Closed-Form Solutions for Current Distribution in Ladder-Type Textile Heaters

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