The Study o 3 rd Overtone Crystal Osillator
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
The Study o 3 rd Overtone Crystal Osillator i
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
909 babu iii
i ii iii iv v vi 1 1.1 1 1.2 2 1.3 11 1.4 11 1.5 12 13 2.1 13 2.2 25 2.3 31 2.4 36 39 3.1 LC 39 3.2 PECL 49 56 57 iv
2 4 12 24 v
1.1 1 1.2 3 1.3 4 1.4 5 1.5 piere 5 1.6 Colpitts 6 1.7 7 1.8 7 1.9 8 1.10 8 1.11 8 1.12 9 1.13 10 1.14 overtone 11 1.15 12 2.1 13 2.2 14 2.3 14 vi
2.4 14 2.5 20 2.6 20 2.7 22 2.8 (1) 25 2.9 (2) 26 2.10 (3) 27 2.11 (4) 28 2.12 (5) 29 2.13 30 2.14 31 2.15 33 2.16 HSPICE 33 2.17 34 2.18 phase noise 34 2.19 layout 35 2.20 36 2.21 36 2.22 38 vii
3.1 39 3.2 Colpitts 40 3.3 40 3.4 M25-93A 42 3.5 42 3.6 43 3.7 44 3.8 44 3.9 45 3.10 45 3.11 46 3.12 48 3.13 49 3.14 PECL 50 3.15 PECL 51 3.16 51 3.17 53 3.18 layout 55 viii
! < CCCC IIII ' ' 1.1 ' /.0 &2 34,$ 5,) % & ( ( ) $ "!# * +,( )- %176 %98:6 1 ;7 /<= = ) ;> 6? @5 &/53+) 5 * A1B CD5E F7GHG5IKJ5L 1
[2] overtone rystal osillator 1.2 2
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 2.9 Q[unloaded] 17483.09 57505.60 s 1 = 2π L C s s p = 2π 1 C0 + Cs Ls C0Cs Ls ( i) Cs ( i) s ( i) 4
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
prq 6
Barkhausen 1.8 LC p -p p Lp Cp 1.9 1.10 7
swv xv y v v y{z v) }2~, sut ƒ z s4 ) 2 8
ˆŠ uš Œ Š Š Œ Š5 ", ŵ 4Ž Ž ˆ{ Žš 9
à 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
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] 1.4 11
, TSMC 2P4M 0.35m 3V 156.27MHz (Vdd=2.5V) 32.1mW( buer) Voh 2.03V Vol 1.2V 1.5 LC network PECL 12
2.1 e ( Z ) C = m 1 2 2 2 3 1 2 2 3 1 3 2 ( g C ) + ω ( C C + C C + C C ) m g C C! " # $ % &('*) +,.- / 0 1 2 3 13
< @*B CDB E B F B ; E*H B IKJL.M Ï N @*A FDG 4 5 687:9 OG M P Q H @P N G. P M 2.2 2.3 2.4 I =?> 14
Vx Vy I = Vt sco + VxsC1 + VxsCgs + V Vy Vx Vy Vy + Vt Vx + + gmvx + = 0 r ds 1 1 1 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
1 1 // rds // V // rds // t Vx scgs + gm + sc + sc + gm + = + Vt sc rds rds Vt + Vt sc2 rds ( // // ) r ds ( ) ( ) 1 2 2 ( // rds // ) 1 1 1 Vx = Vt + sc2 scgs + sc1 + sc2 + gm + gm + rds rds 1 V y 1 1 1 V + sc g + r 1 1 scgs + sc1 + sc2 + gm + gm + r ds ( // // ) t 2 m ds rds ( // rds // ) Vt 16
I 1 Vt + sc2 ( sc1 + scgs ) rds = Vt sco + + 1 1 ( // 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 1 1 1 1 1 + sc2 ( sc1 + scgs ) + + sc2 1 gm + ( // rds // ) rds rds = sco + + 1 1 ( // rds // ) scgs + sc1 + sc2 + gm + gm + r ds 1 17
1 1 // rds // gm + gm + + rds Z = 1 1 2 gm + ω ( C0Cgs + C1C 0 + C2C0 + C2C1 + C2Cgs ) + rds ( gs + 1 + 2 ) s C C C 1 1 // rds // Cgs + C1 + C2 C1 + C gs C // // 2 1 1 rds s Co gm + gm + 1 gm + + + + r ds rds rds ω e { Z} ( 1 2 ) 1 1 // rds // 1 1 2 gm + gm + gm + ω ( C0Cgs + C1C 0 + C2C0 + C2C1 + C2Cgs ) + rds rds = 2 1 1 1 2 1 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 1 2 1 gs 2 ds s Cgs + C + C Co gm + gm + + + + 1 gm + s rds rds s rds // // 2 1 1 rds s Cgs + C1 C2 C1 Cgs C ω Co gm + gm + + 2 1 1 // rds // + + s + + 1 g s rds m + rds s r ds 2 18
uto 1 = 2π gm 1 g m + rds Cgs + C1 + C2 C1 + Cgs C 2 gm ( C0C gs + CC 1 0 + C2C 0 + C2C 1 + C2C gs ) ( Cgs + C1 + C2 ) Co gm + + + rds 19
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
1 w ID = µ ncox Vgs Vt 2 l ( ) 2 wl Cgs + C1 gm ( C2C1 + C2Cgs ) + ( Cgs + C1 + C2 ) rds e{ z} = > 3 2 2 Cgs + C1 ω ( C0Cgs C1C 0 C2C0 C2C1 C2Cgs ) + + + + + C 0gm + rds l m n s 21
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 ) 2 2 + 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
ω uto gm 1 g m + rds = 2 π( Fun. + 10 MHz ) Cgs + C1 + C2 C1 + Cgs C 2 gm ( C0C gs + CC 1 0 + C2C 0 + C2C 1 + C2C gs ) ( Cgs + C1 + C2 ) Co gm + + + rds 23