ౜ޑفࡋٰ࣮Ǵ۰ݢाၲډ 90 ࡋޑ࣬Տୃ౽൩ӵӕע ۰ݢբᑈϩ܈༾ϩǺ^sin^Z^tᆶ^cos^Z^t࣬Տৡ 90 ࡋǴע^sin^Z^tᡂ^cos^Z^tޑБ ݤ൩ࢂҔ༾ϩǶаΠႝၡ(კ 4.25)൩ૈᙁൂޑගٮ༾ϩфૈǴΨёа ᙖҗፓ᏾ౢғ 90 ࡋ࣬Տৡႝၡޑႝࢬελٰၲډόӕελ࣬Տୃ

౽Ƕ

კ 4.25 ٿᅿ Phase Shifter ϐႝၡკ аΠࢂჹ၀ႝၡޑλૻဦբ௢ᏤǺ

(3) Top-Series Quadrature VCO

ᗨฅ”(2)PQVCO with phase shifter ”ύගډёаӧٿ LC-tank ໔Ս

ௗ Phase Shifter ٰׯ๓ Phase NoiseǴ࣬ჹޑႝၡӧ೛ी΢ᡂޑ׳ፄ ᚇǴф౗੃઻ΨӢཥуΕޑႝၡ઻຤׳ӭǴ٬၀ࢎᄬϝό୼ֹ๓Ƕௗ

Πٰ૸ፕޑࢎᄬ൩ࢂճҔ Top-series ޑࢎᄬڗж΢ॊޑ parallel ࢎᄬ (კ 4.26)Ǵౢғ phase noise եΞᙁܰޑ҅Ҭ࣬Տޑᓸ௓᎜ᕏᏔǶ

კ 4.26 Top-Series QVCO

ጠӝႝ඲ᡏჹ(Qcpl1ǵQcpl2)୴᠄ӧॄႝߔႝ඲ᡏჹ(Qsw1ǵQsw2)΢

य़ǴӢࣁጠӝႝ඲ᡏჹࢂ phase noise ޑЬाٰྍǴճҔ೭ঁ୴᠄่ᄬ

ࡕёε൯फ़ե phase noiseǶӧ Parallel QVCO ࢎᄬύQcplǵQswޑελ Ѹ໪཈ᒧǴӢࣁ၀ελ཮،ۓIcplکIswǴ຾Զቹៜ phase noise ک phase errorǴόၸӧ Top-series quadrature VCO ύǴQcplکQswޑελό཮ቹ ៜ phase error ӢࣁIcplکIswӅҔ࣬ӕޑႝࢬྍǴӢԜёаፓ᏾QcplکQsw

ޑελаᕇளന٫ޑ phase noiseǶ

V_in

კ 4.27 Top-Series QVCO ϐ฻ਏъႝၡ

аᜪКႝၡޑλૻဦᏹբٰ࣮Ǵёа௢рQcplޑ noise ჹVoutޑቹ

cpland Rs gm

Զ Top-series ࢎᄬޑ Qvco ΨԖ࣬՟ܭ Parallel ࢎᄬޑѤᅿᏹբރ ᄊკ 4.27a~dǶӧ b Ϸ c ॄႝߔႝ඲ᡏჹࢂೀܭΟભ୔(triode)Զόࢂ

ֹӄޑᜢഈǴ٬ጠӝޑႝ඲ᡏჹૈԖԜჹ triode ႝ඲ᡏޑ degeneration ਏ݀Ǵphase noise ᒿϐफ़եǶόၸ Top-series Qvco ٠ؒݤႽ Parallel Qvco ёаҔᡉԶܰـޑБำԄٰᇥܴ įǴѝૈҔ೬ᡏٰኳᔕǴόၸ (4-5)~(4-9) ޑ฻Ԅ٩ฅ፾ҔǶკ 4.28 Top-Series ѤᅿᏹբރᄊаϷࢬ

