Fabry−Perot cavity antenna structure

The microstrip patch antenna is designed at 4.5 GHz on a substrate with dielectric constant ɛ _r = 4.4 and substrate thickness H _S = 1.6 mm. To construct a metasurface layer, square patches of 10 × 10 array of side D _HOLE = 3.5 mm are etched on a thin dielectric layer (H << Hs) in such a way that each cell is spaced by Dx × Dy = 3.5 × 3.5 mm². This metasurface layer is placed as a superstrate for the patch antenna at a distance H _MS = 0.8 mm above the patch. The dielectric medium between the patch and metasurface is air (ɛ ₀) and between patch and ground plane is FR4 (ɛ _r = 4.4). The feeding transmission line dimensions were optimized to match the 50 Ω feeding port. The detailed metasurface-loaded antenna is shown in Fig. 1(a) for the top view, Fig. 1(b) for the side view, and Fig. 1(c) for the bottom view (the bottom view shows the ground plane as PEC).

Fig. 1.

Geometry of the metasurface antenna (L _P = W _P = 16 mm, W _feed = 13.92 mm L _feed = 41.74 mm, L _MS = W _MS = 131 mm, L _g = W _g = 139 mm, D _X = D _y = 3.5 mm, D _hole = 3.5 mm) (a) top view (b) side view (c) bottom view.

The average tangential (transverse to z) field on it is given by (1) [Reference Lee, Yeo, Mittra and Park13].

(1)$$\left[{\matrix{ E \cr H \cr } } \right] = \displaystyle{1 \over {d^2}}\mathop {\rm \iint }\nolimits_{-{d \over 2}}^{{d \over 2}} \,\left[{\matrix{ e \cr h \cr } } \right]e^{\,jk.\rho }{\rm d}x.{\rm d}y$$

where E and H is tangential electric and magnetic field, d is periodicity, k is transverse wave vector, ρ is arbitrary observation point of the metasurface. Based on the phase reflection optimization properties of the metasurface the patch antenna radiation can be concentrated. In other words, it acts as a lens focusing on the EM radiations.

Fabry−Perot cavity design principles

The 3D geometry of the FPC antenna is shown in Fig. 2. In the design of the reflective structure, the attention was focused on the directive gain improvement and bandwidth enhancement simultaneously. The gain and fractional bandwidth are functions of the reflection coefficient in FP cavity are given by (2) and (3) [Reference Ji, Fu and Gong14, Reference Liu, Lei, Shi and Li15]:

(2)$$G = \displaystyle{{1 + R} \over {1-R}}$$

(3)$$FBW = \displaystyle{{\Delta f} \over {\,f_0}} = \displaystyle{\lambda \over {2\pi L_r}} \times \displaystyle{{1-R} \over {\surd R}}$$

where G is gain, R is the reflection coefficient of PRS, Lr is the resonant length-distance between the ground plane and the PRS, λ is the operating wavelength, Δf is the difference between the high and low frequencies (range of frequencies over which the return loss is acceptable), f ₀ is the operating frequency.

Fig. 2.

Fabry−Perot cavity:(a) enlarged view of the unit cell of superstrate (b) patch antenna with superstrate.

To examine the FPC operation condition, full-wave EM simulation using HFSS specifying periodic boundary conditions (PBCs) and Floquet ports to simulate the infinite periodic model of metamaterial superstrate has been done with simulated reflection coefficient (magnitude and phase) plotted in Fig. 3. It is obvious that the reflection phase (φ) of the proposed metasurface superstrate is 0 degrees and the reflection magnitude (p) is 0.65.

Fig. 3.

Reflection phase and magnitude of proposed superstrate with Floquet port set-up for FEM Analysis.

As per the geometrical optics model [Reference Razi, Bahadori and Rezaei16], the ground plane has a complex reflection coefficient superstrate has a complex reflection coefficient. The ground plane is a metallic conductor with a reflection phase close to π (φ1 ≈ π). The improvement in directivity [Reference Razi, Rezaei and Bahadori17] is given by (4) using the value of (p) from Fig. 3.

(4)$$\Delta D( {dB} ) = 10{\rm log}10\displaystyle{{1 + p} \over {1-p}}\;$$

Hence, ΔD is found out to be 6.7 dB using FEM. Theoretically, the refractive index (η) can be found as in (5).

