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
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–, ĤcñÚ˜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
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.
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< ʨt‚ÈwP"»Å`¤ nø`¤¸i£`¤Æ˛N£1TXrÖ£í<c ʤ>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‘Dñ“
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 . . . 32.1.2 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
3.2 Uà}¶,¿^kÚ®íjKM . . . 22 4 õð!‹Dªœ 25 5 !D„V 35 5.1 ! . . . 35 5.2 „V . . . 35 ¡5d. 36
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. . . 27Ç 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
[ñ“
[ 3.1 â(¡N¶¦)í[b[ . . . 22 [ 3.2 ®jKM[ . . . 22 [ 4.1 ¡5Ú9Ú˜Dd.[8]5d[ . . . 26
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, ĤÚÄÚ9BVBQ, â5V ±B3.3V £B1.8V ¤ÕàS±QÚ˜Š0¾Ê¤ Ì(¦mBVB £ÿB$½b ĤêøQÚ9Q¾Š0í¡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 AT3+ P T AT4 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(−4EkTG) , ÇÕd. [5]uS
àøÅ}–7®–JÒ¨(4 (piecewise linear) V^k 6UàÚ®jKÓʼn“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/◦
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˜ÊÍTvÈjÞxiæíÔ41.4 d-Z
…¹du}üıVn, Î7øıJÕ, cø®ıíqñÜk-: ùı2, ÄѤژ -Z¨ÖڼĶ}, 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!‹Tøêcízp2 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 ʤıøÜútí¡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) Ĥ VGS1 = Vt1+ v u u t 2ID1 µnCOX(WL)1 (2.2) w2IDu¼%MOS í ”Ú¼,Vt1u M1@äÚ9 (threshold voltage), ÄÑID1ID2'ü, /(WL)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
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°, ÄѤژu‚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)
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 KTq (−Vt − N KTq )], VT = κTq 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(KK21) IESK1R ) (2.9) Ç2.6 uQ, í|Ú9DÚÄÚ9íÉ[( BkQ, Ú¼ÄíÿõuâÇ2.2 2ªø M3 Äѧƒ¦−Å|‰) à, U)úÚÄÚ9}ø_×íÑÜ
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 ≥ 3κTq ,(2.8) ª“A ID = KIESexp[ VGS N VT ] (2.12)
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 VCC (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 = κTq uÏÚ9,N uŸ@äb N=2 ∼ 3,K = WL 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)
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 VCC (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(KK21) IES2K2R ) (2.22) Fýu¼MÚ¼Äí|Ú9úÚÄÚ9íÉ[( âÇ2.4Fý¤Ú˜FÛí|üÚÄÚ9ük 1V Ç2.4Ç2.5Ç2.6âõðí!‹ª)øJ,úڼķø_u°íÿõÿçʼn“v, |Ú9}ßÞ—Ë퉓 Wà: Ç2.7í¼MÚ¼Ä|Ú9úÅíÉ[(, ¸Ç2.8íQ, Ú¼Äí|Ú9úÅíÉ[( â (2.7) ¸ (2.20) ªøçʼn“v¥sÚ¼Äí |Ú9}ÄÏÚ9VT ¸`˙¡bIESDÅóÉ7‰, ¤h1ʤl×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
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 VCC (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)
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 ≈ VRCC1 /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¡52 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-:
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) *hcܪ
)|:
VBE(ON )= VT ln(I1T−γE exp(
VG0
VT
)) (2.36)
w2Eub,γ=4 − nÊõÒí?¦Ú˜2, Ú¼I1uÓʼn“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:
2 ı ¡ 5 Ú 9 Ú ˜ Ÿ Ü D - Z
Current Mirror
