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Use full variable names to improve readability
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Put <code> around Modelica variables
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christiankral committed Jun 26, 2021
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26 changes: 13 additions & 13 deletions Modelica/Electrical/Analog/Examples/Lines/CompareLosslessLines.mo
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Expand Up @@ -129,34 +129,34 @@ This example compares three lossless lines with different loads.
Inductance per meter (l=250&nbsp;nH/m) and capacitance per meter (c=100&nbsp;pF/m) are estimated for an average coaxial cable with characteristic impedance z0=&radic;(l/c)=50&nbsp;&Omega;.
The speed of the electromagnetic wave is given by c0=1/&radic;(l*c)=2*10<sup>8</sup>&nbsp;m/s. Using a cable with a length of len=1&nbsp;m, we obtain a delay td=len/c0=5&nbsp;ns.
The sources impress a single voltage pulse with height=10&nbsp;V and lenght=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&nbsp;V.
Simulate for 20&nbsp;ns and compare for each of the lines: <code>v1, v2</code> and <code>i1, i2</code>.
Due to the inner resistances of the sources ri=z0 the pulse at the input of the line (<code>v1</code>) has a height of 5&nbsp;V.
Simulate for 20&nbsp;ns and compare for each of the lines: <code>v1</code>, <code>v2</code> and <code>i1</code>, <code>i2</code>.
</p>
<h4>1. load = idle</h4>
<p>
The voltage pulse at the beginning of the line (v1) starts at 2.5&nbsp;ns and lasts for 2.5&nbsp;ns. It arrives at 7.5&nbsp;ns at the end of the line (v2),
The voltage pulse at the beginning of the line (<code>line1.v1</code>) starts at 2.5&nbsp;ns and lasts for 2.5&nbsp;ns. It arrives at 7.5&nbsp;ns at the end of the line (<code>line1.v2</code>),
and is reflected giving a pulse of 10&nbsp;V (superposition of arriving and reflected pulse).
At 12.5&nbsp;ns the reflected pulse arrives at the beginning of the line, with a height of 5&nbsp;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 (i2) is zero since the load is implemented as an idle.
The current at the beginning of the line i1 is 5&nbsp;V/z0=100&nbsp;mA at 2.5&nbsp;mA and 12.5&nbsp;ns.
The current at the end of the line (<code>line1.i2</code>) is zero since the load is implemented as an idle.
The current at the beginning of the line, <code>line1.i1</code>, is 5&nbsp;V/z0=100&nbsp;mA at 2.5&nbsp;mA and 12.5&nbsp;ns.
</p>
<h4>2. load = z0</h4>
<p>
The voltage pulse at the beginning of the line (v1) starts at 2.5&nbsp;ns and lasts for 2.5&nbsp;ns. It arrives at 7.5&nbsp;ns at the end of the line (v2).
The voltage pulse at the beginning of the line (<code>line2.v1</code>) starts at 2.5&nbsp;ns and lasts for 2.5&nbsp;ns. It arrives at 7.5&nbsp;ns at the end of the line (<code>line2.v2</code>).
Due to load resistance=z0 no reflection occurs.
The current at the beginning of the line i1 is 5&nbsp;V/z0=100&nbsp;mA at 2.5&nbsp;ns.
The current at the end of the line i2 is -5&nbsp;V/z0=100&nbsp;mA at 7.5&nbsp;ns.
The current at the beginning of the line, <code>line2.i1</code>, is 5&nbsp;V/z0=100&nbsp;mA at 2.5&nbsp;ns.
The current at the end of the line, <code>line2.i2</code> is -5&nbsp;V/z0=100&nbsp;mA at 7.5&nbsp;ns.
</p>
<h4>3. load = short</h4>
<p>
The voltage pulse at the beginning of the line (v1) starts at 2.5&nbsp;ns and lasts for 2.5&nbsp;ns.
Since the load is implemented as a short, the voltage at the end of the line (v2) is zero.
The voltage pulse at the beginning of the line (<code>line3.v1</code>) starts at 2.5&nbsp;ns and lasts for 2.5&nbsp;ns.
Since the load is implemented as a short, the voltage at the end of the line (<code>line3.v2</code>) 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&nbsp;ns at the beginning of the line.
The current pulse at the beginning of the line (i1) is 5&nbsp;V/z0=100&nbsp;mA at 2.5 ns.
At the end of the line (i2) a reflection occurs at 7.5&nbsp;ns giving a current pulse of 200&nbsp;mA (superposition of arriving and reflected pulse).
The reflected pulse (100&nbsp;mA) arrives at 12.5&nbsp;ns at the beginning of the line (i1).
The current pulse at the beginning of the line (<code>line3.i1</code>) is 5&nbsp;V/z0=100&nbsp;mA at 2.5 ns.
At the end of the line (<code>line3.i2</code>) a reflection occurs at 7.5&nbsp;ns giving a current pulse of 200&nbsp;mA (superposition of arriving and reflected pulse).
The reflected pulse (100&nbsp;mA) arrives at 12.5&nbsp;ns at the beginning of the line (<code>line3.i1</code>).
</p>
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