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Modeling Coaxial Cables

Coaxial transmission lines can be modeled implicitly as explained in the previous articles. To define a coaxial cable, one needs to know its characteristic impedance (Z0), velocity factor (VF), length, parameters that model losses (K0, K1, K2, etc.), and the shunt admittances at each end (Y1 and Y2). Furthermore, each end or port of the line must be connected to the center of a wire segment. In this implicit model, the electromagnetic interaction between the coaxial cable shield and the wire structure is neglected, and the line ends impose boundary conditions on the voltage and current in the connected segments. However, in certain scenarios, a current can be induced that flows through the outside of the coaxial cable shield, and this current cannot be neglected. To address this, a hybrid model is used, which is explained in detail below.

In the hybrid model, the internal behavior of a coaxial cable is implicitly modeled using its parameters such as Z0, VF, length, etc. On the other hand, the outer shield is modeled by adding a wire that must be divided into segments like the rest of the structure, Fig. 1. This additional wire considers the current induced outside the coaxial cable shield.

Fig. 1: An additional wire is connected between two ends of the ports of a coaxial transmission line to model the cable shield. This wire needs to be divided into segments just like the rest of the structure.

The wire representing the shield should be connected between two ends of the segments where the cable is connected, Fig. 2. Unlike transmission lines that connect in the center of the segments, wires are connected at their ends. Hence, the additional wire representing the shield will be a segment offset from the actual position of the cable. This is not a significant concern since the segments should be small compared to the wavelength.

Fig. 2: Visualization of the sketch in Fig. 1 in the AN-SOF workspace. The short wires, each consisting of one segment, that are required to connect the wire representing the coaxial cable shield are highlighted in red.

Please be reminded that to connect one wire to another and connect the ends of the coaxial cable shield, you will need to manually divide the wires involved, as explained in Connecting Wires.

To simulate the dielectric coating of actual coaxial cables, an outer insulation can be added to the wire representing the shield, and its thickness can be input as well.

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