Design and Optimization of Dual-Band Branch-Line Coupler with Stepped-Impedance-Stub for 5G Applications

A B S T R A C T Article history: Received: 21 January, 2020 Accepted: 23 May, 2020 Online: 11 June, 2020 This paper presents a design optimization of a dual-band branch-line coupler with steppedimpedance-stub lines. This coupler operates over 5G NR frequency bands n5 and n2, developed by 3GPP for the 5G (fifth generation) mobile network, and these two bands are centered at 0.85 GHz and 1.9 GHz respectively. To achieve the design specifications an adjusted Tuning Space Mapping method is used. This method of optimization moves the hardship of optimization from high-fidelity electromagnetic models to low-fidelity tuning models. The simulated and measured results of this enhanced coupler show good dual-band performance at the two bands.


Introduction
The request for mobile communication is more than ever. For this reason, many researchers have focused on the development of a new generation of communication. 5G NR is a new radio access technology developed by 3GPP for the 5G mobile network. We designed the coupler to function in the two bands n5 and n2 from the 3GPP TS 38.101 [1].
This work presents the design of a dual-band BLC with SISBL, designed for 5G NR frequency bands downlink [n2= (0.869 -0.894 GHz) / (n5= (1.930-1.990 GHz)], this bands developed by 3GPP for the 5G (fifth generation) mobile network and centered at 0.85 GHz and 1.9 GHz respectively [1].5G NR, like most modern techniques, demands height accuracy. In many situations like ours, due to microwave structure complexity of SISBL dual-band BLC, the theoretical model only gives the initial design that requires optimization so he can meet the design specifications. In our case, for the optimization, we use an adjusted Tuning Space Mapping, the adjustment is made in the tuning model using our engineering expertise and knowledge of the design problem. The advantage is to reduce time-consuming. The enhanced characteristics of this Dual-Band BLC with SISBL are presented.
The simulated results of this enhanced dual-band BLC show good dual-band performances at n5/n2. The performance of its fabricated prototype has also been validated experimentally. Figure 1.a presents the SISBL containing a signal path (Z3, θ3) tapped with (Z1, θ1) and (Z2, θ2) [10]. By multiplying the ABCD matrices of each cascade component, the ABCD matrix of the SISBL is reached. Since the dual-band branch line behaves as a π/2 line at center frequencies of the two bands (fp and fs), the ABCD matrix is formulated as (1 Where J the characteristic admittance of the π/2 line * arg min ( ( )) The circuit dimensions of the SISBL Figure 1.b can be determined by solving the following equations (1)-(4). Where (θ1, θ2, θ3) the electrical lengths of the lines (1,2,3) respectively, and (Z1, Z2, Z3) the impedances of the lines (1,2,3).
To get a compact dual-band BLC in (2), n takes the value 1.
We cast as free variables, the impedance ratio R= Z1/Z2 and the electrical length ratio U= θ1/θ2. Substituting (2)-(3), Z1=R*Z2 and θ1=U*θ2 into (4) eliminates Z2, leads to (5): Equation (4) has only θ2 for variable since the constants U, R and rf can be pre-chosen. θ2 is found using the graph of each side of the equation (4). Figure 2 presents the variation of the impedances Z1 and Z2 versus frequency ration rf when R and U are both 0.2. That figure shows that both Z1 and Z2 increase as rf increases. Since only an impedance of 20-120 Ω can be realized using microstrip, the range of rf is limited to 1.9<rf<2.5. Dual-band 50/√2 Ω branch line

Tuning Space Mapping
The utilize of electromagnetic software for design optimization can be problematic, because EM simulations are rigorous. By shifting the optimization load onto a coarse model, for example, a circuit equivalent, space mapping (SM) reduces the computational rate of EM simulation. Over an iterative optimization and updating of the low fidelity models, SM achieves efficient optimization. [11].
Tuning space mapping such as SM belongs to a family of surrogate-based optimization techniques [12][13][14][15][16][17][18][19][20][21][22][23]. However, the role of the surrogate model is replaced by a so-called tuning model. By introducing tuning components (circuit-theory base components) into the fine model structure, the tuning model is built up. The original optimization problem is as follow [15]: Where Rf ∈ R m is the response vector, U is an objective function, x is the vector of design parameters, and * is the optimal solution.
At i-th iteration, a tuning model ( ) is constructed based on the fine model data. The alignment process to eliminate the gap between the tuning model response and the response of the fine model at i, it is formulated as: To fit the design specifications, ( ) needs to be optimized with respect to . This is expressed by: The modifications needed for the design variables are determined using a calibration process. Equation (9) express this process:

Results and Discussion
We chose (U, R) = (0.2,0.2), the dimensions of this dual-band BLC have been computed with the use of (2)-(5). Figure 3 illustrates the intersecting points of each side of the equation (4).
The design parameters are x = [L0 L11 L21 L31 L12 L22 L32] T mm. The fine model, as shown in Figure 4, is simulated using a substrate of εr = 4, height H =1.4 mm and loss tangent= 0.0004. Figure 6 shows that S11 and S14 for the second band are below -10dB from 1.76 GHz to 1.88GHz, this is not the entire [1.930 GHz-1.990 GHz] band. And in the same range, the phase difference between output ports (2 and 3) is not 90 °± 10°. For better performance, optimization is needed.
To build the tuning model, we first simulate the fine model with the co-calibrated ports Figure   shows that the simulated S11 and S14 are less than -11dB, within the frequency range of 0.82-0.92 GHz (first band), and within 1.88-2 GHz (second band). Within a similar frequency range, the coupling coefficient is 3 ± 1 dB, the transmission coefficient is 3 ± 1 dB, and the phase difference between output ports (2 and 3) is 90 °± 10°.    Figure 8 shows the photograph of the prototype of the enhanced dual-band BLC fabricated using an LPKF machine. As we can see, its structure is relatively simple as it can be fabricated on a single layer printed circuit board with a simple ground plane.
The measurements of the fabricated prototype are done using 1-Port USB Vector Network Analyzer. Figure 9 plots the simulated and measured (S11), it shows that there is a good match between simulated and measured S11 of this enhanced dual-band BLC.
TABLE I summarized, the results of the simulation for the initial and the optimized dual-band BLC performance, also the measurements of the fabricated prototype. The optimized dualband BLC shows better performances for both 5G NR bands, which the initial does not do.

Conclusion
A dual-band BLC with SISBL for 5G NR applications has been designed. The coupler performance is further improved through optimization of his physical dimensions, using an adjusted Tuning Space Mapping to work for more complex microwave circuits such as our design. The simulated and measured results show that S11 are less than -11dB, within the frequency range of 0.82-0.92 GHz (first band), and within 1.88-2 GHz (second band). The method used permits rapid optimization with accurate results obtained after only one iteration.