Rapid design and size reduction of microwave couplers using variable‐fidelity EM‐driven optimization

In this article, fast electromagnetic (EM) simulation‐driven design optimization of compact microwave couplers is addressed. The main focus is on explicit reduction of the circuit footprint. Our methodology relies on the penalty function approach, which allows us to minimize the circuit area while ensuring equal power split between the output ports and providing a sufficient bandwidth with respect to the return loss and isolation around the operating frequency. Computational efficiency of the design process is achieved by exploiting variable‐fidelity EM simulations, local response surface approximation models, as well as suitable response correction techniques for design tuning. The technique described in this work is demonstrated using two examples of compact rat‐race couplers. The size‐reduction‐oriented designs are compared with performance‐oriented ones to illustrate available design trade‐offs. Final design solutions of the former case illustrate ～92% of miniaturization for both coupler examples (with corresponding fractional bandwidths of 16%). Alternative design solutions pertaining to the latter case show a lesser size reduction (～90% for both examples), but present a much wider bandwidths (～25% for both couplers). The overall computational cost of the design procedure corresponds to about 20 and 10 high‐fidelity coupler simulations for the first and second design example, respectively. Numerical results are also validated experimentally. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:27–35, 2016.     

Design of compact rat‐race couplers with enhanced bandwidth

This article presents a method to design compact rat race couplers with improved bandwidth values. The coupler consists of three coupled‐line sections of different electrical lengths and characteristic impedances. First, design equations are obtained by imposing the coupler conditions using a lossless transmission line model. Input impedance matching, isolation, phase, and amplitude imbalances, all four conditions for both the sum and the difference port excitations are considered for bandwidth calculations. Then, an algorithm is developed to solve for the coupled‐line parameters. Considering the limitations of fabrication, guidelines are provided for selecting the right physical parameters according to bandwidth requirement. As an example, a rat race coupler is fabricated that occupies 10% area of a conventional coupler without compromising the bandwidth values. Measurement results shows that the coupler provides 50% of 15 dB return loss bandwidth, 41.7% of 20 dB isolation bandwidth, 15% of ±5° phase imbalance bandwidth, and 62.5% of ±0.5 dB amplitude imbalance bandwidth which are more than those of a conventional 3λ/2 rat race coupler.     

Analytical method for optimal design of RF dual‐band rat‐race couplers for arbitrary frequency ratios

This article presents an analytical method to design a hybrid structure dual‐band rat‐race coupler at microwave frequencies. The proposed structure uses six identical cells of which each is engineered to work as a quarter wavelength transmission line with proper characteristic impedance at two distinct frequencies having arbitrary frequency ratio. The performances of the π‐ and T‐cells are studied to assess their ability to provide the required electrical parameters for dual‐band operation. It is demonstrated that the single‐section π‐topology can only lead to a suboptimal design for a dual‐band rat‐race cell at two nonharmonic frequencies. In contrast, the proposed double‐section π‐cell structure allows achieving an optimal dual‐band cell design. A dual‐band rat‐race coupler designed at 2.14 and 3.6 GHz has been simulated and fabricated in hybrid microstrip technology. Measurement results agree well with analytically based simulation results, which demonstrate the effectiveness of the proposed structure for dual‐band operation. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22: 690–700, 2012.     

Surrogate‐assisted EM‐driven miniaturization of wideband microwave couplers by means of co‐simulation low‐fidelity models

This article proposes a methodology for rapid design optimization of miniaturized wideband couplers. More specifically, a class of circuits is considered, in which conventional transmission lines are replaced by their abbreviated counterparts referred to as slow‐wave compact cells. Our focus is on explicit reduction of the structure size as well as on reducing the CPU cost of the design process. For the sake of computational feasibility, a surrogate‐based optimization paradigm involving a co‐simulation low‐fidelity model is used. The latter is a fundamental component of the proposed technique. The low‐fidelity model represents cascaded slow‐wave cells replacing the low‐impedance lines of the original coupler circuit. It is implemented in a circuit simulator (here, ADS) and consists of duplicated compact cell EM simulation data as well as circuit theory‐based feeding line models. Our primary optimization routine is a trust‐region‐embedded gradient search algorithm. To further reduce the design cost, the system response Jacobian is estimated at the level of the low‐fidelity model, which is sufficient due to good correlation between the low‐ and high‐fidelity models. The coupler is explicitly optimized for size reduction, whereas electrical performance parameters are controlled using a penalty function approach. The presented methodology is demonstrated through the design of a 1‐GHz wideband microstrip branch‐line coupler. Numerical results are supported by experimental validation of the fabricated coupler prototype.     

