使用簡單的峰值電流鏡電路實現一低電壓低功率17ppm/C參考電壓電路

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國立交通大學

電機與控制工程學系

碩士論文

使用簡單的峰值電流鏡實現㆒低電壓低

功率

17ppm/℃參考電壓電路

A Low-Voltage Low-Power 17ppm/℃ Voltage

Reference Using The Simple Peaking Current

Mirror Circuit

研究生：吳政衛

指導教授：鄭木火博士

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UàÀí¼MÚ¼ŸÚ˜õÛøQÚ9QŠ

0 17ppm/

◦

C ¡5Ú9Ú˜

û˝Þ: Ø\¨

Nû`¤: wƒÊ²=

Å >¦×çÚœD−„ ˙çÍ

¿b

…dT|ø_h/ÝÀíQÚ9QŠ0¡5Ú9Ú˜ ¤¡5Ú9Ú˜Uà¼MÚ¼Ÿ Ú˜Ñ3b-Z, âÚ¼í£Å[b%øÚ®V^kÀšûñ•-Ä”Ú9íŠÅ[bÔ4 âk¼MÚ¼ŸÚ˜5Úñu TÊÿ¥ó–, Ä¤cñÚ˜FÛí¾Š0Ýü, 7/¤Ú˜ ªorÍTkQÚÄÚ9 ¤Ú˜ÝÀ, ÉÛ 6 _jK,4 _Úñ£ 2 _Ú® …d1J« Ú 0.35 µm 3P3M SiGe BiCMOS `˙VõÛ¤¡5Ú9Ú˜ %(¨_Ò!‹ (Post-Sim), …Ú˜5|ü TÚ9Ñ 1.4 V, |Ú9MÑ 710 mV, Å[bÑ 17 ppm/◦

C , |×¾Š0 u 6.68 µW , ÚÄÚ9Æm{„ªÊ1MHz vÑ −84 dB

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A Low-Voltage Low-Power 17 ppm

/

◦

C Voltage

Reference Using Simple Peaking Current Mirror

Circuit

Student: Zheng-Wei Wu

Advisor: Dr. Mu-Huo Cheng

Institute of Electrical and Control Engineering

National Chiao-Tung University

Abstract

This thesis presents a new and extremely simple low-voltage low-power voltage reference circuit. The voltage reference circuit uses the peaking current mirror circuit to extract the current with PTAT (proportional to absolute temperature), and then the current, through a resistor, is used to compensate for the gate-source voltage with the negative temperature coefficient. Since the transistors in the peaking current mirror circuit are operated in weak inversion (subthreshold region), both the power consumption and the required working supply voltage of the reference circuit are all low. The circuit only requires six elements, four transistors and two resistors. The proposed circuit is implemented using the TSMC 0.35um 3P3M SiGe BiCMOS technology. The design IC, after post simulation, attains the minimum supply voltage 1.4 V, output reference voltage 705 mv, temperature coefficient of 17 ppm/◦

C, power consumption 6.68 µW, and power supply noise rejection ratio -84 dB at 1MHz.

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Ðá

¤d?ß‚êA, bÔöyË>áBíNû`¤wƒÊ`¤, Ê¥ssísû˝Þ®2, Ìu&AQÓíy^ö£CµçGíÃã-, ÌUBÊÞº£ç…,×ïGÖ Ä¤Ê…d GF5Ò, úk:£f−¤“í4_,|y£íá< Ê¨t‚ÈwP"»Å`¤ nø`¤¸i£`¤Æ˛N£1TXrÖ£í<c Ê¤>á 5bí: °v>áH“çÅðû ï õãí‹“H−, J£õðíFAº: yÞçÅ ‰ï ¼ TÔ Ê{“,í~}n£Þº,í¡;®x, ÑÓÀ|íû˝ÞºÓ¼.ý H˘ |(b>áBíÂf£ðA, âkFbíG|¸.iË2¥, éB?Ì(è5Rí*9û˝, ß ‚êAç“, 1/?‰Þú-øší˚ØD‘D

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ñ“

2d¿b i Ld¿b ii Ðá _iii Çñ“ vi [ñ“ vii 1 é 1 1.1 ¡5Ú9Ú˜!…Ü . . . 1 1.2 d.èDû˝œ . . . 1 1.3 û˝ñí . . . 2 1.4 d-Z . . . 2 2 ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z 3 2.1 ú!…ABR9Ú¼Ä . . . 3 2.1.1 Vt-¡5Ú¼Ä . . . 3

2.1.2 Q, Ú ¼ Ä (Widlar Current Source) . . . 4

2.1.3 ¼MÚ¼Ä (Peaking Current Source) . . . 6

2.1.4 A B R 9 Ú ˜(Self-Biasing Circuit) . . . 8

2.2 !…?[¡5Ú9Ú˜5«n . . . 10

3 QÚ9QŠ0¡5Ú9Ú˜}&Dql 17 3.1 Ü}& . . . 17

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3.2 Uà}¶,¿^kÚ®íjKM . . . 22 4 õð!‹Dªœ 25 5 !D„V 35 5.1 ! . . . 35 5.2 „V . . . 35 ¡5d. 36