຾ LC-tank ޑႝࢬໆ߄Ƕ

source

) (a

source

I ) 1 ( G

source

) (b

source

) (c

source

I ) 1

( G GIsource

) (d

კ 4.28 Top-Series QVCO ϐѤᅿᏹբރᄊ

კ 4.29 ࢬ຾ LC-tank ޑႝࢬໆ߄

ځԛǴჹܭ΢ॊޑٿᅿ҅ҬਁᕏᏔाӵՖϦѳΞԖཀကޑКၨځ

܄ૈ٠όޔᢀǴӢࣁ phase noise ک phase error ٠όࢂడค࣬ᜢޑୖ

ኧǴӧׯᡂႝၡୖኧٰ෧Ͽ phase noise ޑӕਔǴphase error ࠅᡂৡǶ а Parallel Qvco ࣁٯǴԜٿୖኧڙQswᆶQcplޑႝࢬКٯ௓ڋǴёࢂ

Series QVCO ѝૈᙖׯᡂQswᆶQcplޑελٰׯᡂ phase noiseǴphase errorࣁ΋ۓॶǶ

Qvco܌ౢғޑ҅Ҭ࣬ՏૻဦǴځ໔ޑ phase ک amplitude error Ҟ

߻ࣁЗ٠ؒԖёаޔௗໆෳޑёՉБݤǴѝૈஒᒡрޑ҅Ҭૻဦ០୏

ᚐѦޑ single-sideband upconversion ႝၡǴӆໆෳ upconversion ࡕޑ ך ॺ གྷ ा ᓎ ࢤ ᆶ ᜔ Ⴝ ᓎ ࢤ ޑ ᒡ р ф ౗ К ॶ (image band rejection(IBR))Ƕӧ parallel ࢎᄬύޑQcplႝࢬຫε IBR ຫӳёࢂ phase noise ᡂৡǴҗԜёـǴჹܭόӕࢎᄬޑ Qvco ѝКၨ phase noise ܈ FoMࢂό୼ֹ๓ޑǶКၨӝ౛ޑБݤࢂஒόӕࢎᄬޑ Qvco ೛ीӧ࣬

ӕޑ phase error ࡕӆКၨځ FoMǶ࣬ၨܭ ParallelǴTop-series ࢎᄬޑ phase error ൩ό཮ӢQswᆶQcplޑКॶቹៜǴ܌аךॺёаஒ Parallel

೛ीډᆶ Series ӕኬޑ phase error ࡕӆКѬॺޑ phase noiseǴ൩ёа

҅ዴ࠼ᢀޑКၨځ܄ૈǶ

ᙖҗа΢ޑϩ݋ךॺ൩ёа೛ۓӳ įǵĮǴᡣ Parallel ᆶ Top-series ޑ Qvco Ԗ࣬ӕ phase error ຾Զ଺рϦ҅ޑ phase noise КၨǶ

Top-Series QVCOନΑӢࣁ coscode ࢎᄬᡣ noise फ़եǴவკ 4.23 کკ 4.28 ᗋёᢀჸډќ΋ঁচӢǶჹკ 4.23b ᆶ d ԶقǴҗܭৡ୏ჹ ޑ΋ୁֹӄᜢഈǴӢԜ noise ؒԖၡ৩ࢬډ LC-tankǹՠӧ c ύQcpl1ޑ

noise ൩ёᙖҗQsw2ࢬډ LC-tank ύǶ'I1཮а Ȧout ޑᓎ౗଺ׯᡂ(კ 4.29)Ǵ຾ԶׯᡂΑ Isw,1аϷ Icpl,1ǴനࡕΨׯᡂΑ GMCǶ

Qcpl Q_sw₂

1 I

I '

კ 4.30 კ 4.23c ޑᚇૻྍаϷࢬ຾ LC-tank ޑႝࢬໆ߄

Top-seriesࢎᄬΠQcpl1ӧკ 4.28bǵd ೿Ԗ໒௴Ǵ܌а၀ noise source

཮ჹ I1ᆶ I2଺฻ໆ฻࣬ޑׯᡂǴ൩ 4-6 ԄϷ 4-8 Ԅٰᇥ೭٤ׯᡂ٠ό

཮ቹៜ IQ,1ک II,1Ǵ܌а GMCΨόᡂǶᙖҗ΢ॊޑ૸ፕǴTop-Series Qvco

ࢎᄬᔈёளډၨ Parallel QVCO ӳޑ phase noiseǶ

' 'I₂

I I1'