Inverse modeling for fast design optimization of small‐size rat‐race couplers incorporating compact cells

In the paper, a framework for computationally‐efficient design optimization of compact rat‐race couplers (RRCs) is discussed. A class of hybrid RRCs with variable operating conditions is investigated, whose size reduction is obtained by replacing ordinary transmission lines with compact microstrip resonant cells (CMRCs). Our approach employs a bottom‐up design strategy leading to the development of compact RRCs through rapid design optimization of its building blocks and a subsequent fine tuning to account for parasitic cross‐coupling effects. The fundamental component of the proposed method is an inverse CMRC surrogate model, covering a wide range of cell electrical parameters, and enabling a convenient adjustment of coupler bandwidth. Having the surrogate model established, it is possible to produce close‐to‐optimum CMRC dimensions at a negligible computational cost. The subsequent correction step requires only up to two electromagnetic simulations of the CMRC. The proposed method is demonstrated by designing an RRC for several operational bandwidths. Experimental results are also provided.     

Rapid surrogate‐assisted design optimization of minimum‐size broadband branch‐line couplers with variable topology

This work discusses simulation‐driven design of miniaturized wideband branch‐line couplers with a variable topology. Size reduction is enabled here by replacing uniform transmission lines of the original coupler with slow‐wave structures in the form of cascaded compact cells and meander lines. The primary goal is to determine a number of cells in the cascade and particular cell dimensions for which the minimum size of the coupler as well as its required operating conditions are ensured. To this end, we employ a surrogate‐assisted technique involving a trust‐region gradient search framework. Computational efficiency of the design process stems from estimating the Jacobian of circuit responses at the level of a low‐fidelity model of the cascade. The latter is composed in a circuit simulator from duplicated EM‐evaluated data blocks of a single cell and is well correlated with the corresponding high‐fidelity model. The key advantage of this work is the utilization of a reconfigurable, cheap, and well‐aligned low‐fidelity model. The proposed approach is demonstrated through design of a minimum‐size two‐section branch‐line coupler with quasi‐periodic dumbbell‐shaped cells and meander lines. Excellent circuit performance as well as its small size showcase the reliability and usefulness of the presented method. Experimental verification is also provided.     

Design of an efficiency‐enhanced Greinacher rectifier operating in the GSM 1800 band by using rat‐race coupler for RF energy harvesting applications

Radio frequency energy harvesting (RFEH) circuits can convert the power of communication signals from radio frequencies (RF) in the environment into direct current and voltage (DC power). In this study, the Greinacher full‐wave rectifier circuit topology was combined with a 180° hybrid ring (rat‐race) coupler which was a passive RF/microwave circuit. Thus, higher RF‐DC conversion efficiency was obtained. First, using the Greinacher rectifier topology, RFEH circuit operating at the center frequency of 1850 MHz was designed. Then, at this frequency, designing of the rat‐race coupler having 1000 MHz bandwidth was made. The S‐parameter measurements and simulation data of the designed coupler circuit were compared. Finally, the high efficiency rectifier circuit where these two circuits were used together was designed. The proposed rectifier circuit was constructed on 70 × 70 × 1.6 mm³ FR4 substrate material with a permittivity of 4.3 (ε_r = 4.3). The power conversion efficiency (PCE) of the rectifier circuit, which had 125 MHz bandwidth at the center frequency of 1850 MHz and was developed with rat‐race coupler, was calculated as 71% at 4.7 dBm input power. In addition, with this study, at ?15 dBm input power, which was a relatively low power level, 40% PCE value was obtained.     

