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This example compares three lossless lines with different loads. Inductance per meter (l=250 nH/m) and capacitance per meter (c=100 pF/m) are estimated for an average coaxial cable with characteristic impedance z0=√(l/c)=50 Ω. The speed of the electromagnetic wave is given by c0=1/√(l*c)=2*10⁸ m/s. Using a cable with a length of len=1 m, we obtain a delay td=len/c0=5 ns. The sources impress a single voltage pulse with height=10 V and length=td/2, starting at td/2. Due to the inner resistances of the sources ri=z0 the pulse at the input of the line (v1) has a height of 5 V. Simulate for 20 ns and compare for each of the lines: v1, v2 and i1, i2.

1. load = idle

The voltage pulse at the beginning of the line (line1.v1) starts at 2.5 ns and lasts for 2.5 ns. It arrives at 7.5 ns at the end of the line (line1.v2), and is reflected giving a pulse of 10 V (superposition of arriving and reflected pulse). At 12.5 ns the reflected pulse arrives at the beginning of the line, with a height of 5 V (voltage divider of z0 and ri). Bear in mind that the source voltage is zero at that time, i.e. a short. The current at the end of the line (line1.i2) is zero since the load is implemented as an idle. The current at the beginning of the line, line1.i1, is 5 V/z0=100 mA at 2.5 mA and 12.5 ns.

2. load = z0

The voltage pulse at the beginning of the line (line2.v1) starts at 2.5 ns and lasts for 2.5 ns. It arrives at 7.5 ns at the end of the line (line2.v2). Due to load resistance=z0 no reflection occurs. The current at the beginning of the line, line2.i1, is 5 V/z0=100 mA at 2.5 ns. The current at the end of the line, line2.i2 is -5 V/z0=100 mA at 7.5 ns.

3. load = short

The voltage pulse at the beginning of the line (line3.v1) starts at 2.5 ns and lasts for 2.5 ns. Since the load is implemented as a short, the voltage at the end of the line (line3.v2) is zero. This is possible due to a reflection with negative sign, i.e. the superposition of arriving and reflected pulse gives zero. The reflected voltage pulse arrives at 12.5 ns at the beginning of the line. The current pulse at the beginning of the line (line3.i1) is 5 V/z0=100 mA at 2.5 ns. At the end of the line (line3.i2) a reflection occurs at 7.5 ns giving a current pulse of 200 mA (superposition of arriving and reflected pulse). The reflected pulse (100 mA) arrives at 12.5 ns at the beginning of the line (line3.i1).

• May, 2021 implemented by Anton Haumer, Technical University of Applied Sciences Regensburg