594_set_2

594_set_2 - ECE145C/218C notes M Rodwell copyrighted ECE...

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ECE145C /218C notes, M. Rodwell, copyrighted ECE 145C / 218 C, notes set 2: Transmission Lines Mark Rodwell University of California, Santa Barbara [email protected] 805-893-3244, 805-893-3262 fax
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ECE145C /218C notes, M. Rodwell, copyrighted Transmission Lines Geometries Characteristic Impedances Group Velocity Dispersion 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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ECE145C /218C notes, M. Rodwell, copyrighted Transmission Lines for On-Wafer Wiring H W microstrip line coplanar waveguide 0V 0V 0V +V 0V +V geometry voltages currents I I H W W+2S I 0 I/2 I/2
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ECE145C /218C notes, M. Rodwell, copyrighted Transmission Lines for On-Wafer Wiring coplanar strips slotline 0V 0V +V -V geometry voltages currents H G I 0 0V +V H W W+2S I 0 I -V I
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ECE145C /218C notes, M. Rodwell, copyrighted Substrate Microstrip Line Key advantage: IC interconnects have very low ground-lead inductance Ground-lead inductance: -leads to ground-bounce -is Miller-multiplied by IC gain H W Dominant Transmission medium in III-V microwave & mm-wave ICs Key problems: 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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ECE145C /218C notes, M. Rodwell, copyrighted 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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ECE145C /218C notes, M. Rodwell, copyrighted Transmission Lines: Basic Theory Ldz L Z Cdz gen V s Z LC v C L Z Z v z t V Z v z t V t z I v z t V v z t V t z V dt dV C dz dI dt dI L dz dV o o o / 1 and / where ) / ( ) / ( ) , ( ) / ( ) / ( ) , ( find which we from ) / ( ) / ( and ) / ( ) / ( : line of analysis nodal basic From = = + = + + = = = + +
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ECE145C /218C notes, M. Rodwell, copyrighted Forward and Reverse Waves wave reverse in current ) / ( wave forward in current ) / ( wave reverse in voltage ) / ( wave forward in voltage ) / ( o o Z v z t V Z v z t V v z t V v z t V + + + + +
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ECE145C /218C notes, M. Rodwell, copyrighted Velocity and Characteristic Impedance line the of constant dielectric effective the is and light of speed the is where / length. unit per quantities here are and / 1 and / , , eff r eff r o c c v C L LC v C L Z ε ε = = =
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ECE145C /218C notes, M. Rodwell, copyrighted Reflections () s o o s o s o s s gen s s o l o l l l Z Z Z T Z Z Z Z V T V V Z Z Z Z V V + = + = Γ + Γ = + = Γ Γ = + + and 1 1 where : line of beginning At 1 1 where : line of end At L Z gen V s Z Need good terminations to prevent line reflections and ringing
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ECE145C /218C notes, M. Rodwell, copyrighted Total inductance & capacitance in a length of line o length o length length Z L Z C l τ = τ = is length in that inductance total and is length in that e capacitanc Then total is length line total If l line the on delay" light of speed " / where = = v l length τ
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ECE145C /218C notes, M. Rodwell, copyrighted Lumped models of very short transmission lines L/2 L/2 C L C/2 C/2 Pi-model T-model section or T a as
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594_set_2 - ECE145C/218C notes M Rodwell copyrighted ECE...

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