*3.1. Numerical Analysis*

For numerical analysis of the antenna, CST Studio Suite [43] was used to evaluate the time-domain characteristics of the antenna structure at the three di fferent frequencies. The time-solver calculates the development of the electromagnetic fields through time at certain spatial spots and at discrete-time samples, using Maxwell's equations [44].

The antenna's performance was analyzed both in o ff body and on a body phantom. The phantom model consisted of a 44 mm thick four-layer block. The phantom was modeled as 1 mm of skin, 3 mm of fat, and 40 mm of muscle. The antenna under test (AUT) was placed on top of the four-layer block, leaving a 1 mm air gap in between (see Figure 4a,b). The dielectric properties and conductivity of the three di fferent tissues have been obtained from [45] and are listed in Table 2.

**Figure 4.** (**a**) 2D Body phantom model of four layers and (**b**) 3D body phantom model of four layers.


**Table 2.** Dielectric properties of human tissues at 2.45 GHz [45].

### 3.1.1. Case A at 2.45 GHz

The reflection coe fficient describes how much of an electromagnetic wave is reflected due to a discontinuity in the transmission medium, it is often known as return loss or simply S11. A comparison of the simulated S11 in o ff-body versus on-body is shown in (Figure 5a). As for insertion losses, the presence of a human body barely perturbed the antenna's performance. This is an expected result due to the use of a full ground plane, which isolates the antenna from the body. In fact, this is one of the reasons of choosing a microstrip patch model with a full ground plane, for wearable applications. In addition, the ground plane helped to focus the antenna's radiation on the broadside. The directivity (D) is a parameter that quantifies this ability to focus the radiation from the antenna. For this case, the microstrip patch had a computed directivity of 7.44 dBi towards the expected direction of propagation, and its realized gain (G) was 3.81 dB with an e fficiency (e ff) 43.4%

$$\mathbf{G} = \mathbf{D} \times \mathbf{eff} \tag{7}$$

Simulation results are shown, in 3D, in Figure 5b.

**Figure 5.** (**a**) S11 simulated in both o ff and on body and (**b**) antenna directivity (dBi) in spherical 3D coordinates.

### 3.1.2. Case B (9.5 GHz) and Case C (38 GHz)

For the next two frequencies cases: the case B at 9.5 GHz and the case C at 38 GHz, the analysis was focused on verifying the resonance frequency and the antenna behavior under general conditions. Since the impact of human body can be neglected, as shown before, we have omitted it for these two cases. The return loss for both frequencies and results are shown in (Figure 6a,b), respectively.

**Figure 6.** Return losses simulated for (**a**) S11 at 9.5 GHz and (**b**) S11 at 38 GHz.

### *3.2. Experimental Setup and Results*

A test campaign was carried out at the Antennas Measurement Laboratory facilities of QMUL. To examine radiation patterns at far-field distances, the AUT was placed inside the anechoic chamber (Figure 7a). A diagram of the actual experimental setup used for characterizing the dielectric properties through temperature is depicted in Figure 7b.

**Figure 7.** (**a**) Electromagnetic compatibility (EMC) anechoic chamber at Queen Mary University of London (QMUL) and (**b**) Measurement setup diagram.

The prototypes were placed inside a mobile antenna electromagnetic compatibility (EMC) screened anechoic chamber to examine the radiation patterns of the antenna under test (Figure 7a). The EMC chamber was equipped with two open boundary quad-ridge horn antennas (probe) operating from 400 MHz to 6 GHz (3164-06, ETS-Lindgren, TX, USA) and from 0.8 to 12 GHz (QH800, Satimo, Haydock-MSY, UK), allowing vertical and horizontal linear polarization measurements.

The AUT was located on top of a hot plate (RCT Basic, IKA, Oxford, UK) and a thermocouple as close as possible without interfering to measure hot plate's temperature (Figure 7b). Data from the thermocouple were correlated with the hot plate's internal thermometer to verify the antenna's temperature. To ensure the temperature stability and repeatability in the measurements, a due time of 15 min was allowed and 10 measurements (every ten seconds) were taken for each one of the temperatures. With these waiting periods, we guaranteed that the antenna was under the desired temperature in each step. In order to reduce the possible effects of external factors, and in particular of relative humidity (RH) variations, the setup was placed inside an insulator box made of foam. Coaxial cables close to the hot plate were protected with thermal insulator sleeves to avoid any damage to the equipment used and to minimize the impact on the measured magnitudes.

Return losses were measured with vector network analyzers (VNA) (Keysight Technologies, Reading, UK). A PNA-L N5230C for cases A and B, and PNA-X 5244A for case C. The VNA was

calibrated at the end of the coaxial cable with an E-cal kit to suppress the effects of cables and connectors, and to have the same initial reference for all our measurements.

### 3.2.1. Case A at 2.45 GHz

First, a general test campaign for the organic cotton model at ISM frequency was carried out in order to evaluate the overall performance of the antenna's design. Comparison analysis between numerical and experimental performance was carried for the off body scenario.

Figure 8a shows the computed reflection coefficient of the textile antenna versus the fabricated prototype. The numerical estimation and experimental values of the prototype show a good agreement. The resonant frequency was slightly shifted (45 MHz) towards lower frequencies, due to fabrication tolerances.