(5)$$\eta = \displaystyle{{Im\{ {\ln ( {e^{\,j2nk_od}} ) } \} + 2m\pi -jRe\{ {\ln ( {e^{\,j2nkod}} ) } \} } \over {2k_od}}$$

where k ₀ is the wavenumber in free space, d is HS, n is the integer. Putting values η = 0.4. The reflection coefficient is related to the refractive index by (6).

(6)$$p = \displaystyle{{( 1-e^{( 2k_od) }) \eta } \over {( 1-\eta ^2e^{( 2k_od) }) }}$$

Putting values p = 0.67 and using (4), the improvement in directivity comes out to be 7 dB.

Fabry−Perot cavity design results

The simulated reflection coefficients of the unloaded and metasurface superstrate loaded patch antenna are shown in Fig. 4. The unloaded patch antenna is resonating at 4.5 GHz with a reflection coefficient = 12 dB. When using the metasurface superstrate, strong resonance is generated in the cavity which enhances the matching over a wider band, covering the original frequency (4.5 GHz). The metasurface antenna is in a good matching with a maximum return loss = 23.5 dB, at the resonance frequencies 4.5 and 5 GHz. The bandwidth increases more than four times (4.25 to 4.75 GHz). The FPC antenna with periodic square cells has the maximum impedance matching bandwidth of 11% (in comparison to 2% of the patch antenna).

Fig. 4.

Simulated reflection coefficient for the proposed antenna (without and with using metasurface substrate).

The fabricated antenna porotype is shown in Fig. 5. It is worth commenting that four pin screws of plastic material were used for the assembly of the antenna with superstrate on the top and ground plane on the bottom. A comparison between the reflection coefficient of the simulated and fabricated structures, shown in Fig. 5, is added to Fig. 4. The measurement was done using Keysight RF Fieldfox Network Analyzer. The comparison confirms that the measurement results agree with the simulated ones.

Fig. 5.

Fabricated Fabry−Perot cavity antenna.

To validate the effect of the employed metasurface layers, different loading elements, shown in Fig. 6, as periodic square cells, periodic S-shaped cells, periodic Ω-shaped cells, periodic hole array [Reference Razi and Rezaei18–Reference Rydström and Lindhe21] were examined. In objective of the designing reflective structure, the attention was focused on the directive gain improvement and bandwidth enhancement simultaneously. Many different periodic metamaterial elements such as square cell, S-shaped, Ω-shaped, hole element array, as shown in Fig. 6, have been considered. The PFC antenna loaded with these elements is as the metasurface layer were simulated and the simulated reflection curves are shown in Fig. 7. The periodic square cell elements were used which results in the best enhancement of the reflection coefficient. It has a maximum impedance matching bandwidth (−10 dB condition) of 22.2% in comparison to 8.89% of the patch antenna as calculated from equation 2.

Fig. 6.

Various reflective surfaces used as superstrate in the FPC antenna: (a) square cell, (b) S-element, (c) Ω-element (d) hole element.

Fig. 7.

Simulated reflection coefficient of the loaded patch antenna with S, Omega, patch, periodic holes cells.

Antenna radiation properties

The simulated directive-gain curves in XZ and YZ planes for the conventional patch antenna case and the metasurface superstrate loaded cases are plotted in (Figs 8(a) and 8(b)), respectively. As shown in Fig. 8(a), the peak directivity is 5 dB, and Front to back lobe ratio is 7 dB (5-(−2) dB). On the other hand, in Fig. 8(b), when the superstrate loads the antenna the peak directivity becomes 12 dB, and the front to back lobe ratio is 20 dB (12-(−8) dB). The enhancement in directivity agrees with the previously shown theoretical results (improvement by 7 dB). This leads to a 140% improvement in directivity and 186% improvement in front-to-back lobe ratio along with its physical protection.

Fig. 8.

Simulated directive pattern for the (a) single patch antenna, (b) proposed metasurface superstrate antenna in XZ and YZ planes.

Using AMITEC gain measurement set-up as shown in Fig. 9(a). This setting was placed in an anechoic chamber shown in Fig. 9(b) where we manually had to take this gain measurement setup inside the chamber for measuring the radiation pattern.

