transmission_line_models

transmission_line_models - class notes, M. Rodwell,...

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class notes, M. Rodwell, copyrighted 2009 ECE 145A / 218 C, notes set 1: Transmission Lines Mark Rodwell University of California, Santa Barbara [email protected] 805-893-3244, 805-893-3262 fax
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class notes, M. Rodwell, copyrighted 2009 Transmission Lines Geometries Characteristic Impedances Group Velocity Dispersion kin Effect Losses Skin Effect Losses (substrate) radiation losses Excitation of unwanted modes, suppression Packaging and package resonances
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types of transmission lines
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class notes, M. Rodwell, copyrighted 2009 Transmission Lines for On-Wafer Wiring W microstrip line +V geometry voltages currents I H 0V I W+2S 2 2 coplanar waveguide 0V 0V +V W I I/2 I/2 0V H 0
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class notes, M. Rodwell, copyrighted 2009 Transmission Lines for On-Wafer Wiring coplanar strips geometry voltages currents W+2S -V +V W I I 0V H 0 I I slotline 0V +V G -V 0V H 0
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class notes, M. Rodwell, copyrighted 2009 Substrate Microstrip Line W Dominant Transmission medium in H III-V microwave & mm-wave ICs Key advantage: IC interconnects have very low ground-lead inductance Ground-lead inductance: -leads to ground-bounce Miller ultiplied by IC gain -is Miller-multiplied by IC gain Key problems: rough afer grounding holes (vias) through-wafer grounding holes (vias) coupling to TM modes in substrate Via inductance forces progressively thinner wafers at higher frequencies.
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basic theory L, C, Zo, velocity, Gamma
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class notes, M. Rodwell, copyrighted 2009 Transmission Lines A pair of wires with regular spacing, dielectric loading along the length. These have inductance per unit length and capacitance per unit length. Forward and reverse waves propagate. Reflections will occur if lines are not correctly terminated
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class notes, M. Rodwell, copyrighted 2009 Transmission Lines: Basic Theory Ldz s Z gen V L Z Cdz t I z V d : line of analysis nodal basic From dt dV C dz dI dt dI L dz dV find which we from ) / ( ) / ( and ) / ( ) / ( = = + v z t V v z t V t z I v z t V v z t V t z V ) / ( ) / ( ) , ( ) / ( ) / ( ) , ( + = + + = + Z Z o o where LC v C L Z o / 1 and / = =
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class notes, M. Rodwell, copyrighted 2009 Forward and Reverse Waves ave rward voltage + wave reverse in voltage ) / ( wave forward in ) / ( v z t V v z t V + + wave forward in current ) / ( v z t V + o Z wave reverse in current ) / ( o Z v z t V +
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class notes, M. Rodwell, copyrighted 2009 Velocity and Characteristic Impedance / 1 and / o LC v C L Z = = length. unit per quantities here are and C L and light of speed the is where / , eff r c c v ε = line the of constant dielectric effective the is , eff r ε
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class notes, M. Rodwell, copyrighted 2009 Reflections s Z gen V () o l Z Z + 1 where : line of end At L Z ( ) o l l l Z Z V V + = Γ Γ = : line of beginning At 1 ( ) o s o s s gen s s Z Z Z Z V T V V + = Γ + Γ = + 1 1 where s o o s Z Z Z T + = and Need good terminations to prevent line reflections and ringing
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class notes, M. Rodwell, copyrighted 2009 Total inductance & capacitance in a length of line l length l is length line total If τ is length in that e capacitanc Then total o length Z C = is length in that inductance total and o length Z L τ = g line the on delay" light of speed " / where = = v l length τ
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class notes, M. Rodwell, copyrighted 2009
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This note was uploaded on 12/29/2011 for the course ECE 594A taught by Professor Rodwell during the Fall '09 term at UCSB.

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transmission_line_models - class notes, M. Rodwell,...

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