Closed-form solutions for current distribution in ladder-type textile heaters

Textile heaters are made of knitted conductive yarns integrated into the fabric, making them stretchable, washable, breathable, and suitable for close-to-skin wear. The non-zero resistance in the lead wires, however, causes non-uniform power distribution, presenting a design challenge. To address this, the electrical performance of the heaters is modelled as an n-ladder resistor network. Using the finite difference method, simple, closed-form expressions are derived for networks with the power source connected to input terminals A1B1 and A1Bn, respectively. The results are exact and are used to derive approximations and design criteria. Solutions for ladder networks as presented in this paper apply to a wider class of physical problems, such as irrigation systems, transformer windings, and cooling fins.