PSpice Application Notes

A Step Voltage Input to a Transmission Line: Start of Travel of the Step Let's apply an input step of 0-1V by the voltage source at time t=100ps. The rise time assumed is 1fs for this step. As we saw before, for the step incident at the transmission line input, the transmission line behaves in exactly the same way as a resistor of value √(L/C) =Z0 =50ohms. So, as far the source is concerned, the equivalent circuit right at the instant of application of the step is as depicted in Figure 3. Source Rs 200 R=Z0 50 1V step 0.8V V(x,t)=0.2V (i.e., voltage at the entry point into the transmission line, at the instant of application of the step input.) Figure 3: An equivalent circuit at the step input. So the 1V step is split as 0.8V across Rs and 0.2V across R=Z0 right at the entry point into the transmission line, by simple resistive voltage division action. Now, let us examine the process of propagation of this step injected into the transmission line. As far as the advancing voltage step is concerned, on the transmission line, at any instant of its propagation to the other end until it reaches the end, the impedance=Z0 =50 ohms. Right at the entry point of the transmission line, the input current is a constant current=V/(Rs+Z0). Now, as far as the very first two LC segments in the transmission line are considered, the equivalent circuit as depicted in Figure 4. L1 50p L2 50p C1 20f C1 20f Constant Current I=V/(Rs+Z0) L1 50p C1 20f R=Z0 50 Constant Current I=V/(Rs+Z0) C1 20f R=Z0 50 Constant Current I=V/(Rs+Z0) Figure 4: First two LC segments in transmission line. In other words, it is equivalent to a constant current source=V/(Rs+Z0) driving a parallel RC combination, where R=Z0 and C=the first unit capacitance. Now the voltage across the first unit capacitor increases exponentially with a time constant= RC=Z0C, and the current taken by this capacitor decays exponentially to zero. At the same time, the current injected into the adjacent LC segment increases exponentially. The sum of the two currents is still V= (Rs+Z0). The voltage waveform across the first unit capacitor C1 and the current waveform injected into the adjacent LC segment observed from simulation is illustrated below in Figure 5. The purple waveform is the voltage across the first unit capacitor C1, the green waveform is the current injected into the second LC segment, and the red waveform is the voltage step input applied at t=100ps, probed right at the input of the transmission line (0.2V): www.cadence.com 3 Accurately Modeling Transmission Line Behavior with an LC Network-based Approach

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