AMC design layout with unit cell

The AMC reflects the back lobe radiation of the EM wave, directed toward the source wave. This orientation causes in-phase interference with the source EM wave, which improves the antenna's gain and bandwidth.

Antenna designing begins with metamaterials unit cells; cells' purpose is to achieve resonance from 2.8 to 10 GHz × frequency range. The proposed element cell model is shown in Fig. 1(a); each unit cell is 12 × 12 mm², which involves a pair of copper ring shape patch with a rectangular strip. The dimensions of the designed section are varied so that AMC arrangements and antenna resonant frequency should be matched, and the AMC arrangement length should be less than λ/2. By inserting the inner one rectangle further, the gap in stripes is adjusted. Therefore, AMC size is limited to 12 mm.

Fig. 1.

(a) Unit cell. (b) Outer substrate. (c) Inner substrate. (d) The layered structure of the proposed design.

After designing the AMC structure, a coplanar waveguide (CPW)-fed antenna as the top layer is implemented with this AMC structure. The finishing creation is portrayed in Fig. 1(d). The cavity between the layers is 6.2 mm.

The phase reflection property of the AMC structure is determined by Ansys 15.2, as shown in Fig. 2(a). The AMC is designed by using two uniplanar layers with a square ring stub. Figure 2(b) shows the evolution steps of the AMC structure.

Fig. 2.

(a) Simulated phase reflection of the unit cell. (b) Evolution steps of the unit cell in the AMC structure.

Single ring structure reported in step 1, which exhibits two bands, 3.5–3.9 and 5.9–6.3 GHz, apart from that it also offers a phase reflection from +90 to −90°. In step 2, two square ring slots are used, which results in approximately no change to the first band, but the second band is shifted to the higher side (6.5–7.4 GHz). A phase reflection of +90 to −90° between 6.9 and 7.2 GHz is obtained when the double layer dielectric structure is used with a single square ring resonator, as shown in step 3. Step 3 structure fails to cover our required frequency band. This shortfall can be instigated by using a double layer substrate with a double square ring structure, as shown in step 4.

An AMC based on circular patch is modeled logically by an inductor–capacitor circuit with the characteristic, as shown in Fig. 3. This circuit constitutes surface impedance Z _s whose value depends on the cell geometry, the square patches' capacity, and the inductance produced by the substratum's height. This model gives good results for cell size, whose wavelength is shorter than the phase of the cell.

Fig. 3.

Circuit model for the unit cell.

The resonant frequency can be calculated using the standard formula:

(1)$$f_0 = \displaystyle{1 \over {2\pi \sqrt {LC} }}, \;$$

where C is the fringing capacitor and L is the inductance.

For the fringing capacitor

(2)$$C_{\rm f} = \displaystyle{{\varepsilon _0\varepsilon _{\rm r}A + g} \over {4\pi g}}, \;$$

where A is the area of capacitor and g is the gap between two strips.

For the inductance

(3)$$L = \mu _0\mu _{\rm r}h.$$

It can be found that the equivalent capacitance and inductance can be adjusted correctly by adjusting these parameters. Then the reflection phase bandwidth of two AMC units can be flexibly controlled. The calculated values of C, L and for unit cell are listed in Table 3.

CPW antenna structure

Initially, an antenna was proposed with CPW feed. Owing to its easy availability and cheaper cost, the antenna is made on FR-4 glass epoxy with a thickness of 1.6 mm and a dielectric constant of 4.4 (Figs 4 and 5).

Fig. 4.

Proposed design without AMC.

Fig. 5.

Proposed fabricated CPW-fed antenna.

The 0.5 mm gap is used between the feed line and ground to get wider bandwidth. The strip has a resilient outcome of raising the electrical path in lower and upper operational frequencies.

Antenna results

The double-layer AMC surface structure plays a significant role in enhancing CPW performance, which shows suitability for microwave sensors.

Figure 6 shows the simulated reflection coefficient of the proposed antenna with perfect electric ground (PEC) ground, single layer AMC, dual-layer AMC, without AMC, and measured reflection coefficient with dual-layer AMC. Simulated and measurement results show that the antenna's operating band is 2.1–10 GHz without AMC, with only one resonant frequency of 5.8 GHz. The antenna's working band is 2.8–10 GHz with AMC with two resonant frequencies of 4.8 and 8.8 GHz. The proposed antenna achieves almost the same simulated impedance bandwidth of 130.6% in a 2.1–10 GHz frequency band with different resonant peaks in all cases and achieves measured impedance bandwidth of 122.5% in a 2.8–10 GHz frequency band with dual-layer AMC.

