A paper-based self-inductive folding displacement sensor for human respiration and motion signals measurement

Flexible sensing technologies are promising for human physiological signal detection, soft robotics, and wearable electronics. Inductive sensors are attractive due to low material constraints, compatibility with wireless readout, and high sensitivity for mechanical quantities such as displacement and pressure. Existing flexible inductive sensors include eddy-current, mutual-inductive, and self-inductive types; the first two often require multi-part structures that complicate wearability. Self-inductive sensors can use a single coil whose structural deformation changes inductance, offering better stability for wearable monitoring. However, many flexible sensors rely on costly materials and complex fabrication, and self-inductive sensor models and design principles remain underexplored. This work targets a low-cost, paper-based self-inductive displacement sensor with high performance and simple manufacturing, and proposes a folding strategy to significantly enhance sensitivity while maintaining simplicity. The study aims to establish a sensing mechanism, structural design principles (sensitivity–size trade-off), validate performance, and demonstrate applications in respiration and motion monitoring.

Prior flexible inductive sensing approaches include: eddy-current sensors employing metallic films and planar coils to infer pressure via resonant frequency shifts, and liquid metal-based tri-axial tactile arrays; mutual-inductive sensors where changes in relative coil positions modulate mutual inductance for angle/position monitoring. These typically require at least two separate components, limiting wearability due to structural complexity. Self-inductive sensors have realized angle/bend detection using single-coil structures (e.g., polyester film–coil–magnetostrictive laminates; solenoid coils where bending changes inter-turn angle). Despite advantages, existing flexible sensors often depend on nanomaterials and complex fabrication, increasing cost and limiting scalability. Paper substrates have emerged as low-cost, eco-friendly alternatives for flexible electronics. Sensitivity enhancement in flexible displacement sensors commonly involves additional materials or complex microstructures, increasing cost and fabrication difficulty. This work leverages the foldability of paper to enhance sensitivity via simple folding without added materials or complex structures, and develops a model-driven design framework covering coil shape, duty ratio, turns, and line width.

Sensing mechanism and modeling: The PSIFS uses a planar spiral coil on a paper substrate. Total inductance is the sum of self-inductance of rectilinear segments and their mutual inductance. During deformation (bending or folding), wire lengths remain approximately constant; the dominant change is in mutual inductance due to variation in spacing s between parallel straight segments. Analytical expressions for self- and mutual inductance were adopted from established formulations for rectangular spiral inductors. A simplified low-turn model isolates key interactions between opposing parallel segments. Analysis shows inductance increases with increasing spacing s; thus, as the ends of the sensor separate (larger displacement), inductance rises. The authors derive spacing–displacement relations for bending (Sbend) and folding (Sfold) and show folding induces larger changes in s for the same displacement, predicting greater sensitivity. Finite element simulation: A rectangular planar coil with lead connections was simulated in an AC electromagnetic solver. Boundary conditions: 1 V amplitude at 1 MHz across coil terminals. Simulations visualized voltage distribution and magnetic flux lines and computed inductance across folding angles (30°–180°). Results confirmed inductance monotonically increases as folding angle opens (i.e., displacement increases), matching analytical trends. Fabrication: Substrate: A4 paper (~80 µm). Conductor: copper foil tape (~65 µm) cut to width and length for each side; adhered to paper to form a square spiral. Copper segments were soldered (Sn60Pb40) to ensure continuity and to attach 30 AWG leads. The standard device used a 48 mm × 48 mm square coil with tunable line width (w), duty ratio (DR = w/d), and number of turns (n). Folding creases were introduced manually to implement single- or multi-fold configurations. Performance measurement: Displacement was applied via a precise electric displacement controller (Thorlabs Z825B). Inductance was measured using a precision impedance analyzer (Wayne Kerr WK6500B). Temperature and humidity effects were characterized in a chamber (HT-S-50L). Pressure tests used nonconductive, nonmagnetic PDMS blocks of different mass as loads. For respiration monitoring, the sensor was mounted in a commercial mask (3M 6001CN). Motion monitoring employed medical PE tape to affix sensors to skin or clothing. Response time was derived from measured sensor time (Tmeas) and the known actuator motion time (Tdev), with multiple displacement amplitudes tested. Structural parameter studies: Experiments examined effects of coil shape (square, hexagon, octagon), duty ratio (DR = 0.5, 1, 2), turns (n = 4.5, 6.5, 9.5+), line width (w = 1, 1.5, 2 mm), deformation mode (bending vs folding), and number of folding units (single vs triple). Sensitivity was reported as relative inductance change per displacement (ΔL/L per mm) to normalize across sizes. Trade-offs between sensitivity and sensor size were mapped to identify optimal design choices under a sensitivity–size framework.

