An Optimized Feed Hexagonal Antenna with Defective Ground Plane for UWB Body Area Network Application

Today’s scenario of technology wearable devices has covered almost every sphere. The devices that are put on the body are used for monitoring various vital biomedical parameters, and tracking the movement of the living subjects, for medical, military, security, and business uses [1, 2]. As the number of services offered by these devices increase, the need for antennas operating in specific frequencies of the services have increased. Here multi-band antennas play a major role. A single antenna services multiple frequencies efficiently utilizing the frequency spectrum and eliminates the need for multiple antennas for different frequencies, minimizing the risk of exposure to radiations.

In this paper, we propose a hexagonal antenna. It is fed through one its edges at an inset. The ground plane has been modified to include 16 equal rectangular slots placed equidistant from each other. Due to the hexagonal design, the antenna operates in three bands, with considerable gain and bandwidth. The design can be easily integrated with the printed circuit boards. For improvement of matching of the port to the antenna, the inset feed is used. The length of the inset is optimized through evolutionary algorithm. The algorithm uses Darwinian concept of evolution involving natural selection of fittest individuals from the population. The candidate solutions are selected based on their fitness criteria. The candidates with higher fitness coefficients are included in the search space (population), replacing less fit candidates. The solution with highest fitness coefficient is selected as the optimal solution. The antenna has been designed to operate in Ultra-wideband (UWB) range to allow for design of wearable devices in this range and exploit wider bandwidth and faster data rates. The bands have chosen to avoid interference from other narrow-band services.

The paper describes some related works on multiband antennas for wearable applications in section 2, antenna design using evolutionary algorithm in section 3, results and related discussion in section 4, and concludes with the conclusion section. The works that have been referred to are given in the references section.

3.1 Design of the antenna

The proposed design of the antenna is hexagonal type. As compared to rectangular or circular patch, the hexagonal patch has an inherently multi-band nature, and use the available dielectric area more efficiently. The gains of the hexagonal patch are comparable to rectangular and circular patches. For a comparison, a rectangular, a circular, and a hexagonal patch is designed around 5 GHz on a 70×70×1.6 mm³ FR4-epoxy substrate with a feed width of 3 mm in Figure 1. There is no matching technique used. The ground plane is full. The S11 (dB) and the peak gain (dB) vs frequency are also shown.

Table 1. Summary of results

Step 1: A hexagonal copper patch with a side measuring 24.1 mm is created on a 70mm x 70mm x 1.6 mm substrate (Figure 2(a)).

Step 2: The feed of 5 mm is provided at one of the edges of the hexagon. A lumped port of 50Ω is created at the edge of the feed line (Figure 2(b)).

Step 3. A copper ground plane is created on the other side of the substrate (Figure 2(c)). 16 rectangular slots, each measuring 12mm x 10mm, are cut from the ground plane (Figure 2(d)).

Step 4: The distance of the inset is adjusted after running a Genetic Algorithm optimization to match the input impedance of the patch with the port. The dimensions that led to match are further given in Table 1.

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Figure 1. (A) Different patch shapes, (B) Comparison of S11 vs frequency (C) Comparison of Gain vs frequency

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Figure 2. Design steps

The hexagonal shape of the antenna can be approximated to its circumscribing circle of radius R. The sides of the hexagon subtend an angle of 60 deg (360/6) at the center. If the side of a hexagon is a, then,

$R=\frac{a / 2}{\cos \frac{2 \pi}{6}}=a$           (1)

Then the resonant frequency is given by Eq. (2) [20].

$f_{r}=\frac{8.794}{r_{e} \sqrt{\varepsilon_{r}}} G H z$        (2)

The effective radius r_e is calculated using Eq. (3) [11].

$r_{e}=R\left[1+\frac{2 h_{s}}{\pi R \varepsilon_{r}}\left\{\ln \left(\frac{R}{2 h_{s}}\right)+\left(1.4 \varepsilon_{r}+1.768\right)\right.\right. \left.\left.+\left(\frac{h_{s}}{R}\right)\left(0.267 \varepsilon_{r}+1.649\right)\right\}\right]^{-\frac{1}{2}}$        (3)

where, h_s is the thickness of the substrate and ε_r is the dielectric constant of the substrate.

The effective side length of the hexagonal patch, a_e, can be given as:

$\pi r_{e}^{2}=\frac{3 \sqrt{3}}{2} a_{e}^{2}$         (4)

The antenna is designed on a 70mm x 70mm x 1.6mm FR4-epoxy substrate. It has a relative electrical permittivity of 4.4 and a loss tangent of 0.02. The radiating patch of the proposed antenna has hexagonal shape. The length of each side is 24.1 mm. The ground plane has 16 rectangular slots, each measuring 12mm x 10mm. This modification helps to reduce the back lobe radiations to great extent, and hence the Specific Absorption Rate (SAR). A microstrip line of 5 mm width feeds the antenna at an inset, d from the edge. The feed point is slightly offset from the center. The distance of the inset, d, for best match with the 50Ω port have been determined through Evolutionary optimization.

