868 半导体学报 第26卷 In this paper,we investigate the IV locus of vices are implemented using the minimum gate step-like MOS varactors in a LC-VCO and predict length (0.35um).The open-drain nMOS devices the tuning curves through the oscillating period are the output buffers,which is used to drive the calculation of a serial LC tank in time domaint4.. off-chip bias-T circuits.In order to decrease the An accurate 1.08GHz CMOS LC voltage-con- Miller-effect capacitor,the length of open-drain trolled oscillator is implemented in a 0.35um nMOS devices is 60um.The lengths of current-mir- standard 2P4M CMOS process.The theoretical an- ror are larger than the minimum length so that the alyses agree perfectly with the simulation and channel length modulation(CLM)is attenuated and measurement of a CMOS complementary LC-tank 1/f noise is decreased. VCO. Two additional inductors,Ll &L2,resonate at double frequency with the parasitic capacitors Cl 2 Circuit design &C2 at each common-source node,to avoid Q-deg- radation by triode region MOS transistors in the The complementary cross-coupled negative-Gm stacked differential pairs.The filtering capacitor LC-tank voltage-controlled oscillator in Fig.1 has C3 is used to low the 1/f noise and effect of chan- been implemented in 0.35um 2P4M 3.3V CMOS nel length modulation(CLM). process.On-chip spiral inductor is a symmetric dif- ferential multilayer inductor.Four metals are paral- 3 Frequency tuning characteristic lelly and serially connected with a lot of vias to de- crease the serial resistor of spiral inductor and in- Most of varactors used in LC-tank VCO cir- crease the inductance in unit silicon area.And a cuits are inversion-MOS(I-MOS)and accumula- center-connected patterned ground shield(PGS)is tion-MOS(A-MOS).Their characteristics both are employed to improve quality of inductors at low step-like,and have large nonlinearity.The tuning frequency (1~GHz).On-chip differential spiral curves of an LC-VCO will substantially deviate inductor is 12.4nH,so the single-ended inductor from the ideal curve 1/VLC when a step-like varac- features 6.2nH.The maximum Q arrives seven at tor is usedt.Both I-MOS and A-MOS are step-like 1.1GHz.The compact equivalent PI model shown in Fig.2 is extracted with ASITIC]. capacitors (Figs.3(b)and (c)).The small-signal capacitance is given by 5.78212.38nH5.78 Rs Cmax,V≥V Portlo -oPort2 C(V)= (1) ICuin,V<V 479.5fF 476.9F where V=Van +VTH is effective control voltage 37.122 37.282 (ECV). R Fig.2 PI model of on-chip spiral inductor The transconductances of cross-couple nMOS C.(V) and pMOS devices are chosen to be equal so that DC voltage of LC-tank oscillator is maintained at t C() sign(P) approximately Va/2.First,the oscillating wave- (a) (b) (c) form can have the maximum swing.Secondly,the VCO gain (K)can be decreased and the phase- Fig.3 Serial LC-tank and step-like varactor (a)Serial LC tank;(b)Step-like varactor;(c)Unit step function noise performance can be improved.The MOS de-半 导 体 学 报 第XW卷 L)2<"8.