第5期 Tang Zhangwen et al.An Accurate 1.08GHz CMOS LC Voltage-Controlled Oscillator 869 The presence of on-chip inductors in Fig.1 im- plitude Amin and frequency @min the other is below poses that the DC value of differential oscillating Veu with the amplitude 6Amax(is an ellipse simi- voltages has to be a constant voltage Vde.Neglec- lar factor,ESF)and frequency cmax ting the tank losses in on-chip inductors and varac- (4)When Vde≤V.a≤Vdc十Amax,it consists of tors,the half circuit of LC-tank VCO can be con- two segmental sinusoids joined at ECV.One is a- sidered as a serial LC-tank structure (Fig.3(a)). bove Ve with the amplitude 02Amin(02 is another The value of inductor is L,and the step-like varac- ESF)and frequency wmin;the other is below Ve tors can be mathematically represented as below with the amplitude Amax and frequency @max. C.W)=2C.+C)+ The I-V locus of a step-like varactor in the se- rial LC-tank circuit is shown in Fig.5.It consists of C-C)sign(V-Va)(2) two ellipses of different size joined at the ECV. The above four regions satisfy the following ellip- Figure 4 shows the oscillating voltage wave- ses'equations: forms of the serial LC tank simulated in HSPICE. Each waveform consists of two segmental sinusoids 10F Region(2) 3.61 IECV-3.5V 6 3 0 =2.00V -2 2.25V 3.0 -4 -2.50V 2.75V -6 =3.00V 8 =3251 2.6 =3.50 ECV=25 10 2.4 ECV=2.54 1.41.61.82.02.22.42.62.83.03.23.43.6 Region(3) V 2.0 Fig.5 IV locus of a varactor ECV-2.0V Region(1) (1)When VuVa-Amin,the I-V locus holds )+ =1(3) 0.5 1.0 1.5 2.0 (2)When VeVae +Amax,it holds Time/ns Fig.4 Voltage waveforms of a varactor at different ECV '+-1 (4) (3)When Vae-Amin≤V.≤Vik,two segmental with different size,which join at the effective con- sinusoids respectively hold trol voltage (ECV).With the ECV from low to high,there exist four regions as below: y+广-v≥wm (1)When Veu <Vde-Amin,the oscillating waveform is a sinusoid with the minimum ampli- +(d广=v<v tude Amin and minimum frequency @min (5) (2)When VeVae+Amns,a sinusoid with the where the ESF 0 satisfies Amin/Amnx1.Espe- maximum amplitude Amax and maximum frequency cially when Ve=Vae and 0=1,it satisfies maxi Imax-Cmin Cmax Amin -CmaxCmin Amax (6) (3)When Vde-Amim≤Vet≤Vc,two partial si- where Imax is the maximum current in the inductor nusoids join at ECV.One is over Ve with the am- or varactor.第C期 ’*)3;<*)3]$)6J’?U! E)EHH(1*2$YZ[B0OUNQR,7N\=%2*3$/N=)21=%%$#R8H"%%*2=1 ’<$.1$8$)H$=A=)/H<".")#(H2=18")@"3cY"-/ .=8$82<*22<$4NG*%($=A#"AA$1$)2"*%=8H"%%*2")3 G=%2*3$8<*82=+$*H=)82*)2G=%2*3$##HcF$3%$H/ 2")32<$2*)I%=88$8")=)/H<".")#(H2=18*)#G*1*H/ 2=18"2<$<*%AH"1H("2=A7N/2*)I \NRH*)+$H=)/ 8"#$1$#*8*8$1"*%7N/2*)I821(H2(1$ #@"3cD#*$$c ’<$G*%($=A")#(H2=1"8."*)#2<$82$./%"I$G*1*H/ 2=18H*)+$-*2<$-*2"H*%%&1$.1$8$)2$#*8+$%=] !88##$T Y X#!-*T V!-")$V Y X#!-*T Z!-")$8"3)## Z#$AA$ #X$ @"3(1$a8<=]82<$=8H"%%*2")3G=%2*3$]*G$/ A=1-8=A2<$8$1"*%7N2*)I8"-(%*2$#")O,KLNVc V*H<]*G$A=1-H=)8"828=A2]=8$3-$)2*%8")(8="#8 @"3ca \=%2*3$]*G$A=1-8=A*G*1*H2=1*2#"AA$1$)2VN\ ]"2<#"AA$1$)28"U$"]<"H<>=")*22<$$AA$H2"G$H=)/ 21=%G=%2*3$ #VN\$c!"2<2<$VN\A1=-%=]2= <"3<"2<$1$$T"82A=(11$3"=)8*8+$%=]! #Y$ !<$)#$AA (##H g S-")"2<$ =8H"%%*2")3 ]*G$A=1-"8*8")(8="# ]"2<2<$ -")"-(- *-.%"/ 2(#$S-")*)#-")"-(-A1$J($)H&%-")% #X$!<$)#$AA&##HeS-*T"*8")(8="#]"2<2<$ -*T"-(-*-.%"2(#$S-*T *)# -*T"-(-A1$J($)H& %-*T% #D$!<$)##HgS-")(#$AA(##H"2]=.*12"*%8"/ )(8="#8>=")*2VN\cR)$"8=G$1#$AA ]"2<2<$*-/ .%"2(#$S-") *)#A1$J($)H&%-")%2<$=2<$1"8+$%=] #$AA ]"2<2<$*-.%"2(#$&YS-*T#&Y"8*)$%%".8$8"-"/ %*1A*H2=1"V,@$*)#A1$J($)H&%-*T% #a$!<$)##H(#$AA(##HeS-*T""2H=)8"828=A 2]=8$3-$)2*%8")(8="#8>=")$#*2VN\cR)$"8*/ +=G$#$AA ]"2<2<$*-.%"2(#$&XS-") #&X "8*)=2<$1 V,@$*)#A1$J($)H&%-")%2<$=2<$1"8+$%=] #$AA ]"2<2<$*-.%"2(#$S-*T*)#A1$J($)H&%-*Tc ’<$$"#%=H(8=A*82$./%"I$G*1*H2=1")2<$8$/ 1"*%7N/2*)IH"1H("2"88<=])")@"3cCcL2H=)8"828=A 2]=$%%".8$8=A#"AA$1$)28"U$>=")$#*22<$VN\c ’<$*+=G$A=(11$3"=)88*2"8A&2<$A=%%=]")3$%%"./ 8$8&$J(*2"=)8! @"3cC $"#%=H(8=A*G*1*H2=1 #Y$!<$)#$AA(##HgS-")"2<$$"#%=H(8<=%#8 # Z##H # S-") $ X V $ #%-")!-*TS-") $ X TY #D$ #X$!<$)#$AA&##HeS-*T""2<=%#8 # Z##H # S-*T $ X V $ #%-*T!-")S-*T $ X TY #a$ #D$!<$)##HgS-")(#$AA(##H"2]=8$3-$)2*% 8")(8="#81$8.$H2"G$%&<=%# # Z##H # S-") $ X V $ #%-")!-*TS-") $ X TY" # &#$AA # Z##H # S-*T $ X V $ #%-*T!-")S-*T $ X T&X Y" # ’# ) * + $AA #C$ ]<$1$2<$V,@&Y8*2"8A"$8S-")’S-*T(&Y(YcV8.$/ H"*%%&]<$)#$AAd##H*)#&YdY""28*2"8A"$8 $-*T T%-")!-*TS-") T%-*T!-")S-*T #W$ ]<$1$$-*T"82<$-*T"-(-H(11$)2")2<$")#(H2=1 =1G*1*H2=1c BW‘