Configuration and operating concepts

Geometry of the antenna

The antenna unit consists of two-layer of Rogers 5880 substrate (ε _r = 2.2, tan δ = 0.0009) and two pairs of MED. Stepped microstrip lines coupled by rectangular slits form a feeder network. The height of the upper dielectric substrate is h ₁, and the height of the lower dielectric substrate is h ₂. The electric dipole near the rectangular slit is etched with rectangular tangent corners, and the magnetic dipole is three metal vias of radius “R”, and the center of the metal vias located in the middle of the three metal vias is offset by a distance of “d ₂” from the centers of the other two vias. The other pair of MED is side by side with the first one, with the electric dipoles etching the tangent angles of the triangles and adding elliptical perturbations, the magnetic dipoles are three metal through-holes of radius “R”, centered on the same line. The 3D view (Fig. 1a), side view (Fig. 1b), power feed view (Fig. 1c), and radiation patch view (Fig. 1d) of the antenna are shown in Fig. 1.

Figure 1. Geometry of proposed CP antenna. (a) 3D view, (b) side view, (c) power feed view, and (d) radiation patch view. L = 9.5 mm, W = 9.5 mm, L _p = 1.1 mm, W _p = 4.3 mm, L _pp = 0.97 mm, W _pp = 1.8 mm, R = 0.2 mm, R ₁ = 0.6 mm, d ₁ = 0.57 mm, d ₂ = 0.4 mm, L _px = 0.75 mm, W _py = 3 mm, P _x = 0.15 mm, P _y = 0.15 mm, S _l = 5.4 mm, S _w = 0.8 mm, G _l1 = 0.2 mm, G _w1 = 5 mm, G _l2 = 0.8 mm, G _w2 = 1.6 mm, G _l3 = 3.8 mm, G _w3 = 0.8 mm, h ₁ = 0.508 mm, h ₂ = 0.254 mm.

Operating mechanism

The initial antenna is a pair of MED, a rectangular coupling slot, and a rectangular microstrip line, as shown in Fig. 2a, antenna II is based on antenna I with a rectangular cut angle for the electric dipole, evolution of rectangular microstrip lines into T-shaped microstrip lines, and antenna III is side by side to add a pair of MED and the electric dipole with a triangular cutting angle, evolution of the T-shaped microstrip line into stepped microstrip line. Finally, antenna IV based on antenna III adds an elliptical perturbation, where the axis ratio is obtained by the formula (1), “a” is the long axis of the ellipse and “b” is the short axis of the ellipse:

Figure 2. (a) Configuration evolution of CP antennas, (b) a comparison of the reflection coefficient S11 of four antennas, (c) a comparison of the AR of four antennas, (d) a comparison of the magnitude difference of four antennas, (e) a comparison of the phase difference of four antennas, and (f) a comparison of the electric field vector distribution in T/4 of four antennas at 29.5 GHz.

(1)\begin{equation}AR = 20*{\text{lg}}\left( {a/b} \right)\end{equation}

Figure 2b shows that four antennas obtain a wide IBW, and from Fig. 2c, it can be seen that antenna II with a rectangular cut angle to the electric dipole shows the possibility of adjusting to CP, antenna III achieves an ARBW of 8% from 23.16 to 25.12 GHz, while antenna IV with the addition of elliptical perturbation expands the ARBW by 18.6% from 26.4 to 31.9 GHz. The CP principle of antenna realization is equal amplitude in horizontal and vertical directions and a phase difference of 90°. Simulation results of magnitude difference and phase difference of the four antennas are given in Fig. 2d and e. The results show that antenna I does not satisfy the principle of CP, antenna II has the possibility of realizing CP, antenna III has the performance of CP but with narrow ARBW, and antenna IV has equal amplitude and phase difference of −90°. ARBW is wider and the phase difference of antenna IV is −90°, so the designed antenna is a left-hand CP (LHCP) antenna.

Figure 2f simulates the distribution of the surface currents of the four antennas at 29.5 GHz at different times [Reference Ghosh, Islam and Das12]. The antenna I has no obvious rotation of surface current with time at t = 0 and t = T/4, antenna II has a relatively weak rotation of surface current with time at t = 0 and t = T/4, antenna III has a clockwise rotation of surface current with time at t = 0 and t = T/4, and antenna IV has a clockwise rotation of surface current with time at t = 0 and t = T/4 and strong rotation. The current distributions at t = T/2 and t = 3T/4 are similar to those at t = 0 and t = T/4, respectively, but in opposite directions. Combined with the working principle of CP, we can know that the antenna is an LHCP antenna, and after loading a pair of parasitic patches and adding elliptical perturbation, the ARBW is greatly expanded.

The four perturbation structures with the same equivalent area are compared, and the axial ratio results are shown in Fig. 3a; the circular polarization performance when the perturbation structure is elliptical under the same area is best to analyze the parameters of the elliptical long-axis radius, and the axial ratio results are shown in Fig. 3b; and the circular polarization performance is best when the long axis radius R ₁ = 0.6 mm.

Figure 3. (a) AR of four cases and (b) AR of R ₁.

