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.     

Fast simulation‐driven feature‐based design optimization of compact dual‐band microstrip branch‐line coupler

Design of miniaturized microwave components is a challenging task. On one hand, due to considerable electromagnetic (EM) cross‐couplings in highly compressed layouts full‐wave EM analysis is necessary for accurate evaluation of the structure performance. Conversely, high‐fidelity EM simulation is computationally expensive so that automated determination of the structure dimensions may be prohibitive when using conventional numerical optimization routines. In this article, computationally efficient simulation‐driven design of a miniaturized dual‐band microstrip branch‐line coupler is presented. The optimization methodology relies on suitably extracted features of a highly nonlinear response of the coupler structure under design. The design objectives are formulated in terms of the feature point locations, and the optimization is carried out iteratively with the linear model of the features utilized as a fast predictor. The entire process is embedded in the trust‐region framework as convergence safeguard. Owing to only slightly nonlinear dependence of the features on the geometry parameters of the circuit at hand, the optimized design satisfying prescribed performance requirements is obtained at the low computational cost of only 24 high‐fidelity EM simulations of the structure. Experimental validation of the fabricated coupler prototype is also provided. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:13–20, 2016.     

Compact cell topology selection for size‐reduction‐oriented design of microstrip rat‐race couplers

In this work, we address the problem of compact cell topology selection for miniaturization of rat‐race couplers. The principal objective of the design process is to achieve the smallest possible footprint of the coupler, while maintaining the required levels of electrical parameters imposed on its components. Our approach permits identification of the minimum achievable coupler area, provided that the circuit is composed of a given compact cell and folded lines. This allows for the quantitative assessment of a set of considered cells with respect to the miniaturization capabilities they exhibit under certain design specifications. The proposed method is validated using 6 different cells with unified parameterization to identify the smallest rectangular‐like rat‐race coupler described by 2 design specifications. The obtained results attest that circuit topology and electrical parameters of the reference design are critical factors determining the final miniaturization rate. The proof‐of‐concept prototype devices occupy merely 8% of the conventional coupler area, while preserving fractional bandwidths (20% and 13.5%) of their conventional counterparts. The experimental results confirm the claims inferred from the numerical data.     

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.     

Harmonic suppressed compact wideband branch‐line coupler using unequal length open‐stub units

In this article, the design of a broadband branch‐line coupler (BLC) with reduced size and suppressed harmonic passband response is presented. The proposed approach can be used to replace the low impedance λ/4 lines of the conventional BLC by an equivalent structure almost λ/12 in length. The main advantage of the proposed BLC is that, it has approximately the same bandwidth as that of a conventional BLC. A prototype broadband coupler having fractional bandwidth >50% at 1.1 GHz and of size less than one third of a conventional three‐section wideband BLC topology is realized. In addition, at least 20 dB suppression of up to fourth harmonics is achieved. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

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.     

Novel compact dual‐narrow/wideband branch‐line couplers using T‐Shaped stepped‐impedance‐stub lines

This article presents a compact model to reduce the physical size and increase the frequency ratio between the second and first resonance frequencies of a dual‐function stepped‐impedance‐stub (SIS) line, which was subsequently employed in the realization of dual‐band branch‐line couplers. The proposed model comprises of a loaded spiral T‐shaped SIS that reduces the size of a conventional SIS line as well as improving its frequency ratio. The proposed model behaves exactly similar to the recently developed dual‐band resonators with the advantage of size reduction of ～35% as well as having a wide range of realizable frequency ratios between 1.4 and 3.7 compared to 1.7–2.7 and 1.8–2.3 for the conventional SIS and T‐shaped transmission‐lines, respectively. Dual‐narrowband and wideband branch‐line couplers were developed based on the spiral T‐shaped SIS lines. The dual‐wideband device's bandwidth was enhanced by 2.7% accompanied by a size reduction of 58.6% in comparison with the conventional dual‐wideband couplers operating at the same frequencies. The theoretical results were verified by measurement. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

Design method for quasi‐optimal multiband branch‐line couplers

In this article, the design approach, the implementation, and experimental results of multiband branch‐line couplers operating at arbitrary frequencies are presented. The conventional branch‐line coupler structure is adapted to multiband operation by shunting its four ports with multiband reactive networks. The performance of the proposed multiband couplers is theoretically analyzed and optimized through the even‐odd mode circuit analysis. Dual‐band (2.4–3.5 GHz), triple‐band (1.5–2.4–4.2 GHz), and quad‐band (1.5–2.4–3.5 GHz) microstrip branch‐line couplers have been realized and tested to verify the design method. The good experimental results (input return loss greater than 15 dB and amplitude imbalance lower than 0.7 dB) show excellent agreement with theoretical and simulated ones, thus validating the proposed approach. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:117–129, 2014.     

