**1. Introduction**

Dielectric characterization of materials is crucial to understand the iteration between electromagnetic waves with matters [1,2]. In order to fully develop textile-based technology, the dielectric properties of fabrics need to be quantified. These properties are a ffected by external factors, such as moisture or relative humidity (RH) content and temperature [3]. Previous works [4] have studied the impact of temperature on the dielectric properties of textiles, but without considering the experimental results on several scenarios. There are several cases where textile-based devices must withstand changes in temperature without changing its overall performance, so a deep understanding of the response under di fferent temperature conditions is needed [5]. In addition, an understanding of this phenomenon can be used for sensing applications. Temperature is a crucial parameter to be measured in several fields and applications such as infrastructures, system maintenance, the food industry or body sensing [4,6,7].

Recently developed technologies within the metamaterials discipline have looked into this topic as well. Where the field theory is used to relate electromagnetic fields with parameters such as the permittivity (ε) and how these change as a function of temperature [8,9]. According to microwave theory, material characterization can be performed using two complementary methods: resonant and non-resonant [10,11]. A general rule is to use non-resonant methods when the dielectric properties of a material over a frequency range are unknown and resonant ones for a specific set of discrete frequencies [12]. Among the resonant methods, resonators such as microstrip antennas are simple, low profile non-destructive solutions to evaluate the behavior of fabrics' dielectric properties through temperature. These antennas are mainly a sandwich structure composed of two kinds of materials: one dielectric for the substrate and another one conductive [13–15]. The principle of operation is using the shift of the antenna's resonant frequency (fr) as a passive sensor, due to the e ffect of temperature changes on the dielectric properties of the fabric substrate [4]. In electromagnetism, the absolute permittivity, often known simply as permittivity explains how a material interacts when an electric field is applied to it

$$
\varepsilon = \varepsilon\_{\mathbf{r}} \varepsilon\_0 = \varepsilon' - \mathbf{j} \text{ } \varepsilon'' \tag{1}
$$

where ε0 is the vacuum permittivity (~8.85419 × 10−<sup>12</sup> <sup>F</sup>·m<sup>−</sup>1) and εr is the relative permittivity, also known as the dielectric constant, where ε is the relative permittivity and ε" is the loss index. The dielectric constant accounts for the molecules' polarization in the material, when an electric field is applied. The dielectric constant increases with temperature, due to the increased mobility of polar molecules, which allows them to align more easily with the electric field [16]. The higher the frequency of operation, the more sensitive the antenna is to temperature changes, due to the shorter wavelength. In this study, we did not consider the size variations due to thermal expansion of the antenna, since the porous nature of fabrics, makes this e ffect negligible [3]. In addition, we minimized the e ffect of moisture content, by using encapsulation inside an insulator box and limiting the time of each measurement to 15 min. Other precautions such as thermal sleeves were used during the test campaigns.

In addition to dielectric characterization through temperature, microstrip patches fabricated and tested within this paper can be used for passive temperature sensing within wearable applications. They provide advantages such as low cost, low profile, lightweight, integration into clothing and shielding e ffect of/from the body due to the full ground plane [17,18]. Within wearable systems, flexibility and conformability are fundamental characteristics in order to include the functionality of computers into individuals' daily lives. Allowing the user to benefit from the performance of the system without restricting the user activity and causing any behavior modification [19–21]. Di fferent options for dielectric materials arise for building flexible wearable antennas, such as several types of papers, Kapton, polyethylene terephthalate (PET) [22], polydimethylsiloxane (PDMS) [23], liquid-crystal polymer (LCP) [24] and textiles [25]. Among them, fabrics withstand bending, twisting and stretching. Furthermore, they are thin and have a low dielectric constant (εr) and therefore they are good candidates for flexible wearable antennas as dielectric substrates [26]. In addition to temperature sensing textile-based resonator can plays a key role in the development of a wide range of applications, such as sports analytics [27], healthcare [28], gaming [29], and emergency services [30].

As far as the authors are aware, there is no experimental work carried out on measuring the relationship between dielectric constant and temperature on textile materials. For the first time, a thorough test campaign was carried out and extensive results are presented. Showing a linear relationship between εr and temperature for the three frequencies analyzed and independently of the fabric substrate used. A thermal threshold has been found at 50 ◦C, where the system gets into a saturation status increasing the frequency deviation of the measurements. Adding a constraint to the use of this technique.
