Antenna configuration

The geometry of the proposed dual-polarized IBFD antenna is depicted in Fig. 1. It consists of two square microstrip patches which are built on Rogers RT 5880 substrate (ε_r = 2.2, tan δ = 0.0009) of thickness 1.575 mm. The radiating patch (RP), built on substrate 2 is excited with dual differential feeding. Port 1+ and 1– are used as differential Tx ports while port 2+ and 2– are used as differential Rx ports. The feeding of RP through each differential port is done with the help of a pair of λ/4 resonators. A metallic pin having a diameter dia is placed at the center of the feedline which is shorted to the ground. The parasitic patch (PP) is placed above RP at a height of h on substrate 1. The ANSYS Electronics Desktop (HFSS) is used to design and optimize the structure.

Figure 1.

Proposed design with dimensions (in mm): (a) 3 d view, (b) top view of the bottom layer; l _s = w _s = 100, W ₁ = 37, W ₂ = 38.2, l _r = 19.2, w _f = 4.5, w_r = 1.75, d = 1, dia = 0.3, h = 10.

Operational mechanism

Theoretically, a dual-polarized antenna where Tx and Rx have orthogonal polarization, has infinite isolation between the Tx and Rx port, a favorable condition for the IBFD system. Hence, at Stage 1, a dual-polarized square MPA is excited through direct feeding (insert-fed) at port 1 (Tx port) and port 2 (Rx port). The feeding arrangement shown in Fig. 2(a) ensures that the Tx port is orthogonally polarized with respect to the Rx port. This MPA resonates at a center frequency (f ₀) of 2.5 GHz. It is evident from the S-parameters shown in Fig. 2(a) that in addition to fundamental mode TM ₁₀ (2.5 GHz) of this MPA, other higher order modes TM ₁₁ (3.55 GHz), TM ₂₀ (5.3 GHz) and TM ₂₂ (6.7 GHz) also exist.

Figure 2.

Design evolution of the proposed IBFD antenna and simulated s-parameters: (a) stage 1, (b) stage 2, (c) stage 3, (d) stage 4.

Now, instead of direct feeding, capacitive feeding with the help of pairs of λ/4 resonators is provided to the MPA as shown in Stage 2 of Fig. 2(b). This configuration results in spurious-free characteristics as shown in Fig. 2(b). The suppression of higher-order modes is due to the presence of pairs of λ/4 resonators which are centrally loaded with a shorting pin [Reference Pozar22].

The non-radiating λ/4 resonators along with a shorting pin exhibit resonance at discrete frequencies (nf ₀, where n = 1, 3, .. (2 N + 1)). The MPA is capacitively fed by λ/4 resonators, allowing energy transmission only at discrete frequencies where both the λ/4 resonators and MPA resonate simultaneously. Consequently, it is not possible to excite higher-order modes like TM ₁₁ and TM ₂₂ due to their resonance frequencies not being a multiple of f ₀. For a square MPA, the resonant frequency of the TM ₁₁ and TM ₂₂ modes are 1.414 f ₀ and 2.828 f ₀, respectively.

In addition, the placement of a shorting pin at the center of a feedline results in the creation of an electric field null at the center plane. This configuration prevents the excitation of even order modes, such as TM ₂₀, because the primary requirement to excite any even order mode is to have an electric field maximum in the central plane. Hence, this feeding mechanism shown in Stage 2 of Fig. 2(b) successfully suppresses the second-order modes which are the most critical in any communication system. In spite of good out-of-band performance, this configuration has inter-port isolation of 20 dB as shown in Fig. 2(b) which is insufficient for an IBFD system.

