Unit cell design and characterization

Two different elements are designed to obtain dual resonance in Ku/K frequency bands with a frequency ratio larger than 1.5. The elements are chosen to have varied surface current distribution and thereby reduce the mutual coupling existing between the neighboring RA elements. As researchers in [Reference Misra and Chowdhury13] have experimentally proved that the bandwidth offered by concentric rings is larger than that offered by a single ring or circular patches [Reference Vidhyashree14], the Ku band resonance is achieved using concentric circular rings whose radius b is determined using the expression stated in [Reference Hsieh and Chang15].

(1)$$b = \displaystyle{{3 \times {10}^8} \over {2\pi f_{\rm L}\sqrt {\varepsilon _{reff}} }}$$

where f _L is the Ku band resonant frequency (14.25 GHz), and $\varepsilon _{reff}$ is the effective relative dielectric constant. As the Ku band element is co-centric with the source, a modified Malta cross, placed offset with respect to the source is used as the K band element. These elements are developed on a 0.254 mm thick Rogers RT5870 substrate separated from the ground by a 2 mm air gap. The relative permittivity of the substrate is 2.33 and the loss tangent tan δ is 0.0012. As the element size is 10.5 mm, the periodicity of the integrated elements is 0.5λ ₀ and 0.78λ ₀ at the resonant frequencies 14.25 and 22.5 GHz respectively. The parametric description of the proposed unit cell and its layers are represented in Figs 1(a) and 1(b).

Fig. 1. (a) Unit cell structure, (b) Side view of the unit cell, (c) Infinite array model.

Evolution and parametric analysis

The co-centric and offset alignment of the integrated elements of the dual-band is shown in the infinite array model depicted in Fig. 1(c). The initial design is made in the CST design environment using a circular ring and a Malta cross. The reflection phase and magnitude response of the designed cell is simulated under unit cell boundary conditions in the frequency domain. A phase variation of 290 and 310° are observed at the resonant frequencies through the Floquet ports set. The phase variation is obtained by changing the Malta cross size and the ring size. As the design of RA requires a minimum of 360° phase change, the single circular ring is replaced by a concentric dual circular ring.

As reported in [Reference Narayanasamy, Mohammed, Savarimuthu, Sivasamy and Kanagasabai16], a reduced gap of 0.25 mm (g ₁) is maintained between the concentric rings to increase the mutual coupling between them. The variation in the concentric ring size produces an increased phase variation of 520° at the Ku band resonant frequency, 14.25 GHz. Similarly, the inductive nature of the delay line attached to the Malta cross varies its surface impedance and thereby the current distribution. This variation in the delay line length relative to the Malta size improves the phase range offered by the K band element to 360°. Hence, the minimum 360° phase variation required for designing the proposed dual-band RA is obtained by varying the size of the integrated elements. The evolution of the Ku and K band elements is comparatively portrayed in Figs 2(a) and 2(b) respectively. As the resonance over the two desired bands of operation needs to be individually controlled, the mutual coupling between the integrated elements should be avoided. Hence, the phase variations obtained by controlling their physical changes are done using two independent parameters. The radius, b of the concentric rings decides the resonance frequency. The gap between the concentric rings is maintained minimum to increase their mutual coupling. Hence, the degree of freedom in the Ku band element is restricted to the width of the rings, g.

Fig. 2. Evolution of (a) Ku band element, (b) K band element.

As shown in Fig. 3(a) the ring width is varied and the reflection phase response is observed. Since the phase slope and phase range are almost the same for all three widths, the least value is chosen to avoid the grating lobes which might occur due to the neighboring K band element. As the Malta size, W _p, and the delay line length, d are alone the degrees of freedom in the K band element, the effect of air gap thickness over the phase slope and thereby the bandwidth of the unit cell is analyzed as a common factor. Since, as shown in Fig. 3(b), the 2 mm air gap produces a lower phase slope and increased phase range compared to the other values, the optimized design of the proposed unit cell is made with the parameters as shown in Table 1.

Fig. 3. Reflection characteristics for different (a) Circular ring width, g (b) air layer thickness, t, (c) angles of incidence at Ku band, (d) angles of incidence at K band.

Table 1. Parameters of the proposed unit cell

Further, as the periodicity of the K band element is larger than 0.5λ ₀, the performance of the reflectarray element in both the bands is observed at various angles of incidence as depicted in Figs 3(c) and 3(d). It is evident that the Ku element deviates in performance at lower angle and K element at larger angle.