Fig. 6.

Simulated and measured reflection coefficient of the antenna with PEC ground, without AMC, and with AMC.

The proposed antenna gain is shown in Fig. 7. The proposed antenna's peak gain without AMC, with PEC ground, with single-layer, and dual-layer AMC are 4, 4.5, 8.5, and 12.5 dBi, respectively. The measured peak gain with dual-layer AMC is 12.5 dBi. Figure 8 shows the antenna's 3D polar plot at resonant frequencies of 4.8 and 8.8 GHz that indicate directional antenna radiation.

Fig. 7.

Gain of the antenna without AMC, with PEC ground, and with AMC.

Fig. 8.

Antenna 3D polar plot at (a) 4.8 GHz and (b) 8.8 GHz.

Breast tumor detection

Breast phantom

The electrical properties of tissue in the breast are mentioned in [Reference Michaowska-Samonek, Miaskowski and Wac-Wodarczyk15] considering Gaussian random variables (almost 10% variation from their usual mark) values. Table 4 show the electrical properties of woman breast tissues at a frequency of 6.5 GHz.

Table 3.

Calculated L, C, and f values of the unit cell

Table 4.

Electrical properties of woman breast tissues

Tumor having a conductivity of 4 S/m and relative permittivity of 50 are inserted in the tissue. These tumors have different radii (2.5, 3.5, and 4.5 mm). The simulated 3D phantom model is shown in Fig. 9.

Fig. 9.

3D phantom model (r ₁ = 55 mm, r ₂ = 50 mm, and r ₃ = 40 mm).

Principal component analysis

It is a dimensional reduction technique that identifies the co-relations and patterns in data sets that can be transformed into another data set. In Fig. 10, it is also clear that reflected power is degraded due to the absorption of power by the tumor. The PCAs are carried out on the reflection coefficient to determine the difference between malignant and normal phantoms. The eigenvalue is found with the help of reflection coefficient data, which are given in Table 5. PCA results are obtained with the help of these eigenvalues, as shown in Fig. 11. These results indicate the variation between the normal breast phantom, single-tumor breast phantom, and multiple tumors breast phantom. PCA graph is formed with two-component principal component 1 (PC1) and principal component 2 (PC2), and their corresponding values for different phantoms are provided. With normal phantom, the value of PC1 and PC2 is 0.7 and −0.4, respectively. For single tumor phantom, PC1 = 0.7 and PC2 = 0.4 likewise for multiple tumors PC1 = 0.03 and PC2 = 0.85. Therefore, we can easily differentiate a tumorous phantom from a normal phantom.

Fig. 10.

Simulated reflection coefficient of the antenna without phantom, phantoms with and without tumor.

Fig. 11.

PCA results of the phantoms.

Table 5.

Eigenvalue and variance results of phantoms

Specific absorption rate

SAR can be defined as the amount of EM energy engrossed by any realistic material in the EM field. In humans' case, it is measured as the power absorbed by tissue divided by its mass (W/kg). The SAR value is calculated in two ways first is local SAR, and the second one is Avg. SAR [Reference Xie, Guo, Xu, Li and Stoica16].

Local SAR

A value with a certain mass is found for each point in (W/kg) [Reference Subramanian, Sundarambal and Nirmal17]

(4)$${\rm SA}{\rm R}_{{\rm local}}( {r, \;\omega } ) = \displaystyle{{\sigma ( {r, \;\;\omega } ) {\vert {E( {r, \;\omega } ) } \vert }^2} \over {2\rho ( r ) }}.$$

Avg. SAR

It is the average value for a section. At every point, a particular shape (cube, sphere) with a definite mass is selected. Then by integrating over the cube, power loss density is calculated and after that the calculated power loss density is divided by the cubes or sphere mass [Reference Michaowska-Samonek, Miaskowski and Wac-Wodarczyk15]

(5)$${\rm SA}{\rm R}_{{\rm lAvg}}( {r, \;\omega } ) = \displaystyle{1 \over v}\mathop \smallint \nolimits \displaystyle{{\sigma ( {r, \;\;\omega } ) {\vert {E( {r, \;\omega } ) } \vert }^2} \over {2\rho ( r ) }}, \;$$

where ρ(r) is the mass density at r in (kg/m³), σ(r, ω) is the conductivity (S/m), r is the position vector, V is the volume in (m³), and E(r, ω) is the E-field confined in tissue (V/m).

