1. 1 Interconnect and Packaging Lecture 3: Skin Effect Chung-Kuan Cheng UC San Diego

2. 2 Outlines I.Transmission Line Model II.Spectrum of Configurations III.Skin Effect IV.Coaxial Cable

3. 3 I. Transmission Line Model Voltage drops through serial resistance and inductance Current reduces through shunt capacitance Resistance increases due to skin effect Shunt conductance is caused by loss tangent

4. 4 I. Interconnect Model Telegrapher’s equation: Propagation Constant: Wave Propagation: Characteristic Impedance

5. 5 I. Interconnect Model Propagation Constant: Wave Propagation: Characteristic Impedance

6. 6 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 -12 F/m Magnetic Permeability of Air Characteristic Impedance of Air

7. 7 II. Spectrum of Configurations RLGCRLGC 0001(jwC)Capacitance 0010(G)Shunt 0011(G+jwC)Leaky Capacitance 0100(jwL)Inductance 0101(jwL)(jwC)Lossless LC Line 0110(jwL)(G)Skin Effect Derivation 0111(jwL)(G+jwC)Skin Effect + Permitivity 1000(R)Resistance 1001(R)(jwC)RC Line 1010(R)(G)Leaky Resistance 1011(R)(G+jwC)Leaky RC Line 1100(R+jwL)Lossy Inductance 1101(R+jwL)(jwC)Lossy LC Line 1110(R+jwL)(G)Lossy and Leaky Inductance 1111(R+jwL)(G+jwC)Transmission Line

8. 8 III. Skin Effect Skin Depth (Equivalent Depth of Uniform Current) Assuming that resistance and capacitance are negligible.

9. 9 IV. Coaxial Cable

10. 10 IV. Coaxial Cable: Inductance

11. 11 IV. Coaxial Cable: Inductance

12. 12 IV. Coaxial Cable: Inductance

13. 13 IV. Coaxial Cable: Impedance

14. 14 IV. Coaxial Cable: Impedance

15. 15 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

16. 16 HW1: 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