Fig. 9.

(a) AMITEC gain measurement set-up (b) comparison of directivity (dB) at 4.5 GHz of simulated and fabricated metasurface antenna.

In the setup given by AMITEC [‘https://amitec.co/training/antenna-training-system-ats04/’], transmitted power is −40 dBm, received power is −78.92 dBm, transmitting antenna gain is 10 dB, and the distance between transmitting and receiving antenna is 2 m. Using these values and taking logarithm on both sides of Friis Equation, the antenna-gain values of receiving antenna is 3.63 dB and directivity is 12.2 dB. Therefore, a 2% error in the directivity of the fabricated antenna is obtained when compared with simulated. The errors can be accounted to fabrication tolerances or testing environment etc. The upward shift in boresight gain is mainly due to the tolerance of the dielectric constant of the FR4 substrate that is specified as 4.4 ± 5% [Reference Dubovik and Cheshkov22].

Toroidal metal structure design

It is seen in the previous section that the metasurfaces are capable of improving the bandwidth of the antenna but still not to a level that the antenna could be called broadband (the metasurface is somehow narrowband). This section proposes a toroidal metal structure with the capability of enhancing directivity and bandwidth simultaneously.

As mentioned earlier, the square and circle SRR are two basic metamaterial resonator shapes. In this section, a third basic metamaterial shape i.e. a triangle has been explored. The triangular single ring unit cell (a toroidal metal structure) is shown in Fig. 10. The cell has been designed in such a way that its outer perimeter is the same as that of the circular SRR (r _ext = 6.9 mm). The advantage of using a triangle shape is a better degree of control as it has more variable parameters than a circle or square shape, i.e. length, breadth, height, and angle between two arms.

Fig. 10.

Toroidal metal structure with dimensions dx = 0.5 mm, dy = 1 mm, dx” = 0.5 mm, dy” = 1.3 mm, dx” = 0.15 mm, dy” = 0.3 mm, l = 4.8 mm, b = 4.3 mm, h = 3.5 mm.

The equivalent circuit of the Toroidal metal structure is shown in Fig. 11. The values of C _eq = 70 C _pul (i.e. capacitance per unit length) and LT = 1.59 × 10⁻⁸ H are obtained using the same formula as for square SRR [Reference Radescu and Vaman23]. The average length is calculated to be l _avg = 35.4 mm; thus, C _eq = 1.03 × 10⁻⁹ F. The value of resonant frequency is found out to be 3.93 GHz and for circular-shaped SRR is 4.53 GHz i.e. more than triangular SRR. Therefore, it is observed that the filling ratio i.e. (a/λ) of triangular SRR is more than circular SRR. Hence, it is a better candidate for metamaterial than a circular SRR.

Fig. 11.

Equivalent circuit model of toroidal metal structure.

The advantage of the toroidal cell is it has a high magnetic field as a consequence of toroidal currents in its anti-symmetric arms. Toroidal functionality can be explained by simulating a 2-port unit cell of meta-molecule Fig. 12(a) illustrates the magnetic field intensity distribution in a plane perpendicular to the array and Fig. 12(b) illustrates the surface current distribution forming toroidal moment because of their anti-symmetric flow in both arms. The circular loop current excited on the XY plane of the metasurface creates a magnetic moment on it. Thus, this leads to a toroidal moment oscillating back and forth along the axis of the metal molecule. The two side gaps also support a magnetic quadrupole moment. It is seen that the resonant magnetic fields at the center of two consecutive elements are in phase.

Fig. 12.

Simulated distribution plot of toroidal metal structure for (a) magnetic field (b) surface current.

Mathematical analysis

Considering metasurface superstrate patch antenna loaded with toroidal metal structures, the field reaching the observer plane (OP) can be found by Fourier propagating the field distribution at the intermediate superstrate up to the OP as shown in Fig. 13.

Fig. 13.

Plane setup for measurement of radiation at observer plane.

The total field (E) radiated by a 2 × 2 planar array of toroidal meta-atoms is obtained by summing the contributions from all at the position of the observer is given by (7).

