Lower Band Edge Research Articles

Compact and wideband filtenna for circularly polarised application

A compact single M-shaped probe fed circularly polarised filtenna (filtering antenna) without extra filtering circuit is presented in this study, in which three pair slots with different lengths are etched on its parasitic patch to produce radiation nulls at both band edges of its operating band. Furthermore, a single M-shaped probe feeding structure is used to improve the selectivity, especially for the lower band edge. By merging the filtering circuit into a radiating element, a good selectivity in the gain response can be realised without influencing the operation band aperture efficiency. A sample is fabricated and results show that the proposed filtenna has an operating bandwidth of 13% (| S 11 | < −10 dB, AR < 3 dB) with a centre frequency of 5 GHz, a peak gain of 8.9 dBic, and an average gain of 8.3 dBic within its operating bandwidth. Radiation nulls at 3.93, 5.97 and 6.36 GHz introduced by the three pairs of slots have been successfully generated. The radiation patterns are stable within the whole wide operating band.

A Miniaturized Wideband Bandpass Filter Using Quarter-Wavelength Stepped-Impedance Resonators

In this paper, we present a simple method to design a miniaturized wideband bandpass filter with suppression of the third harmonic, using only two quarter-wavelength stepped-impedance resonators (SIRs). The resonant modes of the quarter-wavelength SIR, depending on the impedance ratio (K) and electrical length ratio (α), are discussed first. As to setting the resonant frequency of the SIR for the lower band edge of the required band, the size parameters of two quarter-wavelength SIRs can be determined by selecting the desired impedance ratio (K) and length ratio (α). By using the opposite directional arrangement of two SIRs with direct taped input/output ports, the wideband response can be formed. A filter example is shown in this study to address this simple design procedure. The measured results of the fabricated filter have a wide passband response from 3.3 to 5.8 GHz, with an insertion loss of 1.5 dB, a return loss of 20 dB, an extended bandwidth ration of 55%, a low-average group delay of less than 0.75 ns, and a stopband from 6 to 12 GHz, with an attenuation level of 20 dB. Due to the similar 0° feeding, a transmission zero at 8.3 GHz appears near the band edge; thus, improving the band selectivity. The proposed filter can have a very simple structure and a miniature size. Simulated results and measured results are in good agreement.

A Simple, Compact Filtering Patch Antenna Based on Mode Analysis With Wide Out-of-Band Suppression

A simple, compact filtering patch antenna with wide out-of-band suppression is presented, where the filtering mechanism is first analyzed and implemented based on mode analysis of a conventional patch antenna. According to the mode analysis, undesired higher-order modes can be effectively suppressed by selecting a proper length ratio of two sides of the patch and the feeding position, thus realizing a wide upper stopband. To further enhance the filtering response, another two simple filtering structures loaded on the patch antenna are also proposed. First, a split-ring-shaped slot is etched on the patch to generate a radiation null at the lower-band edge for improving skirt selectivity. Second, a U-shaped strip is etched underneath the patch and connected with the feeding probe, which can introduce another null at the upper band edge. As a result, a high suppression level of 23 dB in lower and upper stopbands can be realized, respectively, for the proposed filtering antenna, while the upper stopband can extend up to $2.3 f_{0}(f_{0}$ is the center frequency of the antenna). Furthermore, wide passband response can also be achieved by the extra in-band resonances existing in the slot and the strip. A filtering antenna prototype is fabricated and measured for demonstration. Good agreements between the simulated and the measured results are observed, indicating a large impedance bandwidth of 22.6%, high antenna efficiency of 95.6%, and an average gain of about 7.4 dBi. Compared with the reported filtering antennas, the proposed filtering antenna can achieve better wideband filtering response but with a simpler configuration.

