Topological optimization

In the topological structural process, the parametric analysis is one of the important optimization techniques to achieve the desired results with respective proposed microstrip antenna geometry. In this section, we investigated the effect of rectangular slot width and length variation on the circular elements. When there was no additional slot present on the circular patch, the array shows a non-resonance behavior at the desired frequency, and hence, the analysis was arranged in such a way that, the slot width W_slot = 0.5–1.5 mm and slot length L_slot = 1–18 mm. From this observation, resonance varies with respective to return loss, and it has been presented in Figs 3(a) and 3(b). While incorporating the additional slots on the circular patch to enhance the impedance matching of the antenna, the patch resonates at 1.8–3 GHz, and therefore brings the response at desired frequencies of 1.8, 2.1, 2.1, and 2.5 GHz. Further, two more slots are incorporated on the circular patch. Finally, three slots are incorporated on the circular patch then the circular microstrip patch probe array resonated at desired quad-band frequencies; the obtained results are as shown in Figs 3 and 4.

Fig. 3.

(a) Slot width varies with a constant slot length, (b) slot length varies with a constant slot width.

Fig. 4.

The return loss of proposed antenna at 1.8–2.5 GHz.

Figures 3(a) and 3(b) show the impact of slot width on resonant frequency and impedance matching conditions at the circular patch are greater than its length. The resonance frequency is directly proportional to slot width, while impedance remains nearly constant. The detailed descriptions are as follows.

Figure 3a shows the variation of slot width with resonance frequency but slot length should be kept constant at 18 mm. With increasing value of slot width from 0.5 to 1.5 mm, the resonance frequency shifts toward the lower side at 1.5 mm. The acquired desired resonance frequencies are of 1.8, 2.1, 2.45, 2.5 GHz.

Figure 3b demonstrates the circular array element slot length varies from 1 to 18 mm with respective resonance frequency and the slot width kept constant at 1.5 mm; meanwhile, slot length varies from 1 to 18 mm. When the slot length is 1–17 mm, the observed resonance range is of 17–2.45 GHz, and hence, whenever increasing to a further value of 18 mm, the resonance response and enhanced impedance matching have been observed at desired frequencies, therefore, the obtained accurate results are shown in Fig. 4.

Figures 5–9 present the E-field, current distribution, gain, efficiency, and the radiation pattern of the probe array at 1.8–2.5 GHz, as per the theory of fundamental transverse magnetic (TM₁₀) mode in microstrip patch antennas [Reference Balanis16, Reference Garg, Bhartia, Bahl and Ittipiboon17], the E-field is maximum where current is minimum at the center of any patch, both vice versa. In the case of the proposed circular patch probe array, the E-field is maximum toward the probe and the surface current is maximum at the center of the circular patch. The total gain of the array is around 4.3 dB, the efficiency of the array is 80–90% at 1.8–2.5 GHz as shown in Fig. 8, and the circular probe array radiation patterns are omnidirectional and radiation is high at 1.8–2.5 GHz as shown in Fig. 9.

Fig. 5.

Simulated E-field distribution.

Fig. 6.

Surface current distribution.

Fig. 7.

Gain (3D view) of the array.

Fig. 8.

The efficiency of the array.

Fig. 9.

Radiation pattern.

Analytical analysis of electromagnetic wave interaction to human head tissue

When electromagnetic energy interacts with the human head or biological body, it may cause harm to health because of mobile phones and other regularly used RF and microwave communication devices. In the analytical analysis environment, some assumptions are made to predict the electric field and temperature distribution on the human head as shown in equation (15). To verify the assumptions, the 3D human head model has been created in the free space environment with scattering boundary conditions. The interaction of electromagnetic wave propagation on the half-human head model analysis has been presented by using Maxwell equations as follows [Reference Wessapan, Srisawatdhisukul and Rattanadecho18–Reference Shen and Zhang21].

(9)$$\nabla \times \displaystyle{1 \over {\mu _r}}\nabla \times E-\varphi _o^2 \varepsilon _rE = 0, \;$$

(10)$$Z_{in} = \displaystyle{V \over I} = \displaystyle{{E_sl} \over I}, \;$$

where Z_in is the input impedance in (ohms), V is the edge voltage (v), I is the electric field current, l is the edge length,E _s is the E-field of the source, φ_ois the free space wavenumber (m⁻¹).

(11)$$n \times E = 0.$$

For the patch antenna, perfect electric condition (PEC) inner and outer boundary condition (BC) between the two mediums is

(12)$$n \times ( \epsilon _1-\epsilon _2).$$

Truncated free space scattering boundary conditions are

(13)$$\eqalign{n \times ( {\nabla \times E} ) -\sigma \times ( {E \times n} ) & = {-}n \times ( E_i \cr & \times j\varphi ( {n-\varphi } ) {\rm exp}( {-j\varphi.r} ) , \;}$$

where σ = jφn is electric conductivity, E _i is an incident plane wave, j = $\;\sqrt {-1}$, φ is the wavenumber (m−1).

The temperature distribution within the human head has been evaluated by using the penne bio-heat analysis as per Maxwell equations [Reference Wessapan, Srisawatdhisukul and Rattanadecho18, Reference Wessapan, Srisawatdhisukul and Rattanadecho19]. According to the ICNIRP guide standard [1], another definition of SAR in accordance with temperature distribution is given in equation (16).

(14)$$\rho C\displaystyle{{\partial T} \over {\partial t}} = \nabla.( {k\nabla T} ) + \rho _bC_b\omega _b( {T_b-T} ) + Q_{met} + Q_{ext}, \;$$

(15)$$Q_{ext} = \displaystyle{1 \over 2}\;\sigma _{tissue}E^2 = \displaystyle{\rho \over 2}\;.SAR, \;$$

(16)$$SAR = C\displaystyle{{\partial T} \over {\partial t}} = \displaystyle{\sigma \over \rho }\;E^2, \;$$

where ρ is the tissue density (kg/m³), C is the heat capacity of the tissue (J/kg K), δ is the thermal conductivity of tissue (W/m K), T is the tissue temperature (^oC), T _b is the temperature of blood (^oC), ρ _b is the density of blood (kg/m³), C _bis the heat capacity of blood (3960 J/kg K), ω _b is the blood perfusion rate (1/s), Q _met is the metabolism heat source (W/m³), and Q _ext is the external heat source (electromagnetic heat-source density) (W/m³).

The external heat source term is equal to the resistive heat generated by the electromagnetic field [electromagnetic power absorbed (P_a)], which is defined as [Reference Wessapan, Srisawatdhisukul and Rattanadecho18].

(17)$$P_a = Q_{ext\;} = \displaystyle{{\sigma _{tiss}} \over 2}\;E^2 = \displaystyle{\rho \over 2}.SAR.$$

The heat transfer is considered only in the human head, which does not include parts of the surrounding space. As shown in Fig. 10, the outer surface of the human head corresponding to assumption (11) is considered to be a thermally insulated boundary condition as given below in equation.

(18)$$n.( {\delta \nabla T_t} ) = 0.$$

Fig. 10.

Analytically explained the 3D half-human head model.

It is assumed that no contact resistance occurs between the internal organs of the human head. Therefore, the internal boundaries are assumed to be continuous as follows

(19)$$n.( {\delta_u\nabla T_{t_u}-\delta_d\nabla T_{t_d}} ) = 0.$$

Figure 10 portrays an analytical analysis of the electromagnetic spectrum penetration on the human head when we use mobile phones, as well as how electromagnetic radiation pretends to incrementally heat with respect to time. Table 3 showcases the experimental results based on equations (1–4).