# Introduction

The thought of complex electronics often brings up imagery of wires and cables, connecting electrical components on a circuit board to other hardware components. Conventionally, these cables are coaxial (so named due to the central conducting line and the outer braided mesh being aligned along the same center axis) and contain four main layers. Illustrated below, these are the outer jacket, braided shield, dielectric cladding, and central conductor.

Each component has a purpose. The outer jacket protects the fragile inner components from external damage, while the braided shield acts as a “shield” to absorb external electromagnetic waves from penetrating the cable’s inner layers. The next layer is not electrically conductive, and is used to electrically separate the braided shield from central conductor.

To model the interaction between the braided shield and center conductor, there are a couple approaches that could be taken. First, each component could be separated, modeled in CAD software, and attributed with materials. The resulting models could then be imported into a multi-physics simulator and let the algorithms crank away on each of the vertices calculating the response of an impulse electric field. In this study, each component was modeled using Xyce software from Sandia National Laboratories.

A second method might be to separate the shield and conductor into separate components and create an equivalent circuit of each. Once the equivalent circuits are independently validated, the circuits could be modeled together as a feedback loop to model the electrical interaction between them. The latter option is the approach briefly discussed herein. Physically, each electrical component of the equivalent circuit represents a characteristic of the component; for instance, the capacitors, resistors, etc. of the braided cable represent the conductivity of each wire, group of wires, and the gaps between the groups of wires comprising the overall braided geometry. Capacitors represent the shield admittance while inductors represent shield impedance, and resistors represent external loads on the cable and conductor.

Below, a computer-aided design (CAD) model of the center conductor is illustrated next to its equivalent circuit. The circuit diagram consists of different components (resistors, capacitors, etc.), many of which are grouped into a unit cell of length [math] /delta z[/math]. The grouping is done for computational purposes — as the number of unit cells grows, so does the improvement of the approximation of the equivalent circuit.

In a similar manner, the braided shield can also be described via an equivalent circuit (illustrated below). The equivalent circuit for the braid is also defined by a unit cell of width [math] /delta z[/math], built to spatially overlap in lock-step with the unit cell of the center conductor of the same length. In the case of the braided shield, the unit cell contains all electrical elements except the terminal resistor [math]R_1[/math] and voltage source [math]V_0[/math].

With the equivalent circuits defined and validated for the shield and center conductor, a third equivalent circuit can be defined to model the interaction between the shield and conductor. Note that the unit cell of width [math] /delta z[/math] is still defined, and will be iterated over the length of the wire to match the empirical result. In this study, the empirically tested cable was a 22-inch long Belden 9201 cable. Within the combined model, values from the inner conductor and the braided shield will iteratively feed into each other to determine the shielding effectiveness of the braided cable as a function of frequency.

As expected, increasing the number of unit cells within the computational model increases the fidelity of the model. In this study, the number of unit cells was varied from 10 to 2000. The latter case results in a disagreement of 0.03% between the computational model and the analytic solution, illustrated in the shielding effectiveness plot below.