Tumor detection

The SAR value of the breast phantom model is simulated for the tissue at 4.8 GHz. Cancer cells or malignant tumor cells have been located everyplace in the breast tissue model.

Single tumor

The tumor is placed at a location (−5, 16, 30) mm. The radius of the tumor is 2.5 mm. The maximum local SAR values for tumor, glandular tissue, fatty tissues, and skin are 248.45, 1.964, 2.0205, and 44.154 W/kg, respectively. Similarly, the maximum average SAR for the tumor, glandular, fatty, and skin are 70.35, 0.54, 0.954, and 4.650 W/kg, respectively, as mentioned in Table 6.

Table 6.

Simulated SAR_1 g values for 2.5 mm tumor located at (−5, 16, 30) mm co-ordinates

When another tumor of 3.5 mm size has been inserted, the SAR1 g values for the tumor, glandular tissue, fatty tissues, and skin have been given in Table 7.

Table 7.

Simulated SAR_1 g values for 3.5 mm tumor located at (−5, 26, 30) mm co-ordinates

Two tumors

When two tumors (2.5 and 3.5 mm) are present in phantom at co-ordinates (−5, 16, 30) mm and (−5, 26, 30) mm, the SAR values for tumor, glandular, fatty, skin, and the tissue are presented in Table 8.

Table 8.

Simulated SAR_1 g values for two tumors with radii 2.5 and 3.5 mm at (−5, 16, 30) mm and (−5, 16, 30) mm co-ordinates

Simulated SAR values for 2.5 and 4.5 mm tumor located at (−5, 16, 30) mm and (−5, 26, 40) mm coordinates, respectively, are presented in Table 9.

Table 9.

Simulated SAR_1 g values for 2.5 and 4.5 mm tumors at locations (−5, 16, 30) mm and (−5, 26, 40) mm, respectively

Three tumors

Three tumors with radii 2.5, 3.5 and 4.5 mm are introduced at location (−5, 16, 30) mm, (−5, 26, 30) mm, and (−5, 26, 40) mm, respectively. The SAR_1 g values for tumor, glandular tissue, fatty tissues, and skin are presented in Table 10.

Table 10.

Simulated SAR_1 g values for 3.5, 2.5, and 4.5 mm tumor at locations (−5, 16, 30) mm, (−5, 26, 30) mm, and (−5, 26, 40) mm, respectively

Table 11 shows the values of SAR due to tumors at locations (−5, 16, 30) mm, (−5, 26, 30) mm, and (−5, 26, 40) mm with sizes of 4.5, 3.5, and 2.5 mm, respectively.

Table 11.

Simulated SAR_1 g values for 4.5, 3.5, and 2.5 mm tumors at locations (−5, 16, 30) mm, (−5, 26, 30) mm, and (−5, 26, 40) mm, respectively

Figure 12 shows the maximum local SAR values for glandular tissue, fatty tissues, and skin with different tumor locations. This chart indicates that the local SAR value of cancerous tissue is much higher than normal tissue.

Fig. 12.

The maximum local SAR of breast phantom with different locations and different sizes of tumors: (a) without tumor – SAR average and (b) with tumor – SAR average.

The gain of the proposed antenna is upto11.8 dB, and due to the directional pattern, the radiated power of the antenna covers the whole breast for more power absorption. Therefore, the SAR value is very high in the tumor phantom. The proposed antenna's local and average SAR values for phantom without tumor are 24.56 and 7.42 W/kg, respectively. The tumorous phantom absorbs more power than the normal phantom. If the proposed antenna's SAR values for the phantom are >24.56 and 7.42 W/kg, it is considered a tumorous phantom. Figure 13 shows the comparison between breast models with and without tumors. It has been observed that the average and local overall SAR values for the tumorous breast phantom are higher. This system can detect a tumor of size 2.5 mm, so this system can detect cancer at an early stage.

Fig. 13.

Simulated SAR_1 g value for the breast model with tumor and without tumor.