In electromagnetics, optimization problems generally require high computational resources and involve a large number of unknowns. They are usually characterized by non-convex functionals and continuous spaces suitable for strategies based on Differential Evolution (DE). In such a framework, this paper is aimed at presenting an overview of Differential Evolution-based approaches used in electromagnetics, pointing out novelties and customizations with respect to other fields of application. Starting from a general description of the evolutionary mechanism of Differential Evolution, Differential Evolution-based techniques for electromagnetic optimization are presented. Some hints on the convergence properties and the sensitivity to control parameters are also given. Finally, a comprehensive coverage of different Differential Evolution formulations in solving optimization problems in the area of computational electromagnetics is presented, focusing on antenna synthesis and inverse scattering.

Differential Evolution as Applied to Electromagnetics

Before the emergence of ultra-wideband (UWB) radios, widely used wireless communications were based on sinusoidal carriers, and impulse technologies were employed only in specific applications (e.g. radar). In 2002, the Federal Communication Commission (FCC) allowed unlicensed operation between 3.1–10.6 GHz for UWB communication, using a wideband signal format with a low EIRP level (−41.3dBm/MHz). UWB communication systems then emerged as an alternative to narrowband systems and significant effort in this area has been invested at the regulatory, commercial, and research levels.

IEEE Transactions on Microwave Theory and Techniques and Antennas and Propagation Announce a Joint Special Issue on Ultra-Wideband (UWB) Technology

Ferrimagnets having low RF loss are used in passive microwave components such as isolators, circulators, phase shifters, and miniature antennas operating in a wide range of frequencies (1–100 GHz) and as magnetic recording media owing to their novel physical properties. Frequency tuning of these components has so far been obtained by external magnetic fields provided by a permanent magnet or by passing current through coils. However, for high frequency operation the permanent part of magnetic bias should be as high as possible, which requires large permanent magnets resulting in relatively large size and high cost microwave passive components. A promising approach to circumvent this problem is to use hexaferrites, such as BaFe12O19 and SrFe12O19, which have high effective internal magnetic anisotropy that also contributes to the permanent bias. Such a self-biased material remains magnetized even after removing the external applied magnetic field, and thus, may not even require an external permanent magnet. In garnet and spinel ferrites, such as Y3Fe5O12 (YIG) and MgFe2O4, however, the uniaxial anisotropy is much smaller, and one would need to apply huge magnetic fields to achieve such high frequencies. In Part 1 of this review of microwave ferrites a brief discussion of fundamentals of magnetism, particularly ferrimagnetism, and chemical, structural, and magnetic properties of ferrites of interest as they pertain to net magnetization, especially to self biasing, are presented. Operational principles of microwave passive components and electrical tuning of magnetization using magnetoelectric coupling are discussed in Part 2.

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Microwave ferrites, part 1: fundamental properties

We present a new and considerably extended parameterization of the thermodynamic activity coefficient model AIOMFAC (Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients) at room temperature. AIOMFAC combines a Pitzer-like electrolyte solution model with a UNIFAC-based group-contribution approach and explicitly accounts for interactions between organic functional groups and inorganic ions. Such interactions constitute the salt-effect, may cause liquid-liquid phase separation, and affect the gas-particle partitioning of aerosols. The previous AIOMFAC version was parameterized for alkyl and hydroxyl functional groups of alcohols and polyols. With the goal to describe a wide variety of organic compounds found in atmospheric aerosols, we extend here the parameterization of AIOMFAC to include the functional groups carboxyl, hydroxyl, ketone, aldehyde, ether, ester, alkenyl, alkyl, aromatic carbon-alcohol, and aromatic hydrocarbon. Thermodynamic equilibrium data of organic-inorganic systems from the literature are critically assessed and complemented with new measurements to establish a comprehensive database. The database is used to determine simultaneously the AIOMFAC parameters describing interactions of organic functional groups with the ions H^+, Li^+, Na^+, K^+, NH_(4)^+, Mg^(2+), Ca^(2+), Cl^−, Br^−, NO_(3)^−, HSO_(4)^−, and SO_(4)^(2−). Detailed descriptions of different types of thermodynamic data, such as vapor-liquid, solid-liquid, and liquid-liquid equilibria, and their use for the model parameterization are provided. Issues regarding deficiencies of the database, types and uncertainties of experimental data, and limitations of the model, are discussed. The challenging parameter optimization problem is solved with a novel combination of powerful global minimization algorithms. A number of exemplary calculations for systems containing atmospherically relevant aerosol components are shown. Amongst others, we discuss aqueous mixtures of ammonium sulfate with dicarboxylic acids and with levoglucosan. Overall, the new parameterization of AIOMFAC agrees well with a large number of experimental datasets. However, due to various reasons, for certain mixtures important deviations can occur. The new parameterization makes AIOMFAC a versatile thermodynamic tool. It enables the calculation of activity coefficients of thousands of different organic compounds in organic-inorganic mixtures of numerous components. Models based on AIOMFAC can be used to compute deliquescence relative humidities, liquid-liquid phase separations, and gas-particle partitioning of multicomponent mixtures of relevance for atmospheric chemistry or in other scientific fields.