Element design and analysis

To attain dual resonance with reduced optimization complexity and a large frequency ratio, the integrated elements are designed and analyzed using independent equivalent circuits. The researchers in [Reference Hopkins and Free17] have considered the concentric circular ring element as two microstrip lines separated by a small gap. As shown in Fig. 4(a), these lines are represented as parallel RLC combinations. Their values are obtained using equations (2)–(4) reported in [Reference Ketavath18].

(2)$$R_1 = \displaystyle{{Z_0} \over {\alpha [ {2\pi ( {b + g} ) } ] }}, \;\,{\rm and}\,R_2 = \displaystyle{{Z_0} \over {\alpha [ {2\pi ( {b-g1} ) } ] }}$$

(3)$$C_1 = \displaystyle{\pi \over {Z_0\omega _{01}}}, \;\,{\rm and}\,C_2 = \displaystyle{\pi \over {Z_0\omega _{02}}}$$

(4)$$L_1 = \displaystyle{1 \over {C_1\omega _{01}^2 }}, \;\,{\rm and}\,L_2 = \displaystyle{1 \over {C_2\omega _{02}^2 }}$$

where R ₁, L ₁, and C ₁ are the equivalent parameters of the outer ring whose radius is (b + g),

$$\omega _{01} = \displaystyle{{2\pi c} \over {( {b + g} ) }}, \;\;\omega _{02} = \displaystyle{{2\pi c} \over {( {b-g_1} ) }}.$$

Fig. 4. Electrical equivalents of (a) Ku band element, (b) K band element, (c) Equivalent circuit validation using CST and ADS.

Z ₀ is the characteristic impedance, α is the attenuation constant, R ₂, L ₂, and C ₂ are the equivalent parameters of the inner ring whose radius is (b − g ₁), and C _t represents the summation of the capacitance effect due to the gap between rings, the gap between the substrate and ground, and the fringing capacitance.

Similarly, the equivalent circuit of the K band element is obtained as described in [Reference Saravanan and Rangachar19]. The inductive parts of the Malta cross and the four diagonal slots are represented using the parallel LC combinations as depicted in Fig. 4(b). The capacitance between the substrate and the ground is included as C _s in the equivalent circuit. These computations are validated by comparing the corresponding reflection characteristics obtained from CST and the S parameter results of the equivalent circuit simulated in the ADS environment. The comparative results are reported in Fig. 4(c).

Considering the influence of the neighboring Ku band element, the reflection characteristics of the K band element are observed with a fixed-size circular ring within the specified unit cell boundary. The variation in the reflection magnitude w.r.to the incremental values of the Malta cross size, W _p as shown in Fig. 5(a) provides a 92% reflection at 22.5 GHz. To study the influence of the Ku band element over the performance of the K band element, the reflection phase characteristics of the K band element is observed for varying values of circular ring radius, b as shown in Fig. 5(b). Similarly, the reflection characteristics of the Ku band element are observed with a fixed-size Malta cross offset placed within the specified unit cell boundary.

Fig. 5. The reflection characteristics of K band element for Ku element size (a) fixed, (b) varying.

The variation of the phase and magnitude of the reflection coefficient, S₁₁ is analyzed for varying values of the radius of the circular ring, b as depicted in Fig. 6(a). The reflection magnitude of −0.47 dB at the resonant frequency, 14.25 GHz represents 97% reflection offered by the Ku band element. A similar analysis is done with varied values of Malta cross size, W _p as shown in Fig. 6(b). Hence it is evident from Figs 5(b) and 6(b) that the reflection characteristics of the integrated elements in both the bands varies independently w.r.to each other. The enhanced reflection characteristics of the proposed unit cell make it a suitable element for the design of dual-band reflectarray antenna operating in the Ku band uplink (13.51–14.94 GHz), and the K band frequencies (22.2–23.15 GHz). Hence, the proposed RA befits operations involved in fixed satellite services and earth exploration satellites.

Fig. 6. The reflection characteristics of Ku band element for K element size (a) fixed, (b) varying.

