Compact dual band crossover for 5G low and mid band applications using a metamaterial branch line coupler

Abstract

This research paper introduces a compact dual-band crossover designed for the low and mid-band 5G frequencies at 0.7 GHz and 3.5 GHz. The innovative design is achieved by cascading two dual band branch-line couplers (BLCs), which utilize T-shaped transmission lines (TLs) with folded arms and stubs to reduce their overall footprint significantly. Additionally, the integration of metamaterial (MTM) structures, incorporating interdigital capacitor (IDC) unit cells, contributes to an impressive 90% size reduction compared to conventional components. The BLC’s and crossover’s performances were rigorously evaluated using CST Microwave Studio (CST MWS) simulations. Following successful simulations, the BLC and crossover were fabricated on a Rogers Duroid/RT5880 substrate, characterized by a dielectric constant of 2.2 and a thickness of 0.787 mm. A thorough comparative analysis between the simulated and measured results, alongside similar reported works, signifies the exceptional performance of the proposed BLC and crossover. These findings confirm their suitability for sub-6 GHz 5G frequency spectrum applications.

Introduction

Rapid progress in wireless communication technology has opened the door to the revolution of intricate and compact gadgets that were once deemed impossible. Performing effective isolation remains a critical necessity when two RF traces cross on a printed circuit board (PCB), particularly given the compact dimensions of the device. A microwave crossover is a specialized component with four ports. It is designed to connect two transmission lines while preserving essential isolation seamlessly, ensuring proper system operation. Crossovers are commonly used within butler matrices that serve as feeding networks for phased-array antennas. Initially, crossovers were constructed utilizing various three-dimensional (3D) configurations, such as bond wires, via holes, underpasses, and air bridges¹. These designs demonstrated significant loss within the passband and encountered fabrication difficulties². In response to these challenges, alternative branch line configurations have been suggested to achieve compact planar crossovers, offering broader bandwidth and the ability to handle multiple frequency bands^{3,4,5,6,7,8,9,10,11}. Compact dimensions and the ability to operate across multiple frequency bands stand out as the primary criteria for modern wireless technology. As a result, compact planar branch-line crossovers have been developed to achieve dual-band functionality, as demonstrated in^{3,8,9,10,11,12}. Furthermore, dual-band functionality can be achieved using composite right/left-hand transmission lines (CRLH)¹³. Metamaterial (MTM) structures offer improved control over electromagnetic properties, enabling improved performance and miniaturization of microwave devices^14,15.

However, it is important to note that although the earlier methods achieved dual-band functionality, they are primarily effective for handling operating frequency ratios below 3. This constraint emphasizes the need to explore alternative approaches to tackle scenarios where the operating frequency ratio exceeds this threshold. In such cases, developing innovative solutions capable of addressing higher frequency band ratios, such as sub-6 GHz and mmWave 5G systems is imperative. This paper presents a miniaturized dual-band crossover with a higher frequency band ratio designed to function within the low- and mid-band 5G frequencies of 0.7 GHz and 3.5 GHz. The crossover design consists of two developmental stages. Initially, the focus was on the realization of a dual-band branch-line coupler (BLC). This design involved substituting conventional shunts and series branches within the BLC with T-shaped transmission lines (TLs) having folded arms and stubs. This modification aimed to reduce the overall size of the BLC.

In addition, to improve performance and minimize dimensions, an MTM structure was incorporated into the sections utilizing interdigital capacitor unit cells (IDC). There are several MTM (resonant and non-resonant) structures, resonant structures like split ring resonators (SRRs) and complementary split ring resonators (CSRRs) suffer from high losses and limited operational bandwidth due to their strong electromagnetic responses at specific frequencies. These drawbacks make them unsuitable for applications that require low loss and broad bandwidth. On the other hand, non-resonant structures operate without relying on resonance. They adjust the overall configuration to attain the desired properties over a wide frequency range, offering broader bandwidth than resonant structures¹⁴. As a result, IDC as a non-resonant structures are selected for this research. Subsequently, the designed BLC was interconnected in a cascade form in the second phase to realize a compact crossover. The design and simulation of these proposed structures were conducted using CST MW Studio. To validate the effectiveness of the design, prototypes of both the BLC and crossover were fabricated and measured on a Rogers RT5880 substrate. RT/Duroid 5880 with a dielectric constant of 2.2 is an excellent choice for a microwave application due to its low loss, stable properties, and ease of fabrication. This substrate has a low-loss tangent, which results in minimal signal attenuation. This is crucial for high-frequency applications where signal integrity is paramount¹⁶. The dielectric constant of 2.2 is stable across a wide frequency range, ensuring consistent performance in various operating conditions. Moreover, RT/Duroid 5880 offers good mechanical strength and durability, which helps maintain the integrity of the circuit during fabrication and operation. The substrate’s lightweight nature also makes it advantageous for applications where weight is a critical factor, such as aerospace, satellite communications, Wi-Fi, and IoT devices. The main contributions of the proposed work are as follows:

• A key contribution of this work is the 90% reduction in size achieved in the design of the dual-band branch-line coupler (BLC) and crossover. This miniaturization is accomplished by utilizing T-shaped transmission lines (TLs) with folded arms, along with metamaterial (MTM) structures that include interdigital capacitors (IDC). This innovative method enables the miniaturization of dual-band devices without sacrificing performance, particularly at 5G frequencies of 0.7 GHz and 3.5 GHz.