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New and extended parameterization of the thermodynamic model AIOMFAC: calculation of activity coefficients for organic-inorganic mixtures containing carboxyl, hydroxyl, carbonyl, ether, ester, alkenyl, alkyl, and aromatic functional groups

A unified algorithm for elementary functions

Synthesis of unequally spaced linear antenna arrays is considered in this paper. A recently developed new differential evolution algorithm is applied to solve the problem. Both position-only and position-phase synthesis have been studied. Effect of angle resolution has also been investigated. Synthesis results show that our algorithm is able to obtain better synthesis result reliably and efficiently.

Synthesis of Unequally Spaced Antenna Arrays by Using Differential Evolution

In this paper, two- and three-pole microstrip LC constant fractional bandwidth (CFBW) and constant absolute bandwidth (CABW) tunable bandpass filters are proposed. The equivalent-circuit models are presented to study the tunable mechanism. The filter can be reconfigured by changing the capacitance of the LC resonators. Based on electric coupling coefficient compensation, second- and third-order tunable equivalent-circuit models with CFBW/CABW are presented. For demonstration, a semiconductor varactor diode loaded microstrip LC resonator is adopted in our work to design the second- and third-order tunable filters. The S-parameters, group delays, and third-order intercept points for different center frequencies of the filters are presented. Each resonator requires only one varactor diode for both central frequency and resonator coupling coefficient control.

Electrical Tunable Microstrip LC Bandpass Filters With Constant Bandwidth

This letter presents a multilayer approach for suppressing the higher order modes of substrate integrated waveguide (SIW) bandpass filters. Rectangular SIW resonators in multilayer substrates can be vertically coupled with magnetic and/or electric coupling by the proposed apertures etched on the middle metal layer. Harmonic passbands produced by the first higher-order mode $\text{TE}_{102}$ can be suppressed thanks to the proposed weak coupling or mixed coupling schemes in connection with the $\text{TE}_{102}$ mode. Compared with conventional horizontally coupled filter, the proposed filters also show a compact physical size. To demonstrate the proposed design method, two double-layered SIW bandpass filters Filter (I and II) are fabricated and measured. The experimental results show that the maximum rejection levels at the $\text{TE}_{102}$ mode frequencies are below −30 dB and −20 dB for Filter I and II, respectively. Furthermore, simulated and measured results also show a good agreement.

Multilayer Substrate Integrated Waveguide (SIW) Filters With Higher-Order Mode Suppression

This paper presents a two-pole dual-band tunable bandpass filter (BPF) with independently controllable dual passbands based on a novel tunable dual-mode resonator. This resonator principally comprises a λ/2 resonator and two varactor diodes. One varactor is placed at the center of the resonator to determine the dominant even-mode resonant frequency; the other is installed between two ends of the resonator to control the dominant odd-mode resonant frequency. These two distinct odd- and even-mode resonances can be independently generated, and they are used to realize the two separated passbands as desired. Detailed discussion is carried on to provide a set of closed-form design equations for determination of all of the elements involved in this tunable filter, inclusive of capacitively loaded quarter-wavelength or λ/2 resonators, external quality factor, and coupling coefficient. Finally, a prototype tunable dual-band filter is fabricated and measured. Measured and simulated results are found in good agreement with each other. The results show that the first passband can be tuned in a frequency range from 0.77 to 1.00 GHz with the 3-dB fractional-bandwidth of 20.3%-24.7%, whereas the second passband varies from 1.57 to 2.00 GHz with the 3-dB absolute-bandwidth of 120 ± 8 MHz.

Tunable Bandpass Filter With Independently Controllable Dual Passbands

In this letter, a novel quadruple-mode resonator bandpass filter (BPF) with tunable bandwidth is proposed. By using two types of microwave varactors to tune the resonant frequencies and transmission zeros (TZs), the high-side edge of the passband and low-side edge of the passband can be separately varied. Therefore, the bandwidth could be tunable with reasonable adjust of the values of varactors. Theoretical expressions have been derived for the resonant frequencies and the TZs. The measured results of the BPF show that the fractional bandwidth can be tuned from 22% to 34% at a fixed centre frequency 2.0 GHz with a return loss better than dB. The tested results show good agreement with simulated results.

Quanyuan Feng

Papers

Synthesis of Unequally Spaced Antenna Arrays by Using Differential Evolution

Electrical Tunable Microstrip LC Bandpass Filters With Constant Bandwidth

Multilayer Substrate Integrated Waveguide (SIW) Filters With Higher-Order Mode Suppression

Tunable Bandpass Filter With Independently Controllable Dual Passbands

Bandpass Filter With Tunable Bandwidth Using Quadruple-Mode Stub-Loaded Resonator