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

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

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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

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4 I. Interconnect Model Telegraphers equation: Propagation Constant: Wave Propagation: Characteristic Impedance

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

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6 I. Interconnect Model (Constants)

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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

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

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9 III. Skin Effect Boundary condition: Charges at the boundary shield the electric field. Thus, capacitance C does not change with frequency.

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10 IV. Coaxial Cable

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11 IV. Coaxial Cable: Inductance

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12 IV. Coaxial Cable: Inductance

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13 IV. Coaxial Cable: Inductance

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14 IV. Coaxial Cable: Impedance

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15 IV. Coaxial Cable: Impedance

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Skin Effect 16

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