Mixed Coupling Research Articles

Chaotic dynamics of a delayed fractional order MLNCML system

Abstract We present a delayed fractional order spatiotemporal dynamical system using the mixed linear-nonlinear coupling connections between lattices. In the simulation experiments, the dynamical characteristics of the proposed model are looked into and analyzed by using bifurcation diagrams and metric entropy density. The proposed model has fewer periodic windows in its bifurcation diagrams, large key space and strong ergodicity due to the delay. These excellent properties are of great significance in encryption. Moreover, the parameter μ breaks its fixed range in the traditional logistic map, which can contribute to enlarge the key space of cryptosystem. Through numerical simulations and security analysis, it is found that the proposed model is applied for encryption.

High selectivity wideband two‐channel bandpass filter for 5G microwave communication systems

AbstractA two‐channel high‐selectivity, wideband bandpass filter has been presented. This is based on a microstrip mixed‐impedance resonator and defected ground structure with the mixed coupling strategy. Two pairs of peripheral stepped‐impedance resonator (SIR) structures are used as stubs, achieving TZs at the immediate lower and upper cut‐off sides of the passband and control the bandwidth, while the other two transmission zeros on the upper cut‐off side are yielded through the defected ground structure, and the coupling between the SIR and uniform‐impedance resonators components, respectively. A prototype of the circuit is fabricated and measured for validation. The measured results exhibited insertion and return losses better than 1.1 and 20.5 dB, respectively, and high isolation levels exceeding 19 dB. In total, four transmission zeros are achieved. The designed filtering circuit realized a 3‐dB fractional bandwidth of 58.1%. There is a 0.95f0 stopband at the upper cutoff. The fabrication of the prototype shows good agreement between the simulated and measured performance.

The coupling of winds, ocean turbulence, and High Salinity Shelf Water in the Terra Nova Bay Polynya

The Terra Nova Bay (TNB) Polynya in the Western Ross Sea of Antarctica is a major producer of High Salinity Shelf Water (HSSW), a precursor to Antarctica Bottom Water (AABW). Processes occurring in and around the polynya can therefore effect change in the lower limb of overturning circulation in this region. Here, we use data from a densely-instrumented upper-ocean mooring, deployed for 1 year in a region of active HSSW formation within TNB, to examine the coupling of surface brine rejection and vertical mixing to katabatic wind forcing. We find a high correlation between salinity and winds during the wintertime HSSW production season at the mooring site, with a lag-response of 20 h in near-surface (∼47 m) salinity to winds measured at the nearby Automatic Weather Station (AWS) Manuela. Salinity and temperature measurements show a fully destratified water column by June, with a lag-response of near-seabed (∼360 m) salinity to near-surface salinity of just 5 h. Measurements of turbulent kinetic energy (TKE) dissipation rate (ɛ) from moored pulse-coherent acoustic Doppler current profilers (ADCPs) show general agreement with classic boundary layer scaling (BLS), and calculations of a vertical mixing timescale using the Obukhov length scale average to ∼2.5 h during austral winter, consistent with the 5-h lag time observed in the salinity data. Comparisons to data from concurrent mooring deployments along the southern boundary of TNB, as well as to previously published assessments of model simulations and data from Climatic Long-term Interaction for the Mass-balance in Antarctica (CLIMA) moorings, allow us to explore spatial variability in the coupling of winds and salinity across TNB and to speculate on possible HSSW circulation pathways.

Joint action of phase mixing and nonlinear effects in MHD waves propagating in coronal loops

