Research of textile logarithmic-aperiodic antennas with a matching circuit for textronics applications

Abstract

The antenna is the basic element of radio communication systems. Its proper design allows for a sufficiently wide transmission range and quality of data transmission. Most known communication systems operate in a certain frequency range and dipole antennas only work at one frequency of resonance, therefore log-aperiodic antennas are built for covering a wide bandwidth. In a typical configuration, such antennas are made of metal rods; however, in textronics garment applications a flat structure integrated with the textiles is necessary. This article presents the construction and research of a flat antenna entirely made with textile materials and with the use of technologies. Embroidery technology was proposed for the prototyping of antennas for all three communication technologies. Polyester multifilament yarns with a silver top layer were used in the research. A textile impedance matching circuit for the antenna was also built with the use of textile technology. The antennas were designed for the Global System for Mobile Communications, Global Positioning System and WiFi systems, because such wireless technologies have been used in the prototype system for transmitting measurement data of human physiological signals in textronics clothing. Wearable antennas are a part of a device that ensures continuous health monitoring of an elderly person or a patient without hindering his day-to-day activities. The construction of this system was the subject of a project financed by the National Centre for Research and Development in Poland.

The design stage was presented along with the method of connecting the antenna with the transmitter. The repeatability of the antenna parameters was also analyzed and a textile impedance matching circuit was presented. In this article, the author focused on checking the quality and repeatability of electrical and geometric parameters of textile antennas for various types of transmission, including connections in constant environmental conditions.

Keywords

Smart textiles materials measurement protective and other high-performance clothing systems product and systems engineering testing fabrication properties

An antenna is the basic element of radio communication systems. Its proper design allows for a sufficiently wide transmission range and quality of data transmission. Most known communication systems operate in a certain signal frequency range, while dipole antennas only work at one frequency of resonance; therefore, log-aperiodic antennas are built for covering a wide bandwidth. Their structure and design principles were described for the first time at the turn of the 1950s and 1960s.^1
–3 The name of the antenna is related to the uniform distance of each antenna element, which depends on the logarithm of the frequency. These antennas are widely used in television sets,^4,5 due to the wide range of received television channels. These antennas are still the subject of many design and theoretical considerations.^5
–7 In the case of these antennas, it is important to precisely manufacture the elements and calculate the antenna impedance as well as its gain,^8,9 In a typical configuration, such an antenna is made of metal rods, for which dipole antennas are set on two flat bars placed at an angle α to each other. Figure 1 shows a side view of the stick antenna.

Figure 1.
Side view of a typical stick antenna. 1: arm of the dipole of the antenna; 2: metal rod supplying power to the antenna; E: signal transmitter.

Figure 2 shows the Ultralog HL562 antenna by Rohde & Schwarz. Its basic parameters are as follows:

Figure 2.
Ultralog HL562 antenna by Rohde & Schwarz.

frequency range: 30 MHz–3 GHz;

linear polarization;

input impedance: 50 Ω;

voltage standing wave ratio (VSWR) coefficient lower than 2;

gain above 200 MHz, typically 8 dB;

dimensions (W × H × L): 0.6 m × 1.65 m × 1.68 m;

weight: 5 kg.

The VSWR = f(f) characteristic of this antenna is shown in Figure 3.

Figure 3.
Reflection characteristics of the Ultralog HL562 antenna.

In textronics apparel and mobile applications it is necessary to apply a flat structure integrated with the garment. Flat antennas can be made on copper laminates with the use of the etching method, in the same way as electronic printed circuits.^10,11 However, such antennas are not flexible and cannot be fully integrated with textronics clothing.

This article presents the construction and research of a flat antenna entirely made with the use of textile technologies. Textile antennas are used today in many applications, such as military, for soldiers’ live-location tracking, real-time transmission of images and video for instant decentralized communications, etc. These antennas are also used for access/identity management, navigation, radio frequency identification (RFID) applications, etc.^12
–15 The antennas were designed for the Global System for Mobile Communications (GSM), Global Positioning System (GPS) and WiFi systems, because such wireless technologies have been commonly used in textronics systems for transmitting measurement data of human physiological signals before. The system consists of sensors for physiological parameters, such as the pulse, respiratory rate and sub-clothing temperature, and is used for monitoring the health of the elderly in real time. Measurement data is sent with the use of the WiFi technology, while GSM and GPS technologies are used for locating and sending the data to the server where it is gathered and processed.¹⁶ The frequency band ranges for GSM, GPS and WiFi wireless technologies are presented in Table 1.

