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3.4 Mismatched lines - A Physical viewpoint 137 3.4.2 Z L < Z 0 , Z L =25Ω As the switch is closed, the voltage wavefront will make its way down the line just as in the case of a short-circuited line (Figure 2.5-48), since the generator does not know in advance what termination it will encounter! As the end of the line is reached however (Figure 2.5-51), a current is allowed to flow through the termination and into the return wire which is greater than the current that can flow through the transmission line since . Similarly to the case of a short- circuit termination, the rate of flow of charge increases thereby decreasing the charge density in the top wire and increasing that of the bottom wire (blue and yellow circles in Figure 3.4-3). However this differs from the short-circuit case in that the charge concentration in the top wire remains greater than that of the bottom wire and so the voltage maintains the same polarity. However the overall voltage, which is the sum of incident and reflected voltage is lower than the incident one (there is less difference in concentration between blue and yellow carries than between red and black ones). This allows us to infer that the overall voltage is the superposition of an incident voltage and a reflected one of opposite polarity. This ties in well with the reflection coefficient calculation for this termination. Comparative Charge Spacing Figure 3.4-3 Charge distribution and voltage profile for mismatched line with We can also look at things from a circuital point of view by using an equivalent electrical model for our lossless line (Figure 3.4-4). As we get to the end of the line, we encounter a load which opposes less resistance to current flow than the transmission line hence some additional current is allowed to flow. The charges which make up this current must come from somewhere and that somewhere is the last capacitor which discharges a little so as to allow an increase in current through our load. This decreases the voltage across the capacitor to ⁄ E. The current in turn increases to ⁄ I. This is shown in Figure 3.4-4. + _ Zero Volts Vs Vs - 1 3 __ Vs V S Conquer Radio Frequency 137 www.cadence.com/go/awr