1078 半导体学报 第26卷 2 Cm(-1,+I)Cn,+2) Distributed capacitance model ! Inductors that are driven differentially or sin- C(2.2n-2)Cnm(2n-l,3 gle-ended (See Fig.1)have different equivalent (1,2-1)C2n.2) parasitic capactiances (C).The equivalent capaci- tance of the spiral inductor can be expressed asts] Cen=Cm.m+Cm (1) -】 Cm(2) C1) Cm(2n)Cm(2-1) (a) (b) c (a) C(-1+1)Cl(nn+2) Signal ground m3,2n-2)Cm2-]3) ,2n-IC2n,2 C C(+1) C(n) Cm(叶2元 Fig.1 Planar monolithic inductors with the same track (2-20 C(0 width,space,inner,and outer radius (a)Differential- (b) driven symmetric configuration (DSPI);(b)Single-en- ded-driven symmetric configuration (SSPI);(c)Single- ended spiral configuration (SEPI)1,2.3.4.5,and 6 are current flow direction in inductor,i.e.AC signal C.(n-1n) voltage profile or half-turns serial number;Capacitances C(n C.(n-2.n-1 (H+1,n+2) are the equivalently parasitical capacitance of the mono- m(2,3) C(2n-2.2n-1) lithic inductor. m1.2) (2m-1.2) The DSPI can be regarded as two single-ended pla- Cm(2-1)2 2n.0) nar inductors having same the Cm,whose connec- tion point is signal ground and whose Cm.are in se- (c) ries.The Cmm of the DSPI are partly in series con- nection and partly in parallel as shown in Fig.2 Fig.2 Voltage profile and distributed capacitance (a).The Cmm of the SSPI are partly in series con- model of the n-turn planar inductor (a)DSPI;(b) nection and partly in parallel and its Cm are in par- SSPI:(e)SEPI allel as shown in Fig.2(b).The Cm of the SEPI This paper also applies the same method for the are in series connection and its Cm are in parallel. differential inductors.The fundamental assump- Voltage profiles of three inductors are different as tions of the DCM can be derived from the voltage shown in Fig.2. distribution over the inductor,which is called volt- 2.1 Assumptions and definitions age profile.For the conveniences of calculation and analysis,the following assumptions are made. To accurately quantify the Cmm and Cm,inin- (1)The same layer metal traces of the induc- ductors,the DCM can be used to analytically calcu- tor have the same resistivity o,current,metal track late them rather than qualitatively approximate. width w(at least in the same half-turn),and metal The DCM is validated by the previous papersts. thickness t;半 导 体 学 报 第-0卷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‘9@46L>?F9A5@>29A48F>>57CG:49F26F>C5AA>F>7462 289=757D5L,-, +:D "@@;PC>I8<@B<KK=LI<I>I8<@ <96::GF64>@3XG6745A348>.; ;67C.;25757& CG:49F2%48>BOW:67H>G2>C49676@345:6@@3:6@:G& @64>48>; F648>F4867 XG6@54645\>@36??F9R5;64>, <8>BOW52\6@5C64>CH348>?F>\59G2?6?>F2#(%*$ , D5L,- ‘9@46L>?F9A5@>67CC524F5HG4>C:6?6:5467:> ;9C>@9A48>7&4GF7?@676F57CG:49F !6"B"[!&!H" ""[!&!:""J[! <852?6?>F6@296??@5>248>26;> ;>489CA9F48> C5AA>F>7456@57CG:49F2,<8>AG7C6;>746@622G;?& 459729A48>BOW:67H>C>F5\>CAF9;48>\9@46L> C524F5HG45979\>F48>57CG:49F%=85:852:6@@>C\9@4& 6L>?F9A5@>#*$ ,D9F48>:97\>75>7:>29A:6@:G@64597 67C676@3252%48>A9@@9=57L622G;?459726F>;6C>, !)"<8>26;>@63>F;>46@4F6:>29A48>57CG:& 49F86\>48>26;>F>25245\543"%:GFF>74%;>46@4F6:_ =5C48: !64@>6245748>26;>86@A&4GF7"%67C;>46@ 485:_7>22J& )’%1