# 329lect29 - 29 Bounce diagrams • Last lecture we obtained...

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Unformatted text preview: 29 Bounce diagrams • Last lecture we obtained the implulse-response functions Source matched to line: +- +- f ( t ) Z o I ( z, t ) V ( z, t ) z l Z o I ( z, t ) R L V ( z, t ) = τ g [ δ ( t- z v ) + Γ L δ ( t + z v- 2 l v )] and I ( z, t ) = τ g Z o [ δ ( t- z v )- Γ L δ ( t + z v- 2 l v )] for the voltage and current in the TL circuit shown in the margin where the source is matched to the line so that τ g = 1 2 — circuit response with an arbitrary input f ( t ) is obtained by convolving these with f ( t ) (as shown in Example 1 in last lecture). • The impulse-response for V ( z, t ) is depicted in the margin in the form of a bounce diagram , in which z l t τ g τ g Γ L 2 l v l v Bounce diagram – the trajectories of the impulses constituting the impulse response are plotted, with ◦ z axis in the horizontal, and ◦ t axis in the vertical extending from top to bottom – and coefficients of each impulse noted in the diagram next to the trajectory lines. – the blue line sloping down on the top is a depiction of forward propagating impulse τ g δ ( t- z v ) , 1 – the next line down is the depiction of backward propagating im- pulse τ g Γ L δ ( t + z v- 2 l v ) . Bounce diagrams are graphical representations of impulse re- sponse functions derived in TL circuit problems, and are pri- marily used to determine the implulse response functions , rather than the other way around as will be illustrated below....
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329lect29 - 29 Bounce diagrams • Last lecture we obtained...

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