http:∥10.12.240.202，Copyright©2001-2004，Zhangwen Tang Multilayer Spiral Inductor Stacked spiral inductor Miniature 3D spiral inductor M [A.Zolfaghari,B.Razavi,JSSC,April,2001] [C.C Tang,S.I.Liu,JSSC,April,2002] M Differential multilayer inductor M ASIC System State-Key Laboratory,Fudan University -16-
-16- ASIC & System State-Key Laboratory, Fudan University http://10.12.240.202, Copyright © 2001-2004, Zhangwen Tang Multilayer Spiral Inductor Multilayer Spiral Inductor M5 M4 M3 M5 M4 M3 M5 M3 Stacked spiral inductor Miniature 3D spiral inductor Differential multilayer inductor [A. Zolfaghari, B. Razavi, JSSC, April, 2001] [C.C Tang, S.I. Liu, JSSC, April, 2002]
http://10.12.240.202,Copyright@2001-2004,Zhangwen Tang Modeling of On-chip Inductors ● EM Field Solver Characteristic of inductance of a typical ÷High accuracy integrated inductors with frequency Very slow Complex for Spice Inductive Capacitive ● Segmental circuit models Simpler than EM field solver Easy integration into Spice ● Compact,scalable,lumped circuit models Resonance freduency Simple,versatile and robust Physical intuition Frequency ASIC System State-Key Laboratory,Fudan University 17-
-17- ASIC & System State-Key Laboratory, Fudan University http://10.12.240.202, Copyright © 2001-2004, Zhangwen Tang Modeling of On Modeling of On-chip Inductors chip Inductors Characteristic of inductance of a typical integrated inductors with frequency z EM Field Solver High accuracy Very slow Complex for Spice z Segmental circuit models Simpler than EM field solver Easy integration into Spice z Compact, scalable, lumped circuit models Simple, versatile and robust Physical intuition
http:∥10.12.240.202，Copyright©2001-2004，Zhangwen Tang Optimization of Equivalent Capacitance What is the equivalent capacitance At resonance frequency,the peak magnetic and electric energies are equal. Given a peak voltage Vo.electric energy is C2 First resonance frequency fsR fss=(2πVCag)j The proposed equivalent capacitance models Electric energy in interlayer metals,CM-M Electric energy in single metal to substrate,CM-s ASIC System State-Key Laboratory,Fudan University -18
-18- ASIC & System State-Key Laboratory, Fudan University http://10.12.240.202, Copyright © 2001-2004, Zhangwen Tang Optimization of Equivalent Capacitance Optimization of Equivalent Capacitance z What is the equivalent capacitance At resonance frequency, the peak magnetic and electric energies are equal. Given a peak voltage V0, electric energy is z First resonance frequency fSR z The proposed equivalent capacitance models Electric energy in interlayer metals, CM-M Electric energy in single metal to substrate, CM-S 2 C Veq 0 2 ( ) 1 f LC SR eq eq 2π − =
http://10.12.240.202,Copyright 2001-2004,Zhangwen Tang Electric Energy in CM-M and CM-s Electric Energy Ee-立-2cg N M-M m=1 m=12 1 Cw.-w.wl(V-V) AV=K-V- Electric Energy a.-ts m1 CM-S Substrate 69-gM4++% ASIC System State-Key Laboratory,Fudan University -19
-19- ASIC & System State-Key Laboratory, Fudan University http://10.12.240.202, Copyright © 2001-2004, Zhangwen Tang Electric Energy in C Electric Energy in CM-M and CM-S V V 1 2 − i i C C C C C C C C C V V 1 2 − M n M n−1 V1 V2 i C C C C C C C M n V1 C C Substrate V2 V2 V1 ∆VVV = −1 2 CM-M CM-S 1 2 , , 1 1 2 1 2 1 2 1 ( ) 2 m m n n N N eC eC m C m m M M E E CV C wl V V − = = − = = = − ∑ ∑ { } 2 , , 1 1 2 1 1 2 2 1 2 12 1 2 1 ( ) 2 1 6 m m n n N N eC eC m C m m N M S m N M S E E CV C wl m V V N N C wl V V VV = = − = →∞ − = = = −∆ ≈ ++ ∑ ∑ ∑ Electric Energy Electric Energy
http://10.12.240.202,Copyright@2001-2004,Zhangwen Tang Voltage Profile [A.Zolfaghari,B.Razavi,JSSC,April,2001] Turn 2nd Turn 3rd Tum Stacked 21 Substrate [C.C Tang,S.I.Liu,JSSC,April,2002] Vo LTop s Tum 2nd Tum 3rd Turn --5 Cu-s3 Miniature 3D Substrate ASIC System State-Key Laboratory,Fudan University -20-
-20- ASIC & System State-Key Laboratory, Fudan University http://10.12.240.202, Copyright © 2001-2004, Zhangwen Tang Voltage Profile Voltage Profile M5 M4 C1 C2 Substrate M5 M4 C1 C2 Substrate V0 0 2 V CM −S ,1 1st Turn 2nd Turn 3rd Turn CM M− ,1 CM −S ,2 CM M− ,2 CM M− ,3 CM −S ,3 Top Top Top Bottom Bottom Bottom V0 0 2 V CM M− ,1 CM M− ,2 CM M− ,3 CM −S ,3 CM −S ,2 CM S− ,1 1st Turn 2nd Turn 3rd Turn Stacked Miniature 3D [A. Zolfaghari, B. Razavi, JSSC, April, 2001] [C.C Tang, S.I. Liu, JSSC, April, 2002]