• The proposed crossover functions at two distinct frequency bands, 0.7 GHz and 3.5 GHz, resulting in a frequency ratio (K) of 5. This ratio surpasses that of many existing designs, making it ideal for sub-6 GHz 5G applications. Its capacity to manage such a high ratio while remaining compact is a significant contribution to the proposed work.

• The proposed design ensures balanced power distribution across the ports with minimal phase error, nearly reaching 90$^\circ$. For instance, the phase error measures 0.3$^\circ$ at 0.7 GHz and 1.5$^\circ$ at 3.5 GHz, indicating a high level of precision in power division, which is essential for crossover applications in 5G systems.

The experimental results demonstrate the achievable wide frequency band ratio of up to 5, which agrees with the simulation results.

Methods

The typical BLC comprises four ports. Port-1, Port-2, and Port-3 are the input, through, and coupled ports. Meanwhile, Port-4 is an isolated port with minimal or no output power¹⁶.

In this approach, each ($\lambda /4$) segment of the traditional BLC is transformed into a T-section. The details of this conversion process are provided, along with the design flow chart diagram presented in Fig. 1.

The design process starts with a T-shaped dual-band branch-line coupler (BLC) implemented using a stub-tapped T-shaped transmission line (TL) approach, achieving a frequency band ratio of 5. The primitive dual-band BLC, shown in Fig. 5, was designed based on Eqs. (1–16) and occupies an overall circuit size of 162.6 mm $\times$ 161.2 mm.

The second phase utilized the meandered line technique and folded stubs on both the series and the shunt arms of the BLC to achieve a more compact structure. Details of the meandering process and the key equations used to determine the line dimensions are provided in¹⁷. This miniaturization approach led to an approximate 88.4$\%$ reduction in size compared to the original BLC design shown in Fig. 5.

In this phase, the IDC unit cell designed using Eqs. (17–21) was incorporated into the horizontal and vertical arms of the BLC. To achieve the desired performance while minimizing the overall structure size, the dimensions of the transmission lines (TLs) and open stubs were optimized to function at dual-band frequencies of 0.7 GHz and 3.5 GHz. Figure 15 illustrates the simulation of the proposed device using CST Microwave Studio. Compared to the design in Fig. 5, which occupied a total area of 25,438 mm$^2$, the proposed MTM-TL BLC has overall dimensions of 2400 mm$^2$, representing a remarkable 90.56$\%$ reduction in size while maintaining operation within the same frequency bands.

Lastly, the proposed BLC is cascaded using Eqs. (22–14) to implement the crossover illustrated in Figs. 24 and 25. With overall dimensions of 90 mm $\times$ 48 mm, this design provides a compact and robust solution, representing a significant advancement in crossover technology.

Fig. 1

General design flowchart.

The subsequent subsections will demonstrate how this T-section conversion enables dual-band operation for the branch-line coupler.

Dual-band branch-line coupler

The proposed dual-band BLC consists of four standard $\lambda$/4 branches, Fig. 2 that are transformed into T-shaped configurations to determine the dimensions of the active branches in the basic BLC, as shown in Fig. 3. Equation (1) yields the ABCD matrix for the quarter-wave microstrip line with impedance $Z_o$ and electrical length $\theta _o$, as detailed below.

$$\begin{aligned} \begin{bmatrix} A & B \\ C & D \end{bmatrix} = \begin{bmatrix} \cos \theta _o & j Z_o \sin \theta _o \\ \frac{j \sin \theta _o}{Z_o} & \cos \theta _o \end{bmatrix} \end{aligned}$$

(1)

The standard BLC comprises four branches, each with a quarter-wave electrical length. Two of these branches are horizontally oriented and have an impedance $Z_o/\sqrt{2}$, while the other two are vertically oriented with an impedance $Z_o$. The ABCD matrices for these conventional lines with $Z_o$ and $Z_o/\sqrt{2}$, impedances, are presented in (2) and (3) below:

$$\begin{aligned} \begin{bmatrix} A & B \\ C & D \end{bmatrix} = \begin{bmatrix} 0 & \frac{jZ_o}{\sqrt{2}} \\ \frac{j\sqrt{2}}{Z_o} & 0 \end{bmatrix} \end{aligned}$$

(2)

$$\begin{aligned} \begin{bmatrix} A & B \\ C & D \end{bmatrix} = \begin{bmatrix} 0 & jZ_o \\ \frac{j}{Z_o} & 0 \end{bmatrix} \end{aligned}$$

(3)

Fig. 2

Conventional $\lambda /4$ transmission section.

Fig. 3

The ABCD matrix for the T-shaped stub applied in the proposed BLC.

Fig. 4

Layout structure of the T-section branch-line coupler.