Further, to increase the inter-port isolation, differential feeding is provided to Tx and Rx ports which is presented as Stage 3 of Fig. 2(c). To understand the effect of this double differential feeding on inter-port isolation in more detail, a mathematical model is developed based on the analysis proposed in [Reference Chaudhary, Jeong and Jeong13]. To apply the differential feed at both the Tx and Rx ports, two different hybrid couplers can be utilized as shown in Fig. 3. Here, the current at Port 1(Tx) and Port 2(Rx) is represented as I₁ and I₂ respectively. Assuming the lossless hybrid coupler (H.C.), the output currents of H.C. 1 can be written as [Reference Pradhan, Subramanian, Barik and Cheng24]

(1)\begin{equation}{I_{1 + }} = \frac{1}{{\sqrt 2 }}{I_1}{\text{ }}and{\text{ }}{I_{1 - }} = - \frac{1}{{\sqrt 2 }}{I_1}{\text{ }}\end{equation}

Figure 3.

Stage 3 antenna having dual differential feedings realized using identical hybrid couplers.

As the differential port 2 is acting as a receiver port, different currents of H.C. 2 are related to each other as follows:

(2)\begin{equation}{I_2} = \frac{1}{{\sqrt 2 }}({I_{2 + }} - {\text{ }}{I_{2 - }})\end{equation}

Now, let the mutual coupling between port 2₊ (2-) and port 1₊(1-) is represented as S_{2 +1 +} (S_2-1-) and S_{2 +1–} (S_{2-1 +}) denotes the mutual coupling between port 2₊ (2–) and port 1_– (1+), then

\begin{equation*}{I_{2 + }} = \frac{{{I_1}}}{{\sqrt 2 }}{S_{2 + 1 + }} - {\text{ }}\frac{1}{{\sqrt 2 }}{I_1}{\text{ }}{S_{2 + 1 - }}\end{equation*}

(3)\begin{equation} = \frac{{{I_1}}}{{\sqrt 2 }}[{S_{2 + 1 + }} - {\text{ }}{S_{2 + 1 - }}]\end{equation}

(4)\begin{equation}{I_{2 - }} = \frac{{{I_1}}}{{\sqrt 2 }}[{S_{2 - 1 + }} - {\text{ }}{S_{2 - 1 - }}]\end{equation}

Now using eq. (2), (3) and (4), I ₂ can be found as

(5)\begin{equation}{I_2} = \frac{{{I_1}}}{2}\left[ {({S_{2 + 1 + }} - {\text{ }}{S_{2 + 1 - }}} \right) - \left( {{S_{2 - 1 + }} - {\text{ }}{S_{2 - 1 - }}} \right)]\end{equation}

Therefore, based on Eq. (5) the relationship between the current of port 1 and 2 can be expressed as

(6)\begin{equation}\frac{{{I_1}}}{{{I_2}}} = \frac{2}{{\left[ {({S_{2 + 1 + }} - {\text{ }}{S_{2 + 1 - }}} \right) - \left( {{S_{2 - 1 + }} - {\text{ }}{S_{2 - 1 - }}} \right)]}}\end{equation}

The proposed structure is symmetrical and considering the ideal differential operation performed by the hybrid couplers, the coupling between the orthogonally placed ports will be identical ( ${S_{2 + 1 + }} = {\text{ }}{S_{2 + 1 - }} = {S_{2 - 1 + }} = {\text{ }}{S_{2 - 1 - }}$). Hence, it is evident from Eq. (6) that theoretically, infinite inter-port isolation is achieved using this configuration. Nevertheless, in practical use, significantly large inter-port isolation can be achieved by utilizing highly precise hybrid couplers that produce output signals with equal magnitude and out-of-phase characteristics [Reference Chaudhary, Jeong and Jeong13].

It is important to note that double differential feeding deployed at Stage 3 is the major factor in achieving high inter-port isolation. The differential operation performed at the Tx port is responsible for suppressing any Tx-Rx leakage at Rx ports while the differential Rx ports subsequently suppress any further residual self-interference. Hence, the polarization diversity along with double differential feeding yields a high inter-port isolation better than 60 dB for the entire operating band as shown in Fig. 2(c).

The surface currents for Tx and Rx ports are shown in Fig. 4. It is evident that the surface current is oriented in the x (y) direction when differential Tx (Rx) ports are excited while the Rx (Tx) ports are terminated with a matched load. Even though high inter-port isolation is achieved at this design stage, the input matching of this stage is very poor, and impedance bandwidth (|S ₁₁| < − 10 dB) is limited (∼40 MHz).

