Interconnect and Packaging Lecture 3: Skin Effect

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

2. Outlines • Transmission Line Model • Spectrum of Configurations • Skin Effect • Coaxial Cable

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

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

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 8.85x10-12F/m • Magnetic Permeability of Air • Characteristic Impedance of Air

7. II. Spectrum of Configurations

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

9. IV. Coaxial Cable

10. IV. Coaxial Cable: Inductance

11. IV. Coaxial Cable: Inductance

12. IV. Coaxial Cable: Inductance

13. IV. Coaxial Cable: Impedance

14. IV. Coaxial Cable: Impedance

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. 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