Calculating the ABCD matrix for T-shaped branches involves multiplying the ABCD matrices of individual sections, shown in Fig. 3. Similarly, the ABCD matrix for the shunt on the T-shaped stub, denoted by $Z_b$ and $\theta _b$, can be determined using (4). Where (5) represents the ABCD matrix of the overall T-shaped line taking both the main line and stubs into account.

$$\begin{aligned} \begin{bmatrix} A & B \\ C & D \end{bmatrix}_S = \begin{bmatrix} 1 & 0 \\ \frac{j}{Z_o \sin \theta _b} & 1 \end{bmatrix} \end{aligned}$$

(4)

$$\begin{aligned} \begin{bmatrix} A & B \\ C & D \end{bmatrix}_T = \begin{bmatrix} \cos \theta _a & jZ_a \sin \theta _a \\ j \sin \theta _a & \cos \theta _a \end{bmatrix} \begin{bmatrix} 1& 0 \\ \frac{j}{Z_o \sin \theta _b} & 1 \end{bmatrix} \begin{bmatrix} \cos \theta _a & jZ_a \sin \theta _a \\ j \sin \theta _a & \cos \theta _a \end{bmatrix} \end{aligned}$$

(5)

Equations (6) and (7) are derived after the ABCD matrix obtained from the T-shaped stub is simplified and equated with the standard quarter-wave line.

$$\begin{aligned} \tan \theta _a = 2\times \left( \frac{Z_b}{Z_a}\right) \times \cot 2\theta _a \end{aligned}$$

(6)

$$\begin{aligned} Z_o = Z_a \tan \theta _a \end{aligned}$$

(7)

So, for dual-band operations, the necessary conditions indicate that:

$$\begin{aligned} Z_a \times \tan \theta _{af1}=\pm Z_o \end{aligned}$$

(8)

$$\begin{aligned} Z_a \times \tan \theta _{af2}=\pm Z_o \end{aligned}$$

(9)

Furthermore, the electrical lengths of the lines, $\theta _{af1}$ and $\theta _{af2}$ at the lower and upper-frequency bands can be calculated as:

$$\begin{aligned} \theta _{af2}=p\pi \pm \theta _{af1}, \qquad p= 1,2,3, ... \end{aligned}$$

(10)

$$\begin{aligned} \theta _{bf2}=q\pi \pm \theta _{bf1}, \qquad q=1,2,3,... \end{aligned}$$

(11)

$$\begin{aligned} \theta _{af1}=\frac{\pi }{K+1}, \qquad \theta _{af2}=K \times \theta _{af1} \end{aligned}$$

(12)

$$\begin{aligned} \theta _{bf1}=\frac{2\pi }{K+1}, \qquad \theta _{af2}=K \times \theta _{bf1} \end{aligned}$$

(13)

Where the miniaturization factor p$=$ q $=$ 1 for practically small-size TL.

$$\begin{aligned} K=\frac{\theta _{af2}}{\theta _{af2}}=\frac{f_2}{f_1} \end{aligned}$$

(14)

Therefore, the line impedances $Z_a$ and $Z_b$ can be expressed as follows:

$$\begin{aligned} Z_a = \frac{Z_o}{\tan \theta _{af1}} \end{aligned}$$

(15)

$$\begin{aligned} Z_b =\frac{1}{2} \times Z_a \tan ^2 2\theta _{af1} \end{aligned}$$

(16)

The illustrated configuration of the basic coupler is shown in Fig. 4, demonstrating the utilization of four T-shaped branches that replaced the conventional BLC structure. Table 1 presents the calculated parameters for the dual-band BLC implemented with the T-section transmission lines, obtained through (4–16), where both sections have electrical lengths of ($\theta _a=30^\circ$,$\theta _b=60^\circ$). These dimensions are adjusted through EM simulation, demonstrating mutual validation between the simulation and analysis results. Moreover, Fig. 5 illustrates the schematic of the dual-band BLC, designed to operate at frequencies of 0.7 GHz and 3.5 GHz, simulated using CST Microwave Studio.

Table 1 Design parameters for the primitive T-shaped dual-band BLC.

Fig. 5

Layout structure of the primitive T-shaped dual-band branch-line coupler.

Fig. 6

Simulated s-parameters response of the primitive T-shaped dual-band BLC.

Fig. 7

Phase difference at 0.7 GHz frequency band.

Fig. 8

Phase difference at 3.5 GHz frequency band.

The simulation parameters in Fig. 6 demonstrate that the T-shaped dual-band BLC operates effectively at 0.7 GHz and 3.5 GHz, with a $-3\pm 1.5$ dB coupling factor at both frequencies. The simulated reflection coefficients $S_{11}$ and the isolation coefficient $S_{41}$ are below − 20 dB within the specified frequency bands. Due to the reciprocity and symmetrical characteristics of the BLC, both $S_{41}$ and $S_{32}$ show identical values, representing the isolation coefficient. For equal power splitting across Port-2 and Port-3, the T-shaped dual-band BLC design maintains insertion loss $S_{21}$ and coupling coefficient $S_{31}$ at − 3 dB. The simulated results indicate that $S_{21}$ and $S_{31}$ are − 2.8 dB$/$ $-$3.4 dB at lower frequencies and − 2.6 dB$/$ $-$ 3.2 dB at higher frequencies, resulting in average insertion and coupling loss errors of 0.55 dB and 0.6 dB, respectively, closely aligned with the ideal value of − 3 dB. To achieve an optimal power distribution between the output ports, it is crucial to maintain a 90$^\circ$ phase difference between Port-2 and Port-3. Figures 7 and 8 show that when Port-1 is excited, the simulated phase differences ($S_{31}$ $S_{21}$) between Port-2 and Port-3 are 90.3$^\circ$ at 0.7 GHz and 91.5$^\circ$ at 3.5 GHz, resulting in phase errors of 0.3$^\circ$ and 1.5$^\circ$, respectively, slightly deviating from the desired 90$^\circ$. The gray shaded area indicates the device operational bandwidths that cover the ranges between (0.625−0.774) GHz and (3.425− 3.60) GHz in the lower and higher bands, respectively.

