Digital Circuit Boards: Mach 1 GHz

2.21 Transmission Line Networks

A transmission line network includes the conductor pairs that supply or carry energy when a logic transition occurs. When a logic switch closes, waves travel over the entire logic structure. The nearby transmission lines that supply the first energy control the sag in voltage. These lines might be considered the network of interest. This network might include the following:

1. the power path connecting power to the IC (bonds, pads, traces, pins, vias and legs);

2. stubs or branches on the signal path;

3. all traces that are connected to logic 1 at the IC;

4. the ground/power plane;

5. the transmission lines that connect the decoupling capacitors;

6. the transmission lines internal to the decoupling capacitors.

The waves that transition in the network cause the voltage to sag, as energy is moved in the network. In a typical process involving just three transmission lines, 20 or 30 reflections and transmissions can take place before a useful signal might arrive at a logic gate. In practice, the details of these multiple reflections and transmissions are obscured by rise time phenomena and the fact that waves from earlier logic transitions are still creating signals.

The program outlined in the next section ignores rise time and line losses. All interconnected transmission lines are initially set at the power supply voltage. At t = 0, a first wave is generated by a switch closure, and it is assigned the wave number m = 1. Each segment that makes ...