II. SSVA DESIGN AND OPTIMIZATION

The geometric layout of proposed SSVA is shown in Fig. 1(a). This structural modification of radiating fins, stub, and cavity assist in achieving the compactness and electrical dimension of the antenna with high gain. The antenna dimension is 45 mm × 53 mm fabricated on Rogers RT/Druid 5870 substrates with dielectric constant of 2.33 and loss tangent 0.0012. The radiation properties of SSVA are determined by a set of exponential curves, tapered rate, cavity structure, slot line, back wall offset, stub arrangement, feeding position, and the structure of radiating fins.

Fig. 1.

(a) SSVA geometric layout, (b) fabricated prototype (front), (c) fabricated prototype (back).

In SSVA, all these parameters are adjusted and radiating fins are modified by etching several slots. The irregular slot is made to increase the electrical length and achieve higher gain. The main radiating lobe of SSVA is its flare, with height Hf = 43 mm and length Lf = 40 mm with tapered rate R = 0.05 (factor determining the opening rate of the flare) of the inner exponential profile. The exponential curve that employs Vivaldi antenna is defined as:

(1) $$x = \pm C_1e^{Rz} + C_2,$$

$${\rm where\;} \;C_1 = \displaystyle{{x_2 - x_1} \over {(e^{Rz_2} - e^{Rz_1})}}\quad {\rm and}\quad \; \; C_2 = \displaystyle{{x_1e^{Rz_2} - x_2e^{Rz_1}} \over {(e^{Rz_2} - e^{Rz_1})}}.$$

The points (x1, z1) and (x2, z2) are the peak point P2 and the bottom points P1 of the exponential curve. The cavity diameter (Cd) of resonant cavity plays a vital role in return loss characteristic of the proposed antenna. In the proposed antenna, cavity diameter Cd of resonant cavity is kept at 9 mm, to maintain the lower end S ₁₁ ≤ −10 dB limitation at 2.7 GHz. The cavity is adjusted with the equation:

(2) $$C_a = 0.5C_d - 0.5C_d(\cos \theta ),$$

$${\rm \; where}\;\theta = \sin \left( {\displaystyle{{S_w} \over {C_d}}} \right).$$

Table 1 presents the value of antenna parameters. The ratio of slotted (Sa) and non-slotted (Sna) area is 62:38. On both sides, there are three identical slots (S1, S2, S3) and on upper side there is an extra slot S4. The reason of this extra slot is to increase the efficiency, which increases the efficiency about 3%. In the x-axis, the gap of each slot is 4 mm, and in the y-axis, it is from 4.5 to 7.5 mm (S ₁, S ₂, S ₃, S ₄) with single increment. The inner surface is increased by a factor of 2 mm. An identical quadrilateral has taken on the upper back of the radiating fins. The microstrip coupler (Lc) is situated between the microstrip tapper and stub. A 50 Ω SMA connector with 2.08 dielectric constant and 0.000462 S/m conductivity is used to feed the antenna connected to microstrip tapered line.

Table 1.

Structure design parameters of SSVA (in mm).

The effects of slots on the radiating fins to the reflection coefficient and gain are shown in Fig. 2. Without slot S ₁₁ is 3.9–6.4 GHz, with lower slot S ₁₁ is 2.9–6.4 GHz, with the upper slot S ₁₁ is 3.0–6.5 GHz, and for all the slots (proposed), S ₁₁ is 2.7–7 GHz with reflection coefficient <−10 dB. Without slot and with the lower slot, the peak gain is about 6.7 dBi; with the upper slot, the peak gain is 7.1 dBi; but with all slots (proposed), the peak gain is 7.5 dBi.

Fig. 2.

Effect of the slot on the radiating fins to the (a) S ₁₁ and (b) gain.

By using the modified radiating fins (proposed) configuration, better bandwidth (about 1.8 GHz increased) and gain (about 0.8 dBi more) have been achieved. The effect of stub radius to reflection coefficient and gain is shown in Fig. 3. By observing from 8.5 to 10.5 mm, it gives about 500 MHz improved bandwidth and 0.3 dBi higher gain for 10 mm stub radius. It is so, because the stub radius is proportional to the flare height. A strong surface current is raised around the cavity, which influences the directivity of the antenna.

Fig. 3.

Effect of stub radius to the (a) S ₁₁ and (b) gain.

III. ANTENNA PERFORMANCE ANALYSIS

To verify how the side slot structure improves reflection coefficient, gain, and the efficiency with the reduced size, the SSVA is presented in Fig. 1(b). The proposed antenna has been analyzed and optimized using the software CST microwave studio built-in trust region framework under local optimization. The measured results were obtained using the Agilent E8362C vector network analyzer and Satimo near-field measurement laboratory (UKM StarLab) using Satimo passive measurement and SatEnv software. The −10 dB operating bandwidth of proposed SSVA is 2.7–7 GHz with two resonants at 3.83 and 5.56 GHz, which cover typical MBI shown in Fig 4(a). The measured and simulated results have good agreement though a little discrepancy is observed. The discrepancies between simulated and measured results can be attributed to fabrication tolerance and the coaxial cable losses during measurement, which was not considered in simulation.