Miniaturized MTM-based dual-band branch-line coupler

Although the dual-band BLC discussed in Section I demonstrates effective performance across two frequency bands and an improved frequency band ratio, its overall size is substantial, occupying significant space. In addition, the stubs are too long, posing challenges for seamless integration into the design. As a result, MTM unit cells that utilize IDC and multiple right-angle bends have been integrated to reduce their dimension. Reducing the size of this microstrip coupler/crossover is achieved through several techniques, primarily focusing on innovative designs. Employing techniques such as meandered geometric structures effectively increases the electrical length of the stubs without significantly increasing their physical footprint¹⁸. On the other hand, incorporating the IDC could further minimize the size by compactly integrating MTM elements. Finally, optimization helps to reduce the overall size of the proposed coupler/crossover even smaller. These strategies collectively contribute to the miniaturization of the microstrip coupler/crossover while maintaining its functionality and performance merits. The proposed design is an extension of the work reported in¹⁹.

Figure 9 displays the unit cell configuration of the IDC MTM structure. Here, the IDC fingers show a total base width labeled as Bw and a base length referred to as Bl. The distance between the fingers is represented by ‘s’, while ‘g’ signifies the gap at the end of each finger. Furthermore, individual widths and lengths of the fingers are denoted as ‘fw’ and ‘fl’, respectively.

Fig. 9

The structural layout of the IDC unit cell and dimension.

Equation (15) represents the total capacitance of the IDC unit cell²⁰.

$$\begin{aligned} C=(\varepsilon _r+1)fl[(N_f-3)A_1+A_2] \, (\text {pF}) \end{aligned}$$

(17)

Where $N_f$ is the number of fingers, $\varepsilon _r$ is the relative permittivity of the substrate material. $A_1$ and $A_2$ are constants and are represented using (18), and (19) as:

$$\begin{aligned} A_1 = 4.409 \times \tan \left[ 0.55 \left( \frac{h}{Bw}\right) ^{0.45}\right] \times 10^{-6} \, (\text {pF}/\mu \text {m}) \end{aligned}$$

(18)

$$\begin{aligned} A_1 = 9.92 \times \tan \left[ 0.52 \left( \frac{h}{Bw}\right) ^{0.5}\right] \times 10^{-6} \, (\text {pF}/\mu \text {m}) \end{aligned}$$

(19)

The terms $'Bw'$ and $'h'$ denote the base width of the IDC fingers and the height of the substrate material, respectively. So, after selecting the desired number of fingers, (20) and (21) can be used to determine the parameters fw, fl, and $s = 2\times fw/3$

$$\begin{aligned} fw=\frac{Bw}{\left( \frac{5N_f}{s}-\frac{2}{3}\right) } \end{aligned}$$

(20)

$$\begin{aligned} fl\approx \frac{\lambda _g}{8} \approx \frac{c}{8f_o\sqrt{\varepsilon _r}} \end{aligned}$$

(21)

The design of the interdigital capacitor (IDC) unit cells was closely tied to the analysis of material properties, specifically the dielectric constant $\varepsilon$ and magnetic permeability $\mu$ of the substrate material. These parameters play a critical role in determining the electromagnetic behavior of the IDC and its suitability for achieving the desired frequency response. The substrate used, Rogers RT5880, was chosen for its stable dielectric constant ($\varepsilon$ = 2.2) and low-loss tangent, which are crucial for high-frequency applications. The electromagnetic response of the IDC is governed by the effective capacitance and inductance values, both of which are functions of the substrate’s material properties. The results in Fig. 11 demonstrated negative values of $\varepsilon$ and $\mu$ within the operational range, enabling enhanced control over wave propagation. The geometric parameters of the IDC finger width (fw), finger length (fl), and inter-finger spacing (s) were derived based on their relationship to the material properties. The total capacitance of the IDC is expressed in (17). The dimensions of the IDC, optimized for both the series and shunt sections, are as follows: $Bw =$5.7 mm, $Bl =$ 0.3 mm, $s =$ 0.3 mm, and for the finger length (fl) and width (fw), they are 2.6 mm and 0.3 mm respectively. The unit cell design aims to achieve miniaturization at lower frequencies, given that electromagnetic structures intended for such frequencies usually exhibit substantial dimensions. Figures 10 and 11 represent the S parameters and extracted $\varepsilon$ and $\mu$ parameters of the IDC unit cell employed in the MTM-based BLC, determined through the Nicolson Ross Weir (NRW) method^21,22, which indicates that both parameters are negative across the frequency range of 0.2 GHz to 2.6 GHz.

Fig. 10

S-parameters response of the IDC unit cell.

Fig. 11

Extracted $\varepsilon$ and $\mu$ parameters.

