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Page 2 of 15 Romano et al. Soft Sci 2024;4:31 https://dx.doi.org/10.20517/ss.2024.24

INTRODUCTION
In recent years, pressure sensors have attracted considerable interest due to their potential in diverse
applications, ranging from healthcare to robotics. The demand for sensitive pressure sensing media is
increasing significantly . Their versatility is a major reason for this interest; for instance, when embedded
[1-3]
[4,5]
in wearable chest straps, pressure sensors can measure breathing activity , or heart rate by sensing the
[6]
small displacements generated by cardiac mechanics on the chest surface . Additionally, these sensors are
[7]
[8]
utilized in robotics for tactile sensing and human motion monitoring , and in clinical applications, such
as in anesthesiology, to detect the epidural space using the loss of resistance method .
[9]
The main limitation of traditional pressure sensors is their lack of flexibility, which has encouraged the
scientific community to further investigate this field [10-12] . Thus, there is a growing need for tunable and
flexible solutions capable of addressing different types of stimuli and accurately detecting dynamic pressure
across a wide range- from ultra-low (< 1 kPa), low (1-10 kPa), medium (10-100 kPa), to high (> 100 kPa) -
without compromising sensitivity [13,14] . Recent advances have introduced several innovative sensing
solutions, and the concept of soft sensors has emerged [15-17] , especially in human-machine and wearable
electronics [18,19] . Various sensing elements have been proposed, featuring different structures and
transduction mechanisms, including capacitance [20-22] , piezoresistivity [23-25] , and piezoelectricity [10,26,27] .

Among these, piezoresistive flexible pressure sensors have been widely studied due to their simple operating
principle. However, they face limitations such as low sensitivity, nonlinearity, high hysteresis, poor stability,
and unsuitability for low-pressure ranges [7,23,28] . Conversely, capacitive sensors have gained significant
attention due to their advantageous characteristics [29,30] , including low sensitivity to temperature and
[31]
humidity, low power consumption, and highly repeatable response . However, they are typically suitable
for high-pressure range applications and are limited by poor linearity, and susceptibility to parasitic
[32]
[31]
capacitance .
In this context, the magnetic transduction mechanism offers several advantages, such as linearity, reduced
hysteresis, high repeatability and ease of fabrication [7,28,33] . This last factor is particularly noteworthy, as it
contrasts with the previously discussed transduction mechanisms that typically require complex and
challenging manufacturing processes, thereby complicating any modifications to their measurement
range [34,35] . In this context, integrating air chambers into the deformable elements of piezoresistive or
capacitive pressure sensors has shown promising potential for adjusting their stiffness [22,36-38] . However, the
impact of these factors, especially their shape, on soft magnetic sensors remains unexplored. Building on
these insights, we developed pressure sensors consisting of a Hall sensor and a soft element embedding a
magnet. Our study was designed to enhance the tunability of soft magnetic pressure sensors through
variations in the shape and material of the soft element. This methodology aims to extend the maximum
detectable pressure range of these sensors, thereby broadening their applicability without necessitating
changes to the fundamental magnetic and electronic architecture. We produced and metrologically
characterized cylindrical-shaped sensors, implementing a Finite Element Method (FEM) model. These
sensors were realized using five materials with varying stiffnesses and three different shapes: a solid cylinder,
a cylindrical air chamber, and a domed air chamber. Lastly, we demonstrated the applicability of the
produced sensors across various fields, including healthcare and robotics. This was achieved by recording
finger-induced pressures (contact, soft touch, pressing), finger tapping, and chest deformations for non-
intrusive measurement of breathing at different respiratory frequencies.