寬頻雙饋入分佈式功率放大器

୯ҥѠ᡼εᏢႝᐒၗૻᏢଣႝηπำᏢࣴز܌

ᅺγፕЎ

Graduate Institute of Electronics Engineering College of Electrical Engineering and Computer Science

National Taiwan University Master Thesis

ቨᓎᚈ㎸ΕϩթԄф౗ܫεᏔ

Broadband dual-feed distributed power amplifier

ፁ࠹Ӽ Shuan-An Wei

ࡰᏤ௲௤Ǻᐽߞ჏ റγ Advisor: Hsin-Chia Lu, Ph.D.

ύ๮҇୯΋ԭԃϤД

June, 2011

ᇞ ᇞᖴ

Ȩᅈર૖ঞقǴ΋עٌለఽǴ೿قբޣ࿆ǴፔှځύښǶȩӧѠεޑғఱǴ ᒿ๱೭ҁፕЎޑֹԋջஒฝΠѡᗺǴΨ೚ࢂ֋ձᏢғيϩޑ΋ঁҶЗ಄Ǵၸѐ؃

ᏢғఱᗺᗺᅀᅀΨᅌᅌੌ΢ЈᓐǴ྽ύޑለౡᆶधᇺǴߚᒃԾو΋ӣፔΨᜤаᕕ

ှǴՠځύᅿᅿᗺᆚΑၸ۳ӣᏫǴΨᙦ൤ΑԜጇፕЎǶ

ளаֹԋԜፕЎǴךा੝ձགᖴࡰᏤ௲௤ ᐽߞ჏ԴৣǴၸѐٿԃύǴԴৣ஥

๏ךคज़ޑᜢᚶᆶᡫࡘගᗺǶӕਔΨགᖴα၂ہ঩݅ڷՙԴৣǵഋ܃ฅԴৣǵම

ࡿ໢Դৣᆶ݅ے፣ԴৣǶፏՏԴৣвಒޑ᎙᠐ךޑགྷݤᆶЎӷǴ٠வֻᢀޑس಍

فࡋǵᑞஏޑᡄᒠࡘᆢ๏ϒך೚ӭᝊ຦ޑࡌ᝼ǶҁፕЎऩԖ΋ํ׳᎞߈ᏢೌຎഁǴ дॺۚфࣗ଻Ƕ

གᖴӧࣴزޑၸำύǴԖਖҖǵەໜǵֻᅺǵ࢙౰ǵৎሳǵ৚஡ǵಏ๮ǵᅼ

֝ǵ◖߭ᏢߏۆޑࡰᏤᆶڐշǴགᖴߪӼǵξঢ়ǵݯቶǵ࢙▲ӕᏢޑ࣬ϕ૸ፕǴ ΨགᖴϢᝬǵഩЎǵകำǵநԒǵԓ౺Ꮲ׌ޑࠀᓰᆶഉՔǶӧ೭ጇᖴຒύǴךѝ

ૈ૶ᒵգॺޑӜӷǴ٠૶ᒵךჹգॺޑགᖴᆶӅೀޑਔӀǶ

നࡕךाགᖴךޑৎΓǴգॺޑЍ࡭ᆶႴᓰࢂךֹԋᏢ཰ޑനε୏ΚǶ

࠹Ӽ 2011/8/13

ᄔ ᄔा

ҁፕЎམଛЬ೏୏ᇙำǴჴ౜΋ᅿх֖ UWB ᓎࢤޑቨᓎф౗ܫεᏔǴЬ

୏඲Т೽ϩࢂа TSMC 0.18μm CMOS ᇙԋǴམଛٿᅿ೏୏ᇙำǴϩձࣁᐵቺ (Advanced Ceramic X Corp., ACXC)ϦљޑեྕӅᐨഏౠ(low temperature co-fired ceramics, LTCC) ᇙำᆶ୯ৎ඲ТύЈ(CIC)܌ගٮޑᑈᡏ೏୏ϡҹ (intergrated passive device, IPD)ᇙำǴ٠ճҔᙟ඲מೌ่ӝЬ೏୏ᇙำǶ

ךॺ௦Ҕᜪ՟ϩթԄܫεᏔࢎᄬǴ٠ճҔѰѓЋ໺ᒡጕޑϰଛБԄٰග

ܹ S21ޑᓎቨǴ٠Ъ৾௞Α໺಍ϩթԄܫεᏔޑϰଛႝߔǴаයቚуႝၡޑߕ уਏ౗Ǵՠѐନϰଛႝߔ཮ቚуႝၡޑϸ৔ཞ઻Ǵ܌аךॺճҔѳᑽԄܫε Ꮤޑচ౛Ǵམଛቨᓎޑ҅Ҭϩ࣬Ꮤٰቚуႝၡޑ S11ǵS22ᓎቨǶ᏾ᡏԶقǴך ॺׯ๓Αቨᓎф౗ܫεᏔޑᓎቨǵߕуਏ౗ᆶጕ܄ࡋǶӧ TSMC 0.18μm CMOS མଛեྕӅᐨഏౠᇙำΠǴவ 3.1 GHz ډ 10.6GHz ޑᓎ஥ϣǴךॺф౗ߕу ਏ੻ 19~24.5%Ǵቚ੻ 10.8²1dBǴᒡрф౗ OP1dB Ԗ 14.6~16dBmǴOIP3 ၲډ 26.6~27 dBmǶ

ᜢᗖຒǺф౗ܫεᏔǵϩթԄܫεᏔǵຬቨᓎǵᚈ㎸ΕܫεᏔǶ

Abstract

This thesis presents the implementation of ultra-wide band power amplifier by combining both active and passive processes. The active process we used is TSMC 0.18μm CMOS and two passive processes we used are low temperature co-fired ceramics (LTCC) provided by Advanced Ceramic X Corp. (ACXC) and IPD (integrated passive device) provided by Chip Implementation Center (CIC). We use flip-chip interconnects to combine active chips and passive part of power amplifiers.

We use a structure similar to traditional distributed amplifier and CRLH transmission lines are used in matching to improve the bandwidth of S21. One matching resistor in traditional distributed amplifier is removed to increase the PAE, however the removal will degrade the return loss. By using balanced amplifier structure with the broadband quadrature phase power splitter, we increase the circuit's bandwidth of S11 and S22. Overall, we improved the bandwidth of the power amplifier, PAE and linearity. At 3.1GHz~10.6GHz, achievable power-added efficiency is up to 19~24.5%. The amplifier achieves the gain of 10.8±1dB, the output 1 dB compression of 14.6~16 dBm and the output third-order intercept point (OIP3) of 26.6~27 dBm, respectively.

keywords：power amplifier, distributed amplifier, UWB, dual-feed distributed amplifier.

Ҟ Ҟᒵ

ಃ ΋ ക ᙁϟ ... 1

1.1 ୏ᐒ ... 1

1.2 ࣬ᜢࣴزว৖౜ݩ ... 1

1.3 ೏୏ᇙԋϟಏ ... 5

1.3.1 եྕӅᐨഏౠ ... 5

1.3.2 ᑈᡏ೏୏ϡҹ ... 6

ಃ Β ക ѰѓЋ໺ᒡጕ౛ፕᆶϩթԄܫεᏔ ... 7

2.1 ѰѓЋషӝ໺ᒡጕ ... 7

2.1.1 ѓЋ໺ᒡጕኳࠠ ... 7

2.1.2 ѰѓЋ໺ᒡጕኳࠠ ... 10

2.2 ϩթԄܫεᏔޑ୷ҁᏹբচ౛ ... 12

2.3 ᚈ㎸ΕϩթԄܫεᏔ ... 15

2.4 ѳᑽԄܫεᏔ ... 20

ಃ Ο ക ቨᓎᚈ㎸ΕϩթԄܫεᏔ ... 23

3.1 ҅Ҭϩ࣬ᏔᆶൂՏܫεᏔ ... 23

3.2 ቨᓎ೛ीচ౛ ... 28

3.2.1 ൂՏܫεᏔ ... 28

3.2.2 ҅Ҭϩ࣬Ꮤ ... 33

3.3 ჴ౜ൂՏܫεᏔ ... 36

3.3.1 ႝ඲ᡏᒧڗ ... 36

3.3.2 ႝၡѲֽ ... 39

3.3.3 ႝၡኳᔕ่݀ ... 42

3.4 ҅Ҭϩ࣬Ꮤ೛ी ... 45

3.4.1 LTCC製程 ... 47 

3.4.2 IPD製程 ... 50 

3.5  寬頻雙饋入分佈式放大器模擬結果 ... 52 

3.5.1 搭載LTCC製程寬頻放大器 ... 52 

3.5.2 搭載IPD製程寬頻放大器 ... 56 

第 四 章  效能和量測 ... 61 

4.1  量測步驟 ... 61 

4.2  T18CMOS 晶片量測 ... 62 

4.3  低溫共燒陶瓷量測 ... 67 

4.4  積體被動元件量測 ... 73 

第 五 章  結論 ... 79 

參考文獻 ... 83 

კ

კҞᒵ

კ 1-1 ٯη΋ޑႝၡ੝܄[2] ... 2

კ 1-2 ٯηΒޑႝၡ੝܄[3] ... 3

კ 1-3 ٯηΟޑႝၡ੝܄[4] ... 4

კ 1-4 եྕӅᐨഏౠᇙբำׇ[5] ... 5

კ 1-5 IPD ᇙำওय़კ[6] ... 6

კ 2-1 ΋ࢤཱུอ໺ᒡጕޑ฻ਏႝၡ(a)ႝᓸᆶႝࢬۓကϷ(b)໣ᕴ ฻ਏႝၡǶ ... 8

კ 2-2 คཞ઻ѰѓЋషӝ໺ᒡጕޑ฻ਏႝၡǶ ... 10

კ 2-3 όѳᑽషӝѰѓЋ໺ᒡጕ ... 11

კ 2-4 ໺಍ϩթԄܫεᏔ ... 12

კ 2-5 ൑ਏႝ඲ᡏ฻ਏႝၡ ... 13

კ 2-6 ໺಍ϩթԄܫεᏔ࣬ՏҢཀკ ... 13

კ 2-7 (a)႔ཱུጕൂՏϡҹϷ(b)ཱུؕጕൂՏϡҹ ... 14

კ 2-8 ᚈ㎸ΕϩթԄࢎᄬ[11] ... 16

კ 2-9 ᚈ㎸ΕϩթԄࢎᄬ฻ਏႝၡ ... 16

კ 2-10 ᚈ㎸Εࢎᄬޑ S ୖኧკ[12] ... 18

კ 2-11 ᚈ㎸Εࢎᄬᆶ໺಍ࢎᄬޑᒡрф౗Кၨ[12] ... 19

კ 2-12 ᚈ㎸Εࢎᄬᆶ໺಍ࢎᄬޑф౗ߕуਏ౗Кၨ[12] ... 19

კ 2-13 ᚈ㎸Εࢎᄬᆶ໺಍ࢎᄬޑጕ܄ࡋКၨ[12] ... 20

კ 2-14 ٬Ҕ 90^oϩӝݢᏔޑѳᑽԄܫεᏔ ... 20

კ 3-1 ᒡΕૈໆӧᒡΕ୵ࡌ೛܄࣬у ... 24

კ 3-2 ϩݢᏔᒡр࣬Տৡჹႝၡ S11բკ ... 24

კ 3-3 Ѥᗭႝ඲ᡏᚈ㎸ΕϩթԄܫεᏔ ... 25

კ 3-4 ѳᑽԄΠޑှ(΋)ႝၡ೛ी ... 26

კ 3-5 ѳᑽԄΠޑှ(Β)ႝၡ೛ी ... 27

კ 3-6 ѳᑽϩթԄܫεᏔ(a) J ¹⁸⁰180^ooϷ(b) J 00^oo ... 28

კ 3-7 Οᅿ໺ᒡጕ࣬Տკ ... 30

კ 3-8 ගр஌ғਏᔈ٠଺ϰଛ ... 30

კ 3-9 (a)ཱུؕᆄѰѓЋϰଛႝၡϷ(b)႔ཱུᆄѓЋϰଛႝၡ ... 31

კ 3-10 ႝၡ S ୖኧКၨ(a)ႝ඲ᡏ(b)མଛϰଛႝၡ(c)у΢ϰଛႝ ߔ ... 33

კ 3-11 ҅Ҭϩ࣬Ꮤࢎᄬ ... 34

კ 3-12 N ભ࠶ߎහф౗ϩଛᏔ[14] ... 34

კ 3-13 ѰѓЋ໺ᒡጕᆶѓЋ໺ᒡጕ࣬Տៜᔈ[15] ... 35

კ 3-14 ႝ඲ᡏ I-V კ ... 37

კ 3-15 λૻဦ฻ਏႝၡ ... 38

კ 3-16 λૻဦኳࠠᆶ TSMC PDK ኳࠠ S ୖኧКၨკ ... 39

კ 3-17 ൂՏܫεᏔࢎᄬ ... 40

კ 3-18 CMOS 0.18μm ႝ ၡ Ѳ ֽ კ (a)LTCC ᇙ ำ (910μm×950μm)(b)IPD ᇙำ(1030μm×1560μm) ... 41