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Çñ“

Ç 2.1 Vt-¡5Ú¼Ä . . . 4 Ç 2.2 Q , ¡ 5 Ú ¼ Ä . . . 5 Ç 2.3 ¼M¡5Ú¼Ä . . . 6 Ç 2.4 ¼M¡5Ú¼Äí|Ú9úÚÄÚ9íÉ[( . . . 7 Ç 2.5 Vt-¡5Ú¼Äí|Ú9úÚÄÚ9íÉ[( . . . 8 Ç 2.6 Q, Ú¼Äí|Ú9úÚÄÚ9íÉ[( . . . 9 Ç 2.7 ¼MÚ¼Äí|Ú9úÅíÉ[( . . . 10 Ç 2.8 Q, Ú¼Äí|Ú9úÅíÉ[( . . . 11 Ç 2.9 (a) !¦”¡5Ú¼Ä (b) ABR9!¦”¡5Ú¼Ä. . . 12 Ç 2.10 ABR9íj)Ç . . . 13 Ç 2.11 ²ìÍTõ . . . 14 Ç 2.12 !…?[¡5Ú9Ú˜h1. . . 16 Ç 3.1 ¼MÚ¼Ä|Ú¼DpÚ¼íÉ[( . . . 17 Ç 3.2 MOS•-Ä”Ú9DÅíÉ[( . . . 18 Ç 3.3 QÚ9QŠ0¡5Ú9Ú˜ . . . 19 Ç 3.4 ID2DÅíÉ[( . . . 20 Ç 3.5 R1 = 154.602kí|Ú9DÅíÉ[( . . . 21 Ç 3.6 õÒÚ9MD¡Nƒb5ªœ . . . 23 Ç 3.7 õÒÚ¼MD¡Nƒb5ªœ . . . 24 Ç 4.1 Ú˜0Ç . . . 25 Ç 4.2 ¡5Ú9Ú˜5Pre-Sim Ê.°Åí|Ú9 . . . 26 Ç 4.3 ¡5Ú9Ú˜5Post-Sim Ê.°Åí|Ú9. . . 27

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Ç 4.4 d.[8]5|Ú9DÅíÉ[( . . . 28 Ç 4.5 ¡5Ú9Ú˜5Pre-Sim Ê.°ÚÄÚ9í|Ú9 . . . 29 Ç 4.6 ¡5Ú9Ú˜5Post-Sim Ê.°ÚÄÚ9í|Ú9 . . . 30 Ç 4.7 d.[8]5|Ú9DÚÄÚ9íÉ[(. . . 31 Ç 4.8 QÚ9QŠ0¡5Ú9Ú˜5Post-Sim í Innoise . . . 32 Ç 4.9 QÚ9QŠ0¡5Ú9Ú˜5ÚÄÚ9{„ª . . . 33 Ç 4.10 d.[8]5ÚÄÚ9{„ª . . . 34

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[ñ“

[ 3.1 â(¡N¶¦)í[b[ . . . 22 [ 3.2 ®jKM[ . . . 22 [ 4.1 ¡5Ú9Ú˜Dd.[8]5d[ . . . 26

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1 ı

é

1.1 ¡5Ú9Ú˜!…Ü

ÊéªÚ˜¸bPÚ˜íä2, ¡5Ú9ÄÚ˜í@àuÝí˜, Wà: p[ñ bP-é ª²Â (digital-analog converter) éª-bP²Â (digital-analog converter) ’eR¦Í $ (Data acquisition system) N>¿Â (smart sensors) Ú˜ âk IC `¨xXBV Bòü, Ä¤ÚÄÚ9BVBQ, â5V ±B3.3V £B1.8V ¤ÕàS±QÚ˜Š0¾Ê¤ Ì(¦mBVB £ÿB$½b Ä¤êøQÚ9Q¾Š0í¡5Ú9Ú˜, uñ‡ø½bû˝ {æ

1.2 d.èDû˝œ

A* R. J. Widlar [1] T|?¦¡5Ú9Ú˜5(, D¤Ú˜óÉ5û˝d.'Ö Ê P. R. Gray z [2]2íûı, 6‡ú¤Ú˜5-Z, 4?¡b, £Ô4óçêcízp·H ql¡ 5Ú9ÄÚ˜íxXª}Ñsé, øé3bubçÕqlÅ^kÂ, ±Q|Ú9úÅíÑÜ , wÅ[bÑb ppm/◦ C, Ouóú6Ó‹7Ú˜í¾Š0 µÆ¸±QFÛíÚÄÚ 9ªÍTí¸ˇ WàÊd. [3]uSàùŸV^kÚñ!-¦”Ú9íÝ(4á, U|Ú9 úÅíÉ[?Ê/Å?|üí‰, wFàd. [13]Sà .ŒÚ˜ßÞ IP T AT ¸ IN L (¡ NDÅ.óÉíÚ¼) Ê%â P T ATN _{ßÞÂßÞ P T AT}3_{+ P T AT}4 _{V^kÝ(4á d.}

[11]uSà MOS Tkñ¸–1ø -Ä”Ú9¡NA dVDS/dT = AT−α− BT−1 + C , à¤

ªø^kÂíò¼á^k!-¦”Ú9íÝ(4á d. [4]†uSàNbƒb (exponential) j V^k, 7Nbáu‚àÚñí β ¸ÅANbÉ[ β = β∞exp(−4E_kTG) , ÇÕd. [5]uS

àøÅ}–7®–JÒ¨(4 (piecewise linear) V^k 6UàÚ®jKÓÅ‰“íò¼ Ô4V^kàd. [6] d. [10] J,®j¶Êz [7]2ÌFÜ ùé2àd. [8] d. [9], ¥øé3bu‚à MOS Tkÿ¥ó– (weak inversion) ªJTXøüÚ¼íÔ4, w3b íñ™ÿuTXø_'QíÚÄÚ9, / TÚ¼ü, BkwFíd1.i, WàÅ[b®b ppm/◦

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1 ı é Êql¡5Ú9ÄÚ˜2, Ñ7±Q|Ú9úÚÄÚ9íÑÜ·}SàABR9, ú óÉíxXÊ P. R. Gray z [2]2\Ü, Wà:Vt-¡5Ú¼ÄÚ˜àÇ2.1 Fý Q, Ú¼Ä

(Widlar Current Source) àÇ2.2 Fý, ¸¼MÚ¼Ÿ (Peaking Current Source) àÇ2.3 F ý àÇ2.1 2 Vt-¡5Ú˜u‚àÚ® R øVt²AÚ¼ Í7Ñ7fn Tk.Ûbí Tõ, àÇ2.22Q, Ú¼Ä, ¸àÇ2.3¼MÚ¼ÄíÓÜÔ4ÝóN, ·u‚àså MOS í•-Ä ”íÚ9Ï%âøå×Ú®²AÚ¼ âÇ.2-4Fý Vt-¡5Ú¼Ä.âÊÚÄÚ9òk2V vn ?|ø_ ìí|Ú9 âàÇ2.5 FýQ, Ú¼ÄFÛ|üíÚÄÚ9Ñ 1V, âàÇ2.6 Fý ¼MÚ¼ÄFÛ|üíÚÄÚ96Ñ 1V