- Folding vs bending: Analytical and experimental comparisons show folding deformation yields ~3× higher sensitivity than bending for the same geometry and displacement. - Optimal coil shape: Square coils provide the highest sensitivity—about 1.51× that of octagonal and 2.37× that of hexagonal coils—at similar sizes, due to longer opposing parallel segments contributing stronger mutual-inductance changes. - Structural parameters: Increasing turns (n) substantially boosts sensitivity (e.g., 6.5 turns ≈2.29× of 4.5 turns; 9.5 turns ≈4.83× of 4.5 turns), with better sensitivity–size balance than simply widening lines or lowering DR. Larger line width (w) also increases sensitivity (e.g., w = 1, 1.5, 2 mm yields ~0.90–0.98%, 1.23–1.36%, 1.49–1.65% ΔL/L per mm, respectively), but increases overall size. Decreasing DR improves sensitivity modestly while moderately increasing size. Triple-folding further increases sensitivity by ~1.34× over single-fold. - Final design and performance: A 48 mm × 48 mm square coil with w = 1 mm, DR = 1, n = 11.5, single fold, achieves: sensitivity ~4.44% mm⁻¹ over 0–43.2 mm range; hysteresis ~2.4%; maximum error 0.00904 across full range; minimum resolution 20 µm; response time ~81 ms (loading) and ~53 ms (relief) for 2.4 mm, and ~123/122 ms for 19.2 mm, overall ~100 ms considering instrument/controller timing; excellent repeatability between lifting and returning paths. - Stability and environmental robustness: Over >800 cycles (0–9.6 mm), inductance drifted by ~1.02% relative to initial value (long-term stability). Temperature drift ≈0.2% inductance per 10 °C change (~0.045 mm equivalent displacement error). Humidity drift ≈2.5% per 40% RH change (~0.568 mm equivalent). After 1000 full-range cycles, folding crease shows nearly no plastic deformation; adhesion between copper and paper remained intact after multiple concave/convex creases. - Sensing versatility: Angle sensing from 0° to 180° with angle sensitivity ~0.60% per degree; pressure sensing via force–displacement conversion. Respiration monitoring inside a mask distinguished breath holding, feeble, normal, deep, and rapid breathing, robust to head-movement disturbances. Motion monitoring successfully captured finger, wrist, elbow, shoulder, and knee movements, including fast motions.

The study addresses the need for low-cost, wearable, and structurally simple flexible sensors by demonstrating a paper-based self-inductive displacement sensor whose sensitivity is governed by mutual-inductance changes between parallel coil segments under 3D deformation. By exploiting a folding mechanism intrinsic to paper, the sensor achieves substantial sensitivity enhancement (~3×) without added materials or complex microstructures, directly answering the challenge of balancing performance with manufacturability and cost. The design framework systematically maps how coil shape, duty ratio, turns, line width, and folding units influence the sensitivity–size trade-off, identifying square geometry, folding deformation, and increased turns as the most effective strategies. The resulting device attains high sensitivity (4.44% mm⁻¹), wide range (43.2 mm), fine resolution (20 µm), fast response (~100 ms), and good stability, meeting practical requirements for both small and large displacements. Demonstrations in angle, pressure, respiration, and joint motion sensing validate applicability for wearable health monitoring and human–machine interfaces. The findings underscore that simple fabrication on paper can coexist with high performance, and that folding-induced geometric reconfiguration is a powerful route to improve inductive sensing in flexible platforms.

This work introduces PSIFS, a paper-based self-inductive folding displacement sensor that combines ultra-low cost and simple fabrication with high performance. A mechanism-driven design shows that folding deformation amplifies mutual-inductance changes, enabling ~3× sensitivity enhancement. A sensitivity–size design principle identifies square coils, folding deformation, and increased turns as optimal levers. The optimized sensor delivers 4.44% mm⁻¹ sensitivity over 0–43.2 mm, 20 µm resolution, ~2.4% hysteresis, ~100 ms response, and strong long-term stability. PSIFS supports multi-modal sensing—displacement, angle (~0.60% per degree), pressure—and robustly monitors respiratory states and various joint motions, highlighting its potential for wearable applications. Future work could: implement wireless readout leveraging inductive coupling; redesign lead routing (e.g., back-side electrodes) for improved wearability; and employ protective coatings (e.g., Parylene C) to extend lifetime under harsh conditions. Broader integration with textiles and low-power electronics may further advance PSIFS as a practical platform for e-skin and health monitoring.

- Folding structures may not fully self-restore after complete unfolding, motivating a practical measurement range limit (set to 43.2 mm). - Multiple folding units can introduce concave-crease compression that risks conductor fracture; a single-fold configuration was selected for robustness. - Environmental effects exist: temperature (~0.2% inductance drift per 10 °C) and humidity (~2.5% per 40% RH) cause small displacement-equivalent errors; coatings could mitigate drift for extreme environments. - Increasing line width or reducing duty ratio to boost sensitivity enlarges device size, impacting wearability; increasing turns offers a better sensitivity–size balance but still increases footprint compared to minimal designs. - Lead placement at the sensor center can be inconvenient for some wear scenarios, requiring alternative routing (e.g., back-side electrodes).