კ 3-19 ൂՏܫεᏔ S ୖኧ ... 42

კ 3-20 ဂᡏۯᒨਔ໔ ... 42

კ 3-21 ӧόӕᓎ౗ΠൂՏܫεᏔεૻဦൂᓎෳ၂่݀(a)3GHz(b) 4GHz (c)6 GHz (d)8 GHz (e)10 GHz (f)12 GHz ... 44

კ 3-22 ᓎ౗ჹቚ੻ǵP1dB ॶᆶ PAE ॶ ... 44

კ 3-23 ൂՏܫεᏔޑ OIP3 ... 45

კ 3-24 ౛གྷ࠶ߎහф౗ϩଛᏔ S ୖኧ ... 46

კ 3-25 LTCC ᇙำޑ҅Ҭϩ࣬ᏔѲֽკ ... 48

კ 3-26 LTCC ᇙำ҅Ҭϩ࣬Ꮤᒡрਁ൯ѳᑽࡋ ... 48

კ 3-28 LTCC ᇙำ҅Ҭϩ࣬Ꮤဂᡏۯᒨਔ໔ ... 49

კ 3-29 LTCC ᇙำ҅Ҭϩ࣬Ꮤᒡр୵࣬Տৡ ... 49

კ 3-30 IPD ᇙำޑ҅Ҭϩ࣬ᏔѲֽკ ... 50

კ 3-31 IPD ᇙำ҅Ҭϩ࣬Ꮤᒡрਁ൯ѳᑽࡋ ... 50

კ 3-32 IPD ᇙำ҅Ҭϩ࣬ᏔᒡΕཞ઻ᆶᒡр႖ᚆࡋ ... 51

კ 3-33 IPD ᇙำ҅Ҭϩ࣬Ꮤဂᡏۯᒨਔ໔ ... 51

კ 3-34 IPD ᇙำ҅Ҭϩ࣬Ꮤᒡр୵࣬Տৡ ... 52

კ 3-35 LTCC ᇙำܫεᏔ S ୖኧ ... 53

კ 3-36 LTCC ᇙำܫεᏔဂᡏۯᒨ ... 53

კ 3-37 LTCC ᇙำܫεᏔᛙۓࡋϩ݋ ... 54

კ 3-38 ӧόӕᓎ౗Π LTCC ᇙำႝၡεૻဦኳᔕ่݀(a)3GHz(b) 4GHz (c) 6GHz (d) 8GHz (e) 10GHz (f) 12GHz ... 55

კ 3-39 LTCC ᇙำႝၡ OIP3 ჹᓎ౗კ ... 55

კ 3-40 LTCC ᇙำႝၡεૻဦ੝܄ჹᓎ౗კ ... 56

კ 3-41 IPD ᇙำܫεᏔ S ୖኧ ... 57

კ 3-42 IPD ᇙำܫεᏔဂᡏۯᒨਔ໔ ... 57

კ 3-43 IPD ᇙำܫεᏔᛙۓࡋϩ݋ ... 57

კ 3-44 ӧόӕᓎ౗Π IPD ᇙำႝၡεૻဦኳᔕ่݀(a)3GHz(b) 4GHz (c) 6GHz (d) 8GHz (e) 10GHz (f) 12GHz ... 58

კ 3-45 IPD ᇙำႝၡ OIP3 ჹᓎ౗კ ... 59

კ 3-46 IPD ᇙำႝၡεૻဦ੝܄ჹᓎ౗კ ... 59

კ 4-1 ႝၡໆෳБԄ(a)λૻဦໆෳ(b)εૻဦໆෳ ... 62

კ 4-2 ൂՏܫεᏔ඲Тკ(910μm×950μm) ... 62

კ 4-3 ൂՏܫεᏔ S ୖኧໆෳᆶኳᔕКၨ ... 63

კ 4-4 ဂᡏۯᒨਔ໔ໆෳᆶኳᔕКၨ ... 63 კ 4-5 ӧ ό ӕ ᓎ౗ Π ൂՏ ܫε Ꮤ ε ૻဦ ໆ ෳ่ ݀ (a)3GHz(b)

4GHz (c) 6GHz (d) 8GHz (e) 10GHz (f) 12GHz ... 65

კ 4-6 ᓎ౗ჹ P1dB ॶᆶ PAE ॶ ... 65

კ 4-7 ӧόӕᓎ౗Π OIP3 ॶໆෳ่݀(a)3GHz(b) 4GHz (c) 6GHz (d) 8GHz (e) 10GHz (f) 12GHz ... 66

კ 4-8 OIP3 ᆶᓎ౗բკ ... 67

კ 4-9 LTCC ᇙำ҅Ҭϩ໨Ꮤ(9.5mm×8.2mm) ... 68

კ 4-10 LTCC ᇙำ҅Ҭϩ࣬Ꮤ S21 ... 68

კ 4-11 LTCC ᇙำ҅Ҭϩ࣬Ꮤ S31 ... 68

კ 4-12 LTCC ᇙำ҅Ҭϩ࣬Ꮤᒡрਁ൯ѳᑽࡋໆෳ ... 69

კ 4-13 LTCC ᇙำ҅Ҭϩ࣬ᏔᒡΕཞ઻ໆෳ(a)S11Ǵ(b)S22Ϸ(c)S33 ... 70

კ 4-14 LTCC ᇙำ҅Ҭϩ࣬Ꮤᒡр႖ᚆࡋໆෳ ... 70

კ 4-15 LTCC ᇙำ҅Ҭϩ࣬Ꮤᒡр୵࣬Տৡໆෳ ... 71

კ 4-16 ൂՏܫεᏔӧ PAD ෌΢ߎౚ ... 72

კ 4-17 ൂՏܫεᏔᙟ඲ܭ LTCC ᇙำ҅Ҭϩ࣬Ꮤ(9.5mm×15.5mm) ... 72

კ 4-18 ᙟ඲ܭ IPD ᇙำٿঁൂՏܫεᏔ(1030μm×1560μm) ... 73

კ 4-19 IPD ᇙำٿঁ҅Ҭϩ࣬Ꮤ(4.7mm×9.7mm) ... 73

კ 4-20 ൂՏܫεᏔᙟ඲ܭ IPD ᇙำ҅Ҭϩ࣬Ꮤ ... 74

კ 4-21 IPD ᇙำܫεᏔ S ୖኧໆෳ ... 75

კ 4-22 IPD ᇙำܫεᏔ΋ၡൂՏܫεᏔόᏤ೯ϐ S ୖኧ ... 75

კ 4-23 ൂՏܫεᏔ΢ᒴႉౚܫεკ ... 76

კ 4-24 IPD ᇙำܫεᏔဂᡏۯᒨໆෳ ... 76

კ 4-25 ӧ ό ӕ ᓎ౗ Π ൂՏ ܫε Ꮤ ε ૻဦ ໆ ෳ่ ݀ (a)4GHz(b) 6GHz (c) 8GHz (d) 10GHz (e)12GHz ... 77

߄

߄Ҟᒵ

߄ 1-1 ӚႝၡਏૈКၨ ... 4

߄ 3-1 ᚈ㎸ΕϩթԄࢎᄬΠٿಔᙁܰှ(m=0,²2-²3Ǿ) ... 25

߄ 3-2 ࠶ߎහф౗ϩଛᏔ೛ी߄[14] ... 35

߄ 3-3 ႝ඲ᡏλૻဦୖኧ ... 38

߄ 3-4 ႝၡϰଛୖኧ߃ۈॶ ... 40

߄ 3-5 ࠶ߎහф౗ϩଛᏔୖኧ ... 45

߄ 5-1 ൂՏܫεᏔໆෳᆶኳᔕ่݀ ... 80

߄ 5-2 IPDᇙำኳᔕᆶୖԵЎ᝘ਏૈКၨ ... 81

߄ 5-3 LTCCᇙำኳᔕᆶୖԵЎ᝘ਏૈКၨ ... 82

ಃ ΋ കʳ ᙁϟ

Equation Chapter (Next) Section 1 ᙁϟ

1.1 ୏ ୏ᐒ

ຬቨᓎ(UWB)೯ૻ኱ྗࢂᓎቨவ 3.1GHz ډ 10.6GHz ޑ೯ૻᔈҔ[1]Ǵᆶ

໺಍คጕ೯ૻس಍࣬ၨϐΠǴڀԖଯೲၗ਑໺ᒡǵե੃઻ф౗ᆶեғౢԋҁ

฻ᓬ༈Ǵࢂ߈ԃٰπ཰ࣚᔈҔ࣬྽ቶݱޑᔈҔᓎቨǶ

ф౗ܫεᏔӧคጕႝว৔ᆄࢂ࣬྽ख़ाޑ୔༧ǴѸ໪ගٮεޑф౗ᒡр

໺ډࡕᆄޑᘠݢᏔᆶϺጕǴԶቨᓎޑф౗ܫεᏔ׳ࢂ࣬྽֚ᜤޑႝၡǴЬा

ޑࡷᏯࢂૈӕਔᆢ࡭ቨᓎޑቚ੻ǵႝၡϰଛᆶф౗ਏૈǶନԜϐѦǴऩाঋ

៝ጕ܄ࡋǵဂᡏۯᒨᆶቚ੻ޑѳڶࡋǴӧႝၡ೛ी΢Ǵ۳۳ሡाፄᚇޑ่ᄬ

ٰ଺ϰଛႝၡǶ

ฅԶ 3.1GHz ډ 10.6GHz Ԗଯၲஒ߈ 110ʘޑ࣬ჹᓎቨǴ໺಍ޑӭભՍ

ௗႝၡѝૈගٮύ฻ޑᓎቨǴԶЪሡाፄᚇޑᒡрΕϰଛႝၡǴӢԜϩթԄ ܫεᏔ೏ቶݱޑᔈҔܭቨᓎޑф౗ܫεᏔǴՠࢂϩթԄܫεᏔޑф౗ߕуਏ

౗(power added efficiency, PAE)ࠅ۳۳߄౜ό٫ǴҗԜёޕ೛ीຬቨᓎф౗

ܫεᏔ׳ࢂ੻วޑ֚ᜤǶ

ӢԜҁࢎᄬ೛ी׆ఈૈ่ӝϩթԄܫεᏔၨܰޑႝၡᒡрΕϰଛǴЪӕ ਔૈׯ๓ϩթԄܫεᏔၨৡޑф౗ߕуਏ౗Ƕ٬ளቨᓎޑф౗ܫεᏔ׳৒ܰ

೛ीǶ

1.2 ࣬ᜢࣴزว৖౜ݩ

߈ԃٰޑ࣬ᜢࣴزǴךॺᖐр΋٤ӧ UWB ᔈҔᓎࢤՠόӕࢎᄬޑф౗

ܫεᏔٰ଺КၨǴಃ΋ঁٯηࢂ CMOS 0.18μm ᇙำǴ٬ҔႝࢬӆճҔ (Current-reused)کႝߔӣ௤מѯٰቚуф౗ߕуਏ౗ᆶᓎቨǴႝၡ೛ीᓎ౗

ጄൎ 3-7GHzǴቚ੻ 15dBǵOP1dB ࣁ 7dBmǵф౗ߕуਏ౗ 20%ǵဂᡏۯᒨ

²179pSǶ

კ 1-1ʳ ٯη΋ޑႝၡ੝܄[2]

ಃΒঁٯηޑࢎᄬࢂ΋ભ᠄ௗ(cascode)ՍӅྍཱུǴ٠ճҔႝ඲ᡏྍཱུႝ

གଏϯ(source degeneration)Ǵၲډᜪ՟ӣ௤ޑਏ݀Ǵӧ٬Ҕ CMOS 0.18μm ᇙำΠǴ೛ीᔈҔᓎ౗ጄൎ 3-5GHzǴቚ੻ 15.8dBǵOP1dBࣁ 11.4dBmǵф

౗ߕуਏ౗ 14-34%Ƕ

კ 1-2ʳ ٯηΒޑႝၡ੝܄[3]

ಃΟঁٯηࢎᄬࢂϩթԄܫεᏔǴႝၡ΢ԖѤঁൂՏܫεᏔǴ؂ঁൂՏ ܫεᏔࢂҗٿঁ BJT ᠄ௗಔԋǴќѦ೭ϩթԄܫεᏔޑ໣ཱུᆄ໺ᒡጕ٬Ҕ ᒷ׎ϯמѯǴ೭מѯёа࣪௞໣ཱུᆄϰଛޑႝߔаቚуф౗ߕуਏ౗Ƕӧ٬

Ҕ 0.25μm SiGe ᇙำΠǴ೛ीᔈҔᓎ౗ጄൎ 2-12GHzǴቚ੻ 9.5dBǵOP1dB ࣁ 14dBmǵф౗ߕуਏ౗ 6-9%Ƕ

კ 1-3ʳ ٯηΟޑႝၡ੝܄[4]

Π߄᏾౛а΢ႝၡޑӚ໨ႝၡ੝܄ᆶਏૈ

߄ 1-1ʳ ӚႝၡਏૈКၨ

[2]! [3]! [4]!

