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Lec14Smith

# Lec14Smith - ECE 488 RF Circuits and Systems Fall 2009...

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1 1 Swartz 06/2/15 ECE 488 – RF Circuits and Systems – Spring 2009 Lecture 13: ECE 488 RF Circuits and Systems Transmission Lines Smith Charts Impedance Matching Fall 2009 Lecture 14 2009/2/20 2 Swartz 06/2/15 ECE 488 – RF Circuits and Systems – Spring 2009 Lecture 13: Announcements Hand out copies of Smith Charts Pass around samples of transmission lines 4 Swartz 06/2/15 ECE 488 – RF Circuits and Systems – Spring 2009 Lecture 13: The tan-tan Formula – Stub Tuners S tub tuners are short stubs of transmission lines used to cancel out unwanted reactances in RF circuits. o Z 0 = z = z o Z 0 = z = z An open- circuit stub A short- circuit stub ( ) ( ) k j Z X j z Z o tan = = = ( ) ( ) k j Z X j z Z o cot = = = Short open lengths used to cancel unwanted inductive reactances Short shorted lengths used to cancel unwanted capacitive reactances k X 2 π π 2 3 π π 2 2 5 π 0 inductive capacitive k X 2 π π 2 3 π π 2 2 5 π 0 inductive capacitive 5 Swartz 06/2/15 ECE 488 – RF Circuits and Systems – Spring 2009 Lecture 13: Being inductive or capacitive does not mean stubbed transmission lines are the same as lumped elements, since T-Line Capacitors and Inductors is not proportional to as in . The frequency dependence is very different. ω ) / tan( tan ' 0 0 phase v jZ k jZ Z ω = = L j ω 6 Swartz 06/2/15 ECE 488 – RF Circuits and Systems – Spring 2009 Lecture 13: Moving up the transmission line: Position Along the Transmission Line Changes the Reflection Coefficient This is a clockwise rotation in the complex plane.

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