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![Coupled-line bandpass filter [27].](profile/Ezzeldin-Soliman/publication/3131608/figure/fig2/AS:429013924618247@1479296298826/Coupled-line-bandpass-filter-27.png)
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![Fig. 2. Coupled-line bandpass filter [27].](profile/Ezzeldin-Soliman/publication/3131608/figure/fig2/AS:429013924618247@1479296298826/Coupled-line-bandpass-filter-27_Q320.jpg)
![Fig. 3. Electromagnetically coupled microstrip Yagi antenna [27].](profile/Ezzeldin-Soliman/publication/3131608/figure/fig3/AS:429013924618249@1479296298854/Electromagnetically-coupled-microstrip-Yagi-antenna-27_Q320.jpg)
A new technique for design centering of microwave circuits is introduced. This technique exploits the space-mapping interpolating surrogate (SMIS) with a modified ellipsoidal technique. The design centering solution for microwave circuits is obtained with a small number of fine model evaluations and, hence, the number of electromagnetic simulations...
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Citations
... Coupled line microstrip bandpass lters have many desired advantages in terms of low cost, compactness of size and good performance that makes them a favorable choice in modern wireless communication systems. A typical example of 3-section coupled line microstrip band pass lter was optimized in [12] by using space mapping surrogate optimization technique combined with ellipsoidal technique for design centering. The lter response simulation was carried out by Method of Moments (MoM) planar solver [13]- [14]. ...
... The design parameters of the lter are the lengths, widths and spacing of microstrip lines mainly in mm. The design constraints on the lter response are given by (1) The constraints functions have been determined at 11 different frequency values; = 5, 5.75, 6.5, 7.25, 7.75, 8, 8.25, 8.75, 9.5, 10.25, 11 GHz, where the substrate thickness is 1.272 mm and its relative permittivity 'ε r ' is 10, The optimal design parameters of the lter design was obtained as [5.298 12.960 6.052 0.416 2.122 1.099] T with all constraints satis ed [12]. ...
... The deterministic values of the design parameters of the coupled line Bandpass lter[12] The presented stochastic model is built on the Monte Carlo technique, where design parameters of the microstrip coupled line lter are considered as the inputs of the deterministic simulations while the associated operating central frequency and the bandwidth are considered the output parameters. In ...
Coupled Line Microstrip Bandpass Filters are considered as a promising candidate for bandpass filter for wireless and high frequency applications because of their small size, low cost and easy engineered fabrication. In this paper, a stochastic analysis of this coupled line bandpass filter which is based on Monte Carlo Model is developed, where the tolerances in the design parameters of this microstrip bandpass filter and their impacts on the filter performance are investigated. These design parameters include the thickness of the strips of the bandpass filter, their lengths and the spacing between them. The mean, the standard deviations and the probability distribution function of both the central frequency and the operating bandwidth are studied.
... The latter is imperative for compact microwave components, where strong EM crosscoupling effects cannot be adequately represented using simpler methods, e.g., equivalent networks. Conventional uncertainty quantification (UQ) procedures, such as EM-driven Monte Carlo simulation, may incur impractical CPU expenses, whereas robust design (e.g., yield optimization [1], design centering [2]) often turns prohibitive. Acceleration thereof can be achieved by means of surrogate modeling methods, both data-driven [3], and physics-based [4]. ...
... The statistical performance metric utilized in this work is yield Y [2], defined as ...
Improving microwave component immunity to parameter deviations is of high importance, especially in the case of stringent performance specifications. This paper proposes a computationally efficient algorithm for robustness enhancement of compact microwave circuits. The objective is to increase the acceptable levels of geometry parameter deviations under which the prescribed performance specifications are still fulfilled. Our approach incorporates feature-based surrogate models utilized for low-cost prediction of the fabrication yield, as well as the trust-region framework for adaptive control of design relocation and ensuring convergence of the optimization process. The efficacy of our technique is demonstrated using a broadband microstrip filter.
... Surrogate-assisted procedures offer viable workarounds [6,[24][25][26][27][28]. Some of the most popular modeling methods utilized in this context are polynomial approximations [24], space mapping [48], NNs [49], and PCE [50]. As for statistical analysis, the bottleneck is a potentially high cost of the surrogate model setup, related to the dimensionality of the parameter space and parameter ranges. ...