Compact Absorptive Filtering Patch Antenna

This article presents a compact absorptive filtering patch antenna. It consists of a filtering patch antenna and a bandstop filter (BSF), with their transfer functions being complementary to each other. A slot is fabricated in each of the patch and ground, giving a total of two radiation nulls for the lower bandedge. By using a dual-stub feed, two radiation nulls are also obtained for the upper bandedge. For the BSF, a λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> /2 defected ground structure (DGS) and a λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> /4 defected microstrip structure (DMS) are used in the design. It is terminated by a chip resistor. Since the filtering patch antenna and BSF have complementary transfer functions, the incident energy can be radiated effectively in the passband but largely absorbed by the resistor in the stopbands. As a result, only little energy will be reflected over a wide frequency range, giving a reflectionless characteristic. To demonstrate this idea, an absorptive filtering antenna operating at 5.8 GHz was designed, fabricated, and tested. Its impedance is matched from 5 to 6.5 GHz, with the measured out-of-band suppression being higher than 17 and 20 dB for the lower and upper stopbands, respectively. The measured peak realized gain is 7.28 dBi.

Design of Compact, Single-Layered Substrate Integrated Waveguide Filtenna With Parasitic Patch

A compact, single-layered substrate-integrated waveguide (SIW) filtenna with parasitic patch is synthesized and designed. A half-mode substrate-integrated rectangular cavity (HMSIRC) is adopted as the first stage resonator to reduce the circuit size. A parasitic patch functioning as the last stage resonator as well as the radiator is arranged closely to the HMSIRC so as to enhance the operational bandwidth and facilitate the filtering performance. Two broadside radiation nulls are realized at both the upper and lower band-edges to sharpen the band-edge roll-off rate: one is generated by the interaction between the HMSIRC and the parasitic patch, and the other is introduced by placing two pairs of shorting posts under the parasitic patch. The standard filter synthesis technology is utilized to guide the filtenna design. The optimized prototype was fabricated and measured. The measured results, in good agreement with simulated values, indicated the proposed filtenna provides a 5.1% fractional bandwidth, a maximum realized gain of 6.3 dBi, and a flat passband gain response along with excellent out-of-band selectivity, even with ultralow profile 0.015 λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> and small volume 0.005 λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> .

Compact and wideband bandpass filters with analysis of the CRLH-TL characteristics based on stepped impedance resonator

In this paper, we have investigated two unique wideband (WB) bandpass filters (BPFs) based on composite right/left-handed (CRLH) structure that have high performance in C-band. The proposed filters have been implemented with stepped-impedance resonator (SIR) section and interdigital capacitors on it with a parallel coupled-shorted stub (CSS). High selectivity, high out-of-band rejection, low loss and two transmission zeroes at the lower and upper passband/stopband edges have been observed. The out-of-band rejection levels in two filters are better than 17 dB and 20 dB at the lower and upper band edges, respectively. In addition, the return loss and insertion loss of the proposed CSS filter are greater than 17 dB and less than 0.7 dB, respectively. Also, the return loss and insertion loss of the proposed spiral CSS (SCSS) filter are greater than 20 dB and less than of 0.5 dB, respectively. The presented structures have been investigated analytically and experimentally in order to verify balance between the results of the full-wave simulation and the equivalent circuit model with the experimental ones. The dimensions of the suggested filters are 21.6 × 3.06 mm2 and 14.6 × 4.2 mm2. The specifications and compact size of the filters make them suitable for wideband wireless communication systems.

Rationally designed Fe2O3/GO/WO3 Z-Scheme photocatalyst for enhanced solar light photocatalytic water remediation

A novel ternary Fe2O3/GO/WO3 all-solid-state Z-Scheme photocatalyst was rationally designed. Structural, morphological, optical and electronic properties of the synthesized nanocomposite were investigated by XRD, SEM, TEM, UV–vis Diffuse Reflectance and Raman spectroscopy. The results revealed the successful synthesis of the nanocomposite materials. Uniquely, double absorption edges at 2.0 and 2.3 eV for Fe2O3/WO3 and triple absorption edges at 1.5, 1.8 and 2.1 eV for Fe2O3/GO/WO3 were investigated for the first time. Lower absorption band edges dominated for both Fe2O3/WO3 and Fe2O3/GO/WO3, while higher absorption edges dominated for pure nanomaterials. The enhanced interaction among GO, Fe2O3 and WO3 matrix explained the reduction in the CB energy leading to efficient electron separation and transformation and consequently improving the photocatalytic activity. The visible light photocatalytic performance of Fe2O3/GO/WO3 nanocomposites were evaluated for degradation of methylene blue (MB) and crystal violet (CV) dyes as model water pollutants. The photocatalytic activity for degradation of both dyes was found to be greatly enhanced in the presence of ternary Fe2O3/GO/WO3 nanocomposite as compared to nanocomposite systems of Fe2O3/WO3, WO3/GO and Fe2O3/GO or pure Fe2O3 and WO3 nanomaterials. The enhancement in the photocatalytic performance of the ternary Fe2O3/GO/WO3 nanocomposite was expected to be due to the all-solid-state Z-Scheme in which the photogenerated electrons in the CB of photosystem I (WO3) transferred through GO mediator and recombined with the photogenerated holes in the VB of Fe2O3 (photosystem II). So that, the electron-hole pair recombination can be suppressed in both systems. Moreover, the photocatalytic activity of Fe2O3/GO/WO3 nanocomposite has been tested for the degradation of phenol. The results show that 95.4% of phenol was degraded in 120 min. This study provides an efficient green Z-Scheme photocatalyst for water remediation utilizing solar light.