Directional‐coupler‐based microwave sensors for differential angular‐displacement measurement

The novel application of microwave directional couplers to develop angular‐displacement microwave sensors is reported. The proposed sensor approach employs as stator a branch‐line‐type coupler arranged in transversal mode by loading its direct and coupled ports with two distinct‐length open‐ended stubs. Thus, by taking the isolated port of the coupler as the stator output node, a bandpass filtering transfer function with transmission zeros (TZs) is created. Then, a rotor made up of an angularly‐moveable open‐ended stub is attached to a curved section of the longest loading stub of the stator through physical contact, so that their interconnection point varies with the angular‐displacement of the rotor. In this manner, the sensor transfer function is altered with the stub rotation through TZ reallocation, angular‐displacement sensing capabilities are achieved. The theoretical operational foundations of the conceived branch‐line‐coupler‐based microwave angular‐displacement sensor, which features single/multi‐band sensing properties in terms of inter‐TZ spacing and stop band attenuation levels, along with design examples and curves are provided. The extrapolation of this sensor principle to other classes of power‐distribution circuits, such as the rat‐race‐type directional coupler, is also demonstrated. Finally, for experimental‐validation purposes, two 920 MHz microstrip prototypes of the conceived branch‐line‐coupler‐based angular‐displacement microwave‐sensor approach are built and measured.     

Modeling and performance improvement of folded coupled lines in miniaturized Quasi‐lumped directional couplers

An efficient modeling method for folded coupled inductors for application in quasi‐lumped directional couplers designed in both symmetric and asymmetric structures has been proposed. The presented model takes into account the deteriorative effects which occur when coupled inductors realized as electrically short coupled‐lines matched to the high impedance standard are folded into, for example, meander or spiral pattern. The deteriorative influence of coupled‐lines' folding on the performance of the resulting directional coupler has been modeled as additional lumped inductors and capacitors on the schematic diagram of a quasi‐lumped directional coupler's subsection. Moreover, it has been shown that this deteriorative influence can be substantially minimized when values of lumped elements constituting the directional coupler are appropriately changed. The proposed design procedure has been experimentally verified by measurements of two 3‐dB single‐section directional couplers designed in symmetric and asymmetric structures as quasi‐lumped couplers with folded coupled inductors. The measurement results show a good agreement with both circuit and electromagnetic analysis which proves the correctness and usefulness of the presented methods. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:1–9, 2015.     

E and H‐plane wide‐band ridge waveguide couplers

A systematic synthesis procedure for ridge waveguide branch line couplers in both E‐plane and H‐plane configurations is presented. Ridge waveguides are chosen to benefit from their wide mono‐mode band and compact size compared to rectangular waveguides. Equivalent circuit parameters are used to synthesize the coupler sections. Rigorous mode matching method is used for full‐wave analysis and optimization of the couplers. Ridge couplers both in empty waveguide and Low Temperature Co‐fired Ceramic “LTCC” technology are designed using the proposed method and the design is verified with another numerical method. A prototype is built and its response is measured to verify the approach. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.     

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.     

A compact transmission line with two pairs of composite right/left‐handed passbands

A compact transmission line with two pairs of composite right/left‐handed (CRLH) passbands is investigated, and its equivalent circuit is proposed. Compared with the conventional CRLH transmission line (CRLH‐TL), we use the rectangular patches with meander lines and the T‐shaped defected ground structures (T‐DGS) to model the other two resonators, which realize the second left‐ and right‐handed bands. The dispersion relations are analytically derived using the equivalent circuit and Bloch‐Floquet theory. The five‐stage CRLH‐TL is fabricated, and the measured results are in agreement with those of simulation. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.     

