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My issue concern the definition of series connection of multiple transmission lines described by the so called constant parameter model, to be next simulated in EMTP-RV. Let us take as an example two transmission lines of length respectively $$\Delta x_1,\Delta x_2$$ described by the telegapher's equations

$$ L_i\frac{\partial I_i(x,t)}{\partial t}=-R_iI_i(x,t)+\frac{\partial V_i(x,t)}{\partial x}\\ C_i\frac{\partial V_i(x,t)}{\partial t}=-G_iV_i(x,t)+\frac{\partial I_i(x,t)}{\partial x}. $$

with i=1,2. Is it possible to obtain an equivalent aggregated model in the form of telegrapher's equation via linear combination of the two systems? By setting for example $$\Delta x_{eq}=\Delta x_1+\Delta x_2$$ which are the corresponding values of $$L_{eq},C_{eq},R_{eq},G_{eq}$$ ?

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Is it possible to obtain an equivalent aggregated model in the form of telegrapher's equation via linear combination of the two systems?

No, it's not possible.

Reason: at the junction of two real but different transmission lines, there will be a reflection coming back to the source due to the disparity of the two characteristic impedances and, this cannot be adequately modelled by a single "new and modified" transmission line because it will not naturally produce reflections at some distance along its length.

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  • \$\begingroup\$ So how one can usually approach the problem of aggregation for multiple series-connected transmission lines described by telegrapher's equations? Considering that in my case the aggregation is necessary for reducing computational cost, what's your suggestion about the procedure to be followed? \$\endgroup\$ – Daniele Jul 16 '20 at 10:10
  • \$\begingroup\$ There's nothing usual about it when it comes to transmission of data - you will get corruptions so it is to be avoided. If you are, on the other hand, interested in sending carrier modulated RF signals then it's a bit different because you can terminate is apparently the "wrong" impedance and successfully transmit an RF signal. But this requires knowing the length of each t-line and calculating a few things. So, it's not a usual thing to have to do and I've never seen a derivation using the telegraphy equations in this respect. \$\endgroup\$ – Andy aka Jul 16 '20 at 10:15
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As Andy suggests, the discontinuity must be modeled. This upset of 1_D energy movement needs to keep track of bi_directional energy, which is not an assumption or intention of the standard Telegrapher maths.

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