1.3 û˝ñí

ktí¡5Ú9Ú˜íql, …¹uJÚ˜q¶íÔ4VdÅ^k ^kíju‚ àså MOS í•-Ä”Ú9Ï, ¤Ú9ÏúÅuø_øŸ(4íÉ[, à¤Zª.ÛÕql^ kÂV^kÅ[b …¹duO½kQÚ9QŠ0¡5Ú9Ú˜/ÝÀ, ÊQÍTÚ9jÞ uSà¼MÚ¼ÄxQÍTÚ9íÔ4, ¤Üâ}ÊùıÌíÜ ÊQ¾Š0jÞu‚ à MOS Tkÿ¥ó– (weak inversion) xQÚ¼íÔ4y‹,.ÛçÕqlÅ^kÂ, F J¤Ú˜ÊÍTvÈjÞxiæíÔ4

1.4 d-Z

…¹du}üıVn, Î7øıJÕ, cø®ıíqñÜk-: ùı2, ÄÑ¤Ú˜ -Z¨ÖÚ¼Ä¶}, FJBb*z [2]2Tƒ‡úútíÚ¼ÄTÜ1TÀíÅ}&¸ ÍTÚÄÚ9}&, 6}‡úABR9Ú˜íŠà¸Ô4ÌíÜ, àŸZ|êcíQÚ9Q Š0¡5Ú9Ú˜í-Z úı2, Bbl‡úQÚ9QŠ0¡5Ú9Ú˜TÅ}&, Q-V ÜàS‚àbM}&¶ql^kjKíjKM ûı2, Bbø‡úQÚ9QŠ0¡5Ú9Ú˜T ‡0õð (Pre-Sim) ¸(«õð (Post-Sim) , /6‡ú-ZéNíd. [8]Tªœ, BbF×Û í_Ò!‹|Ú9DÅíÉ[ |Ú9DÚÄÚ9íÉ[( ÚÄÚ9{„ª ¸Ú˜0 Ç üı, !, úk…dí!‹Tøêcízp

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2 ı

¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z

2.1 ú!…ABR9Ú¼Ä

ABR9xXí°2ÿuÚ˜ªJAÐßÞø_ ìí¡5Ä, /.ÛçÕ‹R9 Ê¡5Ä Ú˜2à‹³@àABR9íxX, w|ÄúÚÄÚ9}×Û(4É[, ²Æuz, ÿuw| Ú¼úÚÄÚ9íÑÜkø Ê¤ıøÜútí¡5ÄßÞÂ, àVt-¡5Ú¼Ä Q, Ú¼Ä ¼MÚ¼Ä, Bb øJMOS õÛ¥úÚ˜àÇ2.1 Ç2.2 Ç2.3, 1T}&¥úÚ˜íÔ4, ¤zpBbFq lí-Z 2.1.1 Vt-¡5Ú¼Ä Vt-¡5Ú¼ÄàÇ2.1 í3bÔHuø MOS í•-Ä”1:øåÚ®7ßÞÚ¼Ä, M1 T

kñ¸–/ÄÑ M3¸ M4 Aø_Ú¼Ÿ, FJID2kID1 , /ªø ”Ú¼[ýA:

ID1 = ID2 = 1 2µnCOX( W L )1(VGS1− Vt1) 2 _(2.1) Ä¤ VGS1 = Vt1+ v u u t 2ID1 µnCOX(W_L)1 (2.2) w2IDu¼%MOS í ”Ú¼,Vt1u M1@äÚ9 (threshold voltage), ÄÑID1ID2'ü, /(W_L)1

'×, FJ ID1 = ID2 ∼= Vt R (2.3) ¤Ú˜ÄÑuJ#Líql, FJFÛ|üíÚÄÚ96}Ó‹, âÇ2.1 Ç2.5 ªøVt-¡5 Ú¼Ä.âÊÚÄÚ9\VGS1 VGS2VSD3FÌ„, FJÚÄÚ9.âòk 3V vn?|ø_ ìí|Ú9, ,Hÿõ˛Ã½Ì„Vt-¡5Ú¼ÄÊQÍTÚ9í@à

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z M1 M2 M3 M4 R VCC Ç 2.1: Vt-¡5Ú¼Ä

2.1.2 Q , Ú ¼ Ä (Widlar Current Source) Q, Ú¼ÄàÇ2.2í M1¸ M2í(W

L)íªM.ªJó°, ÄÑ¤Ú˜u‚àså.°d

í MOS FßÞíÚ9Ï, yø¤Ú9Ï‹kÚ®,FßÞíÚ¼ ID2, %¬ø Ú¼Ÿ M3M4,

U)ID1 = ID2/ M1¸ M2u Tkÿ¥ó–, FJªøID1 ¸ID2 íÉ[[ýA:

ID = IESK exp( VGS N VT ) (2.4) VGS1 = N VT ln( ID1 IESK1 ) (2.5) VGS2 = N VT ln( ID2 IESK2 ) (2.6)

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z VCC M1 M2 M3 M4 R Ç 2.2: Q , ¡ 5 Ú ¼ Ä

, w2 IES = µnCoxN (VT)2exp[_{N KT}q (−Vt − N KT_q )], VT = κT_q uÏÚ9 κ ušcb

κ = 1.38 × 10−₂₃ , NuŸ@äb N = 2 ∼ 3 ,K u MOS í ÷ªW K = (W L) ∆V = VGS1− VGS2 = N VT ln( ID1K2 ID2K1 ) (2.7) ID1 = ID2 = ∆V R = VGS1− VGS2 R = N VT R ln( K2 K1 ) (2.8) VGS1 = N VT ln( N VT ln(K_K2₁) IESK1R ) (2.9) Ç2.6 uQ, í|Ú9DÚÄÚ9íÉ[( BkQ, Ú¼ÄíÿõuâÇ2.2 2ªø M3 ÄÑ§ƒ¦−Å|‰) à, U)úÚÄÚ9}ø_×íÑÜ

