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

• Telegraphers equation

• Propagation Constant

• Wave Propagation

• Characteristic Impedance

5
I. Interconnect Model

• Propagation Constant

• Wave Propagation

• Characteristic Impedance

6
I. Interconnect Model (Constants)
 
7
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
8
III. Skin Effect
Assuming that resistance and capacitance are
negligible.
Skin Depth
(Equivalent Depth of Uniform Current)
9
III. Skin Effect
 

• Boundary condition
• Charges at the boundary shield the electric
  field.
• Thus, capacitance C does not change with
  frequency.

10
IV. Coaxial Cable
11
IV. Coaxial Cable Inductance
12
IV. Coaxial Cable Inductance
13
IV. Coaxial Cable Inductance
14
IV. Coaxial Cable Impedance
15
IV. Coaxial Cable Impedance
16
Skin Effect