(7)$$ E = \mathop \sum \limits_r E( r ) \approx \displaystyle{1 \over {\Delta ^2}}\mathop \int \limits_{array}^{} d^2rE( r ) $$

Equation (7) holds provided that all meta-atoms oscillate in phase and that the separation between meta-atoms is sufficiently smaller than the wavelength of incident radiation. The latter assumption replaces the sum over the unit cells with an integral over the array area (Δ²). In Fig. 13, three planes have been introduced: the array plane, the superstrate plane (SP), and OP [Reference Tatartschuk, Gneiding, Hesmer, Radkovskaya and Shamonina24–Reference Altshuler, O'Donnell and Yaghjian26]. Y _l,l”,m are the spherical vector harmonics that represent any vector field on the surface of the unit sphere in the same way as spherical harmonics represent any scalar field on the surface of the unit sphere.

The current is given by (8).

(8)$$I_{l, m} = \mathop \int \limits_0^{2\pi } d\varphi ^{\prime}\mathop \int \limits_0^\infty \rho .d\rho .Y_{l, m\;}\,( \theta , \;\varphi ^{\prime} + \pi ) \,{{{\rm exp}( {-ikr} ) } \over r}$$

where ρ and φ” are the radius and the angle specifying the position of toroidal meta-atoms, r is the distance between the observer and toroidal meta-atom, θ is the angle between the line connecting the observer to a toroidal meta-atom and its normal, and R is the distance from the observer to the toroidal array.

The directivity of the antenna is given by (9).

(9)$$D( {\theta , \;\varphi } ) = \displaystyle{{4\pi U( {\theta , \;\varphi } ) } \over {P_{rad}}}$$

where U (θ, φ) represents normalized radiation pattern and is given by (10).

(10)$$U( {\theta , \;\varphi } ) = \displaystyle{{r^2} \over {2\eta }}\vert {E_\varphi^2 + E_\theta^2 } \vert $$

Therefore, to calculate directivity, the equivalent circuit model [Reference Jagtap, Gupta, Chaskar, Kharche and Thakare27] can be used to determine the ratio of the total currents using the equivalent circuit, shown earlier in Fig. 11. In the equivalent circuit, the current entering the toroidal meta-atom is assumed to be Io, and I1 and I2 are the anti-symmetric currents in the triangular SRR. The segment joining the two triangular split rings plays a role in altering the direction of the current. However, its R, L, C can be considered negligible. The current and voltages in each meta-atom can be found out from (11) and (12) where V ₁ is the voltage at the input terminal and V ₂ is the voltage at the output terminal of corresponding rings in meta-atom.

(11)$$V1 = {-}\displaystyle{1 \over {\,j\omega }}.\displaystyle{{( {I_0-I_1} ) } \over C} = ( {R-j\omega L} ) \;I1\;$$

(12)$$V_2 = -\displaystyle{1 \over {\,j\omega }}\cdot \displaystyle{{I_2} \over C} = -( {R-j\omega L} ) I_2$$

Using (11) and (12), the ratio of currents can be found out as in (13)

(13a)$$\displaystyle{{I_1} \over {I_o}} = -\,\displaystyle{{-j\omega C( {R-j\omega L} ) } \over {X( \omega ) }}$$

(13b)$$\displaystyle{{I_2} \over {I_o}} = -\,\displaystyle{{-j\omega ( {-j\omega L} ) } \over {X( \omega ) }}\,$$

(13c)$$\eqalign{X( \omega ) & = -\omega ^3C^2\,[ {-}L^2\omega -2jRL] + \omega ^2[ ( R^2-C^2) -2CL] \cr & -2j\omega RC + 1}$$

A linear array of meta-atoms separated by distance “d” radiating in end-fire direction is formed as shown in Fig. 11 with excitation coefficients as I _o = 1, I _o’ = ±e ^jkd and d = 0.1 λ. The directivity given by (14) was obtained by putting optimal excitation coefficients for currents [Reference Feresidis and Vardaxoglou28] and then doing Taylor series expansion of ratio of excitation coefficients assuming kd << 1.

