.Modelica.Electrical.Analog.Examples.Lines.CompareLosslessLines .Modelica.Electrical.Analog.Examples.Lines.CompareLosslessLinesThis 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.
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.
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.
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).