Table 1.
Most commonly used wireless technologies and their ranges

System f ₁ f ₂

MHz
MHz

GPS 1242 1605

GSM 869 915

WiFi 2401 2495

GPS: Global Positioning System.

In this article the author has focused on embroidery technology to manufacture textile antennas. However, there are very well known other methods and different technologies that are used to incorporate smart electroconductive materials into a textile structure.^12,17 These methods are listed below.
Conductive textiles can be used as yarns to knit or weave the antenna conductive patterns and be stitched together with a non-conductive textile substrate.

Flexible textile antennas can be produced as uniform and thin metallization layers. This can be achieved by affixing non-conductive clothing material to elements such as foil, silver tape or copper.^18,19

The production of conductive patterns using embroidery made from conductive textile yarns on a non-conductive textile substrate.^20–23

The printing of non-conductive textile fabrics by using screen and inkjet printing technology.¹²

Another important problem of the textronics application is the connection of electronic systems with textile antennas. In the article, the author also presents three different methods of connection between textile antennas and a transmitter. These three possibilities are connection with a metal stud, a connector and connection with textile pins – a press stud. The presented connectors are typical ones for connections in mobile applications and can be easily adapted as commercial solutions.²⁴

The author decided not to use elastic connectors, such as textronics Velcro, because this does not have an electrical stable connection and the electrical parameters of contacts depend on pressure force.²⁵

Textile logarithmic-aperiodic antenna design

A general connection diagram inside the log-aperiodic antenna is shown in Figure 4.

Figure 4.
Structure of a log-periodic antenna.

The arms of each dipole are powered alternately from the E source, through a symmetrical line, to ensure the appropriate phase shift. The length of the dipole L₁ is selected for the lowest assumed frequency in the f₁ band according to Equations (1)–(9)
$\frac{L_{(i + 1)}}{L_{i}} = \frac{d_{(i + 1)}}{d_{i}} = T$
(1)

$l_{i} = \frac{L_{i}}{2}$
(2)

$σ = \frac{d_{i}}{2 \cdot L_{i}}$
(3)

$α = \tan^{- 1} (\frac{1 - T}{4 σ})$
(4)

$f_{i} = \frac{f_{1}}{T^{i - 1}}$
(5)

$B = \frac{f_{g}}{f_{1}}$
(6)

$n = 1 - \frac{\log (B)}{\log (τ)}$
(7)

$d_{1} = 2 σ L_{1}$
(8)

$L_{1} = \frac{λ_{1}}{2} = \frac{c}{{2 f}_{1}}$
(9)
where i = 1,2, …, n, n is the number of antenna arms, τ = 0.76…0.95 is the scaling factor, σ = 0.04…0.22 is the distance factor, C = 300 · 10⁶ m/s is the speed of light, f₁ is the lowest assumed frequency, f_g is the highest assumed frequency, B is the assumed frequency band and l_i is the antenna arm.

The constants τ and σ are assumed from the characteristics presented in Figure 5 for the appropriately assumed gain of the G antenna.

Figure 5.
Dependence between the constants for a log-aperiodic antenna.^3,5

Lengths l_i and distances d_i are calculated respectively from Equations (1) and (2). In the case of rod antennas, each arm of the dipoles is set on a separate linear guide arranged in space at a distance at an appropriate angle α, as shown in Figure 4. Next for these constants, the distance d₁ is calculated from Equation (8) and the necessary number of dipoles n is calculated from Equation (7). In a flat textile structure, the arms of the dipoles are placed in two textile layers, as shown in Figure 6.²⁶

Figure 6.
Construction of a textile log-periodic antenna. 1: one electrical conductive layer that contains one arm of the dipole; 2: cotton textile layer; 3: second electrical conductive layer that contains the second arm of the dipole; 4: antenna feeder.

Figure 7.
Microscopic photo of the base fabric.

All textile antennas are made of a cotton raw material base with a twill weave. Cotton fabric (100%) displays excellent durability, good radio frequency (RF) performance and flexibility.²⁷ The fabric thickness is 1.1 ± 0.1 mm. The measurement was performed with an optical thickness gauge in accordance with the standard.²⁸ Microscopic photos of the base material are shown in figure 7.

