The Study of 3 rd Overtone Crystal Oscillator

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1 The Study o 3 rd Overtone Crystal Osillator

2 The Study o 3 rd Overtone Crystal Osillator StudentHsin-Chang Tsai AdvisorPro. Yao-Huang Kao A Thesis Submitted to The Institute o Communiation Engineering College o Eletrial Engineering and Computer Siene National Chiao Tung University In partial Fulillment o the equirements For the Degree o Master o Siene In Communiation Engineering Aug 2004 Hsinhu, Taiwan, epubli o China

3 The Study o 3 rd Overtone Crystal Osillator i

4 The Study o 3 rd Overtone Crystal Osillator StudentHsin-Chang Tsai AdvisorPro. Yao-Huang Kao Institute o Communiation Engineering National Chiao Tung University Abstrat In this thesis, reerene high requeny lok soures are studied. espeially, the 3 rd overtone rystal osillator is oused. Three types are examined. In the irst type, the requeny range o negative resistane is only ontrolled by the eedbak resistane. The origin o the tuning is learly illustrated. The seond type involves external LC network to make iruit resistane positive at undamental requeny. At last, a new design is presented to enhane the positive resistane at undamental requeny, and with PECL output stage, desiring to make 3 rd overtone rystal osillator ombine with digital iruit system more ompatly. ii

5 909 babu iii

6 i ii iii iv v vi LC PECL iv

7 v

8 piere Colpitts overtone vi

9 (1) (2) (3) (4) (5) HSPICE phase noise layout vii

10 Colpitts M25-93A PECL PECL layout 55 viii

11 ! < CCCC IIII ' ' 1.1 ' /.0 &2 34,$ 5,) % & ( ( ) $ "!# * +,( )- %176 %98:6 1 ;7 /<= = ) ;> &/53+) 5 * A1B CD5E F7GHG5IKJ5L 1

12 [2] overtone rystal osillator 1.2 2

13 M/N"O P"Q#S O"T QVU2#W/P"S λ 2 X W"P"Q U/U Y O"S Z9["\ ]^`_2a"b] _2d"bè _/^/b 3λ 2 gh_/^"i j/j \ d"bk l)m l)m nko 3

Fs[MHz] 155.519649 156.2757 Ls[H] 205.755 1481.696 Cs[F] 5.09 0.7 s[] 11.5 25.3 Co[p] 2.7 2.

14 Fs[MHz] Ls[H] Cs[F] s[] Co[p] Q[unloaded] s 1 = 2π L C s s p = 2π 1 C0 + Cs Ls C0Cs Ls ( i) Cs ( i) s ( i) 4

15 Z ( ) ( ) ( ) s i 1 ω s ( i) = L i C i ( ) Q i s s = 1 ω ( i) C ( i) ( i) s s s I 5

16 prq 6

17 Barkhausen 1.8 LC p -p p Lp Cp

18 swv xv y v v y{z v) }2~, sut ƒ z s4 ) 2 8

19 ˆŠ uš Œ Š Š Œ Š5 ", ŵ 4Ž Ž ˆ{ Žš 9

20 Ã ª ª ª Ä ª «ª { : 7 4 " : : ª ªK : :,ª ªK 9 : ª ¹ ± ± ³ ± ±K /À7³ ± : " " ÂÁ 0, 2±² ²³ ±) /À>³ ± : ÅÆ2Ç È ÉKÉ : ª >, /±K²K²³ ±) 0 V ± µ>²k r 0, 2±²K²K³ ±) 0 V ± µ>²k / 2 ¹»º½¼"¾ )œkž,ÿ5ÿ 10

21 Ë Ý Ë 1.3 LC LC overtone 1.14 Þ Ð Ñ"Ò Ô ÔØÙ ÚÜÛ Ï/ÔÖ Ë ÌÝ Ï/ÔÕÖ Þß Ì9Ë Ñ2à Ï2Ñ Ð ÓÒ Ï Ð Ñ/Ò ÊËÌÍhÎ 1.14 overtone [3]

22 , TSMC 2P4M 0.35m 3V MHz (Vdd=2.5V) 32.1mW( buer) Voh 2.03V Vol 1.2V 1.5 LC network PECL 12

23 2.1 e ( Z ) C = m ( g C ) + ω ( C C + C C + C C ) m g C C! " # $ % &('*) +,.- /

24 CDB E B F B ; E*H B IKJL.M Ï FDG :9 OG M P Q N G. P M I =?> 14

25 Vx Vy I = Vt sco + VxsC1 + VxsCgs + V Vy Vx Vy Vy + Vt Vx + + gmvx + = 0 r ds Vx Vt Vx + + = g V rds y m x V V = g V V V r ( // // ) x t x y m x ds Vx Vt V x 1 VxsCgs + Vxgm + gmvx ( // rds // ) rds + V sc + V V sc = 0 ( ) x 1 x t 2 15