IDC parametric study

The performance analysis of the IDC design was carried out to observe the effects of varying three major parameters: interfinger spacing (s), finger length (fl), and finger width (fw) of the IDC with respect to its constitutive parameters $\varepsilon$ and $\mu$, as shown in Figs. 12, 13 and 14. When the space between the fingers of an IDC (s) increases, the capacitance of the IDC also increases, provided that the fw and fl remain constant. This variation in spacing, which ranges from 0.3 mm to 0.6 mm, directly influences the IDC’s performance characteristics. Additionally, as the spacing between the fingers expands, the overall size of the capacitor structure increases, which, in turn, lowers the resonance frequencies. In particular, the increase in size leads to a decrease in the negativity of the constitutive parameters ($\varepsilon$) and ($\mu$), as shown in Fig. 12.

Fig. 12

$\varepsilon$ and $\mu$ parameters for different values of (s).

Fig. 13

$\varepsilon$ and $\mu$ parameters for different values of (fl).

Fig. 14

$\varepsilon$ and $\mu$ parameters for different values of (fw).

On the other hand, increasing the parameters fw and fl while keeping the parameter s constant leads to a reduction in the operation frequency. This modification causes the dielectric constant ($\varepsilon$) and magnetic permeability ($\mu$) to shift toward lower frequencies. The relationship between these parameters and their impact on the operational frequency is crucial for understanding the device’s performance characteristics. As shown in Figs. 13, 14, the influence of these changes on the frequency response is clearly illustrated. The behavior observed in the figures demonstrates how the adjustment of fw and fl affects the overall system. By analyzing the shift in ($\varepsilon$) and ($\mu$), the material properties and their response to varying frequencies are better understood. This information is valuable for designing devices that require precise control over frequency-dependent parameters. Understanding these shifts allows for better tuning of the device’s performance to meet specific requirements, ensuring optimal functionality across different applications.

The proposed dual-band BLC operates at 0.7 GHz and 3.5 GHz frequencies. Its design incorporates modifications to the dimensions of TLs and open stubs to achieve the desired performance while reducing the overall structural footprint. Figure 15 provides a visual representation of the proposed BLC, detailing dimensions such as $W_1$, $W_2$, and $W_3$ measuring 11.40 mm, 4.26 mm, and 12.60 mm, respectively, whereas $L_1$, $L_2$, and $L_3$ correspond to 11.80 mm, 5.60 mm, and 10.60 mm, respectively. This configuration produces a 90$\%$ reduction in size compared to a conventional dual-band BLC operating within the same frequency bands. The proposed dual-band BLC, based on MTM, was implemented by integrating meandered lines, stubs, and IDC MTM unit cells into the horizontal and vertical sections. The structure prototype in Fig. 16 was realized on a single Rogers substrate with a dielectric constant $\varepsilon _r$ = 2.2, and a thickness of 0.787 mm.

Fig. 15

Layout structure of the miniaturized dual-band BLC using CST software.

Fig. 16

Fabricated prototype of the miniaturized dual-band BLC.

Figures 17 and 18 visually represent the current density distribution in the proposed BLC when excited through Port-1 at two specific design frequencies: 0.7 GHz and 3.5 GHz, respectively. These distributions demonstrate the equal division of the input signal between the through port and the coupled port (both yellowish colors), ensuring that the power is distributed evenly. This balanced power distribution is crucial as it significantly enhances the device’s efficiency. Moreover, the figures highlight that Port-4 remains completely isolated (blue color) from the input signal at both frequencies. This isolation is critical as it prevents any unwanted signal leakage or interference, thereby maintaining the integrity of the signal and improving the overall performance of the BLC. Similarly, when Port-2 is excited, the input signal is evenly distributed between Port-1 (through port) and Port-4 (coupled port), while Port-3 remains entirely isolated. This behavior is depicted in Figs. 19 and 20, corresponding to the 0.7 GHz and 3.5 GHz frequency bands, respectively.

Fig. 17

Surface current distribution for Port-1 excitation at 0.7 GHz.

Fig. 18

Surface current distribution for Port-1 excitation at 3.5 GHz.

Fig. 19

Surface current distribution for Port-2 excitation at 0.7 GHz.

Fig. 20

Surface current distribution for Port-2 excitation at 3.5 GHz.

Figures 21, 22 and 23 illustrate the performance of the proposed dual-band BLC, based on MTM, concerning S-parameter characteristics and phase response among the output ports. In Fig. 21, both simulation and measurement results confirm the effective functionality of the BLC across the frequency bands of 0.7 GHz and 3.5 GHz. At both frequencies, the return-loss $S_{11}$ and isolation-loss $S_{41}$ characteristics of the proposed design, as simulated and measured, surpass −20 dB. Additionally, to achieve equal power division between Port-2 and Port-3, the BLC design requires insertion loss $S_{21}$ and coupling loss $S_{31}$ to be approximately − 3 dB. The simulated and measured results for $S_{21}$ and $S_{31}$ show values of approximately − 2.76 dB/−3.06 dB, − 3.4 dB/−3.52 dB at lower frequencies, and − 3.05 dB/− 3.09 dB, − 3.9 dB/− 2.88 dB at upper-frequency bands, respectively. The average insertion loss error is 0.26 dB, and for coupling loss, it is 0.4 dB, closely aligning with the desired value of −3 dB. Consequently, the proposed BLC achieves a coupling factor of approximately − 3±0.5 dB for each frequency band. In Figs. 22, and 23, it is demonstrated that the simulated and measured phase differences between Port-2 and Port-3 are − 89.9$^\circ$/− 89.0$^\circ$ and 88.5$^\circ$/90.1$^\circ$ at 0.7 GHz and 3.5 GHz, respectively. Thus, the average phase error (PE) is 1.3$^\circ$, indicating a slight deviation from the desired value of 90 $^\circ.$

Fig. 21

Simulated and measured S-parameters response for a miniaturized dual-band BLC.