The arms of the antennas are made with the use of the embroidery technique, with electrical conductive multifilament threads. These multifilament yarns are coated with a silver layer of 156.0 tex.

The electrical parameters of the yarn is 14 Ω/m. A computerized embroidery machine (Janome) was used for this purpose. Due to technological and material properties as well as the settings of the yarn tensioner, the average embroidered paths were of 2 mm ± 0.5 mm width. The embroidered paths and their cross-sections are shown in Figures 8(a) and (b). The average value of surface sensor resistance on the knitted substrates was 1.1 Ω/cm. Initial research of the surface resistance measurements was conducted for the prototype antennas. The direct measurement method was used, as well as a recorder – an Agilent 6.5 Digits Millimeter with a resistance accuracy of 0.010 + 0.001 (% of reading + % of range).

Figure 8.
Microscope photos of the antenna arms (a) and the antenna path cross-section (b).

The author is aware of the influence of environmental parameters, that is, changes in air humidity and temperature, on the electrical properties of textile antennas. These studies are widely described, for example, in the literature.^29,30 All tests in the presented work were performed in a climatic chamber, under constant climatic conditions (60% relative humidity (RH), 21ºC ambient temperature). In this way, the author wanted to eliminate the confounding factor. It is necessary to conduct tests in constant conditions, taking into account the principles of repeatability and reproducibility. The next stage of research includes laboratory tests in conditions similar to real ones as well as environmental tests. This procedure enables the necessary corrections to be made in the final product.

Three types of antennas for GSM, GPS and WiFi bands were made according to the frequency characteristics given in Table 2. Figure 7 presents microscopic photo of base cotton fabric and Figure 8 presents a magnification of the embroidered electroconductive path of the antenna.

Table 2.
The thickness of the antenna arm

No. of measurements 12

Minimum 1.71 · 10⁻³ m

Maximum 2.35 · 10⁻³ m

Mean 2.08 · 10⁻³ m

Std. deviation 0.18 · 10⁻³ m

The changes in the thickness of the antenna arms along their length were measured. The measurement results are presented in Table 2.

Table 3 presents the geometrical and electrical parameters of textile antennas for GPS, GSM and WiFi bands.

Table 3.
Parameters of textile antennas for Global System for Mobile Communications (GSM), Global Positioning System (GPS) and WiFi technologies

GSM GPS WiFi

τ 0.96 0.91 0.96

σ 0.06 0.1 0.14

f ₁ MHz 869 1242 2401

f_g MHz 915 1605 2495

n 4 4 2

α ° 9 13 4

G dbi 8 7.5 9.5

l
d
l
d
l
d

Dipol No.
10^–2 m
10^–2 m
10^–2 m
10^–2 m
10^–2 m
10^–2 m

1 8.6 2.1 6.0 2.4 3.1 1.8

2 8.3 2.0 5.5 2.2 3,0 –

3 8.0 1.9 5.0 2.0 – –

4 7.6 – 4.6 – – –

Note: each antenna was designed for the lowest frequency of each f₁ band. The number of dipoles n is a result of the upper frequency f_g.

Table 4.
Calculations of the textile matching system for each technology

Transmission technology
f ₁
f ₂
f ₀
Z_u
Z_b
L
C
Z_upom

MHz MHz MHz Ω Ω nH pF Ω

GSM 869.0 915.0 892.0 50 211.4 18.3 1.7 159.4

GPS 1242.0 1605.0 1423.5 50 293.4 13.5 0.9 116.6

WiFi 2401.0 2495.0 2448.0 50 136.0 5.4 0.8 177.8

Z_u: assumed input impedance of the matching circuit, at f₀; Z_b: impedance of the antenna at f₀; Z_upom: measured input impedance of the matching circuit with the antenna at f₀. GMS: Global System for Mobile Communications; GPS: Global Positioning System.

Table 5.
Geometric parameters of the calculated textile elements based on the capacity L and C from Table 4

Transmission Technology
D
d
a
x

mm mm mm mm

GSM 14.3 2.0 6.4 0.56

GPS 11.8 2.1 4.7 0.56

WiFi 6.7 2.0 4.3 0.56

GMS: Global System for Mobile Communications; GPS: Global Positioning System.