OUT INCurrent 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)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[ýíŃ, ª)||Ú9 Êql?¦¡5 Ú9Ú˜2, Bb|3bíh1uıÅ퉓ú|Ú9êr³ à; Ĥ, 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) Ĥ, ʼn“ú|Ú9í àªâÀø¡bT0V·H, 7T0íM†âNEGV²ì ç|Ú 9ÊT CFkÉ(T = T0)và-: VOU T|T=T0 = VG0+ VT0(γ − α) (2.44)
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
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 NVPTAT BE V T OUT V T C mV/0 0 ~ Ç 2.12: !…?[¡5Ú9Ú˜h13 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 IIN (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}&¸ql3 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 κTq (−Vt− N κTq )], VtuMOS@äÚ9,VT = κTq 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)
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)R9Ú¼ID2ħƒÚÄÚ9¸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)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−VTt − 1) ] (3.8) = N VT ln[ ID2R K2µCOXN (VT)2exp(N V−VTt − 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−VTt − 1)R ] (3.10) = N VT ln[ 1 K2µCOXN VT exp(N V−VTt − 1)R ] (3.11) = N VT ln[ exp( Vt N VT) K2µCOXκqexp(−1)R T (α − 1)] (3.12) = N VT ln[ 1 K2µRCOXκq exp(−1) ] + N VT(α − 1) ln T + Vt (3.13) ID2 = VGS2− VGS3 R = N VT R ln( K3 K2 ) (3.14)
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 K2RµCOXκq exp(−1) ) + N VT(α − 1) ln T + Vt (3.16) = Vt+ [ R1 R + ln( 1 K2RµCOXκq 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[(
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 AT2ò¼áà [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 K2RµCoxκNq exp(−1) )] + κN q (α − 1)(1 + ln T ) (3.19) ílâbçíRûª°) VGS2(T )¸ID2(T )í, ÄÑ̶Äüí`˙¡b, FJªÛSà bM}&¶6ŒBdÄüí}&¸,¿ * (3.13) (3.14) 2ªêÛà‹;dÅ^kªuº ̶)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,íƶBªø˛)øíMHp, 1ª)ƒø _A + BT + CT ln(T )íƒbV¡NHpíM …¹døÔWð„¤¶íªW4, Ê[3.1 2F
3 ı QÚ9QŠ0¡5Ú9Ú˜}&Dql Ôíuâ(¡N¶F×)í[b, Ê[3.2 2FÔíuʤW2®jK¡b, y‚à}¶ Zª,¿|àÇ3.5Fýçb°T = 25◦ c, ʼn“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 <ÏÏw3bŸÄu̶)øõÒÚ®DÅíƒb, FJlvÉ?JÜ;Ú®d}&, Ĥ }¨A<ÏÏ, O¤¶TX7ql6£üíj², 7.uÔñí#ìjKM
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
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
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) mvv -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
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
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[(
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 VCC (Volt) VOUT (Volt) Ç 4.5: ¡5Ú9Ú˜5Pre-Sim Ê.°ÚÄÚ9í|Ú9
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 VCC (Volt) VOUT (Volt) Ç 4.6: ¡5Ú9Ú˜5Post-Sim Ê.°ÚÄÚ9í|Ú9
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 VCC (Volt) V OUT (Volt) Ç 4.7: d.[8]5|Ú9DÚÄÚ9íÉ[(
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)
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
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
5 ı
!D„V
5.1 !
ʤ¹d2FT|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?ƒÚ9ĉú|Ú9퉓, â k.Û5?ƒ¤Ú˜ÊQÚÄÚ9E? T, Bb[JUà Wilson Ú¼ŸÚ˜VTò¤Ú˜í( 4Ä âk¤^@3bŸÄuâk¦−Å|‰ (Channel length modulation) 5^@, ĤB bql M0, £ M1 vuUwÑŦ− 1Áü R1, J±Q|Ú9퉓, *5‡í}&ªêÛ R1 Áü, cñí¾Š0}óúÓ‹, FJ¥uBb@G|íHg Ñ7±Q¦−Å|‰^@7 Lø Ú¼ŸCÓ‹¦−Å, ø}Ó‹FÛ|üíÚÄÚ9 ÊÚ˜}&í¬˙2̶)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¡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.
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.