Reflectarray design

The phase compensation values for the 23 × 23 RA to produce resonance at Ku band center frequency, 14.25 GHz is calculated based on the equation described in [Reference Huang and Encinar20] considering the focal distance as 19.32 cm (f/D = 0.8) [Reference Narayanasamy, Mohammed, Savarimuthu, Sivasamy and Kanagasabai16]. The equation provides the phase value to be offered by each Ku band element considering that the center element is concentric with the source. As the K band elements need to be interleaved between the Ku band elements, the phase compensation to be provided by them is calculated considering that the middle K band element is offset from the source by half of the unit cell size, E _s (5.25 mm). Equation (5) provides the distance, d_i used for calculating the phase compensation required at the K band resonant frequency of 22.5 GHz.

(5)$$d_i( {offset} ) = \sqrt {{\left({x_i-\displaystyle{{E_s} \over 2}} \right)}^2 + {\left({y_i-\displaystyle{{E_s} \over 2}} \right)}^2 + {( f ) }^2} $$

where E _s is the element size and f is the focal distance of the RA.

Comparing the corresponding phase compensation values with the phase curves obtained at Ku and K band resonant frequencies, a 24 × 24 cm² RA is developed on the Rogers RT5870 substrate. As described in the previous section, a 2 mm thick air layer separates the substrate from the ground. Due to the symmetricity in the phase distribution, 78 different sizes of circular rings as shown in Fig. 7(a) are distributed over the substrate. Since the K band elements are placed off-centric with the source, their symmetricity in phase distribution varies as shown in Fig. 7(b). Hence 276 different sizes of Malta cross are distributed over the substrate for K band operation. This arrangement of integrated elements for dual-band operation avoids the optimization of the unit cell for achieving phase matching at the resonant frequencies.

Fig. 7. Phase compensation matrix for 23 × 23 reflectarray (a) Co-centric Ku band elements, (b) Offset placed K band elements.

Note: b_i, W _pi – Varying circular ring and Malta cross sizes

Experimental analysis

The designed RA is fabricated using the conventional photolithography process. Figure 8 depicts the measurement setup of the fabricated prototype. The fabricated RA is placed in an anechoic chamber of size 7 × 3 × 3 m. The pyramidal horn antenna used as the transmitting source is located at the far field distance co-centric with the RA. The source produces a directional beam within a frequency range of 800 to 1800 MHz. The dimensions of the pyramidal horn are a flare length of 54 mm and a waveguide aperture of size 20 mm × 10 mm. The peak gain of the horn is 17.4 dBi at 12 GHz and the beam width is 22°.

Fig. 8. The measurement setup of the fabricated prototype with (a) Ku band receiver, (b) K/Ka receiver.

The Ku band performance of the RA is measured by placing a Ku 5041 model pyramidal receiving horn at the focal distance of 19.3 cm from the prototype. At the same distance, the Ku horn is replaced by a K band receiving horn to measure the performance of the RA within the K band operating range. Similarly, the source is replaced by an 18 to 40 GHz K/Ka pyramidal horn which provides 15.5 dB gain at 22 GHz with 22° beamwidth. The flare length of the horn is 20.5 cm and the aperture size of its waveguide is 20 × 11 mm. The radiation pattern at different frequencies over the operating range in both bands is measured. As shown in Figs 9(a) and 9(b), the simulated and measured patterns are plotted at different frequencies. The relative magnitude of the simulated pattern is 28.4 and 27.1 dB at 14.25 and 22.5 GHz respectively.

Fig. 9. Simulated and measured radiation pattern for different frequencies in (a) Ku band (b) K band, and (c) measured cross-polarization at different frequencies, (d) Gain versus frequency plot.

The simulated SLL at these frequencies is less than −22 and −12 dB respectively. The increased value of SLL at the K band frequency is due to the offset alignment of the K band elements and the resulting phase error. Similarly, the cross-polarization levels observed at these frequencies are less than −32.2 and −30 dB respectively. The measured radiation pattern magnitudes are 28 and 26 dB at the Ku and K band resonant frequencies respectively. The beam width of the measured pattern is 6.5 and 7.1° at 14.25 and 22.5 GHz respectively. The measured SLL and the cross-polarization values are less than −21/−11 dB and −31/−28 dB respectively at both frequencies.