Surrogate modeling for expedited two‐objective geometry scaling of miniaturized microwave passives

Geometry scaling of compact microwave structures is a challenging problem because of complex relationships between the physical dimensions of the circuit and its electrical characteristics, which is mostly caused by considerable cross‐couplings in densely arranged layouts. Yet, possibility of rapid redesign of a structure for various sets of design specification is important from practical point of view. In this article, we develop a procedure for expedited dimension scaling of compact microwave couplers with respect to two independent criteria. Our approach exploits inverse surrogates constructed at the level of equivalent circuit model and correction techniques that permits low‐cost re‐design of the coupler structure (at the level of EM‐simulation model) for a required operating frequency and power split ratio. The procedure is demonstrated using a folded microstrip rat‐race coupler. The scaling range for the considered example is from 0.5 to 2.0 GHz for the operating frequency, and from ?6 dB to 0 dB for the power split ratio. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:531–537, 2016.     

Miniaturized substrate integrated waveguide filter using fractal open complementary split‐ring resonators

A miniaturized substrate integrated waveguide (SIW) bandpass filter using fractal open complementary split‐ring resonators (FOCSRRs) unit‐cell is proposed. The proposed structure is realized by etching the proposed FOCSRR unit‐cells on the top metal surface of the SIW structure. The working principle of the proposed filter is based on the evanescent‐mode propagation. The proposed FOCSRRs behave as an electric dipoles in condition of the appropriate stimulation, which are able to generate a forward‐wave passband region below the cutoff frequency of the waveguide structure. Since, the electrical size of the proposed FOCSRRs unit‐cell is larger than the conventional OCSRRs unit‐cell; therefore, the FOCSRR unit‐cell is a good candidate to miniaturize the SIW structure. The proposed filter represents high selectivity and compact size because of the utilization of the sub‐wavelength resonators. The introduced filter is simulated by a 3D electromagnetic simulator. In order to validate the ability of the proposed topology in size reduction, 1‐ and 2‐stage of the proposed filters have been fabricated based on the standard printed circuit board process. The measured S‐parameters of the fabricated filters are in a good agreement with the simulated ones. The proposed SIW filters have many advantages in term of compact size, low insertion loss, high return loss, easy fabrication and integration with other circuits. It is the first time that the FOCSRR unit‐cells were combined with the SIW structure for miniaturization of this structure. Furthermore, a wide upper‐stopband with the attenuation >20 dB in the range of 3–8 GHz is achieved. The results show that, a miniaturization factor about 75.5% has been obtained.     

Miniaturized wide‐band rat‐race coupler

New designs of wide‐band rat‐race couplers are proposed. The wide‐band operation is achieved with the use of the microstrip nonuniform transmission line sections for the branches of the conventional rat‐race coupler. The design formulas are developed using ABCD matrix and the even‐ and odd‐mode analysis. The theoretical analysis has been verified by measurements of the two manufactured wideband rat‐race couplers, one operate within 0.85–1.92 GHz and other within 1.55–3.55 GHz frequency range with the equal normalized characteristic impedance functions. For both fabricated couplers, the isolation parameter is better than 15 dB over a 77% relative bandwidth. Also, it is shown that the designed wide‐band rat‐race coupler can be realized in higher frequency bands with the fixed fractional bandwidth. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 23: 675–681, 2013.     

EM‐simulation‐driven design optimization of compact microwave structures using multi‐fidelity simulation models and adjoint sensitivities

Reliable design of miniaturized microwave structures requires utilization of full‐wave electromagnetic (EM) simulation models because other types of representations such as analytical or equivalent circuit models are of insufficient accuracy. This is primarily due to considerable cross‐coupling effects in tightly arranged layouts of compact circuits. Unfortunately, high computational cost of accurate EM analysis makes the dimension adjustment process challenging, particularly for traditional methods based on parameter sweeps, but also for conventional numerical optimization techniques. In this article, low‐cost simulation‐driven designs of compact structures were demonstrated using gradient search with adjoint sensitivities as well as multi‐fidelity EM simulation models. The optimization process was arranged sequentially, with the largest steps taken at the level of coarse‐discretization models. Subsequent fine tuning was realized with the models of higher fidelity. Switching between the models was realized by means of adaptively controlled termination conditions. This allowed for considerable reduction of the design cost compared with single‐level optimization. The approach was illustrated using a compact microstrip rat‐race coupler with two cases considered, that is, (i) bandwidth enhancement, and (ii) minimization of the structure size. In both cases, the optimization cost corresponded to a few high‐fidelity EM simulations of the coupler structure. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:442–448, 2016.     