Uncertainty quantification is an important aspect of engineering design, as manufacturing tolerances may affect the characteristics of the structure. Therefore, the quantification of these effects is indispensable for an adequate assessment of design quality. Toward this end, statistical analysis is performed, for reliability reasons, using full-wave electromagnetic (EM) simulations. Still, the computational expenditures associated with EM-driven statistical analysis often turn out to be unendurable. Recently, a performance-driven modeling technique has been proposed that may be employed for uncertainty quantification purposes and can enable circumventing the aforementioned difficulties. Capitalizing on this idea, this paper discusses a procedure for fast and simple surrogate-based yield optimization of high-frequency structures. The main concept of the approach is a tailored definition of the surrogate domain, which is based on a couple of pre-optimized designs that reflect the directions featuring maximum variability of the circuit responses with respect to its dimensions. A compact size of such a domain allows for the construction of an accurate metamodel therein using moderate numbers of training samples, and subsequently, it is employyed to enhance the yield. The implementation details are dedicated to a particular type of device. Results obtained for a ring-slot antenna and a miniaturized rat-race coupler imply that the cost of yield optimization process can be reduced to few dozens of EM analyses.
... A practical limitation is the dimensionality of the parameter space, i.e., the number of training data samples (translating into a computational cost of its acquisition) required for a construction of a reliable surrogate quickly increases with the number of the circuit parameters (also called the curse of dimensionality [17]). Available mitigation techniques include diminishing a number of directly handled dimensions [18], the usage of advanced modeling techniques (e.g., PC kriging, in which traditional trend functions, such as polynomials of low order, are substituted with PCE [19]), incorporation of model order reduction [20], as well as variable-resolution methods (co-kriging [21], space mapping [22]). ...
Fabrication tolerances, as well as uncertainties of other kinds, e.g., concerning material parameters or operating conditions, are detrimental to the performance of microwave circuits. Mitigating their impact requires accounting for possible parameter deviations already at the design stage. This involves optimization of appropriately defined statistical figures of merit such as yield. Although important, robust (or tolerance-aware) design is an intricate endeavor because manufacturing inaccuracies are normally described using probability distributions, and their quantification has to be based on statistical analysis. The major bottleneck here is high computational cost: for reliability reasons, miniaturized microwave components are evaluated using full-wave electromagnetic (EM) models, whereas conventionally utilized analysis methods (e.g., Monte Carlo simulation) are associated with massive circuit evaluations. A practical approach that allows for circumventing the aforementioned obstacles offers surrogate modeling techniques, which have been a dominant trend over the recent years. Notwithstanding, a construction of accurate metamodels may require considerable computational investments, especially for higher-dimensional cases. This paper brings in a novel design-centering approach, which assembles forward surrogates founded at the level of response features and trust-region framework for direct optimization of the system yield. Formulating the problem with the use of characteristic points of the system response alleviates the issues related to response nonlinearities. At the same time, as the surrogate is a linear regression model, a rapid yield estimation is possible through numerical integration of the input probability distributions. As a result, expenditures related to design centering equal merely few dozens of EM analyses. The introduced technique is demonstrated using three microstrip couplers. It is compared to recently reported techniques, and its reliability is corroborated using EM-based Monte Carlo analysis.
... For yield optimization, gradient-based optimizers are often utilized [4], [5], [17], [25]. In [4], three gradientbased optimizers are reviewed for the yield optimization of the microwave circuit models. ...
... In [4], three gradientbased optimizers are reviewed for the yield optimization of the microwave circuit models. To improve the search ability of gradient-based optimization methods, the modified ellipsoidal technique is designed for obtaining the design center of gradient-based optimization methods [17]. A boundary gradient search technique is used for generating a sequence of points on the boundary of the feasible region [25]. ...
... Substituting equations (15), (16), (17), and (18) into equation (21), we obtain ...
Yield optimization aims at finding microwave filter designs with high yield under fabrication tolerance. The electromagnetic (EM) simulation-based yield optimization methods are computationally expensive because a large number of EM simulations is required. Moreover, the microwave filter design usually requires several performance objectives to be met, which is not considered by the current yield optimization methods for microwave filters. In this paper, an efficient yield-constrained optimization using polynomial chaos surrogates (YCOPCS) is employed for microwave filters considering multiple objectives. In the YCOPCS method, the low-cost and high-accuracy of polynomial chaos is used as a surrogate. An efficient yield-constrained design framework is implemented to obtain the optimal design solution. Two numerical examples demonstrate the performance of the YCOPCS method, including a coupling matrix model of a fourth-order filter with cascaded quadruplet topology and an EM simulation model of a microwave waveguide bandpass filter. The numerical results show that the YCOPCS method can obtain the filter designs with higher yield and reduce EM simulations by 80% compared to Monte Carlo-based yield optimization in all testing examples.
... Such object approximates the feasible region, which is identified by the design specifications. The problem's design center is essentially the center of the geometrical body approximating the feasible region [39][40][41]. Among the geometrically based design centering techniques is the normed distances method, which will be used in this work. ...
