\\
\beta (1+\alpha)                    & \beta (1+\gamma)                  & \delta                            & (1+\eta)\sqrt{\frac{Z_4}{Z_3}}    \\
\beta (1+\alpha)                    & \beta (1+\gamma)                  & (1+\delta)\sqrt{\frac{Z_3}{Z_4}}  & \eta                              \\
\end{bmatrix},
\label{eq:differential_load_scattering_matrix}\end{aligned}$$

where $$\begin{aligned}
\alpha &= \frac{(Z_{L_{1}}+Z_3\parallel Z_4)\parallel Z_2 -Z_1}{(Z_{L_{1}}+Z_3\parallel Z_4)\parallel Z_2 +Z_1}\\
\beta  &= \frac{Z_3\parallel Z_4}{Z_3\parallel Z_4 +Z_{L_{1}}}\\
\gamma &= \frac{(Z_{L_{1}}+Z_3\parallel Z_4)\parallel Z_1 -Z_2}{(Z_{L_{1}}+Z_3\parallel Z_4)\parallel Z_1 +Z_2}\\
\delta &= \frac{(Z_{L_{1}}+Z_1\parallel Z_2)\parallel Z_4 -Z_3}{(Z_{L_{1}}+Z_1\parallel Z_2)\parallel Z_4 +Z_3}\\
\epsilon  &= \frac{Z_1\parallel Z_2}{Z_1\parallel Z_2 +Z_{L_{1}}}\\
\eta   &= \frac{(Z_{L_{1}}+Z_1\parallel Z_2)\parallel Z_3 -Z_4}{(Z_{L_{1}}+Z_1\parallel Z_2)\parallel Z_3 +Z_4}
\label{eq:differential_load_scattering_matrix_parameters}\end{aligned}$$ and $Z_{1\dots 4}$ are the reference impedances at port 1…4 respectively and $\parallel$ is the parallel resistance operator.

Measurements results {#sec:comparison_simulation}
====================

In this section, we present measurement results used to justify the need of a mixed-mode cable representation in PLNs.

Our setup is made by a three wire 10 m long power line cable Artic Grade 3183YAG 3x1.5 mm. After measuring its MMSM using a vector network analyzer, we terminated the cable with a load between conductors 1 and 2 having $Z_{L1}=100 \Omega$ and different values of $Z_{P1}$ and $Z_{P2}$. By cascading the cable and load MMSMs, we obtained an equivalent MMSM that has been analyzed as reported in the following.

Assuming to inject only a differential signal between conductors 1 and 2 (corresponding to 