26 1 1 // rds // V // rds // t Vx scgs + gm + sc + sc + gm + = + Vt sc rds rds Vt + Vt sc2 rds ( // // ) r ds ( ) ( ) ( // rds // ) Vx = Vt + sc2 scgs + sc1 + sc2 + gm + gm + rds rds 1 V y V + sc g + r 1 1 scgs + sc1 + sc2 + gm + gm + r ds ( // // ) t 2 m ds rds ( // rds // ) Vt 16

27 I 1 Vt + sc2 ( sc1 + scgs ) rds = Vt sco ( // rds // ) scgs + sc1 + sc2 + gm + gm + r ds 1 Vt + sc2 r 1 1 ds Vt + 1 gm + ( // rds // ) 1 1 ( // rds // ) scgs + sc 1 + sc2 + gm + gm + r ds I V t sc2 ( sc1 + scgs ) + + sc2 1 gm + ( // rds // ) rds rds = sco ( // rds // ) scgs + sc1 + sc2 + gm + gm + r ds 1 17

28 1 1 // rds // gm + gm + + rds Z = gm + ω ( C0Cgs + C1C 0 + C2C0 + C2C1 + C2Cgs ) + rds ( gs ) s C C C 1 1 // rds // Cgs + C1 + C2 C1 + C gs C // // rds s Co gm + gm + 1 gm r ds rds rds ω e { Z} ( 1 2 ) 1 1 // rds // gm + gm + gm + ω ( C0Cgs + C1C 0 + C2C0 + C2C1 + C2Cgs ) + rds rds = gm + ( // rds // ) ω ( C0Cgs + C1C 0 + C2C0 + C2C1 + C2Cgs ) + r ds 1 1 // r // C + C + C C + C C 1 1 // r // 2 ds s gs gs 2 ds s Cgs + C + C Co gm + gm gm + s rds rds s rds // // rds s Cgs + C1 C2 C1 Cgs C ω Co gm + gm // rds // + + s g s rds m + rds s r ds 2 18

29 uto 1 = 2π gm 1 g m + rds Cgs + C1 + C2 C1 + Cgs C 2 gm ( C0C gs + CC C2C 0 + C2C 1 + C2C gs ) ( Cgs + C1 + C2 ) Co gm rds 19

$S:TVUKWX8U Y[Z \ ] ^`_bak dbü e[!$

30 S:TVUKWX8U Y[Z \ ] ^`_bak dbü e[!g h iju k Cgs + C1 gm ( C2C1 + C2Cgs ) + ( Cgs + C1 + C2 ) rds e{ z} = 2 2 Cgs + C1 ω ( C0Cgs C1C 0 C2C0 C2C1 C2Cgs ) C 0gm + rds 20

31 1 w ID = µ ncox Vgs Vt 2 l ( ) 2 wl Cgs + C1 gm ( C2C1 + C2Cgs ) + ( Cgs + C1 + C2 ) rds e{ z} = > Cgs + C1 ω ( C0Cgs C1C 0 C2C0 C2C1 C2Cgs ) C 0gm + rds l m n s 21

32 s o t yyyy zzzz q r ( e( ZC )) max g m > 0 g m = 0, Z C Z 3 1 = Z + Z 1 o(p ( Z + Z ) Z 3 g m = g m, rit g m = g m, opt g m = g m,max Z C ( g m ) t u rwv s*x g =, Z C Z 3 m = {!} { } { } C1C 2 gm < gm, opt = ω C 1 + C2 + C0 { } 22

33 ω uto gm 1 g m + rds = 2 π( Fun MHz ) Cgs + C1 + C2 C1 + Cgs C 2 gm ( C0C gs + CC C2C 0 + C2C 1 + C2C gs ) ( Cgs + C1 + C2 ) Co gm rds 23

LA PRISE DE CALAIS. çoys, çoys, har - dis. çoys, dis. tons, mantz, tons, Gas. c est. à ce. C est à ce. coup, c est à ce

LA PRISE DE CALAIS. çoys, çoys, har - dis. çoys, dis. tons, mantz, tons, Gas. c est. à ce. C est à ce. coup, c est à ce > ƒ? @ Z [ \ _ ' µ `. l 1 2 3 z Æ Ñ 6 = Ð l sl (~131 1606) rn % & +, l r s s, r 7 nr ss r r s s s, r s, r! " # $ s s ( ) r * s, / 0 s, r 4 r r 9;: < 10 r mnz, rz, r ns, 1 s ; j;k ns, q r s { } ~ l r mnz,