Interconnect and Packaging Lecture 3 Skin Effect Chung Kuan Cheng UC San Diego 1 Outlines I II III IV Transmission Line Model Spectrum of Configurations Skin Effect Coaxial Cable 2 I Transmission Line Model Voltage drops through serial resistance and inductance Current reduces through shunt capacitance Resistance Shunt increases due to skin effect conductance is caused by loss tangent 3 I Interconnect Model Telegrapher s equation dV z t dI z t RI z t L dz dt dI z t dV z t C GV z t dz dt Propagation Constant R j L G j C j Wave Propagation V z t V0 e z j z j t v z t Characteristic Impedance Z R j L G j C 4 I Interconnect Model Propagation Constant R j L G j C j 1 j 2 1 j 2 4 LC 2 2 LG 2 RC 2 RG 2 RG 2 LC 4 LC 2 2 LG 2 RC 2 RG 2 RG 2 LC Wave Propagation V z t V0 e z j z j t v z t Characteristic Impedance Z R j L G j C 5 I Interconnect Model Constants AWG American Wire Gauge Wire Diameter 2 54x10 AWG 10 20 Copper p 2 2uohm cm Copper thickness 1oz sqft 36um Electric Permittivity of Air 8 85x10 12F m 7 4 10 H m Magnetic Permeability of Air Characteristic Impedance of Air 376 8 6 II Spectrum of Configurations RLGC R L G 0001 0010 G 0011 G C jwC 0100 jwL 0101 jwL 0110 jwL G 0111 jwL G 1000 R 1001 R 1010 R G 1011 R G 1100 R jwL 1101 R jwL 1110 R jwL G 1111 R jwL G R j L G j C j jwC Capacitance Shunt Leaky Capacitance Inductance jwC jwC Lossless LC Line Skin Effect Derivation Skin Effect Permitivity Resistance jwC jwC RC Line Leaky Resistance Leaky RC Line Lossy Inductance jwC jwC Lossy LC Line Lossy and Leaky Inductance Transmission Line 7 III Skin Effect R j L G j C j LG Assuming that resistance and capacitance are negligible LG LG j 2 2 Skin Depth 2 Equivalent Depth of Uniform Current 8 IV Coaxial Cable ln b a 60 Z0 ln b a 2 r 1 1 1 2 R R 2 a b 2Z 0 d 0 ln b a 1 a b da b a 3 6 Z 0 77 9 IV Coaxial Cable Inductance 2 b I Ir r b dr dr 2 r 2 r a a 2 r I I 2 2 a r ln b a 2 4 a 2 a I LI r b 2 2 rdr 0 a L ln b a 8 2 2 a 10 IV Coaxial Cable Inductance I I Li I rdr 0 p 2p 1 1 1 Li R 2 p p 2 p p 2 R Li 11 IV Coaxial Cable Inductance I 0 a j Zi m 2 a I1 a j j j 12 IV Coaxial Cable Impedance 13 IV Coaxial Cable Impedance 2 2 R RDC RAC 14 HW1 Remarks on z900 Chip Processor 10x17 sqmm 38W 918MHz 250MIPS 128bits to each L2 cache chip 280um pitch chip to MCM MCM 127x127sqmm 5xTerabits s 459MHz 20 Processors 8x4MB Memory 11Knets 95mm max length on critical path 1ns on MCM 1 4ns off MCM 33um think film pitch 396um ceramic substrate 101Kpins 35 3pin sqcm 4224pins 1735pg to PCB 15 Remarks Board 553x447sqmm 1 MCM 64GB memory 24 STI 7 mils pitch 3 3width 4sep 24GB s IO 1GB s bus 240lines MBA 6GB s 10pairs STI 9 signals 1 clock 3516nets 19 788pins signals pg 8pins sqcm 16
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