Pulse Propagation on TLs.
The bounce diagram can be used to analyze the transient response of a TL to other types of excitations besides the unitstep, which is all we’ve considered to this point. For example, another very useful excitation type is the pulse input:
We can easily use a bounce diagram to solve for the voltage (or current) on the TL if we consider this pulse input to be the sum of two unit-step voltages:
The sum of these two unit-step voltages gives the pulse shown
Use Bounce Diagram for V(z,t) vs. t at a Fixed z
To use the bounce diagram in this situation:
(i.) Pick a position z0 at which to plot V ((z0,t) ) versus time.
(ii.) Draw a vertical line at z0. It intersects the sloping lines at points P1 through P12 above.
(iii.) At each of these intersection points, draw horizontal lines and label these times t1 through t12. These are the times at which new wave fronts arrive and abruptly change the voltage at z0.
(iv.) The voltage at z0 versus time is then:
Depending on the width of the input pulse, these voltages will be different, as we’ll see in the next example
Example N15.1: Imagine that a high speed digital logic gate (modeled by a pulse voltage source of amplitude 1 V, pulse width of 200 ps, and output resistance 900 beta) drives a load of 25 beta through a 100-beta microstrip line (u = 200 m/ u s) that is 8 cm long. Sketch the voltage at the load V((L,t )
). We can model this interconnection problem using a transmission line as shown:
For this TL,
At time t = 0+, draw the equivalent lumped-element circuit at the input to the TL:
By voltage division in this circuit
We are requested to plot V( (z = L,t) ). Forz0 = L, since we’re looking at the load end, then referring to the bounce diagram in
Sketch of the output voltage versus time: