In Section 2.12, we discussed wave action where energy flowed from an ideal voltage source through a short transmission line and was dissipated in a resistor. An increment of energy was transferred for each round trip of the wave in the transmission line. In that discussion, reflections occurred at abrupt changes to the characteristic impedance. In the case of a TTL, the reflection process still takes place but on a continuous basis. A linear change in characteristic impedance results in a continuous reflection process. Of course, there is a reflection at the edges of a board, but this occurs at a much later time. The phenomena we consider takes place before the wave action reaches the edge of the board.

To get some idea of how this TTL works, consider the ideal case where the capacitance of the tapered line is charged to a voltage *V*. Assume an ideal logic switch and a load of 5 ohm. When the switch closes, if the tapered entry point looks like 50 ohms, the voltage drops to 9.1% of *V*. We need to find out how long it takes for the voltage at the load to reach 95% of *V*.

At the moment of switch closure, the wave that propagates into the TTL is − 9.909 V. As the wave progresses into the tapered line, the continuous nature of the reflection reduces the magnitude of this wave. Stated another way, as the wave propagates radially, the wave amplitude decreases and the voltage across the leading edge rises. We are interested in the ...

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