I I2'

კ 4.31 ӧკ 4.28bǵd ޑᚇૻྍаϷࢬ຾ LC-tank ޑႝࢬໆ߄

4.4 ჴբ΋ǴQuadrature VCO Using Top-Series Coupling Structure (GaAs HBT 2 ͔m)

Ԝჴբࢎᄬ௦Ҕޑࢂ Top-Series Coupling(კ 4.32)Ǵځࣴز୏ᐒ ᆶࢎᄬᙁϟςӧ 4.3.2 ࿯ύޑ part(3)ᇥܴၸǴௗΠٰޔௗჹႣ՗ೕ਱

ᆶໆෳ่݀բᇥܴǶ᏾ᡏޑႝၡࢎᄬӵკǴ௦Ҕ Emitter coupled pair with cross feedback ޑ ਁ ᕏ Ꮤ ࢎ ᄬ Ǵ Զ feedback ޑ Б ݤ ࢂ ճ Ҕ transformerǴёаᗉխ base-collector junction ӧεᒡрਁ൯ਔᡂԋ໩

ୃǶӧ Varactor ޑ೽ϩ߾ࢂע HBT ႝ඲ᡏޑ base ک collector ௗӧ΋

ଆǴ٬Ҕ base ک emitter ௗय़໔ޑႝ৒ٰჴ౜Ƕ

კ 4.32 Top-series QVCO ϐႝၡკ Symmetric Transformer ϐ੝܄ኳᔕ

Ԝࢎᄬޑ transformer(კ 4.33)ӧϐ߻ςΠၸ TestkeyǴӧႝၡኳᔕ ਔ൩ࢂճҔໆෳޑኧᏵٰ೛ी(კ 4.35)Ǵ٠߈՟΋ಔ discrete ޑ components(კ 4.34)ٰኳᔕ time domain ΢ޑႝၡ੝܄Ǻ

R R6 R=9.237 Ohm R R7 R=7.754 Ohm

L L2 R=

L=1.618 nH L L3 R=

L=2.222 nH

Mutual C=12.305 fF

C C8 C=13.102 fF

C C7 C=0.762 fF C

C6 C=0.008 fF C C11 C=40.853 fF

C C10 C=42.227 fF

კ 4.33 Symmetric Transformer ϐ Layout კ 4.34 Fitted model

0 1 2 3 4 5 6 7 8 9 10

Transmission Coefficient S21(dB)

0 1 2 3 4 5 6 7 8 9 10

K (Coupling Factor)

კ 4.35 Transformer ϐໆෳ่݀

ĺ K=0.66 Transmission Coefficient= -6dB @4.5GHzǶ 4.4.1 Ⴃीೕ਱ӈ߄

Item Spec Supply Voltage 5 V

Current of QVCO core 5.18 mA Current of Output buffer 15.52 mA Power Consumption of core 25.9 mW

Total Power Consumption 103.5 mW Tuning frequency range 4.57GHz~4.67GHz

Phase Noise -102.168dBc/Hz @ 1MHz offset Tuning Range 100MHz

Die size 2000 um × 1000 um

4.4.2 ჴෳ่݀

(1) Output spectrum: 4.0956GHz, -2.3dBm

(2) Phase noise: -120.0203 dBc/Hz

(3) KVCO Ϸ Output power: 25.43MHz/V

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.04

4.06 4.08 4.10 4.12 4.14 4.16

Frequency

Output Power (dBm)

Output Frequency (GHz)

Vtune (V)

-6 -4 -2 0 2

Power

4.4.3 ่ፕᆶ૸ፕ (1) Die Photo:

(2) Chip performance:

Item Measurement Supply Voltage 5 V

Current of QVCO core 5.1 mA Current of Output buffer 15.5 mA Power Consumption of core ~ 25.5 mW