A novel nanocrescent antenna with polarization diversity is introduced. It is formed from a crescent-shaped patch fed with a coupled strip transmission line. The antenna is located on top of a thin film with a shielding ground layer underneath. The structure is supported by an arbitrary substrate. Polarization of the radiated field can be adjusted to be along either one of the two orthogonal polarizations based on which one of the two crescent patch modes is going to be excited. The excitation of either one of these two modes of the patch is achieved by switching between the two propagating modes of the feeding coupled strip transmission line. Using a dual-polarized antenna allows doubling the optical communication system’s capacity via frequency reuse. The new crescent antenna dimensions are optimized to satisfy several goals, such as minimizing the losses, the deviation of the main beam direction away from broadside, and maximizing the radiation efficiency and axial ratio. Through the optimization process, simple surrogate kriging models replace the detailed electromagnetic simulation. The optimal response is achieved by applying two different optimizers. The first optimizer employs the design-centering technique using normed distances. The multiobjective particle swarm with the preference ranking organization method for enrichment evaluations is used by the second optimizer. In order to identify the critical dimensions to which the nanoantenna is most sensitive, a sensitivity analysis is used. The optimized antenna is capable of switching its radiation between two orthogonal pure linear polarizations with maximum radiation along the broadside direction. The size of the proposed antenna is about . Its impedance-matching bandwidth is higher than 30 THz centered around 193 THz (1550 nm). Its gain and radiation efficiency are higher than 5.2 dBi and 85%, respectively, all over the working frequency band.
... Practical EM-driven statistical design can be realized using surrogate modeling techniques [99]- [104]. Widely used methods include response surface approximations [100], neural networks [114], space mapping [115] and polynomial chaos expansion [116]. Although it is possible to set up a single surrogate valid for the entire region of interest (from the point of view of yield optimization), the bottleneck is the curse of dimensionality. ...
In this paper, we outline the historical evolution of RF and microwave design optimization and envisage imminent and future challenges that will be addressed by the next generation of optimization developments. Our journey starts in the 1960s, with the emergence of formal numerical optimization algorithms for circuit design. In our fast historical analysis, we emphasize the last two decades of documented microwave design optimization problems and solutions. From that retrospective, we identify a number of prominent scientific and engineering challenges: 1) the reliable and computationally efficient optimization of highly accurate system-level complex models subject to statistical uncertainty and varying operating or environmental conditions; 2) the computationally-efficient EM-driven multi-objective design optimization in high-dimensional design spaces including categorical, conditional, or combinatorial variables; and 3) the manufacturability assessment, statistical design, and yield optimization of high-frequency structures based on high-fidelity multi-physical representations. To address these major challenges, we venture into the development of sophisticated optimization approaches, exploiting confined and dimensionally reduced surrogate vehicles, automated feature-engineering-based optimization, and formal cognition-driven space mapping approaches, assisted by Bayesian and machine learning techniques.
... Some of the recent approaches are arguably more economical in that sense, e.g., PC kriging [10], where low-order polynomial traditionally employed as a trend function is replaced by the PCE surrogate. Other possibilities include reduction of the problem dimensionality (e.g., using principal component analysis [21]), incorporating variablefidelity simulations by means of space mapping [22], or cokriging [23], as well as combinations of various approaches such as surrogate modeling and model order reduction [24]. ...
... In practice, the methods of choice involve surrogate models [6]- [31]. As mentioned in the previous paragraph, popular techniques include response surface approximations [14], space mapping [8], [22], [32] neural networks [8], and polynomial chaos expansion (PCE) [18]- [20], [33]- [34] . As yield-driven optimization may need to handle considerable ranges of the antenna parameters, a construction of reliable surrogates may become problematic, especially for higher-dimensional spaces. ...
Uncertainty quantification is an important aspect of engineering design, also pertaining to the development and performance evaluation of antenna systems. Manufacturing tolerances as well as other types of uncertainties, related to material parameters (e.g., substrate permittivity) or operating conditions (e.g., bending) may affect the antenna characteristics. In the case of narrow- or multi-band antennas, this usually leads to frequency shifts of the operating bands. Quantifying these effects is imperative to adequately assess the design quality, either in terms of the statistical moments of the performance parameters or the yield. Reducing the antenna sensitivity to parameter deviations is even more essential when increasing the probability of the system satisfying the prescribed requirements is of concern. The prerequisite of such procedures is statistical analysis, normally carried out at the level of full-wave electromagnetic (EM) analysis. While necessary to ensure reliability, it entails considerable computational expenses, often prohibitive. Following the recently fostered concept of constrained modeling, this paper proposes a simple technique for rapid surrogate-assisted yield optimization of narrow- and multi-band antennas. The keystone of the approach is an appropriate definition of the optimization domain. This is realized by considering a few pre-optimized designs that represent the directions of the major changes of the antenna resonant frequencies and operating bands. Due to a small volume of such a domain, an accurate replacement model can be established therein using a small number of training samples, and employed to improve the antenna yield. Verification results obtained for a ring-slot antenna, a dual-band and a triple-band uniplanar dipoles indicate that the optimization process can be accomplished at low cost of a few dozen of EM simulations: 62, 74 and 132 EM simulations, respectively. Result reliability is validated through comparisons with EM-based Monte Carlo simulations.