Measurements and parametric analysis of textile antennas

The parameters that characterize the antennas are gain and VSWR and its impedance. These parameters can be measured with the use of a spectrum or network analyzer in constant climatic condition. Firstly, the analyzer measures the reflected power RL (return losses), the value of which results from the mismatch between the antenna impedance and the impedance of the bridge output, which is usually 50 Ω. with the following formulas. On the basis of the RL value, the remaining parameters are determined, and expressed by the formulas below
$R L = - 20 \cdot \log (Γ)$
(10)

$Γ = 10^{\frac{- R L}{20}} = \frac{Z_{L} - Z_{0}}{Z_{L} + Z_{0}}$
(11)

$VSWR = \frac{1 + | Γ |}{1 - | Γ |}$
(12)

$Z_{L} = - Z_{0} \frac{Γ + 1}{Γ - 1}$
(13)
where RL is the reflected power (return losses), dB; Γ is the reflection coefficient; Z_L is the impedance of antenna, Ω; and Z₀ is the impedance of the source supplying the antenna, Ω. Equations (10)–(13) are valid for some of the real impedances.

If the antenna impedance matches the source impedance then Γ = 0 and VSWR = 1. An increase in the difference between Z_L and Z₀ means that Γ > 0 and VSWR > 1. The Ultralog HL562 antenna by Rhode & Schwarz was used as a test model. All measurements of frequency characteristics were made with the use of the Rhode & Schwarz FSL3 scalar analyzer, which is shown in Figure 9.

Figure 9.
Rhode & Schwarz FSL3 analyzer.

The connection point between the coaxial cable and the textile antenna is important. This connection should be mechanically and electrically stable. The author decided not to use elastic connectors, such as textronics Velcro, because this is not an electrical stable connection and the electrical parameters of the contacts depend on pressure force.³¹ Three possibilities were investigated: connection with a metal stud, with a connector and connection with textile pins – a press stud. Figure 10 shows the different types of antenna-to-transmitter connections.

Figure 10.
Different types of antenna connections with the transmitter: (a) metal stud; (b) connector; (c) press stud.

Figure 11 presents the VSWR characteristics for the mentioned connectors.

Figure 11.
Connections between the Global Positioning System antenna and the coaxial cable: (a) metal stud; (b) connector; (c) press stud.

From among the tested connections, the connectors were selected because in this case the VSWR coefficient is the lowest for the GPS and other transmission (WiFi, GSM) frequency ranges, that is, from 1242 to 1605 MHz. The remaining antennas were also connected via a coaxial cable with mechanical connectors.

Another important parameter is the antenna impedance. The designed antennas have an impedance different from the impedance of the transmitter to which they was connected, which in this case is 50 Ω. For that reason, a textile impedance matching circuit was designed. The electrical diagram of this system is shown in Figure 12.

Figure 12.
Antenna matching circuit.

The input of the circuit is connected to the unbalanced output of the transmitter and the output of the matching circuit is connected to the balanced line that feeds the antenna. The value of the elements of that system is calculated from Equations (14) and (15)
$L = \frac{\sqrt{Z_{u} \cdot Z_{b}}}{2 π f_{0}}$
(14)

$C = \frac{1}{2 π f_{0} \sqrt{Z_{u} \cdot Z_{b}}}$
(15)
where Z is the characteristic impedance of the transmitter port, Ω; Z_b is the impedance of the antenna, Ω; f is the center frequency of the antenna band, Hz; L is the coil inductance, H; and C is the capacitor capacity, F.

In order to fully integrate with the textile substrate, a textile matching system was used. The electrical elements according to Figure 12 were made with the use of the embroidery technology of electrical conductive yarn.

The textile coil was made as a single coil, while the textile capacitor consisted of two facings separated by a layer of raw cotton. This procedure allows one to integrate the antenna with the matching system on a single textile substrate. The geometrical parameters of the coil and the textile capacitor are shown in Figures 13 and 14.

Figure 13.
Single textile coil.

Figure 14.
Textile capacitor.