Technology CMOS 0.18μm CMOS 0.18μm 0.25μm SiGe

Frequency(GHz) 3-7 3-5 2-12

S11(dB) <-6 <-5 <-10

S22(dB) <-7 <-6 <-10

PAE(%) <20 14-34 6-9 Gain(dB) 14.5²0.5 15.2²0.6 9²0.5

OP1dB(dBm) 7 11.4 14

OIP3(dBm) <18 N/A N/A

Group delay(pS) ²179 N/A N/A

DC Power(mW) 24 25 250 B.W.(%) 80% 50% 143%

1.3 ೏ ೏୏ᇙԋϟಏ

ҁፕЎᕴӅճҔٿᅿ೏୏ᇙԋֹٰԋф౗ܫεᏔǴϩձࣁեྕӅᐨഏౠ (LTCC)ᆶᑈᡏ೏୏ϡҹ(IPD)ǴٿঁᇙำᆶЬ୏ᇙำ࣬ၨϐΠ೿Ԗၨեޑཞ

઻ᆶԋҁߡەޑ੝܄ǴԶЪჹܭεႝࢬᆶว዗ୢᚒ೿Ԗ࣬྽ଯޑהڙࡋǴΠ य़ჹٿᅿᇙำբϟಏǶ

1.3.1 եྕӅᐨഏౠ

ךॺ٬ҔޑࢂᐵቺϦљޑ኱ྗᇙำեྕӅᐨഏౠǴӅԖ 17 ቫߎឦٮ٬

Ҕޣ೛ीႝၡǴ؂ቫࠆࡋࣁ 52μmǴH ӧեᓎਔࣁ 7.5Ǵ઻ཞ҅Ϫࣁ 0.005Ǵr

ႝၡϣߎឦ٬ҔሌǴനλޑጕቨጕຯࣁ 100μmǴႝၡᇙբၸำӵკ 1-4 ܌ ҢǶ२Ӄ୷݈চ਑ғԋǴϐࡕࣁ׎ԋቫᆶቫϐ໔ೱ೯Ͼ(VIA)Ǵ٠Ъஒ׎ԋ ϐೱ೯Ͼ༤ᅈߎឦǴϐࡕ཮ӧӚቫ߄य़ӑڇߎឦᏤጕǴฅࡕע܌Ԗቫ᠄ӧ΋

ଆǴ٠ЪӧឪМ 800~900 ࡋΠӅᐨǴӵԜё׎ԋӭቫଯஏࡋഏౠ่ᄬǶ

კ 1-4ʳ եྕӅᐨഏౠᇙբำׇ[5]

1.3.2 ᑈ ᑈᡏ೏୏ϡҹ

ךॺᑈᡏ೏୏ϡҹᇙำࢂҗ୯ৎ඲ТύЈ܌ගٮǴওय़კᜪ՟ӵკ 1-5

܌ҢǴᇙำӅගٮΟቫߎឦٰ೛ीႝၡǴM1 ᆶ M2 ߎឦࠆ 3μmǴM3 ࠆ 10μmǴ ᆶեྕӅᐨഏౠ࣬ၨǴёҔߎឦቫኧၨϿǴՠߎឦ໔ޑ୷݈ࠆࡋᖓࡐӭǴё а೛ी஌ғਏᔈၨλޑ೏୏ϡҹǴЪጕຯёբޑКեྕӅᐨഏౠᆒஏǴՠ M3ᆶ M1ǵM2 ޑຯᚆᡂ౦ၨεǴ܌аၨ፾ӝҔ M3 ߎឦቫ଺ CPW ໺ᒡጕ ޑ׎Ԅٰ೛ीႝၡǶ

კ 1-5ʳ IPD ᇙำওय़კ[6]

ಃ Β കʳ ѰѓЋ໺ᒡጕ౛ፕᆶϩթԄ ܫεᏔ

ѰѓЋ໺ᒡጕ౛ፕᆶϩթԄܫεᏔ

2.1 Ѱ ѰѓЋషӝ໺ᒡጕ

ѓЋ໺ᒡጕԾႝᐒπ཰ว৖аٰǴӧ༾ݢႝၡᆶ৔ᓎႝၡ΢Ӹӧቶݱޑ ᔈҔǴӢѓЋނ፦ࣁԾฅӸӧǶԶѰЋނ፦നԐว৖ܭՋϡ 1968 ԃǴҗ Veselago നӃගр[7]ǴόӕܭѓЋ໺ᒡጕǴѰЋ໺ᒡጕӧჴኧᓎ౗ڀԖॄ

ኧޑϟႝ߯ኧکᅶᏤ౗ǴЪ࣬Տ߄౜΢όӕܭѓЋ໺ᒡጕǴڀԖߚጕ܄ޑ܄

፦ǶՠӧჴሞޑᔈҔύǴѰЋ໺ᒡጕคݤᗉխԾฅӸӧϐѓЋ໺ᒡጕޑៜ ᔈǴ܌а۳۳ӧ૸ፕਔǴ฻ਏኳࠠ཮ӕਔԵໆѰЋ໺ᒡጕᆶѓЋ໺ᒡጕޑ฻

ਏϡҹǴ܌аᆀϐࣁѰѓЋషӝ໺ᒡጕǶEquation Section (Next)

2.1.1 ѓЋ໺ᒡጕኳࠠ

୷ҁႝၡᏢᆶ໺ᒡጕ౛ፕനεޑόӕᗺӧܭϡҹޑႝ਻ελǶ୷ҁႝၡ ᏢύǴଷ೛᏾ᡏႝၡޑނ౛ЁκࣁᇻλܭݢߏǴԶ໺ᒡጕޑߏอࠅёаλܭ

΋ঁݢߏǴΨёаߏډኧঁݢߏǶӢԜǴ໺ᒡጕࢂ΋ঁϩթԄޑᆛၡǴΨ൩

ࢂᇥǴ໺ᒡጕ΢ޑႝᓸॶᆶႝࢬॶ֡཮ᒿߏࡋׯᡂԶԖ܌όӕǶ

໺ᒡጕ೯தࢂаٿచᏤጕٰ߄ҢǴӵკ 2-1(a)܌ҢǴচӢࢂа TEM ݢ

໺ሀޑ໺ᒡጕѸ໪ԿϿх֖ٿঁᏤᡏǴԶკ 2-1 (a)ύ΋λࢤߏࡋࣁ Δz ޑ໺

ᒡጕǴёҔკ 2-1 (b)ޑ໣ᕴϡҹႝၡኳࠠඔॊǴკύޑ RǵLǵG ᆶ C ࣁ

໺ᒡጕ؂ൂՏߏࡋޑނ౛ໆǴځۓကࣁǺ

RɨٿঁᏤᡏύ؂ൂՏߏࡋޑՍᖄႝߔǴൂՏࣁ͈/mǶ LɨٿঁᏤᡏύ؂ൂՏߏࡋޑՍᖄႝགǴൂՏࣁ H/mǶ

Gɨ؂ൂՏߏࡋޑ٠ᖄႝᏤǴൂՏࣁ S/mǶ Cɨ؂ൂՏߏࡋޑ٠ᖄႝ৒ǴൂՏࣁ F/mǶ

Սᖄႝག L ࣁٿᏤᡏύᕴԾགॶǴ٠ᖄႝ৒ C ߾ࢂӢࣁٿᏤᡏޑຯᚆ

᎞߈܌ౢғǴՍᖄႝߔ R ࣁ྽໺ᒡጕᏤᡏڀԖԖज़ޑᏤႝ౗ਔǴ܌ౢғޑ ཞ઻ԶѸ໪ԵቾޑႝߔǴԶ٠ᖄႝᏤ G ࣁϟܭٿᏤᡏ໔ޑϟႝ፦ཞ઻܌

ठǶӢԜǴR ک G ж߄໺ᒡጕޑཞ઻Ƕ΋ࢤԖज़ߏޑޑ໺ᒡጕǴё߄Ңࣁ ӵკ 2-1 (b)ύλࢤ໺ᒡጕՍᖄ܌ಔԋǶ

(a)

(b)

კ 2-1ʳ ΋ࢤཱུอ໺ᒡጕޑ฻ਏႝၡ(a)ႝᓸᆶႝࢬۓကϷ(b)໣ᕴ฻ਏႝၡǶ २Ӄךॺҗკ 2-1 (b)Ǵ࿶җլՋ಻ϻႝᓸۓࡓёள

( , )

( , ) * ( , ) i z t ( , ) 0 v z t R z i z t L z v z z t

t

 '  ' w   '

w (2.1)

࿶җլՋ಻ϻႝࢬۓࡓёள

( , )

( , ) * ( , ) v z z t ( , ) 0 i z t  'G z v z 'z t  'C zw  ' i z 'z t

w (2.2)

ஒ΢य़ٿԄନа'z٠ڗཱུज़' o ǴёаளډႝൔБำԄӵΠ z 0

( , ) ( , )

* ( , ) *

v z t i z t

R i z t L

z t

w   w

w w (2.3)

( , ) ( , )

* ( , ) *

i z t v z t

G v z t C

z t

w   w

w w (2.4)

ӧਔୱޑᛙᄊύǴа࣬ໆ߄ҢǴ(2.5)ԄёᙁϯࣁǺ!

( ) ( ) * ( )

dV z R j L I z

dz   Z (2.5)

( ) ( ) * ( )

dI z G j C V z

dz   Z (2.6)

ஒ(2.5)Ԅᆶ(2.6)ԄᖄҥǴёள໺ᒡጕ΢ႝᓸ V(z)ᆶႝࢬ I(z)ޑݢ୏Бำ Ԅ!

0 0

( ) ^{z z}

V z V e^{ J} V e^{ J} (2.7)

0 0

( ) ^{z z}

I z I e^{ J} I e^{ J} (2.8)

( )( )

j R j L G j C

J D  E  Z  Z (2.9)

ځύe^Jz໨߄Ңݢ۳+z Бӛ໺ኞǴe^Jz໨߄Ңݢ۳-z Бӛ໺ኞǶஒ(2.5) ԄжΕ(2.7)ԄǴёள໺ᒡጕ΢ޑႝࢬࣁǺ

0 0

( ) *[ ^{z z}]

I z V e V e

R j L

J J

J

Z ^{   }

 (2.10)

җ΢Ԅᆶ(2.8)КၨǴёள੝܄ߔל ZoǴځۓကӵΠ!

0

R j L R j L

Z G j C

Z Z

J Z

 

 (2.11)

੝܄ߔל Z^o ೱ่Α໺ᒡጕ΢ႝᓸᆶႝࢬޑᜢ߯ӵΠ

0 0

0

0 0

V V

Z I I

 

 

 (2.12)

Զӧคཞ઻ޑ௃ݩΠǴ(2.9)Ԅᆶ(2.11)ԄёׯቪࣁǺ

, 0 L j LC j Z

J Z E C (2.13)

2.1.2 Ѱ ѰѓЋ໺ᒡጕኳࠠ

ࣁΑᙁϯኳࠠǴךॺӧ௖૸ѰѓЋኳࠠਔଷ೛ԋคཞޑރᄊǴх֖Αѓ Ћ໺ᒡጕਏᔈޑՍᖄႝགᆶ٠ᖄჹӦႝ৒ǴаϷѰЋ໺ᒡጕਏᔈޑՍᖄႝ৒

ک٠ᖄჹӦႝགǴӵკ 2-2 ܌ҢջࣁѰѓЋ໺ᒡጕޑኳࠠ[8]Ƕ

კ 2-2ʳ คཞ઻ѰѓЋషӝ໺ᒡጕޑ฻ਏႝၡǶ

ӕ 2.1.1 ࿯ѓЋ໺ᒡጕϐ߻ޑଷ೛Ǵკ 2-2 ࢂ΋λࢤߏࡋࣁ Δz ޑ໺ᒡ ጕǴ؂ൂՏߏࡋޑߔלᆶᏤયࣁ!