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z VCC R M1 M2 M3 M4 Ç 2.3: ¼M¡5Ú¼Ä

2.1.3 ¼MÚ¼Ä (Peaking Current Source)

¼MÚ¼ÄíÚ˜, àÇ2.3, Ô4¸Q, Ú¼ÄÝóN ¥sÚ˜·u‚àså Tkÿ¥ ó– (weak inversion)NMOSí•-Ä”5ÈíÚ9Ï%âøåÚ®²AÚ¼, FJ;W MOS Tkÿ¥ó– (weak inversion) v, ”Ú¼D•-Ä”Ú9íÉ[: ID = W LµCoxN (VT) 2_{[(1 − exp(−}qVDS κT ))][exp[ q N κT(VGS− VON)]] (2.10) VON = VT + N κT q (2.11) cà -Ä”Ú9 VDS ≥ 3κT_q ,(2.8) ª“A ID = KIESexp[ VGS N VT ] (2.12)

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z 1 1.5 2 2.5 3 3.5 4 4.5 5 0.3864 0.3865 0.3866 0.3867 0.3868 0.3869 0.387 V_CC (Volt) V OUT (Volt) Ç 2.4: ¼M¡5Ú¼Äí|Ú9úÚÄÚ9íÉ[( VGS = N VT ln( ID IESK ) (2.13) IES = µCoxN (VT)2exp[ q N κT(−Vt − N κT q )] (2.14) w2VT = κT_q uÏÚ9,N uŸ@äb N=2 ∼ 3,K = W_L FJ ID2 = K2IESexp( VGS2 N VT ) (2.15) = K2IESexp( VGS2− ID1R N VT ) (2.16) = K2IESexp( VGS1 N VT ) exp(−ID1R N VT ) (2.17) = K2 K1 K2IESexp( VGS1 N VT ) exp(−ID1R N VT ) (2.18) = K2 K1 ID1exp(− ID1R N VT ) (2.19) /ÄÑ M3¸ M4uøúÚ¼Ÿ , FJ ID1 = ID2 (2.20)

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 V_CC (Volt) V G1 (Volt) Ç 2.5: Vt-¡5Ú¼Äí|Ú9úÚÄÚ9íÉ[( ø (2.18) Hp (2.17), %cÜ(ª) ID1 = N VT R ln( K2 K1 ) (2.21) ø (2.19) Hp (2.10) ª) VGS2 = N VT ln( N VT ln(K_K21) IES2K2R ) (2.22) Fýu¼MÚ¼Äí|Ú9úÚÄÚ9íÉ[( âÇ2.4Fý¤Ú˜FÛí|üÚÄÚ9ük 1V Ç2.4Ç2.5Ç2.6âõðí!‹ª)øJ,úÚ¼Ä·ø_u°íÿõÿçÅ‰“v, |Ú9}ßÞ—Ëí‰“ Wà: Ç2.7í¼MÚ¼Ä|Ú9úÅíÉ[(, ¸Ç2.8íQ, Ú¼Äí|Ú9úÅíÉ[( â (2.7) ¸ (2.20) ªøçÅ‰“v¥sÚ¼Äí |Ú9}ÄÏÚ9VT ¸`˙¡bIESDÅóÉ7‰, ¤h1Ê¤l×IíÜ, ÌíRûD }&}Ê-øı‹JÜ 2.1.4 A B R 9 Ú ˜ (Self-Biasing Circuit) Ê¡5ÄÚ˜2ABR9Ú˜í3bŠàu±Q¡5Ú˜í|úÚÄÚ9íÑÜàÇ2.9(b) ¦ Ho‚‚àøåÚ®òQQƒÚÄÚ9àÇ fig2.9(a) 7ABR9Ú˜íh1àÇ2.10, ABR9

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z 1 1.5 2 2.5 3 3.5 4 4.5 5 0.412 0.414 0.416 0.418 0.42 0.422 0.424 0.426 0.428 V_CC (Volt) V CC (Volt) Ç 2.6: Q, Ú¼Äí|Ú9úÚÄÚ9íÉ[( Ú˜´øáÔHÿu…s_ÍTõ, FJ.âçÕqlóÚ˜JZUÚ˜ Tk_çíÍT õ J-BJbçuVõ|ABR9íi4 ílªœÇ fig2.9(a) ¸Ç fig2.9(b) í|ÄúÚ ÄÚ9íÑÜ, *Ç fig2.9(a) ªRû|w|ÄúÚÄÚ9íÑÜ}Ñ (16) IOU T = VBE2 R1 (2.23) VBE2 = VT ln( IIN IS1 ) (2.24) SIOU T VCC = VCC IOU T ∂ ∂VCC VT R1 (ln(IIN) − ln(IS1)) (2.25) = VCC IOU T ∂ ∂VCC (VT R1 ln(IIN IS1 )) (2.26) = VCC IOU T_∂V∂_CC VT R1 (ln(IIN) − ln(IS1)) (2.27) = VT IOU TR1 SII N VCC (2.28)

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z 0 10 20 30 40 50 60 70 80 90 100 0.3 0.32 0.34 0.36 0.38 0.4 0.42 TEMP (°C) V OUT (Volt) Ç 2.7: ¼MÚ¼Äí|Ú9úÅíÉ[( càVCC 2VBE(ON ), †IIN ≈ V_RCC1 /S IOU T VCC = 1, FJ SIOU T VCC = VT IOU TR1 (2.29) *Ç fig2.9(b) 26ªRû|w|ÄúÚÄÚ9íÑÜ (2.28) /IIN = IOU T FJª)| ÄúÚÄÚ9íÑÜÑÉ SIOU T VCC = 0 (2.30) SII N VCC = 0 (2.31) FJ* (2.28) (2.30) ¸ (2.31) 2ªøABR9Ú˜ª××±QÚÄÚ9ú|Äí à