Geometrically progressive stub loading scheme for miniaturization of transmission line‐based components

This paper presents a novel slow wave structure (SWS) using geometrically progressive loaded shunt stubs for miniaturization of microstrip lines. It is observed that, compared to the conventional periodically stub loaded SWS, the proposed technique renders further miniaturization of around 20%, theoretically. Apart from that, this technique also helps in suppression of higher pass bands inherently present in SWSs. A detailed analysis of this technique has been carried out with corresponding design scheme. For proof of concept, this miniaturization scheme is applied to a rat‐race coupler designed at 2 GHz, where 75% reduction in overall footprint is observed. The simulated and measured results are found to be in good agreement with the proposed theory.     

Compact substrate integrated waveguide rat‐race filtering couplers with arbitrary angular interval between ports

A new type of compact filtering rat‐race couplers with arbitrary port direction based on different shape substrate integrated waveguide (SIW) cavity are first proposed in this paper. Different shaped SIW resonators can be combined together to achieve better performance and flexible topology. Resonant frequencies of fan‐shaped SIW cavity with various central angles have been derived to construct the resonant cells and obtain different topological structures. Moreover, interdigital capacitor SIW unit loaded on the common wall between cavities is used to achieve negative coupling structure. The detailed analysis and the design method have been introduced to realize a filtering rat‐race coupler based on substrate integrated fan‐shaped cavity (SIFC) and rectangular cavity. In particular, the combination of different shaped resonators can be selected according to the requirement of port angle interval. In order to further verify the method, the other filtering rat‐race coupler is fabricated using four SIFCs to achieve more available port angle intervals. Compared with other filtering couplers, the proposed designs exhibit good filtering responses, high Q factor, amplitude balance, as well as 0° and 180° phase differences. Furthermore, various angular intervals for input/output ports are convenience to meet the requirement of system topology and interconnect.     

Cost‐efficient design methodology for compact rat‐race couplers

In this article, a reliable and low‐cost design methodology for simulation‐driven optimization of miniaturized rat‐race couplers (RRCs) is presented. We exploit a two‐stage design approach, where a composite structure (a basic building block of the RRC structure) is first optimized using a pattern search algorithm, and, subsequently, the entire coupler is tuned by means of surrogate‐based optimization (SBO) procedure. SBO is executed with the underlying low‐fidelity model implemented as cascaded response surface approximations (RSAs) of the composite structure. Full‐wave analysis of the entire coupler is required at the tuning stage only. By combining SBO with coupler decomposition and RSA surrogates, the overall cost of the design process corresponds (in terms of CPU time) to less than three electromagnetic simulations of the compact RRC, and results in highly miniaturized structure (82% footprint reduction compared to conventional coupler) that exhibits perfect return loss and isolation (almost ?60 dB at the operating frequency), as well as a strong harmonic and spurious suppression (below ?20 dB) in, approximately, 3–9.5 GHz frequency band. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:236–242, 2015.     

Bandwidth improvement of rat‐race couplers having left‐handed transmission‐line sections

A novel broadband rat‐race coupler has been investigated. The coupler utilizes an artificial left‐handed transmission line section for broadband phase response realization. Moreover, a narrowband model of left‐handed section has been shown to prove the couplers equivalent circuit at the center frequency. To broaden the operational bandwidth multisection quarter‐wave transformers have been proposed. The exemplary rat‐race coupler with two‐section impedance transformers has been designed and manufactured. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:341–347, 2014.     

Compact reconfigurable rat‐race coupler with tunable frequency and tunable power dividing ratio

A compact reconfigurable rat‐race coupler with tunable frequency and tunable power dividing ratio is proposed for the first time. Varactors and two single control voltages are used to obtain both the tunable frequency and the tunable power dividing ratio in this article. The structure of the rat‐race coupler involves 50 Ω parallel‐strip lines only and a phase inverter is used for size reduction. Theoretical equations for the relationship among S‐parameters and the capacitance of varactors are derived. The graphic method is used to choose capacitance for the desired operation frequency and the desired power dividing ratio. For demonstration, a prototype is designed and fabricated. The measured results show that the rat‐race coupler's frequency and the power dividing ratio can be effectively tuned in 0.69 GHz ～ 0.81 GHz and 3 dB ～ 14 dB, respectively with isolation better than 20 dB, phase difference less than 7°and return loss better than 20 dB. The theoretical simulation, electromagnetic simulation, and measured results show good agreement in this design.     

