skineffect-presentation-Interconnect.pdf

Skin effect

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 ModelRΔlLΔl
CΔl
RΔlLΔl
CΔl…
i(z,t)
RΔlLΔl RΔlLΔl
⚫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: ),(
),(),(
),(
),(
),(
tzGV
dt
tzdV
C
dz
tzdI
dt
tzdI
LtzRI
dz
tzdV
−−=
−−=
•Propagation Constant:  jCjGLjR +=++= ))((
•Wave Propagation: 

//,),(
0 ===
+−−
tzveVtzV
tjzjz
•Characteristic Impedance )/()( CjGLjRZ  ++=

5. 5
I. Interconnect ModelLCRGRGRCLGLCj
LCRGRGRCLGLCj
2222224
2222224
)(])()[()(
2
1
)(])()[()(
2
1


+−++++
−++++=+
•Propagation Constant:
•Wave Propagation: 

//,),(
0 ===
+−−
tzveVtzV
tjzjz
•Characteristic Impedance )/()( CjGLjRZ  ++=  jCjGLjR +=++= ))((

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 =8.376/ mH/104
7−


7. 7
II. Spectrum of Configurations jCjGLjR +=++= ))((
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

8. 8
III. Skin Effect

2
= 22
))((
LG
j
LG
LGj
CjGLjR



+

++=
Skin Depth
(Equivalent Depth of Uniform Current)
Assuming thatresistance and capacitance
are negligible.

9. 9
IV. Coaxial Cable02
,
2
),
11
(
2
1
Z
R
ba
R ==+= 


 ===
+===
776.3/
/1/ln0
0Zab
baab
da
d )/ln(
60
2
)/ln(
0 ab
ab
Z
r

=

10. 10
IV. Coaxial Cable: InductanceabL
rdr
a
I
brLI
a
/ln
28
2),(
0
2
2






+=
= ab
I
ra
a
I
dr
r
I
dr
a
Ir
r
br
b
a
a
r
/ln
2
)(
4
22
),(
22
2
2
2








+−=
+= 

11. 11
IV. Coaxial Cable: Inductancei
LR= 








2
11
,
2
1
2
2
0
pp
R
pp
L
p
I
rdr
p
I
IL
i
i
====
==

12. 12
IV. Coaxial Cable: Inductance)/()(
/
)(
)(
2
)(
1
0





jj
m
jaI
jaI
a
Z
i
+=
=

13. 13
IV. Coaxial Cable: Impedance

14. 14
IV. Coaxial Cable: Impedance22
ACDC
RRR +=

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