Tuning frequency range

VtuneǺ0~3.5V 4.054 ~ 4.143GHz

KVCO 25.43MHz/V Phase Noise @1MHz offset -120.0203dBc/Hz

FOM -178.21dBc/Hz Output Power ~2dBm

Die size 2000 um Ø 1000 um

ҁԛႝၡჴբዴჴӧ InGaP/GaAs ΢ౢғ Top-Series QVCOǴᒡ рᓎࢤӧ 4GHz ѰѓǴԶ Phase Noise ΨԖ-120dBc/Hz@1MHz offsetǶ ᒡрᓎ౗ޑኳᔕᆶჴෳ่݀ৡຯऊ 527MHzǴёૈӢࣁኳᔕਔ܌٬Ҕ ޑ transformer model όྗዴǶӢࣁ transformer ޑ model ࢂճҔ test-key ޑໆෳ่݀ fitting рٰޑǴӧ fitting ၸำύόࢂ؂ಔ[S]೿ૈֹӄ಄

ӝǴ܌аԜ model ᗋࢂၟჴሞޑ transformer ౢғޑႝགॶԖрΕǴ೷

ԋᓎ౗΢ 11%ޑᇤৡǶӧ DC ک KVCO ޑໆෳ൩ၟኳᔕௗ߈ǴPhase Noise ΨКኳᔕਔाӳǶёૈࢂ၀ᇙԋޑ model ჹႝ඲ᡏޑ flicker noiseؒԖඔॊǴ܌аӧኳᔕਔ࣮όډჴሞޑ noise ੝܄Ƕӧᒡрф౗

Бय़Ǵໆෳ่݀ΨКኳᔕεΑஒ߈ 2dBmǴёૈࢂ QVCO کᒡр጗ፂ ભ໔ؒҔႝ৒ஒ DC ႖๊໒Ǵ܌а QVCO ޑф౗ёаֹӄ໺ډໆෳ

ᐒᏔ΢ǴόၸԜ଺ݤёૈჹ QVCO ௗܭځдႝၡࡕޑᓎ౗ᆶ KVCO

ౢғቹៜǶ

(4) Bottom-Series QVCO Ǻ!

კ 4.36 Bottom-series QVCO ϐႝၡკ

ԜࣁՍௗࢎᄬޑќ΋ᅿௗݤǴஒ Qcplׯܫӧ QswޑΠቫǴёаᡣ

࣬Տᚇૻᡂեՠࢂ཮ཞѨ࣬ՏᇤৡǴ೭ᆶ Top-Series ޑ੝܄খӳϕ

ံǶҗკ 4.27 ޑБݤёаޕၰǴ᠄ܭ΢ԋޑႝ඲ᡏό཮ჹᒡрౢғ noiseǶҗܭ VCO ޑਁᕏౢғЬाڙQswቹៜǴӵ݀עQsw᠄ӧQcpl΢Ǵ

Qswޑ noise ൩ό཮υᘋЬᓎޑਁᕏૻဦǴ܌а Bottom-Series QVCO

཮Ԗၨӳޑ phase noiseǶӕ౛Ǵӵ݀עቹៜٿ VCO ጠӝQcpl᠄ӧ΢ቫǴ ӧౢғ҅Ҭޑၸำύ phase error ൩КၨؒԖ noise ٰυᘋǴ܌а Top-Series QVCO཮Ԗӳޑ phase errorǶ

(5) Superharmonic Coupling QVCO Ǻ!

(1)ډ(4)܌ගޑ҅Ҭᓸ௓᎜ᕏᏔࢎᄬ೿ሡा΋ಔጠӝޑႝ඲ᡏǴ மॐٿঁ VCO ౢғ҅ҬਏᔈǴόၸ೭٤ࢎᄬ཮Ԗ phase noise ᆶ phase errorޑ trade-offǴ܈ࢂӭуႝ඲ᡏ೷ԋф౗੃઻΢ϲǶௗΠٰ૸ፕޑ

