49599

# 49599 - EE 541 Class Lecture Weeks 13-14 Distributed Filter...

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EE 541 Class Lecture Weeks 13-14 Prof. John Choma, Professor Department of Electrical Engineering- Electrophysics 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] Distributed Filter Networks Fall 2006 Semester

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University of Southern California Choma: EE 541 265 Overview Of Lecture Overview Of Lecture z Lumped Line ± Tee Network ± Pi Network ± Synergy With Match Terminated Transmission Line ± Characteristics ² Transfer Function ² Impedance Properties ² Bandwidth ² Delay z Active Line ± Topology ± Design Constraints ± Compensation
University of Southern California Choma: EE 541 266 + Z(s)/2 1 Z(s ) o Z( s ) 2 s ) in o 1 V o V p V i V s s ) out z Circuit z Question ± Can A Load Impedance Be Found So That Z in (s) Z o (s), Independent Of Z 1 (s) & Z 2 (s) ? ± If Such An Impedance Can Be Determined: ² Circuit Emulates Match Terminated Transmission Line ² V i (s) / V s (s) = 0.5 z Answer ± Input Impedance ± Required Load ± Note Output Impedance Is Also Z o (s) When Source Termination Equals Load Termination, Z o (s) Load Source 11 in 2 o o s ) s ) Z (s) Z (s) Z (s) Z (s) 22  =+ +=   1 o1 2 2 Z (s) Z (s) Z (s)Z (s) 1 4Z (s) Tee Network Line Approximation Tee Network Line Approximation

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University of Southern California Choma: EE 541 267 z Circuit z Required Load ± Purely Resistive For ω >> ω l And ω < ω h ± Realizable As Pure Resistance Of Value R o For ω l << ω << ω h ² ω >> ω l Requires Large Shunt Resistance, R ² ω << ω h Requires Small Capacitance For Given R o z Match Terminated Input Port Gain + Z(s ) o Z( s ) in s ) o V o V p V i V s L/2 RC s ) out 1 2 Z (s) sL R s ) 1s R C = = + 2 l oo lh s ω s s ) R ωω   =+ +  o l ho RL C ω 1RC ω 2L C 2 R C = = == i i s V 1 H( s ) V2 Tee Network RLC “Line” Tee Network RLC “Line”
University of Southern California Choma: EE 541 268 do h 2 T( 0 ) RC LC ω == = + Z( s ) R in o V o V p V i V s L/2 R o R o Z (s) R out o i i s V 1 H( s ) V2 =≈ z Circuit ± Frequency Constraints ² Input Impedance ² Output Impedance ± Port Gain Constraint z I/O Transfer Function For R o << 2R ± Butterworth Maximally Flat Magnitude, Third Order Lowpass ± 3-dB Radial Bandwidth Is ω h ± Zero Frequency Delay o o 23 s hhh V 12 s ) V sss 2 ωωω   ++ +  Terminated Tee Network Gain Terminated Tee Network Gain

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University of Southern California Choma: EE 541 269 p p 2 s hh V 12 H( s ) V ss 1 ωω =≈   ++  + Z( s ) R in o V o V p V i V s L/2 RC R o R o Z (s) R out o z Performance Metrics z Interstage Transfer Function ± Not Butterworth MFM ± Unity Quality Factor (Q) ± Peaking, M p , Prevails ± 3-dB Bandwidth o lo ho RL C ω 1RC; R R 2 ω 2L C 2 R C = => > == () p 2 Q2 M 1.155 3 11 2 Q = 2 b 22 h 15 1 1 1 1.272 2 2Q 2Q + =− + + = = ω Terminated Tee Characteristics Terminated Tee Characteristics
University of Southern California Choma: EE 541 270 23 hh h in 2 o ss s 12 2 2 ωω ω Z( s ) R 2 ωω     ++ +   = ++ + s ) R in o V o V p

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