2.2 !…?[¡5Ú9Ú˜5«n

Ê¡5Ú9Ú˜íä2J?¦¡5Ú9Ñ3bxX, …BbøâÓÜÞVRû„p?¼ Ï¡5Ú9ßÞÚ˜ (Bandgap Reference Voltage Generator) 5 TŸÜ£ªW4 íl¡5

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z 0 10 20 30 40 50 60 70 80 90 100 0.34 0.36 0.38 0.4 0.42 0.44 0.46 TEMP (°C) V OUT (Volt) Ç 2.8: Q, Ú¼Äí|Ú9úÅíÉ[(

Ç2.12Ú˜, |Ú9uVBE(ON )‹,NIíVT ; Ñ7²ì N MÛbÖý, Bb.âl)|VBE(ON )í

Å[b, I!”Ú¼, BJT 5VBE(ON )úÅ5É[, Êd. [2]Ñ: VBE(ON ) = VT ln( I1 IS ) (2.32) 7Êd. [2]íøı2)øñ¸Ú¼ DjK!ZíÉ[Ñ IS = qAn2iDn QB = Bn2iDn = B 0 n2iT µn (2.33)

w2 niuÓMýb-ñë (intrinsic minority-carrier concentration)QBu©ÀPÞ !”

¡Æ¾ (total base doping per unit area)µnu!”ÌÚäd0 (average electron mobility

in the base)B¸B0ub, Ê(2.33) 2, Hp=ÄgÉ[µn = (_κTq )Dnª) (2.33) 2

DÅóÉí¾}[ýà-:

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z R1 Iout Q2 VCC Q1 R2 Iin (a) Iout VCC Q1 Q2 Q3 Q4 Iin (b) R1 Ç 2.9: (a) !¦”¡5Ú¼Ä (b) ABR9!¦”¡5Ú¼Ä n2i = DT3exp(− VG0 VT ) (2.35)

w2VG0u¦Ê0◦Kví?¦Ú9(bandgap voltage of silicon extrapolated to),CDub,

úµn7k,n †D!”íEÆ˙É ø (2.32) (2.33) (2.34) (2.35) *hcÜª

)|:

VBE(ON )= VT ln(I1T−γE exp(

VG0

VT

)) (2.36)

w2Eub,γ=4 − nÊõÒí?¦Ú˜2, Ú¼I1uÓÅ‰“7ÝìM, ªJ[ýà-:

I1 = GTα (2.37)

w2Gub, â (2.36) (2.37) ª):

VBE(ON ) = VG0− VT[(γ − α) ln(T ) − ln(EG)] (2.38)

Ç2.122, |Ú9Ñ:

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z

Current Mirror

OUT IN

Current Source

OUT IN VCC Iout Iin Ç 2.10: ABR9íj)Ç ø (2.38) Hp (2.39) ª): VOU T = VG0− VT(γ − α) ln(T ) + VT[N + ln(EG)] (2.40)

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z

Iout

Iin Current mirror Iin=Iout Current source

Desired operating point

Undesired operating point

Ç 2.11: ²ìÍTõ

(2.40) uJÚ˜¡bGαN ¸jK¡bEγ[ýíÅƒ, ª)||Ú9 Êql?¦¡5 Ú9Ú˜2, Bb|3bíh1uıÅí‰“ú|Ú9êr³ à; Ä¤, BbI|Ú9 úÅT}í}MÑÉ, 6ÿu T CF(Temperature coefficient) ÑÉ, Q-Vª°)BbF

ÛbíGαN„øb }à-: 0 = dVOU T dT |T=T0 = VT0 T0 [N + ln(EG)] − VT0 T0 (γ − α) ln T0− VT0 T0 (γ − (α)) (2.41) w2T0ÊVOU TíT CFÑÉvíÅ,VT0ÏÚ9 (thermal voltage) ÊT = T0víM (2.41) ½hcÜ(ª): [N + ln(EG)] = (γ − α) ln T0+ (γ − α) (2.42) ¤j˙ªøBbFÛbíMGαNJjK¡bEγV[ý Q-V, Bbªø (2.42) Hp (2.40) !‹à-: VOU T = VG0+ VT(γ − α)(1 + ln T0 T ) (2.43) Ä¤, Å‰“ú|Ú9í àªâÀø¡bT0V·H, 7T0íM†âNEGV²ì ç|Ú 9ÊT CFkÉ(T = T0)và-: VOU T|T=T0 = VG0+ VT0(γ − α) (2.44)

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z ÔWVz, JBbÊ25◦ cvíT CFkÉ, cqγ = 3.2α = 1, ª)-: VOU T|T=T0=25◦c = VG0+ 2.2VT0 (2.45) ¦í?¦Ú9VG0=1.205, FJ: VOU T|T=T0=25◦c = 1.205V + 2.2(0.026V ) = 1.262V (2.46) â¤!‹ªJõ|, |Ú9ÊÅ[bkÉv(íM'Q¡¦í?¦Ú9M, ¥6£u?¦¡5 Ú9Ú˜±˚ííâ

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2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z PTAT V

generator

N PTAT V NVPTAT C I BE V SUM PTAT BE OUT V NV V T T PTAT V NV_PTAT BE V T OUT V T C mV/0 0 ~ Ç 2.12: !…?[¡5Ú9Ú˜h1

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3 ı

QÚ9QŠ0¡5Ú9Ú˜}&Dql

3.1 Ü}&

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 10−6 0 0.5 1 1.5x 10 −6 I_IN (A) IOUT (A) Ç 3.1: ¼MÚ¼Ä|Ú¼DpÚ¼íÉ[( ¤¹døÿõ[kQÚ9QŠ0¡5Ú9Ú˜, %¬ùı}&úÚ¼ÄÊÍTÚ9íÌ „, FJBSà¼MÚ¼ÄdÑÚ¼Ä, JZ¯¯QÍTÚ9íÔ4, /SàABR9Ú˜JZ±Q |Ú9úÚÄÚ9íÑÜ ÊQŠ0jÞ, u‚à MOS Tkÿ¥ó–xQÚ¼íÔ4, / Ê^kÅ[bv6Zk}&¸ql