Figure 4.

Distribution of surface current on the RP: (i) when differential Tx ports are excited and Rx ports are terminated with matched load, (ii) when differential Rx ports are excited and Tx ports are terminated with matched load.

Although the dual resonant behavior can be observed in antennas of Stage 2 and Stage 3 due to close proximity of λ/4 resonators with the RP (Fig. 2(b) and Fig. 2(c)), the input matching and impedance bandwidth are not sufficient. Therefore, a PP is placed above the RP in Stage 4 as shown in Fig. 2(d). The inclusion of PP has two-fold utility; first, it improves the input matching and then it also improves the impedance bandwidth. It is clear from the S-parameters shown in Fig. 2(d) that the Stage 4 antenna results in a high isolation of 65 dB over the entire operating frequency band (2.30–2.76 GHz).

To illustrate the improvement in input matching, the input impedances of Stage 3 and Stage 4 antennas are plotted in Fig. 5(a). It clearly shows that the Stage 3 antenna exhibits inadequate input matching over the desired operating band.

Now, the air gap between RP and PP facilitates the mixed coupling (electric and magnetic couplings) [Reference Nishiyama, Aikawa and Egashira23]. The effect of this mixed coupling can be observed in Fig. 5(a). This mixed coupling offers either inductive or capacitive impedance across different frequencies. Consequently, an air gap of varying height results in a substantial change in input impedance (the corresponding parametric study is shown in the Section V of this paper). Hence, with the placement of the PP above RP at an optimal height (h) of 10 mm, the imaginary part of Z_{dd 11} of the Stage 4 antenna approaches zero, while the real component of Z_{dd 11} is near to 50 Ω in the entire operating band. This demonstrates the significant improvement of input matching resulting from the strategic placement of PP at an optimal height of h.

Figure 5.

(a) Input impedance matching of stage 3 and stage 4 antenna, (b) Smith chart for impedance matching of stage 3 and stage 4 antenna.

Additionally, the excellent input matching for the entire operating band is also reflected in the Smith Chart shown in Fig. 5(b). The impedance loop of the Stage 4 antenna evidently shifts towards the center of Smith chart which further confirms the substantial improvement in the matching performance due to PP being placed above the RP at a height of h.

Further, the judicious selection of the air gap (h) as 10 mm (∼0.1 λ) facilitates the fundamental mode of PP to resonate with close proximity of the fundamental mode of RP [Reference Naseri, PourMohammadi, Melouki, Ahmed, Iqbal and Denidni25]. Thus, the improved impedance bandwidth (460 MHz) is achieved because three different structures i.e. RP, PP, and λ/4 resonators are resonating in close vicinity. This Stage 4 antenna presented in Fig. 2(d) is our proposed IBFD antenna which has significantly large inter-port isolation over a wide frequency range. Also, this design successfully suppresses the higher-order modes which can be undesirable for other surrounding devices. Table 1 summarizes the key characteristics of antennas of different stages which clearly highlight the achievement of performance improvement of the proposed IBFD antenna in successive stages.

Table 1.

Key features of antennas of different stages

Equivalent lumped circuit model

To gain further insight into the proposed design, an equivalent lumped circuit model of the proposed dual-polarized IBFD antenna is presented in Fig. 6. The differential feeding is provided at both Tx and Rx ports through a microstrip line of characteristic impedance Z ₀. The λ/4 resonator is modeled as a lossless LC circuit (L_ri, C_ri, i varying from 1 to 4). These pair of λ/4 resonators at the Tx and Rx ends are connected in parallel. At one end, these resonators are connected to shorting pins shown as L_{pin 1} and L_{pin 2} at the Tx and Rx ends, respectively. The gap between the feeding circuit and the RP is modeled as a π-network of three capacitances C_{g 1}, C_{g 2}, C_{g 3} and C_{g 4}, C_{g 5}, C_{g 6} at Tx, and Rx ends, respectively. A combination of two parallel RLC circuits i.e. R ₁L ₁C ₁ and R ₂L ₂C ₂ is used to represent the RP when it is excited at differential Tx and Rx ports respectively. It is important to note that, the RP is operating under TM₁₀ mode when excitation is provided at differential port 1 while the dominating mode of operation is TM₀₁ when RP is excited at differential port 2. Similarly, the PP is presented as a parallel resonant circuit R_p1L_p1C_p1 and R_p2L_p2C_p2 when it is excited with differential port 1 and differential port 2, respectively. The resonant frequency $({f_r})$ of each of the three resonators (RP, PP, and λ/4 resonators) can be calculated with the following relation:

(7)\begin{equation}{f_r} = \frac{1}{{2\pi \sqrt {{L_r}{C_r}} }}\end{equation}

where L _r and C _r represent the inductance and capacitance of the corresponding resonator.

Figure 6.

Lumped circuit equivalent model of the proposed antenna: ${L_{pin1}} = {L_{pin2}} = 72.5{\text{ }}nH,{\text{ }}{L_{r1}} = {L_{r2}} = {L_{r3}} = {L_{r4}} = 0.82{\text{ }}nH,{\text{ }}{R_1} = {R_2} = 328{\text{ }}\Omega, {\text{ }}{C_{r1}} = {C_{r2}} = {C_{r3}} =$ ${C_{r4}} = 4.14{\text{ }}pF,{\text{ }}{C_{g1}} = {C_{g4}} = 1.77{\text{ }}pF,{\text{ }}{C_{g2}} = {C_{g3}} = {C_{g5}} = {C_{g6}} = 0.28{\text{ }}pF$, ${L_1} = {L_2} = 0.95{\text{ }}nH,{C_1} = {C_2} = 4.94{\text{ }}p$F, ${L_{c1}} = {L_{c2}} = 0.23{\text{ }}nH$ ${C_{c1}} = {C_{c2}} = 12.86{\text{ }}pF$, ${R_{p1}} = {\text{ }}{R_{p2}} = 15{\text{ }}\Omega $, ${L_{p1}} = {L_{p2}} = 0.28{\text{ }}nH$, ${C_{p1}} = {C_{p2}} = 13.37{\text{ }}pF$.

Further, the mixed coupling (combination of electric and magnetic coupling) between the RP and PP is described as two parallel LC circuits (L_{C 1}, C_{C 1} and L_{C 2}, C_{C 2}). Finally, the mutual coupling between port 1 and port 2 is defined as M₁₂ [Reference Zhang, Ke, Wang, Tang and Chen26,Reference Chen, Ye, Liu and Wu27]. The working mechanism of various components used in the circuit model can be understood by comparing them with the actual elements utilized in the design of the IBFD antenna as tabulated in Table 2. In addition, the ADS software is utilized to design and validate the IBFD antenna equivalent circuit model. A comparison of simulated results obtained from ADS and HFSS is presented in Fig. 7, demonstrating a high level of consistency between the two.

Figure 7.

Comparison between EM simulation and circuit simulation of the proposed IBFD antenna: (a) magnitude plot (b) phase plot (unwrapped).

Table 2.

Relationship of circuit elements used in ADS simulation with their counterpart in EM simulation

Parametric analysis

To elucidate the impact of a few parameters on the performance of the proposed IBFD antenna, two parametric studies are performed. The first study illustrates the effect of variations in d (the gap between a pair of λ/4 resonators and RP) on the input reflection coefficient, as depicted in Fig. 8 (a). For a nominal value of d as 1 mm, all the three reflection poles due to RP, PP, and λ/4 resonators are combined to form a wideband antenna. When the value of d is increased to 1.3 mm, all the reflection poles are merged into a single reflection pole. Additionally, to validate the effectiveness of the proposed equivalent circuit model, one capacitor (C_g1) of the π network (the circuit equivalent of the gap (d) between a pair of λ/4 resonators and RP) is varied and its effect on input reflection coefficient is presented in Fig. 8 (b). It is evident from the Fig. 8 that both EM and circuit simulation leads to a similar conclusion. It is important to note that all parameters except d (C_g1) in EM (circuit) simulation are maintained constant in the aforementioned study.

Figure 8.