҅Ҭ࣬Տ VCO ࢎᄬࢂճҔΒ໘ޑᒋݢ࣬ϕጠӝǴаၲډե phase noise Ϸե੃ᳫф౗ޑٿεҞ኱Ƕ

ӧ ৡ ୏ ޑ ࢎ ᄬ Π ך ॺ ё а ӧ ႝ ၡ ύ ޑ Ӆ ኳ ᗺ (common-mode nodes)ว౜ଽԛ(even)ᒋݢǴځЬाԋҽࢂΒ໘ޑᒋݢǶRategh and Lee ς࿶᛾ܴӧৡ୏ޑਁᕏᏔ΢ǴךॺёаճҔ೭٤ӅኳᗺǴݙΕᆶΒ໘ ᒋݢᓎ౗࣬߈ޑૻဦǴёஒਁᕏᏔᙹӧݙΕૻဦޑΒϩϐ΋ᓎ౗΢Ƕ ѝाਁᕏᏔᆢ࡭ӧᙹՐޑރᄊΠǴךॺёаፓ᏾ݙΕޑᓎ౗ǴԶਁᕏ Ꮤޑ୷ᓎૻဦΨ཮ᒿ๱౽୏٠ᙹۓǶԜ੝܄ёҔٰჴ౜ଯᓎޑନΒႝ

ၡǶ

୷ҁ΢ٿঁৡ୏ޑ VCO ёаᙖҗ΋ጠӝႝၡᡣѬॺޑΒ໘ᒋݢ

ޑ࣬Տև 180⁰Ǵ൩ё០٬ٿঁ VCO ޑৡ୏ᒡрԖ҅Ҭޑਏ݀(კ 4.37)ǶᡣΒ໘ᒋݢև 180 ࡋޑБݤࡐӭǴႽࢂҔ transformer ܈ࢂҔ

ႝ৒ޔௗጠӝډ current source ޑ base ᆄǶ

კ 4.37 Superharmonic coupling QVCO ϐҢཀკ

4.5 ჴբΒǴQuadrature VCO Using Superharmonic Coupling (GaAs HBT 2 ͔m)

Ԝԛჴբޑ VCO core ϝ௦Ҕ”ႝགጠӝᓸ௓ԄਁᕏᏔ”Ǵ೸ၸႝ

གޑጠӝӣډᒡΕᆄǶԜࢎᄬ࣬ၨ”ޔௗӣ௤”ޑӳೀࢂǴᒡрႝᓸޑ

ਁ൯ό཮Ӣ୷ཱུ-໣ཱུௗय़܌ज़ڋǴёᒡрεਁ൯ǴΞёᗉխ٬Ҕႝ

ߔٰ biasǴ܌аёаׯ๓࣬ՏᚇૻǶკ 4.38 ࢂ᏾ᡏޑႝၡࢎᄬǺpart.1

ࢂٿঁᐱҥޑ VCOǹSuperharmonic coupling ޑБݤ߾ࢂҔ transformer ᡣٿ VCO ԋ҅Ҭ࣬ՏǶ

კ 4.38 Superharmonic coupling QVCO ϐႝၡკ

ᡂᓸᏔௗܭٿޑਁᕏᏔޑӅኳᗺǴЪᡣٿୁޑΒ໘ᒋݢև 180⁰

࣬ՏৡǶӧ୏ᄊރᄊΠޑጠӝਁᕏᏔҁيೀܭߚጕ܄ޑႝၡ੝܄Ǵ܌

аᒡрନΑ҅Ҭޑ੝܄ѦΨёૈᡂԋ࣬ϕӕ؁ϯ(࣬Տԋ in-phase ރ ᄊ)Ǵ܈ࢂਥҁᒡр΋٤ᚇ໶ޑૻဦǶᡂᓸᏔޑጠӝமࡋ൩ࢂ،ۓٿ

ਁᕏᏔࢂցԖ҅ҬៜᔈޑᜢᗖाનǶӧךॺ೭ԛޑႝၡ೛ी΢Ǵ൩௦ ҔڀԖၨமጠӝ߯ኧޑ(Coupling factor)ޑჹᆀ(Symmetric)ᡂᓸᏔ(კ 4.39)аቚуΒԛᒋݢޑጠӝໆǴ٬ਁᕏᏔዴჴԖ҅ҬᒡрǶ