(14a)$$D = I_{1optimal} + I_{2optimal} + ee^{ {\pm} kd}$$

(14b)$$\left[{\displaystyle{{I_1} \over {I_2}}} \right] = optimal = \displaystyle{{1-\displaystyle{3 \over 2}pe^{ {\pm} jkd}} \over {e^{ {\pm} jkd}-\displaystyle{3 \over 2}p}}$$

(14c)$$p = \displaystyle{{sin( {kd} ) } \over {kd}}\left[{1-\displaystyle{1 \over {{( {kd} ) }^2}}} \right] + \displaystyle{{cos( {kd} ) } \over {{( {kd} ) }^2}}$$

Using the set of equations (14a)– 14c), D _optimal ≈ 28.57 or 14.5 dB

Energy harvesting applications

A parallel plate system is formed between a plane containing a toroid and a plane containing a superstrate. This is proposed capacitive energy harvester system, where the curling magnetic field density (B) accelerated by toroidal meta-atoms produces the changing electric field (E) as elucidated by Maxwell's equation [Reference Vaidya, Gupta, Mishra and Mukherjee29] as in (15)

(15)$$\nabla XB = \mu _0\varepsilon _0\displaystyle{{\partial E} \over {\partial t}}$$

where μ ₀ is the magnetic permeability and ɛ ₀ is the electric permittivity of free space between the two annular plates. The toroid meta-atoms are spaced at r ₁ and r ₂ from the patch feed point. The curl can now be written as

(16)$$\nabla XB = {-}\displaystyle{{\mu _0I} \over {4\pi }}\displaystyle{{\partial E} \over {\partial t}}\displaystyle{1 \over r}\left[{\displaystyle{\partial \over {\partial r}}\left({\mathop \int \limits_{r_1}^{r_2} \displaystyle{1 \over r}\partial r} \right)} \right]\hat{z}$$

Then by substituting (16) into (15), a model of changing electric field is obtained as

(17)$$\displaystyle{{\partial E} \over {\partial t}} = \displaystyle{{-\mu I} \over {8\pi \mu _0\varepsilon _o}}\left[{\displaystyle{1 \over {r_2^2 }}-\displaystyle{1 \over {r_1^2 }}} \right]\hat{z}\;\;$$

Assuming the time-varying current is to be alternating as a sinusoidal function of time and angular frequency (ω), the electric field between the superstrate and patch plane varying with time comes out to be

(18)$$E = \displaystyle{{-\mu I} \over {8\pi \mu _0\varepsilon _o}}\left[{\displaystyle{1 \over {r_2^2 }}-\displaystyle{1 \over {r_1^2 }}} \right]I_o\omega cos( {\omega t} ) \hat{z}\;\;\;$$

From (18), the induced voltage for capacitive energy harvester is obtained as

(19)$$V = \displaystyle{E \over d} = E = \displaystyle{{-\mu I} \over {8\pi H_{MS}\mu _0\varepsilon _o}}\left[{\displaystyle{1 \over {r_2^2 }}-\displaystyle{1 \over {r_1^2 }}} \right]\;I_o\omega \cos ( {\omega t} ) \hat{z}\;$$

Thus, it can be observed that the proposed capacitive energy harvester is a function of the gap “H _MS” between the plates i.e. the patch plane and SP.

Simulated results

The comparison of simulation of the toroidal metasurface antenna's directivity of a patch antenna with and without toroid is shown in Fig. 14. The patch with toroidal metal structure and superstrate directivity is 15 dB. There is a slight error between the theoretical and simulated values.

Fig. 14.

Comparison of directive gain (dB) at 4.5 GHz of simulated metasurface antenna with toroid /without toroid vs conventional antenna.

The comparison of simulation reflection coefficient curves of a toroidal metasurface antenna with a conventional patch antenna and without toroid is shown in Fig. 15. The 10 dB impedance bandwidth obtained through simulation of the patch with toroidal metal structure and superstrate is 34%. Therefore, the bandwidth increases eight times using the proposed structure comparing with the conventional patch. It can be claimed that this state-of-art improves the bandwidth by 800% and directivity by 200% which is the first-ever proposed in the literature, using a single layer of the metasurface.

Fig. 15.

Comparison of bandwidth at 4.5 GHz of simulated metasurface antenna with toroid /without toroid vs conventional antenna.