' ( _R 1 )

L

Z Z j L

z Z C

Z

' (2.14)

' ( _R 1 )

L

Y Y j C

z Z L

Z

' (2.15)

ӧคཞޑ௃ݩΠǴճҔ΢य़ٿԄёள

2

2

( ) ( ) ' ' ( ) _{R R} 1 ( ^{R R})

L L L L

L C

Z Y S L C

L C L C

J Z E Z Z Z

Z   (2.16)

1

2

1 1

1 min ,

( )

1 1

1 max ,

R L L R

R L L R

if L C L C

S

if

L C L C Z Z

Z

Z Z

*

*

­ § ·½

 

° ¨¨ ¸¸°

° © ¹°

® ¾

§ ·

° ! ¨ ¸ °

° ¨© ¸¹ °

¯ ¿

(2.17)

٩Ᏽ࣬ՏБำύ໒ਥဦޑ่݀Ǵ࣬Տёаࣁપჴኧ܈ޣ຀ኧǶӧ੝ۓޑ

ᓎ౗Πऩ࣬ՏࣁપჴኧǴ߾߄Ңៜᔈࣁ೯஥Ǵϸϐ߾ࣁ࿣஥Ƕځύ࿣஥ޑӸ ӧࣁѰѓЋషӝ໺ᒡጕޑᐱ੝౜ຝǴόӸӧܭપѰЋ܈પѓЋ໺ᒡጕϐύǶ ќѦѰѓЋషӝ໺ᒡጕӧ࣬ೲࡋکဂೲࡋڀԖᐱ੝ޑނ౛܄፦ǴપѓЋ໺ᒡ ጕӧ࣬ೲࡋکဂೲࡋ΢ࣣࣁ҅ኧǴ࣬४ޑ่݀ҭࣁ҅ኧǴԶપѰЋ໺ᒡጕӧ

࣬ೲࡋᆶဂೲࡋޑ४ᑈ΢ࣁॄኧǴӢԜѰѓЋషӝ໺ᒡጕх֖Αٿᅿ໺ᒡጕ ޑ੝܄Ǵӵკ 2-3 ܌ҢǴӧեᓎਔǴ཮р౜ᜪ՟ܭѰЋ໺ᒡጕޑՅණᜢ߯Ǵ ӧଯᓎਔ཮р౜ᜪ՟ܭѓЋ໺ᒡጕޑՅණᜢ߯ǶԶѰѓЋషӝ໺ᒡጕӧ࣬Տ Бำ΢ǴऩวғచҹZ_*1zZ_*2Ǵаႝၡ΢ޑᢀᗺǴջࣁՍᖄޑӅਁᓎ౗ᆶ٠ ᖄӅਁᓎ౗όӕǴΞᆀࣁόѳᑽޑ໺ᒡጕǶךॺёаפډ࿣஥ޑᓎ౗ϟܭZ_*1 ᆶZ_*2ϐ໔Ǵӵკ 2-3 ܌ҢǶ

კ 2-3ʳ όѳᑽషӝѰѓЋ໺ᒡጕ

ฅԶǴऩѰЋکѓЋѳᑽ

1 2 L CR L L CL R

Z_* Z_* o (2.18)

ךॺᆀϐࣁѳᑽ໺ᒡጕ(balanced)Ƕவ(2.18)ԄచҹΠǴ໺ኞதኧёᙁϯ ࣁ!

( ) _{R L R R} 1

L L

L C L C

E Z E E Z

 Z (2.19)

࣬ՏதኧёϩှࣁѰЋ೽ҽᆶѓЋ೽ҽǴӧკ 2-3 ύ࣬Տᙯᡂޑᓎ౗

Z ஒ཮วӧ!0

4 0

1 ,

1 1

,

R R L L

R L L R

unblanced L C L C

balanced L C L C

Z

­ ½

° °

° °

® ¾

° °

° °

¯ ¿

(2.20)

а΢ޑ่݀ှញΑǴ࿣஥ᓎ౗୔ୱஒό཮р౜ӧѳᑽࠠᄊޑѰѓЋషӝ

໺ᒡጕύǴջ٬ β(ω)ࣁ႟ޑ௃׎ΠǴѝԖൂ΋ᓎ౗ᗺࣁ࿣஥ǶճҔ(2.14)Ԅ ک(2.15)Ԅ௢Ꮴр੝܄ߔלࣁ

2 2

0 1

1

balanced

R L R L

L R R L

L C L L

Z L C C C

Z Z



 (2.21)

வ௢Ꮴрޑ(2.21)ԄёளޕǴ੝܄ߔלԄᆶᓎ౗คᜢǶӢԜךॺགྷा೛

ीр΋ঁቨᓎޑѰѓЋషӝ໺ᒡጕǴ൩Ѹ໪ԵቾډѰЋߔלکѓЋߔלޑϰ ଛୢᚒǶ

2.2 ϩ ϩթԄܫεᏔޑ୷ҁᏹբচ౛

კ 2-4ʳ ໺಍ϩթԄܫεᏔ

ϩթܫεᏔޑ୷ᘵࢎᄬӵკ 2-4 ܌ҢǶN ભՍௗޑႝ඲ᡏೱௗٿచ໺

ᒡጕǴځύ႔ཱུೱௗډޑ໺ᒡጕᆀࣁ႔ཱུጕ(gate line)Ǵځύ႔ཱུጕ੝܄ߔל ࣁ Z^g ᆶ࣬Տதኧࣁ β^gǴԶཱུؕೱௗډޑ໺ᒡጕᆀࣁཱུؕጕ(drain line)Ǵځύ

ཱུؕጕӸӧ੝܄ߔלࣁ Zd ᆶ࣬Տதኧࣁ β^dǶϩթԄܫεᏔၮբኳԄࣁᒡΕ

ૻဦ࿶җ႔ཱུጕ໺ሀǴϐࡕӚભႝ඲ᡏᒿ๱႔ཱུᆄޑਁ൯Ǵӧཱུؕᆄౢғ࣬

ჹᔈႝࢬǴฅࡕӧཱུؕጕ΢؂ᗭႝ඲ᡏౢғޑႝࢬ཮ϕ࣬բૻဦషکǴനࡕ ᒡрᆄ཮ࢂ೸ၸӕ࣬Տޑࡌ೛܄࣬уૻဦǶځύ႔ཱུጕᆶཱུؕጕޑ໺ኞதኧ

ᆶႝ਻ߏࡋ཮،ۓനࡕӧᒡрᆄޑૻဦࢂցࣁࡌ೛܄࣬уǴќѦᆄႝߔ R^g ᆶ R^d ߾೛ीҔٰ֎ԏ႔ཱུጕ҅ӛᆶཱུؕጕϸӛ໺ሀޑૻဦǶځύϩթԄܫ εᏔύႝ඲ᡏ႔ཱུᆶཱུؕޑ஌ғਏᔈ཮ճҔ໺ᒡጕ౛ፕӝٳܭ໺ᒡጕ΢Ǵന ࡕ೸ၸ໺ᒡጕቨᓎ੝܄Ǵ٬᏾ᡏႝၡ཮և౜ቨᓎЪܫεޑਏ݀ǶௗΠٰךॺ

ाҗᒡΕᆄႝᓸ௢Ꮴр౛གྷ௃ݩΠϩթԄܫεᏔᒡрᆄޑႝࢬǶ

კ 2-5ʳ ൑ਏႝ඲ᡏ฻ਏႝၡ

ԶϩթԄܫεᏔϣ೽ޑϩ݋Ǵ२Ӄךॺ٬Ҕႝ඲ᡏኳࠠӵკ 2-5Ǵ٠Ъ ᙁϯܫεᏔࣁൂᜐޑࠠᄊ(C^gd=0)ǴӢԜךॺёаஒϩթԄܫεᏔᙁϯࣁٿచ

ॄၩ໺ᒡጕϩձࣁ႔ཱུጕаϷཱུؕጕǴӵკ 2-6Ƕ

კ 2-6ʳ ໺಍ϩթԄܫεᏔ࣬ՏҢཀკ

(a) (b) კ 2-7ʳ (a)႔ཱུጕൂՏϡҹϷ(b)ཱུؕጕൂՏϡҹ

ჹܭϩթԄܫεᏔύ႔ཱུጕᆶཱུؕጕޑ੝܄Ǵךॺёа٬Ҕ໺ᒡጕ౛ፕ

ٰ௢Ꮴ੝܄ߔלᆶ໺ኞதኧ[9]Ǵځύ႔ཱུጕ؂ൂՏߏࡋ฻ਏႝၡӵკ 2-7 (a)Ǵځύ L^g ࣁ໺ᒡጕޑ฻ਏՍᖄႝགǴC^g ߾ࣁ໺ᒡጕޑ฻ਏჹӦႝ৒Ǵ ^g ࣁൂՏϡҹޑނ౛ߏࡋǴ܌аՍᖄߔלᆶ٠ᖄᏤયࣁ

, /

1

gs g

g g

i gs

Z j L Y j C j C

j R C Z Z Z

 Z



g (2.22)

ԶӃ຾ᇙำύ Ǵڂࠠ൑ਏႝ඲ᡏୖኧӧ፾Ҕޑᓎ஥ϣਔǴךॺёаଷ

೛ ωRⁱCgs<<1ǴӢԜ੝܄ߔלёᙁϯࣁ

/

g g

g gs g

Z L

Z Y C C g

(2.23)

ჹܭཱུؕጕǴךॺҭ٬Ҕ࣬ӕଷ೛Ǵ܌а໺ኞதኧёϯᙁࣁ

[ 1 ( / )]

( / )

2

g g g d d ds d

ds d

d

d d ds d

ds d

ZY j L j C C

R

Z j L C C

R

J D E Z Z

Z

  

 

d)]

d

(((

d)

d

 jj L

(2.24)

Կܭቚ੻ޑ௢ᏤǴӵკ 2-6 ܌ҢǴჹܭႝ඲ᡏ؂ભޑᒡΕႝᓸךॺёቪ ࣁ!

( 1)

2 1

( ), 1, 2...

1

k g g

k in

i gs

V V e k n

j R C

J

Z

 



g(

g (2.25)

ךॺҭଷ೛ ωRⁱCgs<<1Ǵ܌аӚભႝ඲ᡏޑᒡрႝࢬࣁ

( 1)

2 ^{g g}, 1, 2...

k

k m k m in

I g V g V e^{  J gg} kk n (2.26)

ӆ࿶җཱུؕጕ໺ሀࡕǴךॺё௢ள߻ӛᕴႝࢬࣁࣁ

1 1 1

( 2 ) ( 2 ) 2 ( )

1 1

1

2 2

d d d d g g g g d d

n n k m in n k n k

forward k

k k

I 

¦

¦ ¦

ځύऩE_{g g}gg EE_dd _ddǴ߾ᒡрᆄᕇளޑႝࢬࣁӄᡏႝࢬᕴکǴԜਔϩթ ԄܫεᏔޑቚ੻ёᐱҥܭᓎ౗ǴচӢࣁ྽ٿచ໺ᒡጕ࣬Տ࣬ӕਔǴ໺ሀӧٿ చ໺ᒡጕ΢ޑૻဦࣁӕ؁Ǵૻဦ۶Ԝ࣬Տ࣬ӕևࡌ೛܄࣬уǴԶ೭Ψࢂϩթ ԄܫεᏔख़ाޑ੝܄ϐ΋ǴჹᏤ೯஥ϣޑૻဦ๏ϒᓎ౗คᜢϐᛙۓቚ੻Ƕ

а΢ךॺவኧᏢϩ݋ޑБԄ௖૸౛གྷ௃ݩΠᒡрΕޑႝᓸႝࢬᜢ߯Ǵऩ

ࢂ૸ፕᒡΕᆄکᒡрᆄޑᒡΕϸ৔ཞ઻Ǵӧ౛གྷޑ௃ݩΠǴᒡΕᆄ࣮ډ႔ཱུ

ጕNE_{g g}gޑႝ਻ߏࡋࡕௗ RgǴӕ౛Ǵᒡрᆄ࣮ډཱུؕጕNE_{d d}dޑႝ਻ߏࡋ ࡕௗ RdǴ႔ཱུᆄ Rg཮ᒧ᏷ᆶ Zg࣬ӕǴཱུؕᆄ Rd཮ᒧ᏷ᆶ Zd࣬ӕǴӢԜᒡ рΕϸ৔ཞ઻೿ࢂคज़εǶ