Differentially Coplanar-Fed Filtering Dielectric Resonator Antenna for Millimeter-Wave Applications

In this letter, a differentially coplanar-fed filtering dielectric resonator antenna (DRA) is proposed for millimeter-wave applications. To realize a low-profile design, a novel coplanar feeding method is presented by incorporating a dielectric resonator and its feeding structure in the same layer, which minimizes the assembly errors. The DRA is shaped by hollowing out the substrate and can be manufactured with a single-layer laminate using standard printed circuit board technology. The DRA operates at TE111 mode that is excited differentially by a pair of microstrip lines with metallic vias. The filtering function is obtained by etching two pairs of slots with different lengths in the ground plane, resulting in two radiation nulls at both upper and lower band edges. For demonstration, a prototype is designed, fabricated, and measured. Good agreement can be observed between simulated and measured results.

Fabrication of CdS quantum dots sensitized ZnO nanorods/TiO2 nanosheets hierarchical heterostructure films for enhanced photoelectrochemical performance

A novel CdS/ZnO/TiO2 hierarchical heterostructure for photoelectrochemical (PEC) application was fabricated by growing ZnO nanorods (NRs) onto TiO2 nanosheets (NSs) with dominant high-energy {001} facets via hydrothermal method, subsequently coated CdS quantum-dots (QDs) sensitized layer via successive ionic layer adsorption and reaction (SILAR) technique. The as-prepared TiO2, ZnO/TiO2 and CdS/ZnO/TiO2 films were characterized by XRD, SEM, TEM, UV–vis absorption spectrum and EIS techniques to investigate the effects of ZnO NRs and CdS QDs on the structure, morphology, optical property and charge carrier transmission characteristics. The results demonstrated that the growth of ZnO NRs obviously enlarges the specific surface area, while the deposition of CdS QDs significantly enhances the light harvesting ability. And the heterojunctions formed among TiO2 NSs, ZnO NRs and CdS QDs effectively promote the photogenerated charge carrier transport and separation, simultaneously inhibit the photogenerated electron-hole recombination. Moreover, it is notable that ZnO NRs trend to grow on the low-energy {101} facets of TiO2 NSs due to the impact of crystal facet controlling agent, which can effectively shorten the electron conduction path-ways and facilitate the photogenerated electron-hole separation due to the lower band edge position of {101} facets than that of {001} facets. As a result, the photocurrent density of the optimized CdS/ZnO/TiO2 composite film enhances to an excellent value of 12.1 mA/cm2 at a potential of 0 V vs SCE, which is more than 27 times higher than that of bare TiO2 NSs films. In addition, the corresponding optimal condition and physical mechanism were also discussed in the paper.