კ 4.39 Symmetric Transformer Layout

ӧӅኳᗺуΕᡂᓸᏔᗋԖ΋ঁᚐѦޑᓬᗺǴ൩ࢂᡣᒡрႝᓸޑਁ

൯уεǴफ़եႝࢬྍჹਁᕏᏔޑႄڋǶ΋૓ޑਁᕏᏔ(კ 4.40(a))ሡा

ӧႝࢬྍᆄ٠ᖄႝ৒ᡣ࣬Տᚇૻफ़եǴՠ཮٬ӧ Vc ӅኳᗺޑΒ໘ᒋ ݢౢғ RC delayǴ೷ԋΒ໘ᒋݢᆶᒡр୷ᓎ(Vn,Vp)ؒԖֹӄჹሸǴ ӧႝ඲ᡏޑ drain ႝᓸѸ໪ଯܭ source ႝᓸޑచҹΠǴᒡрޑ୷ᓎਁ

൯൩Ѹ໪ଯܭ VcǶ

)

(a (b)

კ 4.40(a) VCO without current source filter კ 4.40(b) VCO with current source filter

ӵၸஒᡂᓸᏔௗܭ Vc’ᆄ(კ 4.40(b))ǴҗܭѬҁي൩ࢂႝགǴ٠ ᖄႝ৒٬ѬᒋਁӧΒ७୷ᓎǴᡣ࣮ӛႝࢬྍޑߔל(R)ѝഭჴ೽Ǵஒ RC delayਏᔈ੃ନǶԜਔਁᕏᏔޑᒡрਁ൯ளаගϲǴᡣ࣬Տᚇૻ׳

ӳǶ

ԜѦǴЬᓎޑ஌ғጠӝਏᔈѸ໪ᅰໆᗉխǴӢࣁёૈ٬ਁᕏᏔᡂ ԋ࣬ϕӕ؁(mutual synchronization)ǶԶ೭٤஌ғጠӝਏᔈёૈٰԾӅ

ਁ๚ᙖҗޖ୷݈܈೸ၸᅶ൑གᔈ໺ډᡂᓸᏔǴ܌аᅰёૈஒᡂᓸᏔᇻ ᚆӅਁ๚Ƕ

4.5.1 Ⴃीೕ਱ӈ߄

Item Spec Supply Voltage 5 V

Current of QVCO core 3.752 mA Current of Output buffer 15.68 mA Power Consumption of core 18.76 mW

Total Power Consumption 97.16mW Tuning frequency range 4.34GHz~4.45GHz

Phase Noise -103dBc/Hz @ 1MHz offset Tuning Range 110MHz

Die size 2000 um × 1000 um 4.5.2 ჴෳ่݀

(1) Output spectrum: 5.0371GHz, -5.5dBm

(2) Phase noise: -126.2926dBc/Hz

(3) KVCO Ϸ Output power: 31.25MHz/V

0 1 2 3 4

4.80 4.85 4.90 4.95 5.00 5.05 5.10

Frequency

Output Power (dBm)

Output Frequency (GHz)

Vtune (V)

-6 -5 -4 -3 -2 -1 0 1

Power

4.5.3 ่ፕᆶ૸ፕ

(1) Die Photo:

(2) Chip performance:

Item Measurement Supply Voltage 5 V

Current of QVCO core 3.7mA Current of Output buffer 18.2mA Power Consumption of core ~ 18.5mW