Fig. 22

Simulated and measured phase difference at 0.7 GHz frequency band.

Fig. 23

Simulated and measured phase difference at 3.5 GHz frequency band.

The proposed BLC demonstrates excellent performance in terms of reflection coefficient, transmission coefficient, and isolation loss at 0.7 GHz and 3.5 GHz, occupying merely 90.56$\%$ of the area compared to the primitive T-shaped design. This signifies an improvement over meandered BLCs in¹⁷, as depicted in Table 2, indicating the strong competitiveness of the new design. To address concerns regarding the incremental nature of improvements over previous work¹⁷, we highlight that the integration of the Interdigital Capacitor (IDC) substantially reduces the coupler arms. Despite the similarity in the core methodologies, the novel incorporation of IDC introduces significant advancements, notably improved tuning capability and improved compactness. These refinements are critical for practical integration into advanced RF/microwave systems, ensuring better efficiency and functionality in precision-sensitive, high-frequency applications.

Table 2 Comparison between the primitive BLC, meandered BLC, and proposed BLC.

Table 3 presents a comprehensive comparative evaluation of the proposed dual-band Branch-Line Coupler (BLC) against prior state-of-the-art designs. Through the analysis, it is revealed that the proposed BLC design excels in several key aspects, such as simplicity, compactness, and an expanded frequency band ratio. Specifically, the design achieves a more favorable balance between size and performance, making it particularly advantageous in scenarios where space and efficiency are critical. The broader frequency band ratio of the proposed design ensures greater versatility and adaptability across various applications, representing a significant improvement over previous models. Various dual-band couplers have been reported utilizing composite right/left-handed (CRLH) transmission lines to reduce component size. Designs in²³ implemented an unbalanced CRLH structure for a compact coupler at 2.45 and 5.08 GHz, achieving minimal phase imbalance (± 1.8$^\circ$) and low insertion loss. Similarly²⁴ utilized CRLH baluns, achieving good size reduction and balanced outputs at 2.4 and 5.2 GHz. However, these CRLH approaches typically result in limited bandwidths (below 10$\%$) due to inherent dispersion effects. In comparison, our proposed design in this study employs metamaterial-inspired interdigital capacitor (IDC) unit cells within a T-shaped folded transmission line configuration, achieving exceptional miniaturization (90$\%$) without significantly compromising bandwidth or performance at sub-6 GHz frequencies (0.7 and 3.5 GHz). Islam et al.²⁵ introduced a dual-band coupler with coupled-lines and port extensions to achieve flexible power division and a broader frequency ratio. Their design offers good coupling balance and reasonable bandwidth (16$\%$ at 0.9 GHz and   6$\%$ at 1.8 GHz), but it lacks significant size reduction and simplicity in implementation. Using cascaded dual-band transformers, Naseri et al.²⁶ extended bandwidth coverage (33$\%$ and 14$\%$ at 0.9 and 2.45 GHz, respectively). Though effective in bandwidth expansion, their coupler required additional transmission line segments, slightly complicating the layout and limiting aggressive size reduction. Contrasting these approaches, our proposed coupler uniquely integrates compact IDC-loaded metamaterial lines in a straightforward planar topology, ensuring comparable or superior bandwidth performance and dramatically improved compactness and simpler fabrication, making it highly suitable for compact 5G modules.

Chang et al.²⁷ demonstrated dual-band couplers based on crossed lines and open-ended stubs, enabling arbitrary and distinct power splits at each band. While offering excellent flexibility, this approach necessitates increased complexity through intersecting lines and multiple stubs, potentially complicating fabrication and integration. Zhang and Lee²⁸ employed $\pi$-shaped line sections to achieve dual-band operation (0.9/2.0 GHz), enhancing bandwidth (18.9$\%$ and 10.5$\%$) and introducing harmonic suppression up to 8.3 GHz. Nonetheless, the $\pi$-structured configuration similarly introduced layout complexity due to additional frequency-selective elements. By contrast, the proposed approach delivers robust dual-band operation at widely spaced frequencies (frequency ratio of 5) within a single, extremely compact layout. The straightforward planar construction significantly eases fabrication while ensuring excellent power division accuracy and minimal phase errors ( 0.3$^\circ$ at 0.7 GHz and   1.5$^\circ$ at 3.5 GHz).

Lumped-element approaches proposed in²⁹ introduced couplers with highly customizable power division and phase shifts. Although these configurations achieve considerable size reduction, they typically demand precision tuning and involve intricate component placement, which increases implementation complexity. Koziel et al.³⁰ emphasized efficient design methods and scaling approaches for dual-band circuits but primarily focused on computational methodologies rather than direct hardware miniaturization strategies. In sharp contrast, our metamaterial-inspired design achieves extreme miniaturization, near-ideal coupling and phase balance, wide operational bandwidth, and straightforward manufacturing, thereby combining the benefits of advanced miniaturization techniques with practical implementation simplicity.