Fig. 4.

Simulated and measured (a) S ₁₁, (b) efficiency and gain.

The peak gain of proposed prototype is 7.7 dBi and the radiation efficiency is about 86% on an average over the operating bandwidth shown in Fig. 4(b). Antenna parameter S ₁₁ is affected by stub angle, substrate type, and Cd, whereas gain is affected by stub radius. The modified radiating fins play a vital role on both S ₁₁ and gain. The measured and simulated radiation patterns in two principal planes – namely co-plane and cross-plane at resonant frequencies – are displayed in Fig. 5. According to the satimo measurement laboratory, the xz-plane is taken as co-plane where φ = 0° and z-plane is taken as a cross-plane where φ = 90°. The main beam is in the boresight. More than 10 dB front-to-back ratio and absence of side lobe ensure the higher range of the scattered signal with low unwanted noise and higher directivity, which is required for microwave imaging applications. The slots in the radiating fins remarkably change the antenna characteristics, especially increases the operating bandwidth, gain, and efficiency.

Fig. 5.

Measured and simulated radiation patterns: (a) 3.83 GHz, (b) 5.5 GHz.

The normalized antenna performance in the face-to-face and side-by-side orientation with the distance of 230 mm is shown in Fig. 6. From the transmitting and receiving pulse, it is observed that in the face-to-face orientation the signal has a lower attenuation than that of the side-by-side orientation. For this, the antenna is recommended to use face-to-face orientation in microwave imaging applications. The highest value of cross-correlation among transmitting and receiving pulse evaluates the signal distortion presented as fidelity factor. The fidelity factor for face to face is 0.93 and for side by side is 0.61, which prove the directionality and lower distortion of the signal.

Fig. 6.

Transmitted and received pulse in (a) face to face and (b) side by side.

By considering the physical size of antenna, the minimum quality factor club can be obtained from [Reference Mavridis, Anagnostou and Chryssomallis8] Qlb = ηQ, where Q = 1/k ³ a ³ + 1/ka, wave number k = 2π/λ, and a is the sphere radius, the smallest sphere that encloses the antenna. The upper band of bandwidth efficiency product $(B\eta r)_{ub} = 1/\sqrt 2 [1/ka + 1/k^3a^3]^{ - 1}$ Fig. 7 shows the Qm and (B ηr)ub for the antenna with the peak efficiency 89% and for different values of ka.

Fig. 7.

Theoretical limits and calculated Qa and (B ηr) _ub .

With the value of using the resonant bandwidth of proposed antenna ka = 1.8. From the curve, it can be noted that for ka = 1.8, the minimum limit of Qm is 0.69 and limit of (B ηr)ub is 0.97. The quality factor of the presented antenna is estimated as:

(3) $$Q_a = \displaystyle{{2\sqrt \beta} \over B}\quad {\rm Where}\quad \sqrt \beta = \displaystyle{{s - 1} \over {2\surd s}} \le 1.$$

For the maximum allowable VSWR s = 2, the proposed antenna achieved Qa = 0.73 and B ηr = 0.95. From the graph, the resultant value and the attainable values are close to the antenna parameters which prove the antenna design optimum.

Figure 8 shows the simulation model of breast with proposed Vivaldi antenna. The antenna is kept at the breast phantom and effects of breast tissues are studied. To study the power coupled to the breast tissue, we compute the power radiated from the surfaces of a breast model with radius of 90 mm and height is 100 mm shown in Fig. 8. The antennas are placed at 5 mm distance from breast phantom. The phantom contains four layers, namely, the skin layer, the breast tissue layer or fat, and the normal air layer. The skin layer has the following properties: dielectric constant = 38, thickness = 2.5 mm, and conductivity = 1.49 S/m. The breast tissue layer has a maximum width of 8.75 cm, with conductivity = 0.141 S/m and dielectric constant = 5.14. The radiation efficiency of proposed SSVA prototype with breast model is shown in Fig. 9. The radiation efficiency is around 70% over the bandwidth with breast model whereas without model is more than 80%.

Fig. 8.

Cross-section of breast model simulation setup: (a) front view, (b) perspective view.

Fig. 9.

Radiation efficiency of proposed prototype with breast model.

The near field directivity (NFD) factor is computed using the formula in [Reference Amineh, Trehan and Nikolova9, Reference Amineh, Ravan, Trehan and Nikolova10], which is the ratio of radiated power through the front of the antenna and the total power radiated through the surface of the breast model. Figure 10 shows the NFD factor for proposed SSVA. About 90% of the total power is radiated into the breast tissue.

Fig. 10.

Simulated NFD for the proposed SSVA.