Tuning frequency range

VtuneΚ0~4V 4.913GHz~5.038GHz

KVCO 31.25MHz/V Phase Noise @1MHz offset -126.29dBc/Hz

FOM -187.16dBc/Hz Output Power ~-4dBm

Die size 2000 um ͪ 1000 um

೭ԛჴբр΋ঁ 5GHz ҅Ҭ࣬Տ VCOǴӧ Phase Noise ΢ޑ੝܄

ཱུ٫Ǻ1MHz ޑ offset ၲډ-126dBc/HzǶKVCO ޑჴෳ่݀ၨচӃႣ

՗ޑ 27.5MHz/V ଯ΋٤ǴԖёૈࢂҁႝၡ٬Ҕႝ඲ᡏޑ base-emitter

ႝ৒ٰ྽ varactorǴԶႝ඲ᡏ model ٠όૈֹ᏾ඔॊԜҔݤޑႝ৒੝

܄Ǵ೷ԋऊ 13.6%ޑୃ౽Ƕਁᕏᓎ౗ޑໆෳ่݀ΨᡉҢ۳ଯᓎᅆ୏Α 588MHzǴу΢΢ॊޑ KVCO ᡂεޑ่݀ёа௢ளᔈ၀ࢂჴሞ΢

LC-tankޑႝ৒К೛ीਔλǴ٬ᒡрᓎ౗ᆶ KVCO ΢ϲǶόၸ೭٤ᅆ

୏ࣣࢂӧ 20%аϣǴӧΠԛޑჴբӵ݀ዴჴӃஒᇙำ΢ᜤаᗉխᅆ౽ Եቾ຾ѐǴᔈ၀ёаׯ๓ኳᔕᆶໆෳ΢ޑᇤৡǶ

4.6 ჴբΟǴQuadrature VCO Using Superharmonic Coupling (SiGe HBT 0.35µm)

კ 4.41 ࢂҁԛჴբޑЬाႝၡࢎᄬǴх֖ٿঁЬाޑ೽ҽǺ(1) ৡ୏ᒡрᓸ௓ਁᕏᏔǹ(2) ጠӝᡂᓸᏔ(transformer)ႝၡǶ

(1)ճҔ΋ಔႝ඲ᡏǴஒځ௨ӈԋ Cross-couple ޑࠠԄǴջёаӧ ځᒡрᆄౢғ҅ӣ௤ǴӆճҔᒡрᆄޑ resonator ࿶җ፾྽ޑ೛ीځ Ӆਁᓎ౗Z ¹ LCǴջёӧགྷाޑᓎ౗ౢғڬය܄ޑᒡрǶҁႝၡޑ Ѥঁ࣬ՏᒡрࣣԖᐱԾޑ LC-tankǴӧ cross-couple ၡ৩΢௦Ҕႝ৒բ ࣁӣ௤ϡҹǶԜਔѸ໪ගٮୃᓸႝࢬǴcross-couple ޑႝ඲ᡏωё҅

தπբǶԶ(2)ޑ೛ीБݤ൩ၟ 4.5 ࿯΋ኬǶ

კ 4.41 Superharmonic coupling QVCO ϐႝၡკ

Symmetric Transformer ϐ੝܄ኳᔕ

(1)ጠӝᡂᓸᏔϐኳᔕǺ

ճҔ EM ኳᔕ೬ᡏ(Momentum)՗ᆉᡂᓸᏔޑୖኧϷጠӝ߯ኧ:

ĺ K=-0.835 Transmission Coefficient= -4dB @10GHzǴጠӝ߯ኧࣁॄ

ॶࢂӢࣁךॺעٿЍጠӝޑႝࢬᒡΕᡂᓸᏔޑϸӛᆄǶԜѦǴ߈՟΋

ঁ฻ਏႝၡٰኳᔕ Time domain ΢ޑਏᔈǶ

m12freq=

real(K_sim1)=-0.83510.00GHz

2 4 6 8 10 12 14 16 18

freq, GHz

real(K_sim1)

m12

m14freq=

dB(S(6,7))=-4.84510.00GHz

2 4 6 8 10 12 14 16 18

freq, GHz

dB(S(6,7))

m14

R R6 R=9.237 Ohm R R7 R=7.754 Ohm

L L2 R=

L=1.618 nH L L3 R=

L=2.222 nH

Mutual C=12.305 fF

C C8 C=13.102 fF

C C7 C=0.762 fF C

C6 C=0.008 fF C C11 C=40.853 fF

C C10 C=42.227 fF

4.6.1 Ⴃीೕ਱ӈ߄

Item Spec Supply Voltage 3 V

Current of QVCO core 3.16 mA Current of Output buffer 11.5 mA Power Consumption of core ~ 9.48 mW