3.2 Evolutionary optimization

The Genetic Algorithm optimization was run in Ansys HFSS between 1-10 GHz. The objective is to match the input impedance of the patch with that of the port for maximum power transfer, leading to better radiation efficiency, better gain and bandwidth while reducing the return loss. To find the best length of the feed for matching, we minimize the S11. This also determines the length of the inset, or how deep the inset slot should be etched. The input impedance of the circular patch any radial distance $\rho=\rho 0$ for dominant mode TM11 is given by [20]:

$Z_{i n}\left(\rho=\rho_{0}\right)=\frac{J_{1}^{2}\left(k \rho_{0}\right)}{\left(G_{t} \times J_{1}^{2}(k R)\right.}$      (5)

where, k is the wavenumber, J₁(x) is the Bessel’s function of first kind of order 1, and G_t is the total conductance.

The total conductance, G_t is given by:

$G_{t}=G_{r a d}+G_{c}+G_{d}$          (6)

The conductance between the patch and the full ground plane, G_rad is given by:

$G_{r a d}=\frac{\left(k_{0} R\right)^{2}}{480} \int_{0}^{\frac{\pi}{2}}\left[J_{02}^{\prime 2}+\cos ^{2} \theta J_{02}^{2}\right] \sin \theta d \theta$,          (7)

The ohmic conductance, accounting for ohmic loss, G_c is given by:

$G_{c}=\frac{\epsilon_{m 0} \pi\left(\pi \mu_{0} f_{r}\right)^{-\frac{3}{2}}\left[(k R)^{2}-m^{2}\right]}{4 h_{s}^{2} \sqrt{\sigma}}$          (8)

The dielectric loss is accounted by G_d given by:

$G_{d}=\frac{\epsilon_{m 0} \tan \delta\left[(k R)^{2}-m^{2}\right]}{4 \mu_{0} h_{s} f_{r}}$               (9)

where, $\epsilon_{m 0}=2$ for $m=0, \epsilon_{m 0}=1$ for other m, and f_r is the resonant frequency of the mn0 mode. The reflection coefficient is given by:

$\Gamma=\left(Z_{0}-Z_{L}\right) /\left(Z_{0}+Z_{L}\right)$                 (10)

where, Z₀ = 50Ω and Z_L is given by Eq. (4). Hence the objective function is to keep the reflection coefficient below -20 dB and hence,

$\begin{aligned} S_{11}=-20 \log ((50&\left.-\frac{J_{1}^{2}(k(R-d))}{\left(G_{t} \times J_{1}^{2}(k R)\right.}\right) /(50+\left.\left.\frac{J_{1}^{2}(k(R-d))}{\left(G_{t} \times J_{1}^{2}(k R)\right.}\right)\right) \leq-20 \mathrm{~dB} \end{aligned}$               (11)

where, $\rho 0=R-d$. The constraints for this optimization are:

$d<\frac{a \sqrt{3}}{2}$

The fitness value for each individual is computed [18] as an average of S11 at all desired frequencies sampled at 10 MHz intervals between 0.01 GHz and 10 GHz.

Fitness Value $=\frac{1}{N} \sum_{i=0}^{N} C(f i)$         (12)

where, $C(f i)=\left\{\begin{array}{c}-20, \text { if } S 11(f i) \leq-20; \\ S 11(f i), \text { if } S 11(f i)>-20\end{array}\right.$.

Here, N is the number of sampling points, and C(fi) is the cost function and S11(fi) is the S11 or the return loss at i^th frequency.

3.2.1 Optimization algorithm

Step 1: An initial set of 100 individuals is initialized randomly with different lengths of inset. For each individual, S11 is computed over the entire frequency range using equation (10) and fitness value for each individual is computed using (11). Based on their fitness values, individuals are then sorted.

Step 2: The fittest individuals and some random individuals are selected for reproduction of children through crossover and mutations, respectively. This ensures unbiased exploration of global optimum solutions. The fitness values of the children are also computed.

Step 3: All the individuals from previous generation and children are sorted according to their fitness values. The fittest individuals form the next generation of the population.

Steps 2 and 3 are repeated till fulfillment of the termination criteria.

The minimum and the maximum limit of the length of the inset slot was kept between 0.1 mm and 16 mm. The gap (q) between the feed-line and patch was kept at 1mm on both sides. The lowest cost obtained was for inset size of 13.366837201 mm or 13.37 mm. The antenna with finalized dimensions is shown in Figure 3.

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Figure 3. Antenna after optimization (All dimensions are in mm)