The calculation of the geometric parameters for the inductance L and C is performed according to Equations (16) and (17)

$L = μ_{0} μ_{r} \frac{D}{2} [\ln (\frac{8 D}{d}) - 2]$ (16)

$C = \frac{ε_{0} ε_{r} α^{2}}{x}$ (17)

where $μ_{0} = 4 π 10^{- 7} \frac{H}{m}$ is the magnetic permeability of the vacuum; $ε_{0} = \frac{1}{36 π} 10^{- 9} \frac{F}{m}$ is the dielectric permittivity of the vacuum; D is the diameter of the single coil, m; d is the thickness of the single coil, m; a is the side of the square area of one of the capacitor plates, m; and x is the distance between covers, m. Results of calculation are present in table 4 and 5

The calculations were performed at the center frequency of the f₀ band and assuming that the input impedance of the matching circuit is equal to the impedance Z_u = 50 Ω. After connecting the textile antenna with the textile matching circuit, the VSWR characteristics at the input of the matching circuit were measured. For the f₀ frequency, the Z_upom impedance was determined on this basis. This impedance is lower than the Z_b antenna impedance, which means that the system performs its function, but the impedance is higher than the assumed 50 Ω. This is a result of the tolerances of the manufactured textile elements of the matching system. Figures 15 and 16 present the practical implementation of textile impedance matching circuits.

Figure 15.
Implementation of a textile impedance matching circuit: (a) connection of a textile coil and capacitor as part of a matching circuit; (b) photo of the system structure. 1: textile substrate; 2: a single textile coil; 3: terminals for connecting external elements; 4: textile electrical conductive line; 5: one of the textile capacitor facings placed on the back of the substrate (1); 6: the second textile capacitor facing placed on the same side of the textile substrate (1) as the coil (2).

Figure 16.
Microscope photos of the structure of the matching system: (a) analysis of the thickness of the coil paths; (b) inspection of capacitor connections.

Figures 17 –19 present VSWR measurements for all types of antennas. The characteristics of the antennas were compared with the VSWR characteristics of the matching input after attaching the antennas.

Figure 17.
Global System for Mobile Communications antenna with textile matching circuit.

Figure 18.
Global Positioning System antenna with textile matching circuit.

Figure 19.
WiFi antenna with textile matching circuit.

For each antenna a matching circuit was made to obtain an impedance equal to the impedance of the radio transmitter. The equality of these impedances allows all of the transmitter power to be transferred to the antenna. In this way, signal power losses can be avoided. For these reasons, a textile impedance matching circuit was built to ensure full integration of the transmitter circuit with the textiles.³² Ten antennas were made for each technology in order to statistically evaluate the electrical parameters of the antennas. The VSWR parameter and the impedance of the Z_L antenna were taken into account. All antennas, as before, were made on a raw cotton substrate according to Table 3. Figure 20 presents the implementation of a textile GPS antenna. The remaining antennas were made in the same way and the only difference is the number of dipole arms. Figures 21 –23 show a comparison of the VSWR characteristics of the next 10 antennas for each of the wireless techniques.

Figure 20.
Textile Global Positioning System antenna.

Figure 21.
Reflection characteristics of Global System for Mobile Communications antennas.

Figure 22.
Reflection characteristics of Global Positioning System antennas.

Figure 23.
Reflection characteristics of WiFi antennas.

For each of the wireless techniques, for the frequency band and the midpoint of this band, the mean value, standard deviation from the average value and the coefficient of variation were calculated. The calculations were made for 10 antennas and for the VSWR coefficient and the Z_L impedance
$Z_{Lavg} = \frac{Z_{1} + \dots {+ Z}_{n}}{n} average value$
(18)

$Z_{Lstd} = \sqrt{\frac{\sum_{i = 1}^{n} (Z_{L i} - Z_{Lavg})^{2}}{(n - 1)}} standard deviation$
(19)

$Z_{Lwspzm} = \frac{Z_{Lstd}}{Z_{Lavg}} coefficient of variation$
(20)
where n is the number of antennas.

Tables 6 –8 present the calculated statistical parameters for 10 antennas.