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3 ı QÚ9QŠ0¡5Ú9Ú˜}&Dql 0 10 20 30 40 50 60 70 80 90 100 0.51 0.52 0.53 0.54 0.55 0.56 0.57 TEMP (°C) V G2 (Volt) Ç 3.2: MOS•-Ä”Ú9DÅíÉ[( íl}&Ç2.3¼MÚ¼Ä ID2 = K2IESexp( VGS2 N VT ) (3.1) ID3 = K3IESexp( VGS3 N VT ) (3.2)

w2IES = µnCoxN (VT)2exp[_{N κT}q (−Vt− N κT_q )], VtuMOS@äÚ9,VT = κT_q uÏÚ9κuš

cbκ = 1.38 × 10−₂₃ ,N uŸ@äbN = 2 ∼ 3,K u MOS í ÷ªWK = (W L) (3-1) ÎJ (3-2) , ª) ID2 ID3 = K2 K3 exp(ID2R N VT ) (3.3) (3-3) %cÜ(ª) ID3 = ID2K3 K2 exp(−ID2R N VT ) (3.4) w2²Ï ID3 = [ K3 K2 exp(−1)]ID2 (3.5)

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3 ı QÚ9QŠ0¡5Ú9Ú˜}&Dql

VCC

R

M2

M3

M0

M1

R1

VOUT

Ç 3.3: QÚ9QŠ0¡5Ú9Ú˜ R = N VT ID2 (3.6) fnU)R9Ú¼ID2Ä§ƒÚÄÚ9¸ÕÊ=1í à7ßÞ‰, FJ²Ï_çíRM, 1²Ï M2 ¸ M3 í(W L) , U)ÍTõ£ßu¼MÚ¼Äí¼MÚ¼, àÇ3.1 Fý ÊÅ^kjÞ, íl}&¼MÚ¼ÄíÅÔ4, VGS = N VT ln( ID2 K2IES ) (3.7)

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3 ı QÚ9QŠ0¡5Ú9Ú˜}&Dql 0 10 20 30 40 50 60 70 80 90 100 0.9 1 1.1 1.2 1.3 1.4 1.5x 10 −6 TEMP (°C) I D2 (A) Ç 3.4: ID2DÅíÉ[( = N VT ln[ ID2 K2µCOXN (VT)2exp(_{N V}−V_Tt − 1) ] (3.8) = N VT ln[ ID2R K2µCOXN (VT)2exp(_{N V}−V_Tt − 1)R ] (3.9) ø (3.6) Hp (3.8) , ª)ø (3-5) Hp (3-6) , ª) VGS = N VT ln[ N VT K2µCOXN (VT)2exp(_{N V}−V_Tt − 1)R ] (3.10) = N VT ln[ 1 K2µCOXN VT exp(_{N V}−V_Tt − 1)R ] (3.11) = N VT ln[ exp( Vt N VT) K2µCOXκ_qexp(−1)R T (α − 1)] (3.12) = N VT ln[ 1 K2µRCOXκ_q exp(−1) ] + N VT(α − 1) ln T + Vt (3.13) ID2 = VGS2− VGS3 R = N VT R ln( K3 K2 ) (3.14)

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3 ı QÚ9QŠ0¡5Ú9Ú˜}&Dql âÇ3.2 ¸ (3-13) ª)ø MOS í•-Ä”Ú9uø_ŠÅ[b/uø_Ëbá Åí øŸá ¸Ý(4á FJÊÅ^kjÞ.âßÞø£Å[bjKV^k•-Ä”íŠÅÔ4 àÇ3.3 QÚ9QŠ0¡5Ú9Ú˜u¤¹dFqlí¡5Ú9Ú˜, Sà7¼MÚ¼Äx QÍTÚ9Q¾Š0íÔ4 ÊÅ^kjÞ, â (3-14) 2ªøwõÚ˜…™x ^k vFÛí£Å[bjKID2àÇ3.4, .ÛçÕqlÅ^kÂ, ÉÛQÚ®R1, |cR1Ú®M Uw®ƒÅ^kí^‹, w|Ú9‰Ñ VOU T = ID2R1+ VGS2 (3.15) ø (3.13) ¸ (3.14) uHp (3.15) ª) VOU T = R1 R N VT + N VT ln( 1 K2RµCOXκ_q exp(−1) ) + N VT(α − 1) ln T + Vt (3.16) = Vt+ [ R1 R + ln( 1 K2RµCOXκ_q exp(−1) )](κN q )T + ( κN q (α − 1))T ln T (3.17) 0 10 20 30 40 50 60 70 0.7214 0.7216 0.7218 0.722 0.7222 0.7224 0.7226 TEMPERATURE (°C) VOUT (Volt) Ç 3.5: R1 = 154.602kí|Ú9DÅíÉ[(

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3 ı QÚ9QŠ0¡5Ú9Ú˜}&Dql [b [bM A0 0.8247192351846 A1 -0.0031156571531 A2 0.00038551813486 B0 0.01040873530519 B1 0.00048336389671 [ 3.1: â(¡N¶¦)í[b[ jK±˚ jKM ÀP R1 140 KOhm R 50 KOhm M0 4um/16um M1 4um/16um M2 32um/16um M3 79.04um/16um M4 4um/12um M5 4um/12um M6 4um/12um [ 3.2: ®jKM[