2.3 ᚈ ᚈ㎸ΕϩթԄܫεᏔ

టჴ౜ቨᓎޑф౗ܫεᏔǴϩթԄф౗ܫεᏔࢂࡐӳޑᒧ᏷Ǵӵ 2.2 ࿯

܌قǴճҔᙁൂޑ໺ᒡጕϰଛচ౛ջૈၲډቨᓎޑਏ݀ǴՠϩթԄܫεᏔද ၹٰᇥǴф౗ߕуਏ౗཮КၨեǴԶЪᒿ๱ϩթԄܫεᏔޑભኧຫӭǴӢࣁ

໺ᒡጕ΢ޑཞ઻Ǵຫௗ߈ᒡрᆄޑႝ඲ᡏǴ႔ཱུᆄޑਁ൯ຫλǴຫόૈֹӄ ޑᏹբǶࣁΑׯ๓΢ॊޑୢᚒǴӢԶౢғᚈ㎸ΕϩթԄࢎᄬ[10]Ƕ

კ 2-8ʳ ᚈ㎸ΕϩթԄࢎᄬ[11]

ᚈ㎸ΕϩթԄࢎᄬӵკ 2-8 ܌ҢǴၟϩթԄܫεᏔᜪ՟Ǵѝࢂ႔ཱུጕᆶ

ཱུؕጕޑٿ୵ௗ΢ϩݢᏔǴӢԜӧᚈ㎸ΕϩթԄࢎᄬ΢ؒԖ໕࿼ޑ୵ௗ΢ႝ

ߔஒф౗֎ԏǴ೭Ψࢂф౗ߕуਏ౗К໺಍ޑϩթԄܫεᏔӳޑচӢǶ

კ 2-9ʳ ᚈ㎸ΕϩթԄࢎᄬ฻ਏႝၡ

კ 2-9 ࢂᚈ㎸ΕϩթԄࢎᄬޑ฻ਏႝၡǴௗΠٰाӃ௢Ꮴ႔ཱུᆄᒡΕႝ

ᓸჹᒡрф౗ޑᜢ߯ǴԶ໺಍ޑϩթԄܫεᏔё࣮ԋ EinB ࣁ႟ਔǴѝԵቾ VoutA ޑᒡрǶӵӕ໺಍ϩթԄܫεᏔǴӧԜϩ݋ύǴךॺ଺Α൳ᗺଷ೛ӵ ΠǶಃ΋ᗺଷ೛ӅԖ n ᗭႝ඲ᡏǴךॺճҔ໺ᒡጕ౛ፕǴջ(2.13)Ԅک(2.21) Ԅ฻ϦԄǴ೸ၸϡҹϰଛႝ඲ᡏޑႝ৒ CgsǵCdsǴ٬႔ཱུጕکཱུؕጕӧ೛ी

ᓎࢤਔǴ੝ቻߔלࣁ Z0ǴԶЪӕკ 2-9Ǵ໺ኞதኧࣁ γǴႝ਻ߏࡋࣁ l ܈ / 2l Ƕ

ಃΒᗺଷ೛ךॺёаעૻဦճҔᔎᆢჱচ౛ǴעᒡΕᆄ฻ਏԋٿಔૻဦྍک Z₀ႝߔӧϩݢᏔޑՏ࿼Ǵᒡрᆄ฻ਏԋٿಔ Z0ॄၩ௠ӧϩݢᏔޑՏ࿼Ƕ

࿶ၸ΢य़ޑଷ೛Ǵёޕಃ k ᗭႝ඲ᡏޑཱུؕᆄႝࢬࣁ

dk m gk

I G V (2.28)

Gmࢂႝ඲ᡏεૻဦޑᙯᏤǴךॺճҔख़᠄চ౛ǴӃଷ೛ EinA฻ܭ EǴ EinBࣁ႟ǴӢԜǴಃ k ঁޑ႔ཱུᆄႝᓸࣁ

( ) 1

2

l

l k gk

V E e e

J J

  

(2.29) җ΢Ԅё௢ள

( ) 1

2

l m l k dk

G E e

I e

J J

   (2.30)

྽ᚈ㎸Εٿᆄ೿ԖૻဦਔǴଷ೛ EinA฻ܭ EǵEinBࣁEe^jIǴI^ࣁϩݢᏔ ޑ࣬ՏৡǴٗሶಃ k ᗭႝ඲ᡏޑ႔ཱུႝᓸ཮җٿᆄޑᒡΕૻဦಔӝӵΠ

( ) 1 ( ) 2

l

l k l n k j

gk

V E e e e e

J J J I

 ª¬      º¼ (2.31)

җ΢Ԅё௢ள

( ) 1 ( ) 2

l

l k l n k j

m dk

G E e

I e e e

J J J I

 ª¬      º¼ (2.32)

ཱུؕᆄႝࢬ཮ϩࢬ۳ VoutAک VoutBᆄǴॄၩࣁٿঁ Z0ႝߔ٠ᖄǴӢԜ

ॄၩߔלࣁ ⁰ 2

Z Ǵ่ӝ(2.32)Ԅё௢ளཱུؕᆄႝᓸࣁ

2 1 1 2

2 2

0 ... ( ) ( ) ( ) ( ) ....

2 ^{k k k k k}

l l l l

dk d d d d d

V Z e ^J I e ^J I I e ^J I e ^J I

   

   

ª       º

¬ ¼ (2.33)

၀Ԅࢂଷ೛ಃ k ঁཱུؕᆄႝᓸࢂҗ؂ঁႝ඲ᡏႝᓸϩࢬᕴکӆ४΢ॄ

ၩԶٰǶԶ؂ঁႝ඲ᡏᒡрф౗ёҗΠԄीᆉ 1 *

Re( )

2 ^{dk dk}

Pout  V I (2.34)

ట٬ᒡрф౗നεǴவ(2.32)ᢀჸǴѸ໪ᅈى(e^{Jl k}) ^1ک(e^{Jl n k}) ^ e^jIӕ࣬

ՏǴӢԜё᏾౛ϦԄӵΠǺ

1 2 1

(e^{Jl k}) ^ (e^{Jl n k}) ^ e^jI Ÿ(e^Jl) ^{k n } e^jI (2.35) ऩࢂӧคཞЪૈໆࣣࢂࡌ೛܄࣬уޑ௃ݩΠǴ໺಍ޑϩթԄܫεᏔᒡр

ф౗ࣁ

2

0

1 | |

out 2 outA

P V

Z (2.36)

Զᚈ㎸Εޑࢎᄬᒡрф౗ࣁ

2 2

0

1 (| | | | )

out 2 outA outB

P V V

Z  (2.37)

྽ύ|V_outA| e^JlV_dnǴ|V_outB| e^JlV_d1Ƕவ(2.36)Ԅᆶ(2.37)Ԅё࣮рᚈ

㎸ΕࢎᄬёК໺಍ϩթԄܫεᏔቚу 3dB ޑቚ੻Ƕ

[12]ճҔᚆණϡҹٰᡍ᛾΢ॊ౛ፕǴҔᚈ㎸ΕϩթԄܫεᏔᆶ໺಍ϩթ ԄܫεᏔբКၨǴ٠ჹٿᅿࢎᄬޑ੝܄բკӵΠǶ

კ 2-10ʳ ᚈ㎸Εࢎᄬޑ S ୖኧკ[12]

კ 2-10 ܌ҢǴᚈ㎸ΕࢎᄬёаԖ S21ቨᓎޑ੝܄Ǵவ฻ਏႝၡკ 2-9

ٰ࣮Ǵ႔ཱུጕ΢ޑႝᓸਁ൯ჹ࣬٩ႝࢬྍ Idi ౢғᒡрႝࢬǴႝࢬவཱུؕጕ

΢ࢬӛٿᆄᒡрǴԶ࣬٩ႝࢬྍ Idiᐱҥܭᓎ౗ӢનǴӢԜ S21ቨᓎǶ

კ 2-11ʳ ᚈ㎸Εࢎᄬᆶ໺಍ࢎᄬޑᒡрф౗Кၨ[12]

კ 2-12ʳ ᚈ㎸Εࢎᄬᆶ໺಍ࢎᄬޑф౗ߕуਏ౗Кၨ[12]

வკ 2-11 ᆶკ 2-12 ύǴךॺёаᡍ᛾Ӣࣁѐନ௞໺಍ࢎᄬ΢ޑ Rg ᆶ RdǴٿಔࣁΑׯ๓ᒡΕཞ઻ԶӸӧޑႝߔǴӢԜׯ๓Αႝၡቚ੻ᆶф౗ߕ уਏ౗Ƕ

კ 2-13ʳ ᚈ㎸Εࢎᄬᆶ໺಍ࢎᄬޑጕ܄ࡋКၨ[12]

ᗨฅᚈ㎸Εࢎᄬׯ๓Αႝၡቚ੻ᆶф౗ߕуਏ౗Ǵՠጕ܄ࡋࠅК໺಍ࢎ

ᄬৡǴӵკ 2-13 ܌ҢǶ

2.4 ѳ ѳᑽԄܫεᏔ

ѳᑽԄܫεᏔࢎᄬӧ 1965 ԃҗنᅟჴᡍ࠻ޑ R. S. Engelbrecht ගр [13]ǴԜࢎᄬ΋໒ۈӧեᚇૻܫεᏔ΢٬ҔǴѬૈᡣႝၡന٫ϯᚇૻਏ੻ޑ ӕਔගٮӳޑᒡрΕϸ৔ཞѨǴϐࡕѳᑽԄܫεᏔΨӢࣁૈගٮቨᓎޑᒡр ΕϰଛԶቶݱޑᔈҔӧቨᓎႝၡ΢Ƕ

კ 2-14ʳ ٬Ҕ 90^oϩӝݢᏔޑѳᑽԄܫεᏔ

კ 2-14 ࢂѳᑽԄܫεᏔޑ౛ፕࢎᄬǴ၀ࢎᄬࢂҗٿঁъႝၡܫεᏔᆶ ٿঁ 3-dB 90^oБӛጠӝᏔ܌ಔԋǴጠӝᏔޑ႖ᚆᆄ୵೯த೛ी௠΢ Z0 Ω ޑ

ॄၩǴ၀ॄၩёа֎ԏவъႝၡܫεᏔϸ৔ӣٰޑૈໆǴ၀୷ҁᏹբচ౛ӵ ΠǺಃ΋ঁ 90±БӛጠӝᏔஒᒡΕૻဦ֡ϩࣁٿঁ࣬Տৡ 90±Ъ฻ਁ൯ૻ

ဦǴ٠ӕਔ㎸Εٿ࣬ӕޑъႝၡܫεᏔǴٿঁ㎸Εૻဦё߄Ңࣁ

1 1

1

A 2

V^ V^ (2.38)

1 1

B 2

V^ jV^ (2.39)

ځύV₁^ࣁΕ৔ႝᓸݢǶಃΒঁ 90rБӛጠӝᏔૈஒٿܫεᏔޑᒡр࣬

уǴځᒡрႝᓸё߄Ңࣁ

2 2 2 1 1 1

1 1

( )

2 ^A 2 ^B 2 ^{A A} 2 ^{B B} 2 ^{A B}

j j j

V^  V^  V^  G V^  G V^  V^ G G (2.40)

܌а S21ёቪԋ

2 21

1

( )

2 ^{A B}

V j

S G G

V



   (2.41)

(2.41)Ԅё᛾ܴѳᑽԄܫεᏔϐቚ੻ǴࣁٿܫεᏔቚ੻ޑѳ֡ॶǶԶᒡ Εᆄޑᕴϸ৔ႝᓸǴёਥᏵ 90rБӛጠӝᏔᒡрޑ࣬Տᜢٰ߯᛾ܴǴऩٿܫ

εᏔֹӄ࣬ӕǴ߾ٿܫεᏔᒡΕᆄ܌ౢғޑϸ৔ݢǴ཮ӧ 90rጠӝᏔޑᒡΕ ᆄ۶Ԝ࣬ϕܢᎍǴځኧᏢᜢ߯Ԅࣁ

1 1 1 1 1 1

1 1

( )

2 ^A 2 ^B 2 ^{A A} 2 ^{B B} 2 ^{A B}

j j j

V^ V^   V^  * V^   * V^ V^ *  * (2.42)

܌а S11ёቪԋ

1 11

1

1( ) 2 ^{A B} S V

V



 *  * (2.43)

ӢԜऩٿܫεᏔֹӄ࣬ӕǴ߾GA GBЪ* *A BǴ(2.43)Ԅ᛾ܴ S11=0Ǵ (2.41)Ԅ᛾ܴѳᑽԄܫεᏔޑቚ੻ǴᆶঁձܫεᏔޑቚ੻࣬ӕǶԶѳᑽԄܫ εᏔޑᒡрᆄΨёа೸ၸᜪ՟ޑ௢Ꮴ᛾ܴǴٿܫεᏔֹӄ࣬ӕਔ S22=0Ƕ