A novel frequency‐tunable branch line coupler

This article introduces a novel two‐section frequency‐tunable branch line coupler, which is realized by inserting a narrow band frequency‐tunable phase inverter into a wideband two‐section branch line coupler's middle branch line. Such frequency‐tunable method is different from the conventional one. Furthermore, in this bias feeding design, there are only one control voltage, two varactors, two resistors, and two capacitors are utilized. The measured results show that the operation frequency of the branch line coupler can be tuned from 0.73 to 1.33 GHz, and the return loss is >20 dB, the isolation >20 dB, the amplitude imbalances <1 dB, and the phase imbalances is <2°. Through the comparison, the measured results basically conform to the simulated results in this design.     

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.     

Low‐cost multiband compact branch‐line coupler design using response features and automated EM model fidelity adjustment

Design closure of compact microwave components is a challenging problem because of significant electromagnetic (EM) cross‐couplings in densely arranged layouts. A separate issue is a large number of designable parameters resulting from replacement of conventional transmission line sections by compact microstrip resonant cells. This increases complexity of the design optimization problem and requires employment of expensive high‐fidelity EM analysis for reliable performance evaluation of the structure at hand. Consequently, neither conventional numerical optimization algorithms nor interactive approaches (e.g., experience‐driven parameters sweeps) are capable of identifying optimum designs in reasonable timeframes. Here, we discuss application of feature‐based optimization for fast design optimization of dual‐ and multiband compact couplers. On one hand, design of such components is difficult because of multiple objectives (achieving equal power split and good matching and port isolation for all frequency bands of interest). On the other hand, because of well‐defined shapes of the S‐parameter responses for this class of components, feature‐based optimization seems to be well suited to control multiple figures of interest as demonstrated in this work. Two‐level EM modeling is used for further design cost reduction. More importantly, we develop a procedure for automated determination of the low‐fidelity EM model coarseness that allows us to find the fastest possible model that still ensures sufficient correlation with its high‐fidelity counterpart, which is critical for robustness of the optimization process. Our approach is illustrated using two dual‐band compact couplers. Experimental validation is also provided.     

Penta‐band notched ultra‐wideband monopole antenna loaded with electromagnetic bandgap‐structures and modified U‐shaped slots

In this article, a planar monopole penta‐notched ultra‐wideband (UWB) antenna is designed and investigated. Three notches (2.81 GHz radar surveillance, 3.38 GHz WiMAX, and 3.87 GHz C‐band satellite downlink) have been realized by integrating three modified U‐shaped slots on the radiating surface. Furthermore, to create two additional notches (2.33 GHz ISM band and 5.75 GHz WLAN), two meander line electromagnetic bandgap (EBG); one located near to the feed line and another on the radiating surface, have been introduced in the design. These unit cells play a fundamental role in generating notches at higher as well as lower frequencies. The proposed antenna possesses an overall size of 34.9 × 31.3 × 1.6 mm³ and has been designed over FR4 substrate. A 50 Ω microstrip line is used to feed the antenna. The antenna without any extra arrangement exhibits an impedance bandwidth of 7.6 GHz. A parametric analysis is studied in detail to observe the band rejection characteristics. The ANSYS HFSS simulation software is used for simulating the proposed design structures. For validation purpose, a prototype is fabricated and characterized. A very good agreement is achieved between simulated and measured results.     

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.     

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.     

Novel compact planar electromagnetic band‐gap structure using for ultra‐wideband simultaneous switching noise suppression

In this article, by analyzing the equivalent circuit mode for electromagnetic bandgap (EBG), a novel compact planar EBG structure is proposed for overcoming the drawback of narrow bandwidth of conventional EBG structures. The novel design is based on using meander lines to increase the effective inductance of EBG patches. The simulated and measured results demonstrate the simultaneous switching noise (SSN) can be mitigated with an ultra‐wideband from 280 MHz to 20 GHz at the restraining depth of ?40 dB. Compared with the traditional L‐bridge and meander lines EBG structures, this novel structure has the advantages of suppression bandwidth and fabrication cost. Moreover, signal integrity is achieved by the time‐domain simulation. The proposed structure provides a new kind of theoretical designing reference for EBG structure to improve the bandwidth of restraining SSN. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:429–436, 2014.