PSpice Application Notes

Figure 5: Voltage waveform across the first unit capacitor C1 and the current waveform injected into the adjacent LC segment As seen earlier, the input current into the second LC segment is an exponential one with time constant=Z0C. Now the equivalent circuit for the second and third LC segments becomes: L2 50p L3 50p C2 20f C3 20f Exponential Current Input with Time Constant=Z0C L2 50p C1 20f R=Z0 50 Exponential Current Input with Time Constant=Z0C C2 20f R=Z0 50 Exponential Current Input with Time Constant=Z0C Figure 6: A step voltage input to a transmission line: Start of travel of the step (continued) The current into the second unit capacitor C2 initially increases with an increasing exponential profile to a point, after which the current shunted away from it by R=Z0 starts becoming significant and the current into C2 starts reducing and finally becomes 0, at which point voltage across C2=V*Z0/(Rs+Z0) = 0.2V in this case. The voltage and current profiles for the first six capacitors in the transmission line are illustrated below in Figure 7. The screen shot shows that the rise time of the voltage waveform keeps on slowing down as we progress down the transmission line, due to the change in profile of the currents going into each capacitor as we move down the transmission line. In this manner, the step input injected into the transmission line propagates towards the end. Note that during this process, the nature of termination of the transmission line is immaterial until the propagating wave reaches at the end of the transmission line. Until that point, during its traversal, the propagating waveform is blind to the kind of termination on the transmission line and can only see Z0 at each point it reaches. Figure 7: Voltage and current profiles for the first six capacitors in the transmission line (step applied at t=100ps) www.cadence.com 4 Accurately Modeling Transmission Line Behavior with an LC Network-based Approach

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