*.$1!]$")G$82"3*2$2<$$"# %=H(8=A 82$./%"I$QR,G*1*H2=18")*7N/\NR*)#.1$#"H2 2<$2()")3H(1G$82<1=(3<2<$=8H"%%*2")3 .$1"=# H*%H(%*2"=)=A*8$1"*%7N2*)I")2"-$#=-*")"a!‘# c E) *HH(1*2$ YZ[B0OU NQR, 7N G=%2*3$/H=)/ 21=%%$# =8H"%%*2=1 "8 "-.%$-$)2$# ") * [ZDC$- 82*)#*1#XKaQ NQR,.1=H$88c’<$2<$=1$2"H*%*)/ *%&8$8 *31$$ .$1A$H2%& ]"2< 2<$ 8"-(%*2"=) *)# -$*8(1$-$)2=A*NQR,H=-.%$-$)2*1&7N/2*)I \NRc + /H?MIH>K=@HRF ’<$H=-.%$-$)2*1&H1=88/H=(.%$#)$3*2"G$/@- 7N/2*)IG=%2*3$/H=)21=%%$#=8H"%%*2=1")@"3cY<*8 +$$)"-.%$-$)2$#")[ZDC$- XKaQ DZD\ NQR, .1=H$88cR)/H<".8."1*%")#(H2=1"8*8&--$21"H#"A/ A$1$)2"*%-(%2"%*&$1")#(H2=1c@=(1-$2*%8*1$.*1*%/ %$%%&*)#8$1"*%%&H=))$H2$#]"2<*%=2=AG"*82=#$/ H1$*8$2<$8$1"*%1$8"82=1=A8."1*%")#(H2=1*)#")/ H1$*8$2<$")#(H2*)H$")()"28"%"H=)*1$*cE)#* H$)2$1/H=))$H2$#.*22$1)$#31=()#8<"$%#$K0,%"8 $-.%=&$#2="-.1=G$J(*%"2&=A")#(H2=18*2%=] A1$J($)H&$Y’X0OU%"C# cR)/H<".#"AA$1$)2"*%8."1*% ")#(H2=1"8YXZa)O!8=2<$8")3%$/$)#$#")#(H2=1 A$*2(1$8WZX)Oc’<$-*T"-(- %*11"G$88$G$)*2 YZY0OUc’<$H=-.*H2$J("G*%$)2KL-=#$%8<=]) ")@"3cX"8$T21*H2$#]"2<E,L’LN"W# c @"3cX KL-=#$%=A=)/H<".8."1*%")#(H2=1 ’<$21*)8H=)#(H2*)H$8=AH1=88/H=(.%$)QR, *)#.QR,#$G"H$8*1$H<=8$)2=+$$J(*%8=2<*2 4NG=%2*3$=A7N/2*)I=8H"%%*2=1"8-*")2*")$#*2 *..1=T"-*2$%&###&Xc@"182!2<$=8H"%%*2")3 ]*G$/ A=1-H*)<*G$2<$-*T"-(-8]")3c,$H=)#%&!2<$ \NR3*") $&\ %H*)+$#$H1$*8$#*)#2<$.<*8$/ )="8$.$1A=1-*)H$H*)+$"-.1=G$#c’<$ QR,#$/ G"H$8*1$"-.%$-$)2$# (8")3 2<$ -")"-(- 3*2$ %$)32< $[ZDC$-%c’<$=.$)/#1*"))QR,#$G"H$8 *1$2<$=(2.(2+(AA$18!]<"H<"8(8$#2=#1"G$2<$ =AA/H<".+"*8/’ H"1H("28cL)=1#$12=#$H1$*8$2<$ Q"%%$1/$AA$H2H*.*H"2=1!2<$%$)32< =A =.$)/#1*") )QR,#$G"H$8"8W[$-c’<$%$)32<8=AH(11$)2/-"1/ 1=1*1$%*13$12<*)2<$-")"-(-%$)32<8=2<*22<$ H<*))$%%$)32<-=#(%*2"=)$N7Q%"8*22$)(*2$#*)# Y&5)="8$"8#$H1$*8$#c ’]=*##"2"=)*%")#(H2=18!7Y j 7X!1$8=)*2$ *2#=(+%$A1$J($)H&]"2<2<$.*1*8"2"HH*.*H"2=18NY j NX*2$*H<H=--=)/8=(1H$)=#$!2=*G="#%/#$3/ 1*#*2"=)+&21"=#$1$3"=) QR,21*)8"82=18")2<$ 82*HI$##"AA$1$)2"*%.*"18"P# c’<$A"%2$1")3H*.*H"2=1 ND"8(8$#2=%=]2<$Y&5)="8$*)#$AA$H2=AH<*)/ )$%%$)32<-=#(%*2"=)$N7Q%"Y# c U 5?=YI=FM<>IFHFRMG;?;M>=?H@>HM Q=82=AG*1*H2=18(8$#")7N/2*)I \NRH"1/ H("28*1$")G$18"=)/QR,$L/QR,%*)#*HH(-(%*/ 2"=)/QR,$E/QR,%c’<$"1H<*1*H2$1"82"H8+=2<*1$ 82$./%"I$!*)#<*G$%*13$)=)%")$*1"2&c’<$2()")3 H(1G$8=A*) 7N/\NR ]"%%8(+82*)2"*%%& #$G"*2$ A1=-2<$"#$*%H(1G$Y&%.! ]<$)*82$./%"I$G*1*H/ 2=1"8(8$#"D# c5=2<L/QR,*)#E/QR,*1$82$./%"I$ H*.*H"2=18$@"38cD$+%*)# $H%%c’<$8-*%%/8"3)*% H*.*H"2*)H$"83"G$)+& !88$#%T !-*T! # &#$AA ’!-")! # ’#$AA $Y% ]<$1$#$AAd#H21%e#’O "8$AA$H2"G$H=)21=%G=%2*3$ $VN\%c @"3cD ,$1"*%7N/2*)I*)#82$./%"I$G*1*H2=1 $*%,$1"*% 7N2*)I($+%,2$./%"I$G*1*H2=1($H%_)"282$.A()H2"=) BWB