LectureAid3-4

LectureAid3-4 - EE 541 Prof John Choma Professor Class...

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EE 541 Class Lecture Weeks 3 & 4 Scattering Parameter Models & Analysis Fall 2008 Semester Prof. John Choma, Professor Ming Hsieh Department of Electrical Engineering University of Southern California University Park; MC: 0271; PHE #604 Los Angeles, California 90089-0271 213-740-4692 [USC Office] 213-740-7581 [USC Fax] [email protected]

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University of Southern California EE 541 Fall 2008/ Choma 38 Overview of Lecture Overview of Lecture z Reflection Coefficients ± Voltage ± Current ± Power z Two Port Scattering Parameters ± Measurement ± I/O Transfer And Impedance Characteristics ± Relationship To Conventional Two Port Parameters z Lossless Two Port Networks ± Lossless Network Implications Of Scattering Matrix ± Fundamental Loss Filter Scattering Parameter Constraint ± Filter Design Example ² Third Order Lowpass Filter ² Topological Realization ² Confirmation Of Design Propriety Through Simulation
University of Southern California EE 541 Fall 2008/ Choma 39 rr ii IV ρ ± ir VV V =+ Reflection Concepts Reflection Concepts z Simple One Port Network z Electrical Variables ± Current ² I i Is Incident Component Of Actual Load Current ¾ Actual Current Flowing When Z l = R o (Load Matched To Characteristic Source Impedance) ¾ Incident Current: ² I r Is Reflected Component Of Load Current ± Voltage ² V i Is Incident Component Of Actual Load Voltage ¾ Actual Load Voltage Developed When Z l = R o (Load Matched To Characteristic Source Impedance) ¾ Incident Voltage: ² V r Is Reflected Component Of Load Voltage ± Reflection Coefficient ² Measure Of Matching Between Impedance And A Reference ² When Load Is Matched To Source Impedance, Reflection Coefficient Is Zero Z l I + V s + V R o III =− is o 2 R = 2 =

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University of Southern California EE 541 Fall 2008/ Choma 40 Reflection Coefficient Reflection Coefficient z Current z Voltage Z l I + V s + V R o lo ss ir i ol o ZR l o s ri i oo l loo VV III ; I RZ 2 R Z R V II I ρ I 2R R Z Z R = =− = = + ⎛⎞ ⎜⎟ = = = ++ ⎝⎠ ls s i s l o s i ZV V V ; V 2 V Z R V V ρ V 2 2 = =+ = = + = = = () r il o r o o ii o rr i i I ρ IZ R V ρ VZ R R0 VI 0R I1 ρ I V1 ρ V == + + ⎡⎤ ⎤⎡ = ⎢⎥ ⎥⎢ ⎦⎣ ⎣⎦
University of Southern California EE 541 Fall 2008/ Choma 41 Power Scattering Power Scattering z Input ± Sinusoid Of Amplitude V s ± Power ² Incident Power To Load Is P i When Z l = R o ² Reflected Power Is P r ² Total Average Power Is P = P i –P r z Average Power Dissipated In Load z Scattering Z l I + V s + V R o () 2 2 s s i oo 2 2 sl l 2 ol V2 2 V P R8 R VR I PR 2 2R Z == ⎛⎞ ⎜⎟ ⎝⎠ + ( ) 2 i r ii 2 i PP P ρ P1 ρ P =−

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University of Southern California EE 541 Fall 2008/ Choma 42 Re( ) ρ Im( ) ρ 1 1 -1 -1 ρ r ρ i | ρ Reflection Coefficient Significance Reflection Coefficient Significance z Reflection Properties ± Magnitude Is At Most One ± Load Impedance z Load Impedance Properties ± Positive Real Parts Lie Within Unit Circle ± Negative Real Loads Lie Outside Of Unit Circle ± Resistive loads Lie Along Horizontal Axis ±
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LectureAid3-4 - EE 541 Prof John Choma Professor Class...

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