3.2 Uà}¶,¿^kÚ®íjKM

Êd.è2Tƒ¡5Ú9Ú˜íÅ0^k2w2øéu`TP T AT2_{ò¼áà [5]^} kÝ(4á, 7^kÂíqlYWu‚àÊ/øÅË¡U|Ú9‰“|ü, 6ÿué|Ú9Ê /øÅË¡ø¼}ÑÉ ù¼}ÑÉ, é|Ú9Ê/øÔìÅË¡uœÑ ì ∂VOU T ∂T = ∂ID2 ∂T R2 + ∂VGS2 ∂T (3.18) = κN q [ R1 R + ln( 1 K2RµCoxκN_q exp(−1) )] + κN q (α − 1)(1 + ln T ) (3.19) ílâbçíRûª°) VGS2(T )¸ID2(T )í, ÄÑÌ¶Äüí`˙¡b, FJªÛSà bM}&¶6ŒBdÄüí}&¸,¿ * (3.13) (3.14) 2ªêÛà‹;dÅ^kªuº Ì¶)ø`˙¡b, FJ‚àbM}&¶(¡N¶¡NVGS2¸ID2, )ƒVGS2(T )ID2(T ) (

¡N¶uøJ5íb_õàø‘(¡N¥b_õ, wbç[ýÑ M IN N X i=1 [Gi− (A + BTi+ CTiln(Ti))]2 (3.20) w2A + BT + CT ln T u;b¡Níƒb%, â,íÆ¶Bªø˛)øíMHp, 1ª)ƒø _A + BT + CT ln(T )íƒbV¡NHpíM …¹døÔWð„¤¶íªW4, Ê[3.1 2F

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3 ı QÚ9QŠ0¡5Ú9Ú˜}&Dql Ôíuâ(¡N¶F×)í[b, Ê[3.2 2FÔíuÊ¤W2®jK¡b, y‚à}¶ Zª,¿|àÇ3.5Fýçb°T = 25◦ c, Å‰“b°|ü, %}¶,¿|íR = 154.602K 7õÒ,, çT = 25◦ c, }ÑÉFÛí154.602K w|Ú9DÅíÉ[àÇ3.5 Fý 270 280 290 300 310 320 330 340 350 0.525 0.53 0.535 0.54 0.545 0.55 0.555 0.56 0.565 0.57 TEMPERATURE (°K) V G2 (Volt) Hspice data curve data Ç 3.6: õÒÚ9MD¡Nƒb5ªœ âÇ3.6¸Ç3.7ªø‚à(¡N¶, F¡NíƒbDõÒ<íÏæ, w2¨A,¿M¸õÒM <ÏÏw3bŸÄuÌ¶)øõÒÚ®DÅíƒb, FJlvÉ?JÜ;Ú®d}&, Ä¤ }¨A<ÏÏ, O¤¶TX7ql6£üíj², 7.uÔñí#ìjKM

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3 ı QÚ9QŠ0¡5Ú9Ú˜}&Dql 270 280 290 300 310 320 330 340 350 0.14 0.145 0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 TEMPERATURE (°K) V R1 (Volt) Hspice data curve fitting Ç 3.7: õÒÚ¼MD¡Nƒb5ªœ

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4 ı

õð!‹Dªœ

Êõð2, …Ú˜¸d. [8]íÚ˜jKÌSà TSMC 0.35um 3P3M SiGe BiCMOS`˙, Ç4.1uÚ˜0Ç, [??FýuQÚ9QŠ0Dd. [8]ªœ5d[, âÇ[2ªø¤Ú˜F Ûb|üíÚÄÚ9u1.4V |Ú9u0.71 |× TÚ¼u2.23uA, Å[bu16.8ppm/◦

c

Ç 4.1: Ú˜0Ç

ÊÇ[2ªøÊÚ˜¾Š0ü 1.5I, X@Ú¼˛øš 7ÚÄÚ9jÞd. [8]ÍT¸ ˇ˛ó¡ ÊÅjÞ…Ú˜œi¡ 4 I Ê4.6 2ÚÄÚ9{„ªíòä¶}ªy|«1Qø _ÚñZª××ZªÚÄÚ9{„ª

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4 ı õð!‹Dªœ ¡b d. [8] QÚ9QŠ0¡5Ú9Ú˜ ÀP X@Ú¼ 2.163 2.23 µA ¾Š0 _10.221 _6.68 _µW p¡5Æmò _758.045 _15.6 µV Hz0.5 |Ú9 _0.72 _0.71 _V ÚÄÚ9{„ª -70(1 Hz) -109(1 Hz) dB -70(1KHz) -109(1 kHz) -67(1 MHz) -84.05(1MHz) (4Ä _-1.76(◦ c) 4.3(◦ c) mv_v -0.6(70◦ c) 3.7(70◦ c) Å[b _43.3 _16.8 _ppm/◦ C [ 4.1: ¡5Ú9Ú˜Dd.[8]5d[ 0 10 20 30 40 50 60 70 80 90 100 0.7124 0.7126 0.7128 0.713 0.7132 0.7134 0.7136 0.7138 TEMP (°C) VOUT (Volt) Ç 4.2: ¡5Ú9Ú˜5Pre-Sim Ê.°Åí|Ú9

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4 ı õð!‹Dªœ 0 10 20 30 40 50 60 70 80 90 100 0.7118 0.712 0.7122 0.7124 0.7126 0.7128 0.713 0.7132 TEMP (°C) VOUT (Volt) Ç 4.3: ¡5Ú9Ú˜5Post-Sim Ê.°Åí|Ú9

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4 ı õð!‹Dªœ 0 10 20 30 40 50 60 70 80 90 100 0.723 0.7235 0.724 0.7245 0.725 0.7255 0.726 0.7265 0.727 0.7275 TEMP (°C) VOUT (Volt) Ç 4.4: d.[8]5|Ú9DÅíÉ[(

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4 ı õð!‹Dªœ 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 0.45 0.5 0.55 0.6 0.65 0.7 0.75 V_CC (Volt) VOUT (Volt) Ç 4.5: ¡5Ú9Ú˜5Pre-Sim Ê.°ÚÄÚ9í|Ú9