Performance‐driven modeling of compact couplers in restricted domains

Fast surrogate models can play an important role in reducing the cost of Electromagnetic (EM)‐driven design closure of miniaturized microwave components. Unfortunately, construction of such models is challenging due to curse of dimensionality and wide range of geometry parameters that need to be included in order to make it practically useful. In this letter, a novel approach to design‐oriented modeling of compact couplers is presented. Our method allows for building surrogates that cover wide range of operating conditions and/or material parameters, which makes them useful for design purposes. At the same time, careful definition of the model domain permits dramatic (volume‐wise) reduction of the of the design space region that needs to be sampled, thus, keeping the number of training data samples at acceptable levels. The proposed technique is demonstrated using a compact rat‐race coupler modeled for operating frequencies from 1 to 2 GHz and power split of ?6 to 0 dB. Benchmarking and application examples for coupler design optimization as well as experimental validation are also provided.     

A planar ultra‐wide band asymmetric rat‐race hybrid coupler

In this article, an asymmetric ultra‐wideband rat‐race hybrid coupler with 180° phase shift is proposed. The primary goal of this work is to design a planar ultra‐wideband hybrid coupler with a microstrip structure by avoiding via holes and multi‐layer design. The bandwidth of an asymmetric ring hybrid is enhanced using shorted coupled lines, perturbation impedance techniques, and matching stubs. This hybrid coupler was designed and fabricated using Taconic TLX‐8 substrate with a thickness of 0.5 mm. The results of the simulation and measurement are promising and meet the desired specifications. This hybrid coupler yields a fractional bandwidth of 56% at the center frequency of 5.95 GHz based on ±1 amplitude imbalance between two output ports.     

A novel super compact half‐mode substrate‐integrated waveguide filter using modified complementary split‐ring resonator

A novel super compact filter based on half‐mode substrate‐integrated waveguide (HMSIW) technology loaded by the modified complementary split‐ring resonator (MCSRR) is proposed. The working principle of the proposed filter is based on the evanescent‐mode propagation technique. According to this technique, by loading the complementary split‐ring resonator (CSRR) on the metal surface of the substrate‐integrated waveguide (SIW) structure, an additional passband below the SIW cutoff frequency can be obtained. In order to miniaturize the physical size of the conventional CSRR, a new method is introduced. In the proposed MCSRR unit‐cell, the meander slots are carved inside all of the interior space of the ring. Accordingly, the length of the slot is increased which leads to an increase in the inductor and capacitor of the proposed structure without occupying the extra space. Therefore, the electrical size of the proposed MCSRR unit‐cell is reduced. Consequently, the resonance frequency of the proposed MCSRR unit‐cell is decreased compared to the conventional CSRR with the same sizes. Namely, the lower resonance frequencies can be achieved by using this technique without increasing the size of the unit‐cell. In order to confirm the miniaturization technique, two HMSIW filters loaded by the proposed MCSRR unit‐cell are designed, fabricated, and experimental verifications are provided. The results show that a miniaturization about 67% is achieved.     

Design of a miniaturized planar half elliptical ultra‐wideband dipole using a concaved arm

This article presents the miniaturization of a planar half elliptical ultra‐wideband dipole. By simply placing a concaved arm in close proximity to the original structure, a 45% area reduction in terms of electrical wavelength can be achieved. The proposed antenna exhibits a wide measured return loss bandwidth of 2 to 9.9 GHz and omnidirectional radiation patterns across the band. The design features a footprint size of 41.5 × 41.5 mm² and an electrical size of 0.28λ × 0.28λ at 2 GHz. Compared with some previously reported planar designs, the proposed antenna presents a more compact electrical dimension and better or comparable bandwidth. Critical geometric parameters of the structure, particularly the concaved arm, are investigated to understand the miniaturization and operating mechanism of the design. Satisfactory correlation between the simulation and measurement data is obtained.