The effect of variations in (a) d (b) C_g1 on the input reflection coefficient.

Subsequently, in another parametric study, the effect of variations in the air gap (h) between RP and PP is analyzed, as shown in Fig. 9(a). It clearly demonstrates that the judicious selection of the airgap (h) as 10 mm is essential for the fundamental mode of PP to resonate with close proximity of the fundamental mode of RP which results in a good impedance matching over a wideband. Furthermore, as discussed in the previous section, the air gap between RP and PP facilitates the mixed coupling (electric and magnetic couplings) to improve the input matching. This can be further verified from the parametric variation in C _c1 (parallel combination of C _c1 and L _c1 is circuit equivalent to mixed-coupling provided by the air gap between RP and PP) performed in circuit simulation as shown in Fig. 9(b). Hence, the prudent selection of air gap to obtain a good input matching over a wideband is justified with the help of EM and circuit simulation as illustrated in Fig. 9.

Figure 9.

The effect of variations in (a) h (b) c_c1 on the input reflection coefficient.

Results and discussion

To validate the functionality of the proposed design, a prototype is implemented using RT Duroid substrate, and the nylon screws are used to hold both substrate layers. The fabricated prototype is shown in the inset of Fig. 10(a). To provide differential signals at Tx and Rx ports, an ultra-wideband hybrid coupler proposed in [Reference Ta and Trong9] is used. The magnitude and phase imbalance between the two output ports of this coupler is within the limit (±0.2 dB and ±2.5^◦ respectively) over a large frequency range (1–10 GHz).

Figure 10.

Measured results of the proposed IBFD antenna: (a) out of band performance, (b) reflection coefficients and inter-port isolation, (c) realized gain, (d) e-plane and h-plane radiation pattern of Tx port at (i) 2.4 Ghz (ii) 2.65 Ghz.

The S − parameters of the proposed dual-polarized IBFD antenna are measured using the Agilent Vector Network Analyzer [N5247A] and presented in Fig. 10. The improved out-of-band characteristic of the proposed structure can be observed in Fig. 10(a) which clearly shows that it possesses spurious free characteristics. Moreover, as shown in Fig. 10(b), the measured impedance bandwidth is ∼20% (2.26–2.76 GHz) which is somewhat larger than the simulated results. Also, the measured isolation between Tx and Rx ports is better than 58 dB for the entire operating range (2.26–2.76 GHz) while in simulation it was obtained as 65 dB. The discrepancies between the simulated and measured results are due to cable losses and misalignment of the PP with respect to the driven patch.

The far-field parameters are measured in an anechoic chamber and the measured realized gain and radiation pattern are presented in Fig. 10(c) and Fig. 10(d), respectively. It is important to note that the proposed design is symmetrical with respect to Tx and Rx ports. Thus, the measured results are presented only for the differential Tx ports for brevity. The peak values of measured realized gain and radiation efficiency are 9.1 dBi and 92%, respectively. The cross-polarization better than −30 dB at boresight direction is measured at two operating frequencies 2.4 GHz and 2.65 GHz in both E and H planes. It is evident from the measured results that these are in close agreement with the simulated results.

A detailed comparison of the proposed structure with other reported dual-polarized IBFD antennas is presented in Table 3. The present design offers the largest fractional bandwidth (|S ₁₁| < −10 dB) of 20% among all the designs listed in Table 3. Though the designs presented in [Reference Chaudhary, Jeong and Jeong13] and [Reference Wang, Tang, Yang and Chen14] offer better inter-port isolation, these multi-radiator-based designs have very narrow bandwidths and possess lower values of peak gain. Moreover, none of the aforementioned IBFD structures provide suppression of higher-order modes. Hence, it can be concluded that the proposed shared radiator-based design provides significantly larger isolation of 58 dB over a wide bandwidth of 20% along with a large peak gain of 9.1 dBi and an excellent out-of-band performance.

Table 3.

Comparison of the proposed work with reported works

DPA: Dielectric Patch Antenna, DRA: Dielectric Resonator Antenna, MED: Magneto Electric Dipole, N.P.: Not Provided