Design of Dual-Band Bandpass Filters With Fixed and Reconfigurable Bandwidths Based on Terminated Cross-Shaped Resonators

Based on a novel microstrip terminated cross-shaped resonator (TCSR), the dual-band bandpass filters (DB-BPFs) with fixed and reconfigurable bandwidths are proposed in this brief. In addition to the basic TCSR’s three poles and four zeros, the extra four poles and three zeros can be introduced with the help of a pair of symmetrical parallel-coupled lines and open-ended stubs. Therefore, a planar DB-BPF with multiple transmission poles and zeros can be realized. To achieve the reconfigurable bandwidths, a capacitor is inserted into the basic TCSR’s lower stub. It is found that the lower bandedge of the first passband can be tuned while the other three bandedges are kept unchanged. Two prototypes, including fixed-bandwidth filter (Filter I) with 3-dB fractional bandwidths (FBWs) of 20.8% and 17.3%, and reconfigurable-bandwidth filter (Filter II) with 3-dB FBW variation from 22.5% to 34.7% for the first passband and 19.8% for the second passband, are designed, fabricated, and experimentally characterized. The experimental characterizations of these two filters verify the proposed design.

A Broadband Filtering Patch Antenna Using T-Probe, Transverse Stubs, and U-Slots

This paper presents a broadband filtering patch antenna. This antenna consists of a rectangular patch, a rectangular ground plane, and an upright substrate. A coplanar waveguide (CPW) with T-probe is printed on the front side of the substrate, which can engender the broadband characteristic. On the back side, two transverse stubs cross the slots of CPW. The two transverse stubs can not only broaden the bandwidth but also improve the selectivity of the realized gain and reflection coefficient. Two U-slots are etched on the patch for providing a radiation null at the lower band edge as well as increasing the selectivity of out-of-band edge. Ultimately, an impedance bandwidth of 71.17% (2.48–5.22 GHz) and an average realized gain of 4.2 dBi are obtained. Moreover, two radiation nulls occur at 2.25 and 5.3 GHz. The simulated results are in good agreement with the measured results.

Compact Dual-Band Dual-Polarized Base-Station Antenna Array With a Small Frequency Ratio Using Filtering Elements

This paper presents a compact dual-band ±45° dual-polarized base-station array based on embedded filtering elements. The proposed antenna array consists of 9 dual-band antenna units, which operate at the lower band (LB) of 790-862 MHz and the higher band (HB) of 880-960 MHz with a small frequency spacing. In each unit, one antenna element is embedded into the other one, featuring a very compact size. To alleviate the serious cross-band mutual coupling between the two elements, the LB patch antenna generates a boresight radiation null at its higher band edge, and the HB element is designed with a band-stop response at its lower band edge. In this way, high cross-band isolation between the two embedded elements can be obtained. For demonstration, a compact dual-band ±45° dual-polarized filtering antenna array with 9 units is designed and fabricated to fit the specification of LB and HB bands (|S 11 | <;-15 dB). The overall width of the array is only 280 mm, which is much narrower than that of typical industrial products using two side-by-side sub-arrays (~576 mm). The measured performance of the antenna array can meet the requirement of base stations.

Frequency Response of a Moving Two-Dimensional Defect in Magnetic Flux Leakage Inspection

The detection of magnetic flux leakage (MFL) enables nondestructive detection and characterization of defects in magnetic structures. In this letter, Fourier transforms of the leakage fields from a two-dimensional surface defect are evaluated to produce analytical expressions for the frequency response of MFL signals detected by a flux-sensitive sensor. The expressions show the correlation between the spectral response of the leakage fields, defect dimensions, and sensing element lift-off spacing as a product of frequency-dependent defect-width loss function, spacing loss function, and thickness enhancement function. The lower and upper band edges of the band-limited leakage magnetic fields are theoretically identified. A spectral method for sizing of defects is proposed based on the frequency response.

Characteristics of low-frequency noise elimination in a fluid-filled pipe of dark acoustic metamaterial type