Context. The evolution of Alfvén waves in cylindrical magnetic flux tubes, which represent a basic model for loops observed in the solar corona, can be affected by phase mixing and turbulent cascade. Phase mixing results from transverse inhomogeneities in the Alfvén speed, causing different shells of the flux tube to oscillate at different frequencies, thus forming increasingly smaller spatial scales in the direction perpendicular to the guide field. Turbulent cascade also contributes to the dissipation of the bulk energy of the waves through the generation of smaller spatial scales. Both processes present characteristic timescales. Different regimes can be envisaged according to how those timescales are related and to the typical timescale at which dissipation is at work. Aims. We investigate the interplay of phase mixing and the nonlinear turbulent cascade in the evolution and dissipation of Alfvén waves using compressible magnetohydrodynamic numerical simulations. We consider perturbations in the form of torsional waves, both propagating and standing, or turbulent fluctuations, or a combination of the two. The main purpose is to study how phase mixing and nonlinear couplings jointly work to produce small scales in different regimes. Methods. We conducted a numerical campaign to explore the typical parameters, such as the loop length, the amplitude and spatial profile of the perturbations, and the dissipative coefficients. A pseudo-spectral code was employed to solve the three-dimensional compressible magnetohydrodynamic equations, modeling the evolution of perturbations propagating in a flux tube corresponding to an equilibrium configuration with cylindrical symmetry. Results. We find that phase mixing takes place for moderate amplitudes of the turbulent component even in a distorted, nonaxisymmetric configuration, building small scales that are locally transverse to the density gradient. The dissipative time decreases with increasing the percentage of the turbulent component. This behavior is verified both for propagating and standing waves. Even in the fully turbulent case, a mechanism qualitatively similar to phase mixing occurs: it actively generates small scales together with the nonlinear cascade, thus providing the shortest dissipative time. General considerations are given to identify this regime in the parameter space. The turbulent perturbation also distorts the background density, locally increasing the Alfvén velocity gradient and further contributing to accelerating the formation of small scales. Conclusions. Our campaign of simulations is relevant for the coronal plasma where Reynolds and Lundquist numbers are extremely high. For sufficiently low perturbation amplitudes, phase mixing and turbulence work synergically, speeding up the dissipation of the perturbation energy: phase mixing dominates at early times and nonlinear effects at later times. We find that the dissipative time is shorter than those of phase mixing and the nonlinear cascade when individually considered.

Leveraging Insulator's Tacticity in Semiconducting Polymer Blends.

Blending conjugated polymers with insulating matrices is often utilized for engineering extrinsic properties in organic electronics. Semiconductor/insulator blends are typically processed to form a uniformly distributed network of conductive domains within the insulating matrix, marrying electronic and physical properties from individual components. Understanding of polymer-polymer interactions in such systems is thus crucial for property co-optimization. One of the commonly overlooked parameters is the structural configuration of the insulator on the resulting properties, especially the electronic properties. This study investigated how the tacticity of the matrix polymer, among other relevant parameters in play, impacts solid state crystallization in semiconductor/matrix blends and hence the resulting charge transport properties. We found an intricate dependence of the film morphology, aggregation behavior, electronic charge transport, and mixed ionic-electronic coupling properties on the insulator's tacticity. Our experimentally iterative approach shows that for a given application, when selecting semiconductor/insulator combinations, the tacticity of the matrix can be leveraged to optimize performance and vary solid-state structure.

Mixed Couples, Mixed Attitudes: How Interracial Couples in Marketing Appeals Influence Brand Outcomes

Abstract Interracial couples are increasingly featured in marketing messages, yet little is known about how their representation influences consumer behavior. Across six experiments (N = 4,956) and a field study on Facebook, interracial couples in marketing appeals enhance brand outcomes relative to monoracial dominant (i.e., White) couples, but decrease brand outcomes relative to monoracial nondominant (i.e., minority) couples. These effects stem from how the racial composition of dominant (vs. nondominant) members within a couple either amplifies or dilutes perceived warmth. Monoracial couples possess consistent stereotype attributes, with dominant (vs. nondominant) groups typically seen as lower in warmth. Thus, monoracial couple warmth is amplified: monoracial dominant couples are seen as less warm (i.e., negative amplification), and monoracial nondominant couples as warmer (i.e., positive amplification) than the individuals in the couple. Interracial couples possess inconsistent racial attributes, inducing stereotype dilution with intermediate levels of perceived warmth. Warmth drives brand outcomes above and beyond brand diversity, social desirability, and brand morality. Effects are moderated by consumers’ social dominance orientation and whether the monoracial dominant couple is nondominant along another dimension (i.e., sexual orientation). This work holds theoretical implications for stereotyping research and provides practical insight into multiracial marketing.

