Printed Electronics: Effects of Bending and a Self-Compensation Means

Abstract

A highly-worthy attribute of printed electronics is its possible realization on flexible-substrates that can be molded/bent. Heretofore, investigations into the effects of bending to printed circuit-elements/circuits remain not only largely incomplete, but an electronic/layout-means to mitigate said effects remains unreported/unresolved. We present a comprehensive investigation into the effects of concave/convex bending to printed circuit-elements and basic-circuits. The variations of said circuit-elements range from mild to severe, depicting that for accurate transfer-functions, capacitor-based circuits are preferred; and the variation directions of capacitors and resistors are the same, but the converse of transistors. For the inverter and ring-oscillator, the variations range from moderate-to-very-severe and severe-to-extremely-severe respectively for diode-connected and zero- $V_{GS}$ connected topologies. This depicts that diode-connected circuits are preferred; and for speed, concave-bending is preferred. For the op-amp, the gain and gain-bandwidth variations range from mild-to-severe; and concave- and convex-bending is respectively preferred for gain-bandwidth and gain. By leveraging on the process-simplicity of our fully-additive all-air low-temperature printing processes, we propose a novel localized self-compensation means involving the partition of a given circuit-element/circuit into two-halves, each placed on the top/bottom of the flexible-substrate surface. The proposed means is highly efficacious– the reduction of variations ranges from $\sim 2\times $ to $> 100\times $ , yet without power, hardware or substrate-area overheads.