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:
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 up the network is assigned a unique location number. Consider a wave number 7 in segment 4. The voltage of wave 7 is WV(7). The location of wave 7 is LOC(7) = 4. The direction of WV(7) is given by DIR(7), which can be + 1 or −1. The transit time for every line segment is one of the initial parameters. The arrival time for WV(7) is the wave start time plus the transit time. The arrival time for WV(7) is given by TM(7).
When the first wave reaches the end of its segment, new waves are generated. These wave voltages are perhaps WV(2) and WV(3). If WV(2) is the transmission of WV(1) into segment 2 then we can assign LOC(2) = 2 and DIR(2) = 1. If wave WV(3) is reflected back on to line 1 then LOC(3) = 1 and DIR(3) = − 1. The wave voltage WV(2) = WV(1) × TTL12 and wave voltage WV(3) = WV(1) × RTL21. The term TTL12 is read, transmission from transmission line 1 to 2. The term RTL21 is read, reflection from line 2 back into line 1. After this transition, wave W(1) is no longer active and a flag FLG(1) is set to 1.
The program must provide reflection and transmission coefficients for both ends of every transmission line segment. The reflection coefficient for a zero impedance point (voltage source) is −1. The reflection coefficient for an open circuit is + 1. The transmission and reflection coefficients at a simple transition in characteristic impedance are discussed earlier in this chapter. If a line branches into two lines then six coefficients are required for that junction.
The program starts by incrementing time. The active waves are examined one at a time in a program loop using a counter n. If the program time is greater than an arrival time then a wave has reached its segment end. The program then generates new waves and the old wave is flagged (it is now inactive). The voltage on each segment at any time is the initial voltage plus the sum of all the flagged waves that have traveled along that segment.