The suppression and absorption of low-frequency noise for a fluid-filled pipe system has become a challenging task. Inspired by the properties of acoustic metamaterials, we construct a fluid-filled periodic pipe system, consisting of small-size short acoustic pipes mounted on a fluid-filled main pipe system equidistantly along the axial direction of main pipe. The short acoustic pipe is filled with fluid and gas, and the fluid section is connected to the main pipe that is filled with the same liquid. In such a periodic pipe system, an ultra-low frequency and ultra-broad band gap of acoustic waves can be generated, making the acoustic waves transmitting in the pipe system effectively attenuated within the band gap frequency range. Since the attenuation effects of the band gap on the low-frequency sound are so strong (the acoustic waves almost cannot be transmitted through the pipe system) that the periodic pipe system is referred to as a dark acoustic metamaterial (DAM)-type fluid-filled pipe system. The formation mechanism of the first band gap can be ascribed to the co-resonance of the short acoustic pipe array in the piping system, and this band gap is categorized as resonant-type BG (RBG). The contribution of short acoustic pipes is to introduce a low-frequency and large impedances spatially into the system, whereupon the transmitting waves will experience a tempestuously resonance in the pipe. As a result, the transmission of acoustic waves within the RBG is stopped. The second band gap in a higher frequency range is classified as Bragg-type band gap (BBG), since it is induced by the effects of interference between the incident, the reflected and the transmitted acoustic waves existing in the periodic units. The interference effect on the suppression of wave transmission is strengthened by the ceaselessly repeating uniform cells. The lattice constant change can bring in a modulation effects on both the BBG and the upper band edge of RBG. Increasing the volume of gas chamber in the short acoustic pipe will result in a shift of lower band edge of RBG towards the low-frequency range but has no action on the upper band edge; similarly, the augment of the liquid volume of the short acoustic pipe also lowers the band edges of RBG, however, bandwidth of the RBG will be reduced. A membrane may be used to physically separate the gas from the fluid in the short acoustic pipe, rendering the design more feasible to be realized in practical engineering. The installation of membrane will not change the low-frequency band gap properties of the DAM pipe. The obtained results show that the proposed design in this study may provide a new way to solve the defiant problem of noise control in the low frequency range for fluid piping systems.

Absolute instability and transient growth near the band edges of a traveling wave tube

An electron beam in the slow wave structure of a traveling wave tube may be subjected to absolute instability at the lower and upper band edges, where the group velocity is zero. From a careful re-examination of the immediate vicinity of these band edges, we use the Briggs-Bers criterion to show that, contrary to previous findings, an absolute instability may arise at the lower band edge if the beam current is sufficiently high, even if the beam mode intersects with the circuit mode with a positive group velocity. However, the upper band edge was found to be more susceptible to absolute instability than the lower band edge. The threshold condition for the onset of absolute instabilities is derived analytically at both band edges. The Green's function shows possible transient temporal growth with an exponentiation rate proportional to t1/3, whether or not the band edge is subject to an absolute instability.

High‐efficiency circular dense dielectric patch antenna with frequency selectivity

A circular dense dielectric (DD) patch antenna realised by stacking an upper DD patch on the lower DD patch is proposed to achieve high efficiency and frequency selectivity. The high efficiency is attributed to the non-metallic radiators and the radiations of both lower and upper DD patches operating at TM11 mode. To achieve higher frequency selectivity than that of the reported DD patch antennas, the opposite E-field distribution inside the upper DD patch and the quarter-wavelength open-circuit stub produce two radiation nulls near the lower band-edge, while the opposite E-field distribution inside the lower DD patch and the opposite E-field distribution at the edges of the two DD patches produce two radiation nulls near the upper band-edge. For demonstration, a prototype covering the fifth generation (5G) band (3.4–3.6 GHz) achieves the simulated radiation efficiency of 96%, the measured peak gain of 9.2 dBi, 10 dB impedance bandwidth of 12.3%, four radiation nulls, and the cross-polarisation rejection larger than 22 dB within the 3-dB beam range at the centre frequency. The results show the features of high efficiency, multiple radiation nulls, wide bandwidth and high gain simultaneously while the reported DD patch antennas just have part of the features.

Mean-field model for the density of states of jammed soft spheres.

We propose a class of mean-field models for the isostatic transition of systems of soft spheres, in which the contact network is modeled as a random graph and each contact is associated to d degrees of freedom. We study such models in the hypostatic, isostatic, and hyperstatic regimes. The density of states is evaluated by both the cavity method and exact diagonalization of the dynamical matrix. We show that the model correctly reproduces the main features of the density of states of real packings and, moreover, it predicts the presence of localized modes near the lower band edge. Finally, the behavior of the density of states D(ω)∼ω^{α} for ω→0 in the hyperstatic regime is studied. We find that the model predicts a nontrivial dependence of α on the details of the coordination distribution.