྽೛ी΋ঁൂᆄޑեᚇૻܫεᏔ܈ф౗ܫεᏔਔǴԵໆډᚇૻ܈ᒡрф

౗ޑਏ੻ǴᏤठܫεᏔԖၨৡޑᒡрΕϸ৔ཞ઻ǴԜਔ೸ၸѳᑽԄܫεᏔޑ

ࢎᄬǴёаӕਔᆢ࡭ᚇૻ܈ᒡрф౗ޑਏ੻аϷׯ๓ᒡрΕϸ৔ཞ઻Ƕӕ

౛Ǵӧ UWB ޑᔈҔύǴऩܫεᏔाԵໆډቚ੻ѳڶࡋᆶᓎቨԶԖၨৡޑᒡ рΕϸ৔ཞ઻ǴΨёа೸ၸԜࢎᄬׯ๓Ƕ

ନΑׯ๓ᒡрΕϸ৔ཞ઻ѦǴѳᑽԄܫεᏔΨԖΠӈޑӳೀǺ

ቚуф౗ܫεᏔޑᒡрф౗Ǻф౗ӝԋᏔࢂᇙբф౗ܫεᏔதҔޑמ ѯǴٿঁൂᆄф౗ܫεᏔёа೸ၸф౗ӝԋᏔගଯᒡрޑф౗ǴԶѳᑽԄܫ εᏔޑࢎᄬΨԖ࣬ӕޑ੝܄Ƕ

೛ीᓎ஥ϣӳޑᛙۓࡋǺѳᑽԄܫεᏔ΋૓ٰᇥ཮Ԗ׳ӳޑᛙۓࡋǴচ ӢӧႝၡϣޑൂᆄܫεᏔᒡрΕޑߔלၨڰۓǴ೯தӧ 50ΩǴऩѳᑽԄܫε ᏔᒡрΕޑॄၩׯᡂǴՠჹൂᆄޑъႝၡܫεᏔޑॄၩׯᡂໆ೯தόεǴϸ ᢀऩόࢂѳᑽԄܫεᏔǴ߾ॄၩׯᡂ཮ޔௗቹៜډႝၡǴЀځࢂф౗ܫε ᏔǴऩࡕᆄௗޑࢂ஥೯ԄᘠݢᏔǴѝԖӧ೛ीᓎ஥ϣࢂ 50ΩǴ೛ीᓎ஥Ѧॄ

ၩၨᜤ՗ीǴ۳۳཮೷ԋܫεᏔႝၡ᎜ᕏǶ

ႝၡё᎞ࡋၨଯǺӵ݀ѳᑽԄܫεᏔޑъႝၡࡺምǴ߾ܫεᏔޑѝቚ੻

෧Ͽ 6dBǶऩӧ΋ঁس಍܈ܫεᏔޑՍӈǴѳᑽԄܫεᏔѝࢂځύޑ΋ભǴ ऩъႝၡܫεᏔวғࡺምǴ߾ჹ᏾ᡏޑቹៜջቚ੻෧Ͽ 6dBǴϸᢀऩόࢂѳ ᑽԄܫεᏔ߾᏾ঁس಍೿όૈ٬ҔǶ

ၨӳޑጕ܄ࡋǺӢࣁӧѳᑽԄܫεᏔύǴᒡΕъႝၡܫεᏔޑૈໆѝԖ

΋૓ឲΕൂᆄܫεᏔޑΒϩϐ΋(ջࢂϿ 3dB)Ǵ߾ OIP3 ၟൂᆄܫεᏔ࣬ၨ

ϐΠΨ཮ගଯ 3dBǶ

ಃ Ο കʳ ቨᓎᚈ㎸ΕϩթԄܫεᏔ Equation Section (Next)

ቨᓎᚈ㎸ΕϩթԄܫεᏔ

3.1 ҅ ҅Ҭϩ࣬ᏔᆶൂՏܫεᏔ

ᗨฅӧ౛གྷ௃ݩޑϩ݋΢Ǵᚈ㎸ΕϩթԄܫεᏔࢎᄬૈቚуܫεᏔޑф

౗ߕуਏ౗Ǵՠӧႝၡ೛ी΢ࠅӸӧ΋٤લᗺǶځ΋Ǵᚈ㎸Εࢎᄬޑጕ܄ࡋ

཮КൂᆄޑϩթԄܫεᏔৡ[12]ǴځΒǴᚈ㎸ΕࢎᄬޑϩݢᏔᒡрޑٿঁ୵ ٠ߚᐱҥǴӵკ 2-9 ྽ύޑ EinAᆶ EinBǴऩ EinAᒡΕޑૈໆؒԖӧ໺ᒡጕ΢

੃઻ᆶ֎ԏǴ߾཮வ EinB ᒡΕೀϸឲӣϩݢᏔǴඤقϐǴEinA ᒡΕૈໆᆶ E_inBᒡΕૈໆஒ࿶ၸ႔ཱུጕࡕӧᒡΕ୵ࡌ೛܄࣬уǴӵკ 3-1 ྽ύޑٿచၡ ৩܌ҢǴ೷ԋޑਏ݀ࢂ᏾ᡏႝၡޑϸ৔ཞ઻཮ࡐৡǶךॺፓ᏾ϩݢᏔޑᒡр

࣬فৡ٠ჹ᏾ᡏႝၡޑ S11բკǴӵკ 3-2 ܌ҢǴკύऩϩݢᏔᆶ႔ཱུጕࣁ

౛གྷރᄊǴջคཞރᄊǴ߾ૈໆֹӄϸቸԿᒡΕ୵Ǵӕ౛Ǵவᒡр୵ϩ݋

S₂₂ Ψ཮Ԗ࣬ӕޑ௃ݩǶӢࣁа΢ޑٿঁচӢǴךॺ೛ीਔעϩݢᏔٿᆄޑ ᒡрΕ୵ׯԋᐱҥǴ่ӝѳᑽԄܫεᏔࢎᄬٰׯ๓ጕ܄ࡋᆶϸ৔ཞ઻Ƕ

კ 3-1ʳ ᒡΕૈໆӧᒡΕ୵ࡌ೛܄࣬у

კ 3-2ʳ ϩݢᏔᒡр࣬Տৡჹႝၡ S11բკ

ךॺа n=4 ޑᚈ㎸ΕϩթԄܫεᏔࣁٯǴӵკ 3-3 ܌ҢǴn=4 жΕ(2.35) ԄǴךॺёளډΠԄ

2 5

(e^Jl) ^k e^jI (3.1)

კ 3-3ʳ Ѥᗭႝ඲ᡏᚈ㎸ΕϩթԄܫεᏔ

Զ(3.1)Ԅёаளډٿಔᙁܰޑှёаᡣૈໆӧᚈ㎸ΕϩթԄࢎᄬύࡌ

೛܄࣬уǴӵ߄ 3-1 ܌ҢǶ

߄ 3-1ʳ ᚈ㎸ΕϩթԄࢎᄬΠٿಔᙁܰှ(m=0,²2-²3Ǿ) J

J e^Jl I

ှ(΋) 180^o -1 180 ^o²360 ^o m

ှ(Β) 0 ^o 1 0 ^o²360^o m

ӧှ(΋)ޑႝၡ೛ीΠǴკ 3-3 ྽ύޑ AǵB ٿᗺখӳࢂϩݢᏔٿᆄᒡ Εޑઇᚯ܄࣬уޑ࿯ᗺǴΨ൩ࢂԜٿᗺႝᓸᔈؒԖਁ൯٠ЪႝࢬനεǴӢԜ

೛ी၀ᗺௗӦǴ٬ϩݢᏔٿᒡΕ୵ᐱҥǴӢԜךॺளډΠკ 3-4Ƕ

კ 3-4ʳ ѳᑽԄΠޑှ(΋)ႝၡ೛ी

ӵკ 3-4 ܌ҢǴϩݢᏔٿᒡΕ୵ᐱҥǴԶკύ*_inё࣮ډ 900 ໺ᒡጕௗ

ӦǴջࣁ* _in 1ǴவϩݢᏔᒡΕޑૈໆӧ၀࿯ᗺ࣮ډ* _in 1཮ֹӄϸ৔Ǵૈ

ໆϸቸӣ႔ཱུጕԿϩݢᏔǴԶᒡΕޑૈໆᆶϸ৔ޑૈໆӧႝ඲ᡏ႔ཱུᆄࣣࣁ ࡌ೛܄࣬уǴӧԜރᄊΠǴᒡΕޑૈໆஒӧ႔ཱུጕ΢׎ԋᎫݢǴԜᎫݢޑݢ ঢ়ݢك೛ीӧႝ඲ᡏޑ႔ཱུᆄǶ

ᆶᚈ㎸ΕϩթԄࢎᄬКၨǴٿޣࣣૈӧႝ඲ᡏ႔ཱུᆄԖࡌ೛܄࣬уǴৡ ձӧѳᑽԄࢎᄬࢂ೸ၸϩݢᏔൂ΋୵ޑૈໆϸ৔ǴԶᚈ㎸Εࢎᄬ߾ࢂᆶϩݢ Ꮤќ΋୵ޑૈໆ࣬уǴவ(2.7)ک(2.8)ёޕǴѳᑽԄࢎᄬࢂӧคཞޑ௃ݩΠǴ ႔ཱུጕ΢ႝᓸᡂٿ७ǴԶؒԖႝࢬǶӧკ 2-5 ൑ਏႝ඲ᡏ฻ਏႝၡύёޕǴ

࣬٩ႝࢬྍ Gm཮ᒿ႔ཱུጕ΢ޑႝᓸਁ൯ᡂٿ७Զౢғٿ७ޑཱུؕႝࢬǶ ӧ΢ॊ૸ፕύǴϩ݋ӧှ(΋)ރᄊΠǴϩݢᏔٿ୵ᐱҥᆶց٠όቹៜႝ

ၡቚ੻ǴՠऩϩݢᏔගٮޑ࣬Տৡࣁ 180 ^o²360^o×m (m=0,²2-²3Ǿ)Ǵ߾ႝၡ ޑϸ৔ཞ઻ϝฅࡐৡǴ٠҂ׯ๓ϸ৔ཞ઻ǴӢԜϩݢᏔޑ࣬Տৡ೛ीԋගٮ 90^o࣬ՏৡǴ೭ኬϸ৔ޑૈໆ཮ӵӕѳᑽԄܫεᏔࢎᄬ΋ኬǴ੃઻ӧϩݢᏔ

ᐱҥ୵΢ޑႝߔǴаዴߥႝၡޑϸ৔ཞ઻ǶՠࠅΨӢࣁׯᡂϩݢᏔޑ࣬Տ ৡǴૈໆߡόૈֹӄӕ࣬Տޑ࣬уǴ࣬Տᆶӕ࣬Տ࣬у࣬ৡΑ 90^oǴӢԜૈ

ໆѝԖֹӄ࣬уޑ 1 2Ƕ

ӕ౛Ǵ߄ 3-1 ྽ύޑှ(Β)ΨёׯԋѳᑽԄࢎᄬǴচҁೱ่ಃΒکಃΟ ᗭႝ඲ᡏ໺ᒡጕΨࣁ 0^oǴՠךॺёаӃ࣮ԋ 360^o໺ᒡጕǴӵკ 3-5(a)ǴԶ

໺ᒡጕύЈՏ࿼җϩݢᏔ໺ٰޑૻဦ࣬ӕǴӢԜёע໺ᒡጕύЈՏ࿼ AǵB

ೀᘐ໒Ǵவ*_in࣮ډ 180^o໺ᒡጕ໒ၡǴΞёа฻ਏԋ 0^o໺ᒡጕ໒ၡǴӵკ 3-5(b)܌ҢǶ

(a) (b) კ 3-5ʳ ѳᑽԄΠޑှ(Β)ႝၡ೛ी

ӵӕှ(΋)ޑϩݢᏔޑ࣬Տৡሡፓ᏾ԋ 90^o࣬ՏৡǴှ(Β)ޑϩݢᏔ΋ኬ Ѹ໪ׯԋ 90^o࣬ՏৡǴωૈගٮӳޑႝၡϸ৔ཞ઻Ƕ

೭࿯ךॺගٮΑٿಔᚈ㎸ΕϩթԄܫεᏔޑှǴ٠ЪࣁΑှ،ᚈ㎸Εϩ թԄႝၡޑϸ৔ཞ઻ᆶׯ๓ႝၡጕ܄ࡋǴ׳ׯԋѳᑽԄႝၡࢎᄬǴ٬ளϩݢ Ꮤᒡрޑٿ୵ϕ࣬ᐱҥǴᆶᚈ㎸ΕϩթԄႝၡࢎᄬനεޑৡ౦Ǵӧ٬ႝ඲ᡏ ႔ཱུᆄႝᓸਁ൯ቚуޑ׎ԋচӢǴԶϩݢᏔᒡрௗډޑъႝၡǴךॺᆀϐࣁ