Tuning frequency range 5.006GHz~5.529GHz

KVCO 523MHz/V Output Power -1.328dBm @ 5.529GHz

-2.783dBm @ 5.006GHz Phase Noise -107dBc/Hz @ 1MHz offset

Die size 1355 um × 1182 um 4.6.2 ჴෳ่݀

(1) Output spectrum: 4.159GHz, -13.05dBm

(2) Phase noise: -116.2831dBc/Hz

(3) KVCO Ϸ Output power: 23.1MHz/V

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

4.02 4.04 4.06 4.08 4.10 4.12 4.14 4.16 4.18 4.20 4.22

-7.0 -6.5 -6.0 -5.5 -5.0 -4.5 -4.0 -3.5 -3.0

Output Power (dBm)

Frequency (GHz)

Vtune (V)

4.6.3 ่ፕᆶ૸ፕ

(1) Die Photo:

(2) Chip performance:

Item Measurement Supply Voltage 3 V

Current of QVCO core 3.2mA Current of Output buffer 33.94mA Power Consumption of core ~ 9.6mW

Tuning frequency range

VtuneǺ0~2.6 4.14 ~ 4.20GHz

KVCO 23.1MHz/V Phase Noise @1MHz offset -116.28dBc/Hz

FOM -178.80dBc/Hz Output Power ~-6dBm

Die size 1355 um Ø 1182 um ೭ԛΠጕ܌٬ҔޑႝၡࢎᄬǴࢂஒٿঁ࣬ӕ LC-tank VCO ճҔ Symmetricޑ transformer բ Superharmonic couplingǴаౢғ҅Ҭ࣬Տ ޑ LO ૻဦǶҗໆෳ่݀ᆶኳᔕ่݀բКၨǴӧਁᕏᓎ౗΢ୃ౽Αஒ

߈ 900MHzǴ೷ԋޑচӢёૈࢂኳᔕਔ٬Ҕޑϡҹ model ᆶჴሞ΢ޑ ॶԖрΕǶҗܭҁႝၡԖ٬Ҕډ PN-junction ޑ varactorǴЪԜԛΠጕ

߻ TSMC SiGe 0.35µm ޑ model ۘ҂ׯހǴӧኳᔕ model ᆶ Layout

΢٠҂᏾ӝǴӵ݀у΢ႝགޑᕴୃ౽ໆၲ 56%Ǵ൩཮ளډҁԛޑໆෳ

่݀Ƕҗ tuning range ؒၲډႣ՗ॶёа௢ϐǴᔈ၀ࢂ varactor ޑ model

΢วғୢᚒǶԜѦǴSymmetric ޑ transformer ٠҂Πၸ testkeyǴᗨฅ ӧኳᔕਔς࿶Ҕ EM ೬ᡏႣ՗ځ੝܄Ǵόၸჴሞ΢ޑਏ݀ᗋࢂளΠ testkey ٰ ᡍ ᛾ Ƕ ӧ Phase noise ΢ ޑ ੝ ܄ ൩ ӳ ࡐ ӭ Ǵ ၲ ډ -122dBc/Hz@1MHz offsetǶф౗੃઻Бय़ΨᆶႣය࣬߈Ƕ

4.7 ჴբ΋ǵΒǵΟϐКၨ

Coupling Method Top-Series Superharmonic Superharmonic Technology InGaP/GaAs

2͔m HBT

InGaP/GaAs 2͔m HBT

SiGe 0.35͔m BiCMOS HBT Output Frequency

range (GHz) 4.054 ~ 4.143 4.913 ~ 5.038 4.14 ~ 4.20 Power

Consumption (mW)

25.5 18.5 9.6

KVCO (MHz/V) 25.43 31.25 23.1

Output Power

(dBm) ~ 2 ~ -4 ~ -6

Phase noise

@1MHzOffset -120.02dBc/Hz -126.29dBc/Hz -116.28dBc/Hz

FOM (dBc/Hz) -178.21 -187.16 -178.80

߄ 4.1 ჴբ҅Ҭ࣬ՏਁᕏᏔϐКၨ

ಃϖക

่ፕ

ҁፕЎճҔ GCT 2.0 um InGaP/GaAs HBT Ϸ SiGe 0.35µm

在文檔中高速除頻電路與正交相位振盪器之設計 (頁 68-0)