Simulated Current Distribution

The simulated current distribution at 4.5 GHz is shown in Fig. 16(a) for a single microstrip patch and Fig. 16(b) for the metasurface-loaded patch antenna. When the Fourier transform of a short pulse is taken, a broad frequency spectrum is obtained. This analogy is used in determining the radiation pattern of an antenna: the pattern can be thought of as the Fourier transform of the antenna's current or voltage distribution [Reference Singh, Abegaonkar and Koul30]. As a result, small antennas have broad radiation patterns (low directivity), and antennas with large uniform voltage or current distributions have very directional patterns (and thus, a high directivity) as evident from Fig. 16(b). This further confirms the directivity enhancement.

Fig. 16.

Simulated current distribution plot of (a) conventional patch antenna (b) metasurface superstrate antenna (c) antenna with proposed toroidal metal structure and superstrate.

The patch antenna is further loaded with four toroidal metal structures at areas where current density was comparatively higher (as shown in Fig. 16(b). As a consequence, the current distribution is more uniform and higher on the patch as seen in Fig. 16(c). There is a 38% increase in current density i.e. from 5 to 24 A/m on the patch.

Fabrication measured results

The fabricated prototype of the metasurface superstrate toroid antenna is shown in Fig. 17. The antenna performance was evaluated by checking its matching properties and EM radiation properties as shown in Fig. 18 by plotting the simulated and measured reflection coefficient. It is obvious that the results agree with each other and also both of them are lower than – 10 dB from almost 3.7 to 4.4 GHz and 4.42 GHz to near 6.5 GHz.

Fig. 17.

Fabricated toroid metasurface superstrate antenna.

Fig. 18.

Comparison of reflection coefficient at 4.5 GHz of simulated metasurface antenna with toroid vs fabricated antenna.

A comparison between simulated and measured antenna radiation patterns and reflection curves at 4.5 GHz is shown in Fig. 19. The results are close to each other. As shown in Fig. 19(a), the peak directivity is 15 dB, and Front to back lobe ratio is 20 dB (15-(−5) dB). The enhancement in directivity agrees with the previously shown theoretical results. This leads to a 200% improvement in directivity and 800% improvement in bandwidth with a 20 dB front-to-back lobe ratio along with its physical protection.

Fig. 19.

Comparison of directive gain (dB) at 4.6 GHz of simulated metasurface antenna with toroid vs fabricated antenna.

Using AMITEC gain measurement set-up as shown in Fig. 9(a), the radiation pattern was measured and plotted in Fig. 19(a). In the setup given by AMITEC, transmitted power is −40 dBm, received power is −75.09 dBm, transmitting antenna gain is 10 dB, and the distance between transmitting and receiving antenna is 2 m. Using these values and taking logarithm on both sides of Friis Equation, the antenna-gain values of receiving antenna is 6.6 dB and directivity is 15.2 dB. Therefore, a 2% error in the directivity of the fabricated antenna is obtained when compared with the simulated (shown in Fig. 14). The discrepancy between the simulated and measured results for reflection coefficient as shown in Fig. 19(b), the difference in peaks can be accounted to the tolerance of the dielectric constant of the FR4 substrate that is specified as 4.4 ± 5% [Reference Altshuler, O'Donnell and Yaghjian26] and to fabrication tolerances or testing environment, etc. However, the 10 dB bandwidth is measured the same as the simulated one.

Finally, a comparison of the proposed antenna with existing state of art antenna structures [Reference Jagtap, Gupta, Chaskar, Kharche and Thakare27–Reference Chacko, Augustin and Denidni31] using FPC has listed in Table 1. All the reference antennas have larger dimensions except [Reference Chacko, Augustin and Denidni31, Reference Vaid and Mittal32]. The bandwidth of the proposed antennas is significantly more than the reference antennas. In [Reference Oliner33, Reference Monsoriu, Depine and Silvestre34], the antennas are wideband as they use superstrate but this has led to a decrement in the directivity of the antenna. Also, in [Reference Jagtap, Gupta, Chaskar, Kharche and Thakare27, Reference Vaidya, Gupta, Mishra and Mukherjee29], the antennas have high directivity at the expense of decreasing the antenna bandwidth. It is noticeable that the proposed antenna has the highest front-to-back lobe ratio. Therefore, it can be claimed that the proposed antenna which is designed using just a single layer of superstrate improves the antenna directivity and bandwidth simultaneously and has a compact size and lower height in comparison with the reported antennas.

Table 1.

Comparison of proposed work with reference antennas.