Design of Filtering-Radiating Patch Antennas With Tunable Radiation Nulls for High Selectivity

This communication demonstrates a method to design filtering antennas by using the filtering-radiating patch (FRP). The so-called FRP is a structure of a rectangular patch etched with slots. It inherits the radiation performance of conventional patch antennas, and more importantly, introduces filtering feature with a radiation null at either the upper or lower band edge of radiation efficiency curve. The frequencies of radiation nulls are easy to control. Based on the FRP, a novel filtering antenna is proposed. Two radiation nulls are realized at both band edges of the antenna efficiency curve, leading to a sharp band skirt and good selectivity in the boresight gain response. The locations of the two radiation nulls can be flexibly controlled by the lengths of slots. A prototype is fabricated and tested. The measured results show an impedance matching bandwidth of 7% with a center frequency of 5.24 GHz, two radiation nulls at 4.7 and 5.85 GHz, respectively, a realized gain of 6.6 dBi, the cross-polarization rejection larger than 23.4 dB, and the front-to-back ratio better than 15 dB. The presented method demonstrates the capability of not only achieving good filtering-radiating performances but also possessing very simple structures by only etching slots on the patch of a conventional microstrip antenna.

CdSe Species Decorated TiO2 Nanotubes Film Via Chemical Bath Deposition for Enhancing Photoelectrochemical Water Splitting Performance

Background: The conversion of sunlight to electrical power has been dominated by solidstate junction devices, often made of silicon. However, this dominance is now being challenged by the emergence of the new generation of water splitting cell (integration of photovoltaic system with an electrolyzer to generate clean and portable H2 energy carrier. This cell normally is based on nanocrystalline materials, which offers the prospect of cheap fabrication together with other attractive feature such as high chemical stability and flexibility in aqueous solution under evolving oxygen (O2) gases. However, nanocrystalline materials are facing few drawback such as recombination losses of charge carriers and less response under visible spectrum. Therefore, an effort to minimize the recombination losses of charge carriers and extended the spectral response of TiO2 NTs into visible spectrum by incorporating an optimum amount of lower band gap and suitable band edge position semiconductor (cadmium selenide [CdSe]) into the lattice of TiO2 NTs. Methods: An efficient approach has been demonstrated in this research work to enhance the solardriven photoelectrochemical (PEC) water splitting performance by decorating CdSe species into highly ordered TiO2 nanotubes (NTs) film through a facile and cost-effective chemical bath deposition. Morphology, chemical properties, and electronic structures have been studied. Results: A maximum photocurrent density of ~2.50 mA/cm2 at 0.6V versus Ag/AgCl electrode was exhibited by TiO2 NTs with the presence of approximately 1 at % of CdSe species. The presence of CdSe species offered an improvement of photocurrent density under solar irradiation due to the effective mediators to trap the photo-induced electrons and minimizes the recombination of charge carriers within the lattice of TiO2 NTs. Conclusion: Hybrid CdSe-TiO2 NTs were successfully fabricated through chemical bath deposition method in order to study the synergistic coupling effect of CdSe with TiO2 NTs on the PEC performance. By bathing pure TiO2 NTs film in a 5 mM CdSe precursor solution extensively covered by approximately 1 at % CdSe exhibited the highest jp of 2.50 mA/cm2 among the samples. However, excessive deposition (≥5 mM) was neither negatively affected by the self-organized NTs nor decreased in jp. This condition inferred that higher ionic product (Cd and Se ions) leaded to rapid ion-by-ion condensation or adsorption of colloidal particles clogged the opening pore’s mouth of TiO2 NTs. Thus, an improvement in the photoresponse was observed when optimum amount (~ 1 at %) of the CdSe was deposited on TiO2 NTs film.

One-dimensional photonic crystals bound by light

Through rigorous simulations, the light scattering induced optical binding of one-dimensional (1D) dielectric photonic crystals is studied. The optical forces corresponding to the pass band, band gap, and band edge are qualitatively different. It is shown that light can induce self-organization of dielectric slabs into stable photonic crystals, with its lower band edge coinciding with the incident light frequency. Incident light at normal and oblique incidence and photonic crystals with parity-time symmetry are also considered.