Since the substrate thickness is just 0.254 mm, the arrangement of a 2 mm air gap between the substrate and ground and the alignment of the prototype in the measurement setup, causes unavoidable phase errors resulting in the deviation of the measured values from the simulated results. The cross-polarization levels at different frequencies in both bands are presented in Fig. 9(c). The measured and simulated gain of the RA calculated from the pattern magnitudes using the Friss transmission formula is plotted against the operating range of frequencies as shown in Fig. 9(d). The 529 Ku band elements and the 529 K band elements offer a simulated peak gain of 28.62 dBi at 14.25 GHz and 26.92 dBi at 22.5 GHz. The corresponding measured values are 28 and 26.4 dBi respectively. Though an equal number of elements are utilized for the dual resonance operation, the gain offered by the K band elements is slightly lesser than the Ku gain because of the phase error introduced due to their offset alignment with respect to the source. Due to the fabrication errors and the misalignment error during measurement, the measured gain is slightly lesser than the simulated results. The concentric circular rings offer a 1 dB gain bandwidth of 9.8% (13.5–14.9 GHz) at the Ku band and the modified Malta cross offers a bandwidth of 3.5% (22.3–23.1 GHz). Though the percentage bandwidth is less, it covers the entire Ku band uplink frequency range required for fixed satellite services and the K band range needed for earth exploration satellites. The roll-off rate between the two bands of operation is high providing good isolation between the bands. The aperture efficiency, A _e of the proposed antenna with gain in dB is calculated as

(6)$$A_{\rm e} = \displaystyle{{c^2 \times {10}^{G( {dB} ) /10}} \over {\,f^2 \times 4\pi \times A_{\rm p}}} \times 100\% $$

where A _p is the physical aperture of the antenna and f is the resonant frequency. Therefore, the measured aperture efficiency is 38.65% at 14.25 GHz and 10.72% at 22.5 GHz. Due to the non-uniformity in the thin substrate and the thin airgap maintained between the substrate and the ground causes much reduced efficiency in the K band. To attain a better efficiency, the arrangement of the elements is reversed compared to the proposed design and simulated. The K band elements are arranged co-centric with horn and the Ku band elements are placed off-centered in the alternate design. The simulated gain obtained from this design is 29.5 dBi at 22 GHz and 27.8 dBi at 14 GHz. The corresponding calculated aperture efficiency is 38.24% at 14 GHz and 22.9% at 22 GHz. A comparison of the measured performance characteristics and the physical aspects of the proposed dual-band RA with other works discussed in the literature is reported in Table 2. Based on the comparison the following inferences are made:

1. 1) The design of the dual resonant elements in [Reference Su, Yi and Wu3, Reference Zhu, Yang, Mcgloin, Liao and Xue8, Reference Hamzavi-Zarghani and Atlasbaf10] and [Reference Saravanan and Rangachar19] requires the matching of phase response obtained at the resonant frequencies through complex optimization procedures. The proposed RA uses integrated elements with different phase responses. Hence optimization of the unit cell is not required.

2. 2) The maximum reduction in gain in the frequencies between the bands of dual resonance in the proposed RA is 6 dB. This value is 3 dB larger than [Reference Zhu, Yang, Mcgloin, Liao and Xue8], and 4 dB larger than [Reference Hamzavi-Zarghani and Atlasbaf10].

3. 3) The gain offered by the proposed RA is at least 3 dB more than the gain reported in [Reference Zhu, Yang, Mcgloin, Liao and Xue8] and 5 dB larger than that in [Reference Hamzavi-Zarghani and Atlasbaf10]. The gain reported in [Reference Saravanan and Rangachar19] is much larger because of the utilization of the sub-reflector.

4. 4) Within the reduced aperture size, nearly 400 more elements are accommodated in the proposed RA compared to the RA described in [Reference Zhu, Yang, Mcgloin, Liao and Xue8] and [Reference Saravanan and Rangachar19].

5. 5) The cross-polarization level of the proposed RA is at least 1 dB less than [Reference Hamzavi-Zarghani and Atlasbaf10] and [Reference Saravanan and Rangachar19].

6. 6) The SLL value of the RA designed with co-centric elements is 5 dB less than those reported in [Reference Su, Yi and Wu3, Reference Hamzavi-Zarghani and Atlasbaf10] and [Reference Saravanan and Rangachar19]. Even the SLL value of the off-centered elements is 1 dB less than [Reference Su, Yi and Wu3].

Table 2. Comparison of the proposed RA with previous works

BW, Bandwidth; NR, Not reported in the paper

Hence the enhanced dual-band performance of the proposed RA is more useful for fixed satellite services and the all-weather, day and night, global observations of the earth and its atmosphere.