Table 6.
Statistical parameters for Global System for Mobile Communications (GSM) antennas

Statistical parameters for GSM

f MHz 8.73E+08 8.96E+08 9.19E+08

VSWR_avg 4.0 3.1 3.1

VSWR_std 0.8 0.6 0.5

VSWR_CV 0.2 0.2 0.2

Zl_avg Ω 199.1 155.6 156.2

Zl_std Ω 42.3 27.9 24.0

Z_lCV Ω 0.2 0.2 0.2

Table 7.
Statistical parameters for Global Positioning System (GPS) antennas

Statistical parameters for GPS

f MHz 1.2432E+09 1.4284E+09 1.6079E+09

VSWR_avg 3.6 2.9 2.9

VSWR_std 0.5 0.4 0.6

VSWR_CV 0.1 0.2 0.2

Zl_avg Ω 181.0 143.6 147.5

Zl_std Ω 22.9 22.3 30.5

Zl_CV Ω 0.1 0.2 0.2

Table 8.
Statistical parameters for WiFi antennas

Statistical parameters for WiFi

f MHz 2.41E+09 2.45E+09 2.50E+09

VSWR_avg 3.2 2.2 3.4

VSWR_std 0.3 0.2 0.2

VSWR_CV 0.1 0.1 0.1

Zl_avg Ω 161.4 112.0 171.0

Zl_std Ω 14.3 8.8 11.0

Zl_CV Ω 0.1 0.1 0.1

The coefficient of variation shows a maximum 20% of variability of the electrical parameters of the textile antenna made with the use of the embroidery technology. These are acceptable deviations for using textile antennas in particular transmission systems.

Discussion and conclusions

In textronics apparel applications it is necessary to construct flat textile antennas. All requirements, such as flexibility or integration with clothing, are met by the structure presented in the study. Research on the correct design of textile antennas is very important from the point of view of specific absorption rate (SAR) limits for wireless devices to ensure acceptable radiations level in the human body.³³ Therefore, the repeatability of the antenna parameters is important. Tests of parameter changes under the influence of bending and operational tests are the next step in the research. The current research is at the fourth level of technological readiness. The next step on the fifth technology level will be laboratory tests in conditions similar to real ones.

The transmitting antennas were made in the form of textile and will be placed on the back of the garment as a detachable clothing module in the form of a lining. The antennas are designed as broadband to cover the entire band used by wireless transmission technology. These antennas were made for three technologies used in textronics system, that is, WiFi, GSM and GPS, with the use of one technique for this purpose – the embroidery technique. The embroidery method is recommended in this case due to the possibility of making the antenna in one technological process. However, this method cannot be performed on all textile substrates, and thus a cotton one was chosen. Cotton fabric displays excellent durability, good RF performance and flexibility. However, there may be some limitations, for example, in the case of vapor-permeable membranes or specialized protective clothing. Another limitation is the dispersion of the dimensions of the tracks, in particular their thickness, which affects the antenna impedance. It is also influenced by the relatively high linear resistance of the electrical conductive yarn.

This discrepancy in the tests carried out was a few ohms per meter. It was caused by the non-homogeneous structure of the textile products, for example, the variation in weight along the length of the yarn and the inhomogeneity of the base material surface, such as the used fabrics. The fact that modern embroidery machines are fully computerized is a plus, which allows for the precise design of the geometric shapes of the applied paths. These machines are also characterized by a certain flexibility in terms of the selection of threads that are used for embroidery due to the possibility of selecting technological parameters such as the type and geometrical dimensions of the stitch as well as the embroidery speed. In the conducted research, multifilament polyester yarns coated with a silver layer were used, which were ideally suited for this type of application. A positive aspect of the design of antennas with the use of textile technologies is also the possibility of using modified clothing connections as elements connecting the antennas with the transmitter, for example, with the use of textile connectors, which has a positive effect on integration with textiles. The embroidery method also allows one to design a textile antenna matching system, which is important from the point of view of the energy efficiency of the antenna system. The coefficient of variation of the antenna electrical parameters is a maximum of 20%, which is a value comparable to the variability of the textiles parameters. The improvement of the transmission parameters of the antennas together with the textile matching system were observed for each of the three types of transmission. If the antenna impedance matches the source impedance, Γ = 0 and VSWR = 1. In this case, antennas are better manufactured. An increase in the difference between Z_L and Z₀ means that Γ > 0 and VSWR > 1. When VSWR is around 2–3 it means that RL is from about 11% to 25%. This is due to the antenna impedance mismatching the source impedance. The reason may be the discrepancies in the electrical properties of the textile embroidered antenna arms. Variability of electrical parameters occurs as a function of, for example, changes in stitch density, the geometry of embroidered paths, change in yarn resistance, etc.

