Lec13Tlines

# Lec13Tlines - 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 Reflection Coefficients Fall 2009 Lecture 13 2009/2/16(18) 4 Swartz 06/2/15 ECE 488 – RF Circuits and Systems – Spring 2009 Lecture 13: Modeling a Transmission Line (1) Transmission line effects become important When their length becomes comparable with a fraction of a wavelength. When the time to propagate to the other end becomes comparable to other circuit response times. This model uses lumped elements Series inductances – slow build up of currents at other end Parallel capacitances – shunt off currents before reaching other end No resistances shown here (usually small, but can be added to model as a series element if losses need to be modeled) . 5 Swartz 06/2/15 ECE 488 – RF Circuits and Systems – Spring 2009 Lecture 13: Modeling a Transmission Line (2) Consider a transmission line with a characteristic impedance of Z 0 , attached to of load of impedance Z 0 , then its input impedance is Z 0 . Adding the lumped elements of model Cannot change input impedance L has units of H/m; C has units of F/m. 6 Swartz 06/2/15 ECE 488 – RF Circuits and Systems – Spring 2009 Lecture 13: Modeling a Transmission Line (3) Compute the input impedance: 0 0 0 0 0 1 1 1 xZ C j Z x L j x C j Z x C j Z x L j Z Z δ ω + + = + + = + 0 0 1 xZ C j Z + 2 0 0 ) ( 0 2 lim xZ C j Z x = Consider the second term: = 0 0 1 1 xZ C j xZ C j 2 0 2 2 2 0 0 ) ( 1 ) 1 ( Z x C xZ C j Z + 7 Swartz 06/2/15 ECE 488 – RF Circuits and Systems – Spring 2009 Lecture 13: Modeling a Transmission Line (4) Reducing to ) ( 2 0 0 2 0 0 0 Z C L x j Z xZ C j Z x L j Z Z + = + = + ωδ What happens when ? C L Z = 0 0 0 Z Z Z = + What does this mean?

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Lec13Tlines - ECE 488 RF Circuits and Systems Fall 2009...

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