... Due to its importance, system design centering has been discussed and developed by many researchers in several publications. [1][2][3][4][5][6][7][8][9][10][11][12][13] Generally, design centering approaches can be categorized into two main classes, namely, geometrical and statistical approaches. For geometrical approaches, the yield function is implicitly optimized by fetching the feasible region center and use it to approximate the design center. ...
... In this regard, the feasible region could be approximated by a convex body, eg, hyper-sphere, a hypercube or a hyperellipsoid, then use the center of this body as the design center. 1,[5][6][7][8][9][10]12 On the other hand, statistical approaches utilize statistical analysis approaches to explicitly optimize the yield function with no restrictions on the problem size. [1][2][3][4]11 In general, yield function value at a given nominal parameter values could be estimated by generating a set of sample points in the design parameter space using a predefined probability distribution of the system parameters. ...
... This makes the design centering of the microwave systems practically prohibitive. 1 To overcome this problem, the exact calculations using the simulator (high fidelity accurate model) could be performed, instead, using a cheaper surrogate model. 1,3,7,10 Space mapping (SM) technology 17,18 introduces efficient SM surrogate models that can be used to reduce the simulation cost. SM technology exploits fast, yet inaccurate, cheap coarse models to construct SM surrogate models that replace the time-consuming, computationally CPU intensive full-wave fine models. ...
System design centering process looks for nominal values of system designable parameters that maximize the probability of satisfying the design specifications (yield function). Statistical design centering implements a statistical analysis method such as Latin hypercube sampling (LHS) for yield function estimation and explicitly optimizes it. In this paper, we introduce a new statistical design centering technique for microwave system design. The technique combines a modified surrogate‐based derivative‐free trust region (TR) optimization algorithm and the generalized space mapping (GSM) technique. The modified TR algorithm is a derivative‐free optimization algorithm that employs quadratic surrogate models to replace the computationally expensive yield function over hyperelliptic trust regions in the optimization process. TR algorithms exhibit global convergence features irrespective the starting point setting. The new design centering approach utilizes the GSM technique to approximate the feasible region in the design parameter space with a sequence of iteratively updated space mapping (SM) surrogates. At each SM iteration, the modified TR algorithm optimizes the yield function for the current SM region approximation to get a better center. Two microwave circuit examples are used to show the effectiveness of the new design centering technique to obtain an optimal design in few SM iterations. In the design process, we employ Sonnet em for the bandstop microstrip filter design and CST Studio Suit for the ultra‐wideband (UWB) multiple‐input‐multiple‐output (MIMO) antenna.
... Surrogates are particularly useful for speeding up numerical procedures involving massive EM evaluations of the system under design. These include local [16], [17], and global parametric optimization [18]- [20], multi-criterial design [21]- [24], yield-driven optimization [25], or statistical analysis [26], [27]. There are two main groups of replacement models: approximation (or data-driven) [28], [29], and physics-based (e.g., space mapping [30], shape-preserving response prediction [31], etc.). ...
Full-wave electromagnetic (EM) analysis has been playing a major role in the design of microwave components for the last few decades. In particular, EM tools allow for accurate evaluation of electrical performance of miniaturized structures where strong cross-coupling effects cannot be adequately quantified using equivalent network models. However, EM-based design procedures (parametric optimization, statistical analysis) generate considerable computational expenses. These can be mitigated using fast surrogate models, yet their construction is hindered by the curse of dimensionality but also the utility requirements: a practically useful model needs to cover sufficiently broad ranges of geometry/material parameters as well as operating conditions. The recently proposed constrained modeling methods—both forward and inverse—work around the above issues by setting up the surrogate only in the relevant regions of the parameter space, i.e., containing designs that are of high quality with respect to the assumed performance measures. The model domain is established using pre-optimized sets of reference points. The high cost of generating such designs may significantly diminish the computational savings achieved by operating in confined domains. This article discusses a technique for fast reference design acquisition, involving inverse gradients, and expedited local refinement aided by the response feature technology. The presented approach is validated using a branch-line coupler and miniaturized rat-race coupler. It is also demonstrated to considerably reduce the cost of constructing performance-driven surrogates as well as setting up efficient procedures for fast geometry scaling of microwave components.