**Figure 8.** Antenna on cotton fabric at 2.45 GHz; (**a**) reflection coefficient S11 computed vs measured and (**b**) radiation pattern Phi (φ) 90 computed vs measured.

The radiation pattern properties in an off-body environment were measured in an anechoic chamber at the QMUL antennas laboratory, showing an expected behavior of a standard high Q-factor microstrip patch antenna. The E-plane cut shows that measurements match simulations fairly well, in terms of radiation pattern and directivity (Figure 8b), and behave as expected from a directional microstrip patch antenna.

### Thermal Characterization at 2.45 GHz

The initial thermal characterization using the test setup exemplified in (Figure 7b) was performed for the woven and knitted textiles (four initial fabric substrates: cotton, jeans, viscose and lycra).

The thermal test campaign consists of taking ten measurements of the resonant frequency for each temperature step (20 ◦C, 30 ◦C, 40 ◦C, 50 ◦C to 60 ◦C). The average frequency shifts (in MHz) of each fabric are listed in Table 3. Results of all measurements are depicted in the graphs below, for organic cotton (Figure 9a), jeans cotton (Figure 9b), viscose (Figure 9c) and lycra (Figure 9d).

**Table 3.** Frequency shift over temperature sweep (20–60 ◦C per 10 ◦C) at 2.45 GHz (measured results).


**Figure 9.** Measured frequency vs temperature representation. Case A at 2.45 GHz: 20–60 ◦C/10 ◦C steps for: (**a**) Cotton; (**b**) Jeans; (**c**) Viscose and (**d**) Lycra.

From the test campaign, a linear behavior between εr and temperature was observed. An average shift of 10 MHz per 10 ◦C increment was measured for all four textiles substrates up to a temperature of 50 ◦C, which according to Equations (2)–(4) is equivalent to approximately a 1.67 × 10−<sup>2</sup> change in the dielectric constant for each step. All results are shown in the first row of the first column of Tables 4 and 5. For all four textiles, there was a 10% of frequency deviation (1 MHz) and thermal threshold at 60 ◦C where the resonant frequency tended to saturate. At the thermal threshold, the standard deviation of the resonant frequency showed a larger standard deviation, as well.


**Table 4.** Frequency shift over temperature sweep (measured results in MHz).

**Table 5.** Dielectric constant change over temperature sweep (measured results Δεr).


### 3.2.2. Case B at 9.5 GHz

The same thermal measurements were done for the second antenna, case B (Figure 10a). In this case, a 40 MHz decrement per 10 ◦C increase was measured. Following the same mathematical approach as in 3.2.1., the equivalent change in the dielectric constant is equal to 1.67 × 10−2. The result matches the one from the previous case A independently on the final resonant frequency. In this case the frequency deviation is 2.5 MHz (6.25%). Final results are summarized in the first row of the second column of both tables, Tables 4 and 5.

**Figure 10.** Measured frequency vs temperature representation. Cotton Case B at 9.45 GHz for: (**a**) 20–60 ◦C/10 ◦C steps and (**b**) 20–40 ◦C/5 ◦C steps.

We performed a finer temperature sweep from 20 ◦C to 40 ◦C using 5 ◦C steps. A 20 MHz shift for each step were measured (Figure 10b), half from the 10 ◦C case, with a variation of 8.35 × 10−<sup>3</sup> (εr). These results show that the relative change of the resonant frequency with temperature had a clear linear behavior. The set of results are listed in the second row of the second column of Tables 4 and 5.

### 3.2.3. Case C at 38 GHz

Finally, for the third case, the same procedure as in the previous ones was used. First, measurements from 20 to 60 ◦C in steps of 10 ◦C and second from 20 to 40 ◦C with increments of 5 ◦C (Figure 11a,b) were taken. Shifts of 150 MHz and 75 MHz respectively were measured, corresponding to Δ<sup>ε</sup>r of 1.67 × 10−<sup>2</sup> and 8.35 × <sup>10</sup>−3, with a frequency uncertainty of 5 MHz (3.33%) for this scenario. The increase in frequency shifts allowed a finer temperature sweep. In this case, an extra measurement was added to cover the ambient temperature range from 20 ◦C to 24 ◦C, with a 1 ◦C steps (Figure 11b). The resonance change measured for each step was of 15 MHz, Δ<sup>ε</sup>r of 1.67 × 10−3.

**Figure 11.** Measured frequency vs temperature representation. Cotton Case C at 38 GHz for: (**a**) 20–60 ◦C/10 ◦C steps and (**b**) 20–40 ◦C/5 ◦C steps and 20–24 ◦C/1 ◦C steps.

Results for case C are in good agreemen<sup>t</sup> with previous cases, A and B, showing a linear behavior as expected, independently of the resonant fr. The mmW prototype improves the sensitivity in an order of magnitude, up to 1 degree Celsius. It can be seen that increasing the sensing frequency, increases the frequency deviation in the measurement.

All the quantitative results for both frequency and dielectric constant are shown in the third column of Tables 4 and 5.
