Interconnect and Packaging Lecture 3: Skin Effect

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Interconnect and PackagingLecture 3 Skin Effect
Chung-Kuan Cheng UC San Diego
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Outlines

• Transmission Line Model
• Spectrum of Configurations
• Skin Effect
• Coaxial Cable

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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

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I. Interconnect Model

• Telegraphers equation

• Propagation Constant

• Wave Propagation

• Characteristic Impedance

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I. Interconnect Model

• Propagation Constant

• Wave Propagation

• Characteristic Impedance

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I. Interconnect Model (Constants)

• AWG (American Wire Gauge
• Wire Diameter 2.54x10-(AWG10)/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

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II. Spectrum of Configurations
RLGC R L G C
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
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III. Skin Effect
Assuming that resistance and capacitance are
negligible.
Skin Depth
(Equivalent Depth of Uniform Current)
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IV. Coaxial Cable
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IV. Coaxial Cable Inductance
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IV. Coaxial Cable Inductance
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IV. Coaxial Cable Inductance
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IV. Coaxial Cable Impedance
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IV. Coaxial Cable Impedance
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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

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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