In summary, the proposed dual-band couplers notably surpasses existing designs (Table 3) in achieving an optimal balance between extreme compactness (90$\%$ size reduction), broad and widely spaced frequency coverage (0.7 and 3.5 GHz, frequency ratio of 5), minimal insertion loss, and near-ideal coupling and phase performance. The innovative use of IDC-based metamaterial cells within a folded T-shaped transmission line configuration uniquely positions our design as highly attractive for next-generation compact and efficient 5G sub-6 GHz applications.

Table 3 Comparative analysis of the proposed dual-band BLC with other related works.

Proposed compact dual-band MTM-based crossover

The crossover was developed by sequentially integrating two BLCs from the previous section. The structure is an extension of the work presented in³¹. Figures 24 and 25 illustrate the simulated layout and physical prototype of the proposed crossover setup. It is crucial to note that the dimensions of the IDC and stub lines in the crossover were maintained to match those utilized in the BLCs. The width of the middle section of the crossover ($W_x$ = 3.8 mm) is obtained per (20–22)³², and optimized to achieve resonance within the designated frequency bands. The overall dimensions of the crossover are 0.31 $\lambda _g$ $\times$ 0.16 $\lambda _g$, respectively.

Fig. 24

Structural layout of the proposed dual-band crossover.

Fig. 25

Fabricated prototype of the proposed dual-band crossover.

$$\begin{aligned} Z_1=Z_o= 50\, \Omega \end{aligned}$$

(22)

$$\begin{aligned} Z_2=\frac{Z_o}{\sqrt{2}}=35.35 \, \Omega \end{aligned}$$

(23)

$$\begin{aligned} Z_3=50\times \frac{Z_2^2}{Z_o^2}=25\, \Omega \end{aligned}$$

(24)

The impedance ($Z_3$) of the middle section of the crossover is converted to a T-shaped dual-band section using (15) and (16). Since the electrical lengths of the lines remain unchanged ($\theta _a$ = 30$^\circ$,$\theta _b$ = 60$^\circ$), the calculated impedances of the middle section and its stubs are 43.3 $\Omega$ and 64.95 $\Omega.$

A detailed parametric analysis was performed to investigate the impact of varying the center widths ($W_x$) and lengths ($L_y$) on the system’s performance. The results of this study are depicted in Figs. 26, 27, 28 and 29, which illustrate the frequency responses corresponding to different values of these parameters.

In Fig. 26, the influence of varying the physical width $W_x$ on $S_{11}$ values is observed, indicating a notable decrease across all frequency bands with increasing width. This trend also affects $S_{31}$ values, as illustrated in Fig. 27. After careful analysis, a width of $W_x$ = 3.8 mm is identified as optimal, demonstrating superior performance across the desired operational parameters. Increasing the length Ly has minimal impact on the $S_{11}$ values across both frequency bands, as depicted in Fig. 28. However, achieving an $S_{31}$ value of 0 dB is paramount for effective signal routing in 5G applications. This criterion ensures low insertion loss and high isolation, critical for minimizing power loss and preventing crosstalk. As $L_y$ is extended, insertion loss decreases at both frequency bands, with a more noticeable reduction observed at higher frequencies as observed in Fig. 29. Therefore, selecting $L_y$ = 7.5 mm is deemed optimal to attain peak performance.

Fig. 26

The parametric study of $S_{11}$ as a function of Wx.

Fig. 27

The parametric study of $S_{31}$ as a function of Wx.

Fig. 28

The parametric study of $S_{11}$ as a function of Ly.

Fig. 29

The parametric study of $S_{31}$ as a function of Ly.

Figures 30 and 31 present a detailed performance evaluation of the proposed 0 dB dual-band crossover. The evaluation focuses on analyzing the S-parameters and phase differences among adjacent output ports. In both the 0.7 GHz and 3.5 GHz frequency bands, Fig. 30 demonstrates that the simulated and measured reflection coefficient ($S_{11}$) characteristics remained below − 18 dB, indicating excellent performance. At 0.7 GHz, the transmission coefficient values at the diagonal ports ($S_{31}$ and $S_{24}$) were recorded at − 0.29/− 30 dB, while at 3.5 GHz, these values were slightly better at − 0.23/− 0.22 dB. Furthermore, Fig. 31 highlights the simulated and measured phase differences of 0.12$^\circ$/– 0.20$^\circ$ and 0.17$^\circ$/– 0.35$^\circ$ between $S_{31}$ and $S_{24}$, which consistently closed to the ideal value of 0$^\circ$ at 0.7 GHz and 3.5 GHz frequency bands, respectively. This consistency demonstrates the crossover’s effectiveness in maintaining minimal phase deviation, thus ensuring optimal signal integrity across the specified frequency bands.

Fig. 30

The simulated and measured S-parameters response of the proposed crossover.

Fig. 31

The simulated and measured output phase difference ($\angle$ $S_{31}-$ $\angle$ $S_{24}$) between the diagonal ports.

Table 4 provides a comprehensive comparative analysis of the MTM-based dual-band crossover introduced in this study in contrast to recent dual-band crossover approaches. The comparative performance analysis highlights key advancements and trade-offs in dual-band crossover designs presented in previous literature, as compared to the proposed work. The work² introduced a frequency-reconfigurable crossover capable of electronically tuning its operating band between approximately 1.41 GHz to 2.05 GHz, achieving a substantial tuning range of 36.9$\%$. Despite its versatility, the crossover supports only a single active frequency band at a time and necessitates mechanically tunable dielectric components, adding complexity.

