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Unformatted text preview: 30 Multi-line circuits • In this lecture we will extend the bounce diagram technique to solve distributed circuit problems involving multiple transmission lines. • One example of such a circuit is shown in the margin where two distinct TL’s of equal lengths have been joined directly at a distance l 2 away from the generator. +- f ( t ) R g = 2 Z 1 R L = Z 2 z l Load Z 1 Z 2 = 2 Z 1 l 4 81 τ g = Γ g = Γ 12 = 1 3 τ 12 = 4 3 Γ L = 0 1 3 1 9 1 27 1 81 4 9 t l/ 2 v 2 = 2 v 1 v 1 – The impulse response of the system can be found by first con- structing the bounce diagram for the TL system as shown in the margin. – In this bounce diagram, z = l 2 happens to be the location of ad- ditional reflections as well as transmissions because of the sudden change of Z o from Z 1 to Z 2 = 2 Z 2 . These reflections and transmissions between line j and k — transmis- sion from j to k , and reflection from k back to j — can be computed with reflection coefficient Γ jk = Z k- Z j Z k + Z j and transmission coefficient τ jk = 1 + Γ jk that ensure the voltage and current continuity at the junction 1 – Z j is the characteristic impedance of the line of the incident pulse, while – Z k is the impedance of the cascaded line into which the transmitted...
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This note was uploaded on 12/04/2010 for the course ECE 329 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.
- Fall '08