ൂՏܫεᏔǴԶϩݢᏔவচҁᚈ㎸ΕϩթԄࢎᄬਔǴёࣁ 0^o܈ 180^o࣬ՏৡǴ

ࣁΑ಄ӝѳᑽԄႝၡࢎᄬǴࣣׯԋᒡр 90^o࣬ՏৡǴࢂࣁ҅Ҭϩ࣬ᏔǶ

3.2 ቨ ቨᓎ೛ीচ౛

ӧ΢΋࿯ύǴךॺ૸ፕൂՏܫεᏔک҅Ҭϩ࣬ᏔǴऩךॺा೛ीቨᓎႝ

ၡǴٗሶൂՏܫεᏔک҅Ҭϩ࣬Ꮤ೿Ѹ໪ाԖቨᓎޑ੝܄ǴௗΠٰा૸ፕा

ӵՖჴ౜ቨᓎޑѳᑽϩթԄႝၡࢎᄬǶ

3.2.1 ൂՏܫεᏔ

΢΋࿯ύǴךॺᖐрٿᅿှޑѳᑽϩթԄൂՏܫεᏔǴϩձࢂ J 180180^oo ޑှ(΋)Ǵӵკ 3-6(a)Ǵќ΋ᅿࢂ J 00^ooޑှ(Β)Ǵӵკ 3-6(b)Ƕ྽ύJJ ޑفࡋࢂךॺႝၡ೛ीᓎࢤޑفࡋǴाૈᡣൂՏܫεᏔቨᓎǴٗሶѸ໪ᡣ

J

J ޑفࡋᒿᓎ౗ᡂ౦ໆόεǶӵკ 3-6 ܌ҢǴٿᅿൂՏܫεᏔ೿Ԗٿచૈ

ໆၡ৩Ǵკ 3-6(a)ޑၡ৩Β཮Кၡ৩΋ӭو 360˚ǴԶკ 3-6(b)ޑၡ৩Βᆶၡ ৩΋ޑفࡋ࣬ӕǴࡺӧ೛ीᓎࢤύǴٿޣࣣࣁࡌ೛܄࣬уǶᒿޣᓎ౗ׯᡂǴ ଷ೛ၡ৩ΒКၡ৩΋ӭوޑٿࢤ໺ᒡጕӚׯᡂ Δθ ޑفࡋǴӅ 2ΔθǴऩ| T |

Z w w ॶຫλǴ߾ႝၡቨᓎǶ

(a) (b) კ 3-6ʳ ѳᑽϩթԄܫεᏔ(a) J 180180^ooϷ(b) J 00^oo

ӧคཞޑ௃ݩΠǴ໺ᒡጕفࡋёቪԋ

T EE ^(3.2)

җ΢Ԅё௢ள

( ) ( )

T E E

Z Z Z

w w  w w w (wE)

) ( EE ) (

)) (3.3)

ՠӢࣁ ࢂჴᡏߏࡋǴ٠όᒿᓎ౗ׯᡂǴ܌а ( ) 0 w oZ

ww ) 0Ǵךॺёள ( )

T E

Z Z

w # w

w w (3.4)

வ(3.4)ԄޕǴा٬| T | Z w

w ॶ෧λǴךॺሡ٬ ෧λǶᢀჸკ 3-6 ޑ(a)ǵ(b) ٿკǴ׆ఈ ॶλǴӢԜךॺᒧ᏷ႝ਻ߏࡋ 0˚ޑ(b)კࢎᄬǴ٠Ъз ॶᖿ߈ ܭ႟ǶӧԜǴךॺԖΟᅿБԄٰჴ౜Ԝࢤ໺ᒡጕǴಃ΋ᅿࢂ໺಍ѓЋ໺ᒡጕǴ

ಃΒᅿࢂΓ೷ѓЋ໺ᒡጕǴಃΟᅿࢂΓ೷ѰѓЋ໺ᒡጕǶऩ٬Ҕ໺಍ѓЋ໺

ᒡጕǴᓬᗺࢂૈၲډၡ৩΋ᆶၡ৩ΒԖനλޑ࣬ՏৡǴՠલᗺࢂൂ٬Ҕ໺಍

ѓЋ໺ᒡጕǴ٠คݤံᓭႝ඲ᡏޑ஌ғႝ৒ CgsǵCdsǹԶऩ٬ҔΓ೷ѓЋ໺

ᒡጕǴᓬᗺࢂૈံᓭႝ඲ᡏޑ஌ғਏᔈǴՠલᗺࢂ࣬ՏৡၨεǴਥᏵ(2.13) ԄǴऩाံᓭ஌ғႝ৒ CgsǵCdsǴЪ Z0،ۓǴ߾Սᖄႝག߾೏،ۓǴӢԜ β ॶΨ೏،ۓǴӢԜคݤԖᖿ߈ܭ႟ޑႝ਻ߏࡋǶԶಃΟᅿΓ೷ѰѓЋ໺ᒡ ጕǴӢࣁૈӧեᓎਔගٮ҅࣬ՏǴӢԜᓬᗺࢂӧႝၡ೛ीޑύЈᓎ౗ё೛ी

ᆒྗޑ 0˚࣬ՏৡǴ٠ЪΨૈԖံᓭ஌ғਏᔈޑᓬ༈ǴՠલᗺၟѓЋ໺ᒡጕᜪ

՟ǴਥᏵ(2.19)Ԅᆶ(2.21)ԄǴZ0ک β Ψ൩೏،ۓΑǴԜѦǴѰѓЋΓ೷໺ᒡ ጕӢࣁ β^Lᆶ ω ԋϸКǴ܌аӧեᓎਔǴ( E)

Z w

w ॶനεǴΨ൩ࢂ| T | Z w

w ॶനεǴ კ 3-7 ࢂΟᅿ໺ᒡጕޑ࣬ՏკǴёаܴᡉޑ࣮р΢ॊޑᓬલᗺǶ

კ 3-7ʳ Οᅿ໺ᒡጕ࣬Տკ

җ΢ॊϩ݋ǴࣁΑ؃നεᓎቨǴךॺ٬Ҕ໺಍ѓЋ໺ᒡጕǴ٠ЪӢࣁႝ

਻ߏࡋཱུλǴӢԜךॺଷ೛ԋ 0˚Ǵ٠עӚঁ஌ғޑႝ৒ CgsǵCds౽ډ໺ᒡጕ ѦǴᕴӝ஌ғႝ৒ C_gs’ǵC_ds’଺ϰଛǴ ӵკ 3-8 ܌ҢǶ

კ 3-8ʳ ගр஌ғਏᔈ٠଺ϰଛ

ϰଛႝၡϩԋ႔ཱུᆄϰଛႝၡᆶཱུؕᆄϰଛႝၡǴԶךॺ،ۓӧ႔ཱུᆄ ϰଛႝၡ٬ҔΓ೷ѓЋ໺ᒡጕϰଛǴཱུؕᆄϰଛႝၡ٬ҔΓ೷ѰѓЋ໺ᒡጕ

ጕǴԶ၀ࢤ໺ᒡጕ೷ԋޑႝ਻ߏࡋૈ೏҅Ҭϩ࣬Ꮤ֎ԏǴவ҅Ҭϩ࣬Ꮤٰ

࣮Ǵᒡрޑᚈ୵Ӛගٮ฻࣬Տޑ໺ᒡጕǴ٠όቹៜډᒡрޑ 90˚࣬ՏৡǶ

(a) (b) კ 3-9ʳ (a)ཱུؕᆄѰѓЋϰଛႝၡϷ(b)႔ཱུᆄѓЋϰଛႝၡ

ךॺᒧ᏷ཱུؕᆄ٬ҔѰѓЋϰଛႝၡޑচӢǴࢂ׆ఈႝ඲ᡏޑཱུؕᆄё аճҔѰЋϡҹ྽ύޑჹӦႝགගٮཱུؕᆄႝᓸǴӢࣁ႔ཱུᆄόሡԖޔࢬႝ

ࢬǴךॺ௦Ҕεႝߔ๏႔ཱུᆄୃᓸǴӢԜᒧ᏷ѓЋϰଛႝၡǶ

ႝ඲ᡏޑ࣬٩ႝࢬྍᐱҥܭᓎ౗ǴӢԜךॺൂՏܫεᏔޑᓎቨ୷ҁ΢ࢂ

җံᓭ஌ғਏᔈޑϰଛႝၡ܌،ۓǴѓЋ໺ᒡጕᜪ՟ե೯ᘠݢᏔǴѬޑᄒЗ ᓎ౗ࣁ

2 2

RH 1

c

R R

f S L C ^(3.5)

ѰѓЋ໺ᒡጕᜪ՟஥೯ᘠݢᏔǴѬޑᄒЗᓎ౗[8]ࣁ

1 1 1 1

1 1

4

LH RH

c c

L L R R

f f

L C L C

S ^Ε S ^(3.6)

܌а᏾ঁൂՏܫεᏔޑᄒЗᓎ౗ᔈ၀ࣁ

1 1 1 1 2 2

1 1 1

min ,

4

LH RH

c c

L L R R R R

f f

L C L C L C

S S S

­ ½

° °

® ¾

° °

¯ ¿

Ε (3.7)

೸ၸ΢ॊޑϰଛႝၡǴൂՏܫεᏔޑ฻ਏႝၡǴёа࣮ԋவᒡрΕ୵ௗ

໺ᒡጕǴو΋ࢤႝᏔߏࡋࡕ໒ၡǴԶ႔ཱུጕ΢ޑႝᓸਁ൯Ǵ཮೸ၸ؂ᗭႝ඲

ᡏϣޑ࣬٩ႝࢬྍǴౢғܫεޑႝࢬૻဦǴ၀ႝࢬૻဦӧཱུؕጕ΢բࡌ೛܄

࣬уǴനࡕࢬӛᒡрॄၩǶ᏾ᡏԶقǴൂՏܫεᏔԖቨᓎޑ S21Ǵՠϸ৔ཞ

઻٠҂೸ၸ၀ϰଛႝၡׯ๓ǴՠΨӢԜቚу႔ཱུጕ΢ޑႝᓸਁ൯ελᆶཱུؕ

ጕ΢ႝࢬޑൂӛ܄Ƕམଛკ 3-10Ǵკ 3-10(a)ࢂႝ඲ᡏޑ S ୖኧǴӧ҂ϰଛ

߻Ǵቚ੻ࡐόѳڶǴᓎቨΨ࣬྽ઞǴӧу΢ϰଛႝၡࡕǴS ୖኧӵკ 3-10(b)Ǵ ϰଛႝၡׯ๓ S21ѳڶࡋǴᡣᓎቨ׳ቨǴՠӢࣁ࣪ѐΑϩթԄܫεᏔࢎᄬ΢

ளϰଛႝߔǴӢԜϸ৔ཞ઻ϝ҂ׯ๓Ǵךॺ၂๱עϰଛႝߔу΢ǴS ୖኧӵ კ 3-10(c)Ǵךॺёаவკύว౜у΢ϰଛႝߔׯ๓Αϸ৔ཞ઻ǴՠΨӢԜ ᡣႝၡቚ੻Πफ़೚ӭǴӢԜךॺа٬Ҕϰଛႝၡՠ࣪ౣϰଛႝߔٰ೛ीךॺ ޑൂՏܫεᏔǶ

(a)

(b)

(c)

კ 3-10ʳ ႝၡ S ୖኧКၨ(a)ႝ඲ᡏ(b)མଛϰଛႝၡ(c)у΢ϰଛႝߔ ᗨฅ 3.2.1 λ࿯ӧ૸ፕਔǴ೿а n=4 ٰբϩ݋Ǵՠӧჴ଺ਔǴךॺёа ٩Ᏽ܌ሡाޑᒡрф౗ᆶႝၡޑ೛ीᓎࢤٰׯᡂ n ॶǴ྽ n ॶຫεǴ߾Ⴋک ᒡрф౗཮ຫεǴՠ࣬ჹ஌ғႝ৒ C_gs’ǵC_ds’Ψ཮ᒿ n ॶ΢ϲǴ຾Զቹៜډ ϰଛႝၡޑᓎቨǶ

