Multiple OLine

Multiple Coupled Lossy Transmission Line

 Description The Multiple OLine (or M OLine) component models coupled lossy transmission lines. It consists of several segments and several coupled single lines. Each segment consists of resistors and inductors that are connected in series in each single line, and of capacitors and conductors both between the lines and to the ground. The inductors are coupled to each other like in the M Transformer model. The following diagram shows the schematic of a segment with four single lines (lines=4): To achieve a symmetric model, half-valued resistors and inductors are used for the end segments. The resistance per unit length, $r$, is specified as a vector of length $\mathrm{lines}$, which each element the resistance per length of the corresponding line. The per-unit-length capacitance, conductance, and inductance parameters, $c$, $g$, and $\ell$, respectively, are vectors of length $\frac{1}{2}\mathrm{lines}\left(\mathrm{lines}+1\right)$ which specify the partial rows of the upper-triangular portion of a symmetric $\mathrm{lines}×\mathrm{lines}$ matrix. For the segment shown in the first schematic, the capacitance matrix is so the parameter $c$ is $\left[23.8,101,85.6,5.09,27.1,20.9,71.6,18.3,123,20.7\right]{10}^{-12}$. The $g$ and $\ell$ parameters are specified in the same manner. To connect to a particular line of the model, make the connection to the desired end, then select the line and use the drop-down menu in the Connections Manager to make the the connection to the desired line. The Connections Manager is found under the Properties tab whenever you select a connection line in the Model Workspace.

Connections

 Name Description Modelica ID $p$ Positive pin p $n$ Negative pin n $\mathrm{Heat Port}$ heatPort

Parameters

 Name Default Units Description Modelica ID $\mathrm{length}$ $0.1$ $m$ Length of line length $\mathrm{lines}$ 2 Number of lines lines $N$ $5$ Number of lumped segments N $c$ $\left[1,0.1,1\right]$ $\frac{F}{m}$ Capacitance per meter [1] c $g$ $\left[0.1,0.1,0.1\right]$ $\frac{S}{m}$ Conductance per meter [1] g $\ell$ $\left[1,1,1\right]$ $\frac{H}{m}$ Inductance per meter [1] l $r$ $\left[0.1,0.1\right]$ $\frac{\mathrm{\Omega }}{m}$ Resistance per meter, vector of length $\mathrm{lines}$ r ${\mathrm{\alpha }}_{G}$ $0$ $\frac{1}{K}$ Temperature coefficient of conductance, ${g}_{\mathrm{actual}}=\frac{g}{1+\mathrm{\alpha }\left(T-{T}_{\mathrm{ref}}\right)}$ alpha_G ${\mathrm{\alpha }}_{R}$ $0$ $\frac{1}{K}$ Temperature coefficient of resistance,${r}_{\mathrm{actual}}=r\left(1+\mathrm{\alpha }\left(T-{T}_{\mathrm{ref}}\right)\right)$ alpha_R $T$ $293.15$ $K$ Fixed device temperature if Use Heat Port is false T ${T}_{\mathrm{ref}}$ $300.15$ $K$ Reference temperature T_ref Use Heat Port $\mathrm{false}$ True (checked) means heat port is enabled useHeatPort

[1] The $c$, $g$, and $\ell$ vectors are of length $\frac{1}{2}\mathrm{lines}\left(\mathrm{lines}+1\right)$ and specify the upper-right triangular portion of a $\mathrm{lines}×\mathrm{lines}$ symmetric matrix.

 Modelica Standard Library The component described in this topic is from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here.