Single-layer tri-state switching as an economical method to address linear light-emitting diode arrays

This paper reports on new schemes based on the concept of tri-state switching for routing linear arrays of light-emitting diodes (LEDs) on slim substrates. The schemes use a minimal number of wires in single-metal planar technologies, where wires are not allowed to cross. They have in common that the number of LEDs, N_L, addressable by N_W wires is given by N_L = 4N_W − 6. The designs are built on a family of hierarchically interconnected structures with (2ⁿ⁺¹ − 2) LEDs and (2ⁿ⁻¹ + 1) wires, for positive integers n. A process termed linear expansion straightforwardly extends them to arbitrary values of N_W and adds 4 LEDs with each additional wire. Expressions for series resistances and the average wire length normalized to the array length are derived. In hierarchical designs, the average normalized wire length asymptotically approaches 7/12 for large n. A matrix formulation graphically elucidates the new interconnection schemes.