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4 ı õð!‹Dªœ 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 0.45 0.5 0.55 0.6 0.65 0.7 0.75 V_CC (Volt) VOUT (Volt) Ç 4.6: ¡5Ú9Ú˜5Post-Sim Ê.°ÚÄÚ9í|Ú9

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4 ı õð!‹Dªœ 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 0.6 0.62 0.64 0.66 0.68 0.7 0.72 V_CC (Volt) V OUT (Volt) Ç 4.7: d.[8]5|Ú9DÚÄÚ9íÉ[(

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4 ı õð!‹Dªœ 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6x 10 −3 Frequency (Hz)

input reference noise RMS (V)

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4 ı õð!‹Dªœ 0 1 2 3 4 5 6 7 8 9 10 x 105 −115 −110 −105 −100 −95 −90 −85 −80 −75 Frequency (Hz) PSRR (dB) Ç 4.9: QÚ9QŠ0¡5Ú9Ú˜5ÚÄÚ9{„ª

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4 ı õð!‹Dªœ 0 1 2 3 4 5 6 7 8 9 10 x 105 −70 −69.5 −69 −68.5 −68 −67.5 −67 Frequency (Hz) PSRR (dB) Ç 4.10: d.[8]5ÚÄÚ9{„ª

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5 ı

!D„V

5.1 !

Ê¤¹d2FT|øÝÀ7/QÚ9QŠ0¡5Ú9Ú˜ ¤Ú˜%‡0_Ò (Pre-Sim) ¸(«_Ò (Post-(Pre-Sim) w!‹uÅ[bÑ 16.8ppm/◦

c ÚÄÚ9{„ª -84 dB |× ¾Š0Ñ 6.68uW, FÛí|üÚÄÚ9Ñ1.4V. Bb65?ƒÚ9Ä‰ú|Ú9í‰“, â k.Û5?ƒ¤Ú˜ÊQÚÄÚ9E? T, Bb[JUà Wilson Ú¼ŸÚ˜VTò¤Ú˜í( 4Ä âk¤^@3bŸÄuâk¦−Å|‰ (Channel length modulation) 5^@, Ä¤B bql M0, £ M1 vuUwÑÅ¦− 1Áü R1, J±Q|Ú9í‰“, *5‡í}&ªêÛ R1 Áü, cñí¾Š0}óúÓ‹, FJ¥uBb@G|íHg Ñ7±Q¦−Å|‰^@7 Lø Ú¼ŸCÓ‹¦−Å, ø}Ó‹FÛ|üíÚÄÚ9 ÊÚ˜}&í¬˙2Ì¶)øÌ í`˙¡bFJBb«àbM}&2í(¡N¶UBbíÊqlí¬˙2y‹Z¡/Äü

5.2 „V

Ê…d2J¼MÚ¼ÄÑ!‚àABR9xXê|øÀíQ Ú9QŠ0¡5Ú9Ä, 1«àÚ˜q¶så MOS Tkÿ¥ó–í•Ä”Ú9ÏxDÅøŸáíÉ[V^kÅ [b, à¤Z.ÛçÕqlÅ^kÂ, â¤cñíÚ˜-Z‰AÝÀ, 7/¾Š0ü, Ou Ú˜2í(4|c´Zªí˛È, ÄÑÊÚ˜2ÍTÚ9¸(4|cíÔ4}ó§½, FJ¥j Þ@vuM)Êû˝íËj

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¡5d.

[1] R. J. Widlar, “New developments in IC voltage regulators,” IEEE J. Solid-State Circuits, Vol. SC-6, pp. 2-7, Feb. 1971.

[2] P. R. Gray, Analysis and Design of Analog Integrated Circuits, John Wiley & Sons ,2001.

[3] B. S. Song and P. R. Gray, “A precision curvature-compensated CMOS bandgap reference,” IEEE J. Solid-State Circuits, Vol. SC-18, pp. 634-643, Dec. 1983.

[4] I. Lee, G.Kim and W.Kim, “Exponential curvature-compensated BiCMOS bandgap reference,” IEEE J. Solid-State Circuits, vol. 29, pp. 1396-1403, Nov. 1994.

[5] G. A. Rincon-Mora and P. E. Allen, “A 1.1-V current-mode and piecewise-linear curvature-corrected bandgap reference,” IEEE J. Solid-State Circuits, vol. 33, pp. 1551-1554, Oct. 1998.

[6] J. M. Audy, “Bandgap voltage reference circuit and method with low TCR resistor in parallel with high TCR and in series with low TCR portions of tail resistor,” U. S. Patent 5,292,122, March 1994.

[7] G. A. Rincon-Mora, Voltage References-From Diodes to Precision High-Order Bandgap Circuits,New York: Wiley, 2002.

[8] X. B. Ye and Z. L. Chen, “Low Voltage Self-biasing Reference Circuit,” 2001. Pro-ceedings. 4th International ASIC Conference, pp. 23-25, Oct. 2001.

[9] G. Giustolisi, G. Palumbo, M. Criscione, and F. Cucutri, “A Low-Voltage Low-Power Voltage Reference Based on Subthreshold MOSFETs,” IEEE J. Solid-State Circuit, vol. No.38, pp. 151-154, Jan. 2003.

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5d. [10] K. N. Leung, P. K. T. Mok, and C. Y. Leung, “A 2-V 23-uA 5.3-ppm/◦

c Curvature-Compensated CMOS Bandgap Voltage Reference,” IEEE J. Solid-State Circuits, vol. 3833, pp. 561-564, Mar. 2003.

[11] O. Salminen and K. Halonen, “The Higher Order Temperature Compensation Bandgap Voltage Reference ,” IEEE International Symposium on Circuits and Sys-tems , vol. 3, pp. 1388-1391, May 1992.

[12] C. Popa, “A new curvature-corrected voltage reference based on the weight differ-ence of gate-source voltages for subthreshold-operated mos transistors,” IEEE Inter-national Symposium on Circuits and Systems, vol. 2 ,pp. 585-588, July 2003.