3.2.2 ҅ ҅Ҭϩ࣬Ꮤ

ךॺճҔѰѓЋ໺ᒡጕᆶѓЋ໺ᒡጕޑ࣬ՏৡǴаϷ΋ঁ 0˚࣬Տৡޑ࠶

ߎහф౗ϩଛᏔǴಔӝԋ҅Ҭϩ࣬ᏔႝၡǶा٬҅Ҭϩ࣬Ꮤႝၡቨᓎх֖

UWBᓎ஥ǴԖٿঁచҹाᅈىǴځ΋Ǵ࠶ߎහф౗ϩଛᏔǵѰѓЋ໺ᒡጕ ᆶѓЋ໺ᒡጕࣣ໪ቨᓎǴځΒѰѓЋ໺ᒡጕᆶѓЋ໺ᒡጕሡߥ࡭ቨᓎޑ 90˚

࣬ՏৡǶ

კ 3-11ʳ ҅Ҭϩ࣬Ꮤࢎᄬ

೛ीቨᓎޑ࠶ߎහф౗ϩଛᏔǴ२Ӄ،ۓଯ೯஥ᆶե೯஥ޑᄒЗᓎ౗

ᗺǴϩձࣁ f2ک f1Ǵीᆉ f2/f₁ॶٰᒧ᏷ф౗ϩଛᏔࢎᄬǴӵკ 3-12 ܌ҢǴ ऩሡाᓎቨຫቨǴ߾ N ॶሡຫεǴՠ࣬ჹ࿯ኧຫଯǴႝၡཞ઻཮ຫεǶ،

ۓ f2/f₁ॶࡕǴୖྣ߄ 3-2[14]Ǵёள Z1ډ ZNϷ R1ډ RNޑॶǴϐࡕ೛ी໺

ᒡጕࢎᄬǴӵ༾஥ጕǵCPWǵGCPW ฻Ǵӧႝၡ೛ीᓎ஥ޑύЈᓎ౗೛ी

࣬ف͟ޑ໺ᒡጕǴϐࡕ٩ྣკ 3-12 ჴ౜ջёǶ

კ 3-12ʳ N ભ࠶ߎහф౗ϩଛᏔ[14]

߄ 3-2ʳ ࠶ߎහф౗ϩଛᏔ೛ी߄[14]

೛ीѰѓЋ໺ᒡጕᆶѓЋ໺ᒡጕޑ࣬ՏৡǴךॺёаୖྣ[15]ගٮޑ؁

ᡯǴ२Ӄ΋ኬӃ،ۓ೛ीޑᓎ஥ጄൎவ f1ډ f2Ǵҗკ 3-13 ܌ҢǴךॺёа வѓЋ໺ᒡጕ،ۓѰѓЋ໺ᒡጕޑ࣬ՏI_MM1کI_MM2Ƕ

კ 3-13ʳ ѰѓЋ໺ᒡጕᆶѓЋ໺ᒡጕ࣬Տៜᔈ[15]

ѰѓЋ໺ᒡጕ܌ගٮޑ࣬ՏǴਥᏵ(2.19)ԄǴёаϩԋѰЋ໺ᒡጕගٮ

࣬ՏᆶѓЋ໺ᒡጕගٮ࣬ՏޑᕴکǴӢԜёቪԋΠԄ

1( )1 ( )1 ( )1 1 / 1

MM f RH f LH f Pf Q f

I I I   (3.8)

2( 2) ( 2) ( 2) 2 / 2

MM f RH f LH f Pf Q f

I I I   (3.9)

྽ύP I_RH / f_iǴQ ˜f_i I_LHǶԶ΢य़ٿԄёှᖄҥள

1 1 2 2

2 2

2 1

MM MM

f f

P f f

I  I

 (3.10)

2 2

1 2 1 1 2 2

2 2

2 1

MM MM

f f f f

Q f f

I  I

 (3.11)

Զ،ۓޑ f1ǵf2ǵI_MM1ᆶI_MM2жΕ΢य़ٿԄёளPǵQ ॶǴPёаϸ௢

рI ॶǴԶѰЋ໺ᒡጕޑϡҹॶ L_RH LǵCLᆶ Q ޑᜢ߯ёቪԋ

2 _{L L} Q N

S L C ^(3.12)

N ж߄ՍௗӭϿ࿯ޑѰЋ೽ϩٰಔԋѰѓЋ໺ᒡጕǴճҔ΢Ԅᆶ(2.21) ԄёှᖄҥளډL_LǵC_LॶǶ

3.3 ჴ ჴ౜ൂՏܫεᏔ

3.3.1 ႝ඲ᡏᒧڗ

ႝ඲ᡏኳࠠჹךॺ೭ঁႝၡ೛ी࣬྽ख़ाǴЀځࢂѸ໪ाံᓭޑ஌ғႝ

৒ Cgsک CdsǴԶ஌ғਏᔈελҗ(3.7)،ۓᓎቨǴךॺᒧႝ඲ᡏޑБݤ२Ӄ،

ۓ΋߃ۈୃᓸǴ೛ۓ Vds=1.8VǵVgs=1VǴϐࡕךॺԵໆᒡрф౗ᆶᓎቨǴ

྽ႝ඲ᡏᕴቨࡋ،ۓǴ߾஌ғਏᔈᆶനεᒡрф౗Ψ೏،ۓǴεठ΢ٰᇥǴ ऩᕴቨࡋຫεǴ߾ёᒡрຫεޑф౗Ǵՠ஌ғਏᔈΨ࣬ჹ΢ϲǴӧ߃ۈୃᓸ ΠǴךॺ៾ᑽᒡрф౗ᆶႝၡᓎቨǴᒧ᏷ߏࡋࣁ 0.18μmǴᕴӅቨࡋࣁ 80μmǶ ࣁΑႝၡጕ܄ࡋԵໆǴךॺᒧҔ A ᜪܫεᏔǴᒧ᏷ୃᓸБԄࢂճҔլٚද ථ(Cripps)ॄၩጕǴӧႝ඲ᡏ I-V კύǴᒧ᏷፾྽ୃᓸᗺǴӵკ 3-14 ܌ҢǴ m1ᗺࢂᙯשႝᓸǴm2 ߾ࢂךॺᒧޑୃᓸᗺǴ၀ॄၩጕന٫ޑ RLoadࣁ 100ΩǴ

ԶךॺޑൂՏܫεᏔӅ٬Ҕٿᗭႝ඲ᡏǴӢԜٿᗭႝ඲ᡏޑന٫ॄၩࣁ 50ΩǴջࣁϰଛႝၡௗ҅Ҭϩ࣬ᏔޑॄၩǶ

ӧႝ඲ᡏᒧڗਔǴѸ໪ݙཀႝၡҁيޑᔈҔǴ྽ᒧڗޑᕴቨࡋຫεǴа Ϸຫӭᗭႝ඲ᡏਔǴႝၡޑᕴᒡрф౗཮΢ϲǴՠᓎቨΨ཮Πफ़ǴӧҁፕЎ

ࢂа UWB ᔈҔǴUWB ӧೕጄ΢ሡाຬቨᓎޑ੝܄Ǵՠόሡाεф౗ᒡрǴ ӧᒧ᏷ୃᓸаϷॄၩጕਔǴҭѸ໪Եໆډ᏾ᡏس಍ᔈҔޑᒡрф౗ᆶ໺ᒡຯ ᚆǶ

კ 3-14ʳ ႝ඲ᡏ I-V კ

،ۓႝ඲ᡏελࡕǴ๧ڗ஌ғਏᔈډ 20GHzǶλૻဦ฻ਏკӵკ 3-15Ǵ Զ܌Ԗୖኧӈܭ߄ 3-3Ƕ

კ 3-15ʳ λૻဦ฻ਏႝၡ ߄ 3-3ʳ ႝ඲ᡏλૻဦୖኧ

LG LS LD RG RS

0 nH 0 nH 0.014 nH 5.3 Ω 3.3 Ω

R_D R_bx R_gs R_ds C_bx

2.1 Ω 293 Ω 0 Ω 467 Ω 130 fF

C_gs C_ds C_gd g_m

103 fF 35 fF 26 fF 48 mS

Πკࢂךॺ๧ڗрٰޑኳࠠ(ᙔ)ᆶ TSMC ܌ගٮ PDK ኳࠠ(आ)ޑ S ୖኧ КၨკǶ

კ 3-16ʳ λૻဦኳࠠᆶ TSMC PDK ኳࠠ S ୖኧКၨკ

3.3.2 ႝ ႝၡѲֽ

ਥᏵ 3.2.1 ࿯ޑ௢ᏤǴёޕൂՏܫεᏔࢎᄬӵკ 3-17 ܌ҢǴ႔ཱུᆄճҔ εႝߔ๏ୃᓸǴճҔѓЋ໺ᒡጕኳࠠϰଛ஌ғႝ৒ C_gs’ ǴԶཱུؕᆄճҔѰ ѓЋ໺ᒡጕኳࠠϰଛ஌ғႝ৒ C_ds’Ǵ٠ЪճҔѰЋჹӦႝག๏ϒୃᓸǶ

კ 3-17ʳ ൂՏܫεᏔࢎᄬ

ୖྣ߄ 3-3ǴӃ۹ౣځᎩޑ஌ғਏᔈǴ߃؁՗ᆉ C_gs’ᆶ C_ds’ॶǴϩձࣁ 206pF ᆶ 330pFǴճҔ(2.21)Ԅǵ(2.13)Ԅᆶ(3.7)ԄǴё،ۓႝၡ΢ϰଛႝၡ ޑ߃ۈॶǴӈ߄ӵΠ

߄ 3-4ʳ ႝၡϰଛୖኧ߃ۈॶ

CR1 CL1 CR2

660 fF 513 fF 412 fF

LR1 LL1 LR2

1.65 nH 1.28 nH 1.03 nH

ע߄ 3-4 ॶжΕ(3.7)ԄीᆉǴӧ౛གྷ௃ݩΠǴf_c^LHёԿ 2.2GHzǴf_c^RHё

ၲډ 13.2GHzǴՠӢࣁ஌ғਏᔈǴךॺѸ໪ӆ଺༾ፓǴቹៜၨεޑЬӢԖٿ

ঁǴځ΋ࢂ Cgdޑӣ௤ႝ৒Ǵᡣ႔ཱུᆄکཱུؕᆄ࣮຾ѐޑ੝܄Ⴝߚጕ܄ႝ৒Ǵ ቹៜΓ೷໺ᒡጕޑϰଛǴќѦࢂϰଛϡҹޑ Q ॶǴQ ॶϼե೷ԋଯᓎޑཞ

઻ᡂεǴ཮෧Ͽ 3dB ᓎቨǶႝၡѲֽკӵკ 3-18 ܌ҢǶ

(a)

(b)

კ 3-18ʳCMOS 0.18μm ႝၡѲֽკ(a)LTCC ᇙำ(910μmØ950μm)(b)IPD ᇙำ (1030μmØ1560μm)

კ 3-18 ޑٿᅿൂՏܫεᏔϩձჹᔈډٿᅿ೏୏ᇙำޑൂՏܫεᏔǴԶ IPD ᇙำޑय़ᑈၨεǴচӢࢂ඲༝ቷӧᔅךॺႝၡ଺ᙟ඲ਔԖा؃നλय़ ᑈǴӢԜךॺעკ 3-18(a)ޑႝၡբ᜔৔ǴעٿঁൂՏܫεᏔբӧӕ΋ঁ඲

Т΢Ǵа಄ӝႝၡ೛ीೕ߾Ƕ

3.3.3 ႝ ႝၡኳᔕ่݀

ൂՏܫεᏔךॺ߃؁ޑኳᔕ่݀ӵΠ

კ 3-19ʳ ൂՏܫεᏔ S ୖኧ

კ 3-20ʳ ဂᡏۯᒨਔ໔

S ୖኧኳᔕ 3dB ᓎቨவ 2.2GHz ډ 12.2GHzǴλૻဦቚ੻നεॶऊࣁ 13dBǴऩࢂӧ UWB ᔈҔᓎࢤǴλૻဦቚ੻ࣁ 12.2²0.5dBǴဂᡏۯᒨਔ໔ࣁ 114.5²47.5pSǴკ 3-19 ޑ S11ᆶ S22߾ࢂӢࣁ࣪ౣΑচҁϩթԄܫεᏔࢎᄬ ޑϰଛႝߔǴӢԜϸ৔ཞ઻ၨৡǴऩу΢ϰଛႝߔ߾ϸ৔ཞ઻཮ׯ๓ǴՠΨ

཮ੁ຤ૈໆӧ၀ႝߔǶჹܭၨৡޑϸ৔ཞ઻ǴϐࡕճҔ҅Ҭϩ࣬Ꮤٰׯ๓Ƕ

(a) (b)

(c) (d)