Dual-band designs were significantly advanced by³³, utilizing a two-section branch-line structure, achieving a frequency ratio of approximately 2.3 (1.0/2.3 GHz). This design presented excellent isolation (> 20 dB), minimal insertion loss (0.26−0.57 dB), and strong impedance matching (return loss − 24 dB). However, its fractional bandwidth per band remained relatively narrow. Subsequently, Reference³⁴ introduced an asymmetrical $\pi$-shaped transmission line crossover, expanding the achievable frequency ratio to 3 (0.5/1.5 GHz) and providing compact sizing (0.38$\times$0.38$\lambda _g$). It maintained low insertion losses (0.45/0.75 dB) and high isolation (> 20 dB), though bandwidth constraints persisted similarly to³³.

Authors in³⁵ further increased the achievable frequency ratio to 4 (1.0/4.0 GHz), utilizing cascaded branch-line hybrids with $\pi$- or T-network topologies. Despite achieving nearly ideal insertion loss ( 0.4dB at low band), it encountered higher insertion losses (1.1 dB at high band) and comparatively moderate isolation (15 dB). Its main drawback was a narrow operational bandwidth at each frequency band. To address bandwidth limitations, Authors³⁶ adopted multisection coupled-line branch-line couplers, significantly enhancing bandwidth ( 225–269 MHz per band at 1.0/2.6 GHz). However, this advantage came with increased complexity, size, and a moderate frequency ratio (2.6).

A unique balanced crossover using composite right/left-handed (CRLH) transmission lines and defected ground structures (DGS) was proposed by³⁷. Operating at 1.8/4.2 GHz, this crossover demonstrated effective common-mode suppression and negligible insertion loss in differential mode. However,frequency ratio (2.3) and moderate bandwidth, combined with with the added complexity due to CRLH and DGS implementation, are not good enough.

In comparison, the proposed metamaterial-based dual-band crossover surpasses prior works by achieving an unprecedented combination of high frequency ratio (5:1 at 0.7/3.5 GHz), compactness (90$\%$ size reduction), low insertion loss (0.3 dB), and high isolation. Although fractional bandwidth remains similar to the narrower designs, the proposed crossover uniquely balances ultra-wideband separation and minimal complexity. This positions the current design as particularly suitable for sub-6 GHz 5G systems, effectively integrating and enhancing the advantageous features found individually across references in Table 4.

Table 4 Comparative analysis of the proposed dual-band crossover with other related works.

From the outset, the primary challenge faced was selecting the appropriate substrate materials. The proposed devices are designed to operate within a lower frequency range (0.7 GHz and 3.5 GHz). At these frequencies, microwave devices tend to be physically large, occupying significant space. To address this, using a substrate material with a high dielectric constant can reduce the size of the devices and lower costs. However, this comes at the expense of increased signal losses³⁸. On the other hand, a substrate material with a low dielectric constant offers reduced losses and improved bandwidth but is generally more expensive¹⁶. After careful consideration, the RT/Duroid 5880 substrate, with a dielectric constant of 2.2, was selected as a balanced compromise between performance and cost.

The future of microstrip coupler/crossover design is set for significant advancements, driven by the growing demand for compact, high-performance RF and microwave components in emerging technologies like 5G, IoT, and satellite communications. Innovations in materials, such as low-loss dielectrics and flexible substrates, will enhance the efficiency and miniaturization of these couplers. Moreover, the integration of advanced simulation tools and artificial intelligence will allow designers to optimize performance parameters such as bandwidth, selectivity, and power handling more effectively. Additionally, the use of metamaterials and novel geometries may lead to the creation of multifunctional couplers capable of operating across multiple frequency bands, addressing the diverse needs of modern communication systems³⁹. Consequently, the future will likely feature highly integrated, versatile, and cost-effective microstrip filtering couplers that meet the stringent requirements of next-generation applications.

Conclusion

This study presents a novel MTM-based dual-band crossover design characterized by compact size and enhanced frequency band ratio. The design integrates meandered lines and an interdigital capacitor (IDC) unit cell, creating a composite right/left-handed transmission line (CRLH-TL) architecture. This innovative approach led to the development of a compact dual-band T-shaped branch-line coupler, which forms the basis for the proposed crossover by cascading two of these BLCs.

To validate the design, both the branch-line coupler and crossover were fabricated on a single Rogers RT5880 substrate and subsequently measured. The simulated and experimental results demonstrate the outstanding performance of these devices across the 0.7 GHz and 3.5 GHz frequency bands. Notably, the proposed branch-line coupler and crossover exhibit significantly reduced dimensions, measuring 0.17$\lambda _g$ $\times$ 0.16$\lambda _g$ and 0.31$\lambda _g$ $\times$ 0.16$\lambda _g$, respectively, representing a size reduction of approximately 90$\%$ compared to conventional T-shaped structures. Overall, the key innovation is the integration of metamaterial structures, interdigital capacitors, and CRLH-TL architecture, resulting in a remarkable 90% size reduction for dual-band crossovers. It also supports a high-frequency ratio of 5, making it highly suitable for compact 5G applications. This design delivers excellent performance across both low and mid-band frequencies while addressing the size and complexity challenges found in other approaches.