Proposed structure

The schematic representation and design steps of the proposed structure are presented in Figs 1 and 2. An equilateral triangular patch of edge S is taken as a reference in Fig. 1(a). This equilateral triangular patch is fed by a microstrip line of length L _ml and width W _ml. The input impedance of the patch is matched with the characteristics impedance of microstrip line through inset feed of length y ₀ and slot width w ₀. The structure is designed for 5 GHz and detailed parameters are given in Table 1.

Fig. 1. Schematic representation of the triangular patch antenna with (a) inset feed and (b) asymmetric offset inset feed.

Fig. 2. Schematic representation and step-by-step evolution of the proposed design; (a) case I – Ant_1, (b) case II – Ant_2, (c) case III – Ant_3, (d) case IV – Ant_4, and (e) case V – Ant_5.

Table 1. Design specification of antenna designs along with their metamaterials

Length L _ml of the microstrip line is calculated as [Reference Kumar and Ray24, Reference Balanis25]

(1)$$L_{ml} = \displaystyle{c \over {4f_r\sqrt {\varepsilon _{effml}}}}, $$

where

(2)$$\; \varepsilon _{effml} = \displaystyle{{\varepsilon _r + 1} \over 2} + \displaystyle{{0.5(\varepsilon _r - 1)} \over {\sqrt {1 + 12(h/W_{ml})}}}, $$

(3)$$S = S_{eff} - \displaystyle{{4h} \over {\sqrt {\varepsilon _r}}}, $$

where S, S _eff, h, and ε _r are the edge of the equilateral triangular patch, the effective length of the edge of the equilateral triangular patch, height of the dielectric substrate, and relative dielectric constant of the dielectric substrate, respectively.

Effective length S _eff is calculated as [Reference Balanis25]

(4)$$S_{eff} = \displaystyle{{2C} \over {3f_r\sqrt {\varepsilon _{eff}}}}, $$

where C, ε _eff, and f _r are the speed of light in free space, effective dielectric constant, and resonance frequency, respectively.

Further, the asymmetric feed is introduced in the equilateral triangular patch as shown in Fig. 1(b). The microstrip line is shifted toward its right by a distance d for asymmetric feed. Offset feed method for triangular patch antenna has been reported for the enhancement of impedance bandwidth [Reference Thomas and Sreenivasan11, Reference Ammann and Chen12]. Asymmetric feed provides directional radiation in the end-fire direction (z-direction) as shown in Fig. 3. It is observed that antenna starts to radiate in the end-fire direction as the offset distance d is increased to the value of S/4.

Fig. 3. The radiation pattern of a triangular patch antenna for different values of offset distance d; (a) E-plane, (b) H-plane.

The schematic representation and step-by-step evolution of the proposed structure are shown in Fig. 2. In case I, offset feeding is introduced in the equilateral triangular patch to achieve the directional radiation pattern and the antenna structure is referred as Ant_1, which is shown in Fig. 1(b).

For case II, a dipole is designed for 2.5 GHz and embedded with a triangular patch, which is referred as Ant_2 and shown in Fig. 2(b). Half-length of the dipole is embedded with a patch on the signal plane, whereas a slot of length (Ln ₁ + x ₁) is embedded on the ground plane; in which, x ₁ is the width of the connecting strip. The length L _n1 and width W _n1 of the first dipole are calculated from equations (5) and (6), respectively.

Half-length L _n/2 of the dipole is the quarter wavelength and calculated as

(5)$$\displaystyle{{L_n} \over 2} = \displaystyle{{\lambda _{eff}} \over 4} = \displaystyle{c \over {4f_r\sqrt {\varepsilon _{eff}}}}, $$

where c, ε _eff, and f _r are the speed of light in free space, effective permittivity (ε_eff ≤ ε_r), and resonating frequency of dipole, respectively. Resonant frequency f _r of the dipole is taken as 2.5 GHz in this study.

Width W _n1 of the dipole corresponding to its length L _n1 is related to its impedance and calculated by equation (6) [Reference Balanis25]. The impedance of the dipole is matched to the input impedance of the edge of the microstrip patch.

(6)$$W_n = \displaystyle{{\pi L_n} \over {exp((R_{in}(x = 0)/120) + 2.25)}},$$

where R _in (x = 0) is the input impedance at the edge of microstrip patch antenna and calculated by equation (7) [Reference Kumar and Ray24]:

(7)$$R_{in}(x = 0) = \displaystyle{{50} \over {cos^2(\pi S_0/S)}},$$

where S is the edge of the equilateral triangular patch and S ₀ is the length of the transmission line corresponding to 50 Ω impedance.

In case III, one more dipole is embedded and the structure is referred as Ant_3, which is shown in Fig. 2(c). The second dipole is designed for 4 GHz, and the length L _n2 and width W _n2 are calculated by equations (5) and (6), respectively. Their relevant values are adjusted up to the minimum extent to maintain the resonant peak at the specific frequency by parametric analysis.

In case IV, an inter digital capacitor-loaded loop resonator (IDCLLR) [Reference Tong13, Reference Peng and Zhang14] is embedded below the right corner of the edge of the triangular patch as shown in Fig. 2(d) and the structure is referred as Ant_4.