Despite potential problems, textile antennas integrated with clothing seem to be a very attractive solution in mobile applications. They have a wide range of applications for various wireless transmission methods. They are characterized by flexibility. The antennas can be made with the use of conventional textile methods, such as knitting, embroidery and printing.

System	f ₁	f ₂
	MHz	MHz
GPS	1242	1605
GSM	869	915
WiFi	2401	2495

No. of measurements	12
Minimum	1.71 · 10⁻³ m
Maximum	2.35 · 10⁻³ m
Mean	2.08 · 10⁻³ m
Std. deviation	0.18 · 10⁻³ m

		GSM	GPS	WiFi
τ		0.96	0.91	0.96
σ		0.06	0.1	0.14
f ₁	MHz	869	1242	2401
f_g	MHz	915	1605	2495
n		4	4	2
α	°	9	13	4
G	dbi	8	7.5	9.5
	l	d	l	d	l	d
Dipol No.	10^–2 m	10^–2 m	10^–2 m	10^–2 m	10^–2 m	10^–2 m
1	8.6	2.1	6.0	2.4	3.1	1.8
2	8.3	2.0	5.5	2.2	3,0	–
3	8.0	1.9	5.0	2.0	–	–
4	7.6	–	4.6	–	–	–

Transmission technology	f ₁	f ₂	f ₀	Z_u	Z_b	L	C	Z_upom
GSM	869.0	915.0	892.0	50	211.4	18.3	1.7	159.4
GPS	1242.0	1605.0	1423.5	50	293.4	13.5	0.9	116.6
WiFi	2401.0	2495.0	2448.0	50	136.0	5.4	0.8	177.8

Transmission Technology	D	d	a	x
GSM	14.3	2.0	6.4	0.56
GPS	11.8	2.1	4.7	0.56
WiFi	6.7	2.0	4.3	0.56

Statistical parameters for GSM
VSWR_avg	4.0	3.1	3.1
VSWR_std	0.8	0.6	0.5
VSWR_CV	0.2	0.2	0.2
Zl_avg	Ω	199.1	155.6	156.2
Zl_std	Ω	42.3	27.9	24.0
Z_lCV	Ω	0.2	0.2	0.2

Statistical parameters for GPS
VSWR_avg		3.6	2.9	2.9
VSWR_std	0.5	0.4	0.6
VSWR_CV	0.1	0.2	0.2
Zl_avg	Ω	181.0	143.6	147.5
Zl_std	Ω	22.9	22.3	30.5
Zl_CV	Ω	0.1	0.2	0.2

Statistical parameters for WiFi
VSWR_avg	3.2	2.2	3.4
VSWR_std	0.3	0.2	0.2
VSWR_CV	0.1	0.1	0.1
Zl_avg	Ω	161.4	112.0	171.0
Zl_std	Ω	14.3	8.8	11.0
Zl_CV	Ω	0.1	0.1	0.1

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This work was supported by Founds in the framework of the project LIDER IV, titled “Textronics system for protecting elderly people” and financed by The National Centre for Research and Development in Poland.

ORCID iD

Michal Pawel Frydrysiak

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Statistical parameters for GSM
f	MHz	8.73E+08	8.96E+08	9.19E+08
VSWR_avg		4.0	3.1	3.1
VSWR_std		0.8	0.6	0.5
VSWR_CV		0.2	0.2	0.2
Zl_avg	Ω	199.1	155.6	156.2
Zl_std	Ω	42.3	27.9	24.0
Z_lCV	Ω	0.2	0.2	0.2

Statistical parameters for GPS
f	MHz	1.2432E+09	1.4284E+09	1.6079E+09
VSWR_avg		3.6	2.9	2.9
VSWR_std		0.5	0.4	0.6
VSWR_CV		0.1	0.2	0.2
Zl_avg	Ω	181.0	143.6	147.5
Zl_std	Ω	22.9	22.3	30.5
Zl_CV	Ω	0.1	0.2	0.2

Statistical parameters for WiFi
f	MHz	2.41E+09	2.45E+09	2.50E+09
VSWR_avg		3.2	2.2	3.4
VSWR_std		0.3	0.2	0.2
VSWR_CV		0.1	0.1	0.1
Zl_avg	Ω	161.4	112.0	171.0
Zl_std	Ω	14.3	8.8	11.0
Zl_CV	Ω	0.1	0.1	0.1