Equivalent circuit model

In order to explain the working principle of the designed CP antenna more clearly, the equivalent circuit characteristics of the CP antenna are analyzed and its model is shown in Fig. 4a. The input port is equivalent to a resistor of 50 Ω, and the feeder line can be equivalent to an inductor L ₁ and a series resistor R ₁. The input signal passes through substrate 1, which can be equivalent to Tx line 1 and reaches the uppermost radiation patch through the rectangular slot and substrate 2. The rectangular slot is equivalent to the band-pass filter of the inductor (L ₂) in series with the capacitor (C ₂), and substrate 2 can be equivalent to Tx line 2. The metal via etched in substrate 2 can be equivalent to shunt inductance (L ₃), in which the Tx line 2 is connected in parallel. The radiation patch of the antenna can be equivalent to the series connection of radiation resistance (Rrad), inductance (L ₄), and capacitance (C ₁). The overall circuit is drawn in Advanced Design System (ADS) software, and the parameters are as follows: L ₁ = 0.6 pH, R ₁ = 26.8 Ω, L ₂ = 35.5 pH, C ₂ = 29.7 fF, L ₃ = 30.5 pH, Rrad = 63.8 Ω, C ₁ = 8.4 fF, and L ₄ = 3.4 fH. A good agreement between the simulated high-frequency structure simulator (HFSS) response and the numerically calculated advanced design system(ADS) result is observed in Fig. 4b.

Figure 4. (a) Equivalent circuit modeling and (b) results of ADS and HFSS.

The design of the antenna array

To obtain higher antenna gain in the application, a four-way microstrip power divider is designed [Reference Bai, Wang and Zou13], and four radiating elements are arranged into a periodic structure, which forms a planar 2 × 2 antenna array. The antenna is designed and optimized using Ansys full-wave electromagnetic simulation software. The power divider and the antenna array are shown in Fig. 5a, and the S-parameters of the power divider are shown in Fig. 5b. To investigate the effect of the spacing between the antenna units on the antenna array S11 and AR, a parametric analysis was performed, the results for antenna arrays S11 and AR corresponding to different unit spacing are shown in Fig. 5c. From Fig. 5b, it can be seen that S11 of input port #1 within the IBW of the antenna is lower than −15 dB, #2, #3, #4, and #5 the insertion loss is −6 dB between the four output ports and input port. The isolation between the output ports S23/S45/S25/S34 is lower than −25 dB, which indicates that the mutual coupling between the output ports is weak. The optimal cell spacing Dis = 9.5 mm can be obtained from Fig. 5c, and five circular holes with DD = 2 mm diameter were etched around the antenna for fixation; to reduce the loss, the compensation structure is designed in the feed network, that is the angle is cut, in which w, x, d, and m are indicated in Fig. 5a, and the best way to cut the angle can be obtained by formula (2):

(2)\begin{equation}m = 0.52 + 0.65 \times {e^{\left[ { - 1.35{*}\left( {w/h} \right)} \right]}}\end{equation}

Figure 5. (a) Antenna array and power divider, (b) S-parameters of the power divider, and (c) S11 for different parameters of Dis.

where w = 0.8 mm, h = 0.254 mm, and, therefore, the “m” is calculated at around 0.529.

Next, the gain of the unit or array and the half-power beamwidth are compared, and the result is shown in Fig. 6. The gain increases and half-power beamwidths narrow of antenna arrays. Where the gain can be obtained by the formula (3), “D” is the directivity of the antenna, and “λ ₀” is the wavelength:

(3)\begin{equation}{\textrm{Gain}} = 10{\textrm{lg}}\left\{ {4.5{*}\!\left({D \over {\lambda 0}}\right)\!{^\wedge{}}2} \right\}\end{equation}

Figure 6. (a) The gain of the antenna unit and array and (b) the HPBW of the antenna unit and array.

Simulation and measurement

Figures 7a and b show the top view and bottom view of the antenna. Respectively, simulations and measurements were performed for the proposed antenna. Figure 7c shows the simulated and measured S11 as well as the AR of the antenna array. It can be seen that the measured and simulated curves of the antenna match well, and a relative bandwidth of 41.6% (22.28–33.97 GHz) and an ARBW of 16.6% (26.42–31.21 GHz) are obtained. The measured peak gain of the antenna reaches 13.89 dBic as seen in Fig. 7d. The radiation efficiency of the antenna is higher than 89% in the whole operating band. The radiation efficiency can be obtained by the formula (4), where “D” and “Ap” are the directivity and aperture size of the antenna and “λ ₀” is the wavelength:

(4)\begin{equation}{\text{ Efficiency}} = \frac{{D\lambda 0^\wedge{} 2}}{{4\pi Ap}}\end{equation}

Figure 7. The fabricated antenna and the simulated and measured results. (a) The top view, (b) the bottom view, (c) S11 and AR, and (d) gain and radiation efficiency.

Figures 8a and b give the measured and simulated directional diagrams of the xoz-plane and yoz-plane at 27 GHz and 31.5 GHz. It can be seen that the simulated and measured radiation patterns coincide with each other. The main polarization is LHCP, the right-hand CP (RHCP) level is low, and the measured cross-polarization is below −20 dB in the whole operating band. The antenna achieves a stable radiation performance.

Figure 8. xoz-plane and yoz-plane radiation patterns (a) at 27 GHz and (b) at 31.5 GHz.

To better illustrate the value of the antenna array designed in this paper for millimeter-wave applications, Table 1 [Reference Xu, Li, Liu, Zhou and Wei14–Reference Midya, Ghosh and Mitra17] shows the comparison of the proposed antenna with other CP antenna arrays in terms of IBW, ARBW, gain, shape, and size. As can be seen from Table 1, the antenna array designed in this paper has significant advantages over arrays of the same size, both in terms of IBW and ARBW, and ensures gain and overall size.

Table 1. Performance comparison with the proposed antenna