In case V, a slot and a slit of rectangular split-ring resonators (SRR) [Reference Lin and Cui15, Reference Siddiqui16] are embedded in the left corner of the triangular patch as shown in Fig. 2(e) and the structure is referred as Ant_5. The top and bottom views of a schematic representation of the proposed Ant_5 (case V) are shown in Figs 4(a) and 4(b), respectively. The dimensions of a single unit cell of rectangular SRR and IDCLLR are shown in Fig. 5, and the real permittivity, permeability, and refractive index of the unit cell are shown in Figs 6(a) and 6(b). The detailed dimensions of all the structures are listed in Table 1.

Fig. 4. Schematic representation of the proposed design Ant_5; (a) top view, (b) ground plane, (c) side view, and (d) fabricated prototype.

Fig. 5. Schematic representation of a single unit; (a) rectangle SRR, (b) IDCLLR.

Fig. 6. Metamaterial characteristic of a single unit; (a) rectangular SRR, (b) IDCLLR.

Analysis and result discussion

The FR-4 Epoxy substrate of dimensions 35 mm × 35 mm × 1.5748 mm is used to analyze the proposed antennas. Fabrication is done by standard photolithography process and measurement is done by Agilent™PNA-L Series Network Analyzer and Agilent™ Spectrum Analyzer. A fabricated prototype of Ant_5 is depicted in Fig. 4(d). Figure 7 shows the S ₁₁ variation with the frequencies Ant_1, Ant_2, Ant_3, and Ant_4 corresponding to cases I–IV. Ant_5 shows five resonating frequency bands with very small frequency ratios as shown in Fig. 8. S ₁₁ and VSWR characteristics with the frequency of Ant_5 is shown in Figs 8(a) and 8(b), respectively. All five resonating bands are achieved by the presented mathematical design equations; however, the least parametric analysis is done to achieve sharp resonance for the specific applications. Ant_5 resonates at 2.58, 3.17, 3.42, 4.0, and 5.3 GHz with very small frequency ratios of the values 1.2286, 1.078, 1.169, and 1.325 between two consecutive resonant frequencies, respectively. A comparative study is shown in Table 2.

Fig. 7. S ₁₁ characteristics with the frequency of Ant_1, Ant_2, Ant_3, and Ant_4.

Fig. 8. Measured and simulated characteristics with the frequency of the proposed antenna Ant_5; (a) S ₁₁, (b) VSWR.

Table 2. Frequency ratio of the proposed design Ant_5 in comparison with recent works

The current distribution of the proposed antenna Ant_5 at each resonant frequency is shown in Fig. 9. The working mechanism of the proposed antenna could be defined with the help of the shown current distribution: (i) dipoles embedded in the front of the triangular patch and ground are mainly contributing to generate 2.58 GHz frequency as shown in Fig. 9(a); (ii) 3.17 GHz frequency is achieved due to a slot and a slit of rectangular SRR, which can be clearly observed in Fig. 9(b); (iii) IDCLLR combined with a slit and a slot are playing a role in generating 3.42 GHz frequency; and finally (iv) 4 and 5.3 GHz frequencies are achieved due to the triangular patch with inset feed as shown in Figs 9(d) and 9(e), respectively.

Fig. 9. Current distributions at (a) 2.58 GHz, (b) 3.17 GHz, (c) 3.42 GHz, (d) 4 GHz, and(e) 5.3 GHz.

Radiation patterns of the proposed antenna Ant_5 are shown in Fig. 10. E-plane patterns of Ant_5 are shown in Figs 10(a), 10(c), 10(e), 10(g), and 10(i); whereas H-plane patterns are shown in Figs 10(b), 10(d), 10(f), 10(h), and 10(j) at 2.58, 3.17, 3.42, 4.0, and 5.3 GHz frequencies, respectively. It is observed from Fig. 10 that Ant_5 shows good radiation characteristics in both major planes. Measured results are in good agreement with the simulated results.

Fig. 10a. Measured and simulated normalized radiation pattern of the proposed antenna; (a) E-plane at 2.58 GHz, (b) H-plane at 2.58 GHz, (c) E-plane at 3.17 GHz, (d) H-plane at 3.17 GHz, (e) E-plane at 3.42 GHz, (f) H-plane at 3.42 GHz, (g) E-plane at 4 GHz, (h) H-plane at 4 GHz, (i) E-plane at 5.3 GHz, and (j) H-plane at 5.3 GHz.

Fig. 10b. Continued.

Figure 11 shows the measured gain variation with the frequency of the proposed antenna. Ant_5 shows antenna gain of about 3.23, 2.9, 2.8, 4.01, and 3.49 dBi at frequencies 2.58, 3.17, 3.42, 4, and 5.3 GHz, respectively. Antenna efficiency is shown in Fig. 12, and it is observed that the proposed antenna Ant_5 shows antenna efficiency around 87.5, 83.05, 82.45, 89.35, and 88.93% at respective bands. Performance of proposed Ant_5 is compared in Table 3.

Fig. 11. Measured gain variation with the frequency of the proposed antenna.

Fig. 12. Measured antenna efficiency variation with the frequency of the proposed antenna Ant_5.

Table 3. Performance of the proposed design Ant_5 in comparison with recent works