Definition of a beam-like reduced order model element by means of a mixed dimensional coupling

The use of Reduced Dimensional Models (RDM) discretized like beams, plates and shell elements drastically decreases the computational cost of solving a full 3D elastic problem with a Finite Element Method (FEM). However, its kinematic assumptions are only applicable to bodies with regular sections or continuous layouts. For the correct analysis of irregular regions, it is necessary to rely on bi-dimensional or solid models that fully reproduce the geometry of the body and its behavior but have a much higher computational cost. The Mixing Dimensional Coupling (MDC) technique allows linking models discretized with elements of different topologies, allowing the possibility of considering the most cost-effective model in each region. This coupling takes place at the interface that delimits both models and relies on the equilibrium of work and reactions on its two faces. In this paper, the formulation is presented for coupling beams with laminar sections and 2D Plane-Stress (PS) models demonstrating its proper behavior. Finally, this coupling is used for defining a new beam element, the Beam-Like Reduced Order Model (BLROM), which is obtained from a Plane-Stress model of their longitudinal section.

Synchronization of Neural Networks Involving Distributed-Delay Coupling: A Distributed-Delay Differential Inequalities Approach.

In this article, we address the synchronization issue for coupled neural networks (CNNs) with mixed couplings by way of the delayed impulsive control, where the delay is distributed. Particularly, mixed couplings comprise the current-state coupling and the distributed-delay coupling, where influences on network connections caused by the past information of CNNs over a certain period are considered. First, we propose a novel array of delayed impulsive differential inequalities involving distributed-delay-dependent impulses, where distributed delays can be relatively larger. Second, we apply such delayed inequalities to analyze the problem of synchronization for CNNs with two different topologies. Sufficient criteria and distributed-delay-dependent impulsive controller are derived thereby. Furthermore, using techniques of matrix decomposition, several low-dimensional criteria are set out, which are appropriate for applications of large scale CNNs. Finally, a numerical example of CNNs with both the current-state coupling and the distributed-delay coupling involving three cases, are exhibited to exemplify the validity and the efficiency of the obtained theoretical results.

In Situ Surface-Enhanced Raman Spectroscopy on Organic Mixed Ionic-Electronic Conductors: Tracking Dynamic Doping in Light-Emitting Electrochemical Cells.

In the domain of organic mixed ionic-electronic conductors (OMIECs), simultaneous transport and coupling of ionic and electronic charges are crucial for the function of electrochemical devices in organic electronics. Understanding conduction mechanisms and chemical reactions in operational devices is pivotal for performance enhancement and is necessary for the informed and systematic development of more promising materials. Surface-enhanced Raman spectroscopy (SERS) is a potent tool for monitoring electrochemical evolution and dynamic doping in operational devices, offering enhanced sensitivity to subtle spectral changes. We demonstrate the utility of SERS for in situ tracking of doping in OMIECs in an organic light-emitting electrochemical cell (LEC) containing a conjugated polymer (poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene]; MEH-PPV), a molecular anion (lithium triflate), and an electrolyte network (poly(ethylene oxide); PEO). SERS enhancement is achieved via an interleaved layer of gold particles formed by spontaneous breakup of a deposited thin gold film. The results successfully highlight the ability of SERS to unveil time-resolved MEH-PPV doping and polaron formation, elucidating the effects of triflate ion transfer in the operating device and validating the electrochemical doping model in LECs.

Effect of flame characteristics on an isolated ethanol droplet evaporating through stagnation methane/air flames: An experimental and numerical study

A single ethanol droplet evaporation through laminar methane/air stagnation flame is investigated at lean, stoichiometric and rich conditions experimentally and numerically. For the droplets having initial diameters of 20-70μm, the particle Reynolds number is measured via PIV/PTV, resulting in the slip velocity between the droplet and gas flow being small and the surrounding gas being able to carry without any significant convective effects. Evaporation rates, computed from Abramzon–Sirignano for a moving droplet towards a stagnation flame field, satisfy the ones computed from empirically determined evaporation rates from ILIDS measurements as a function of flame temperature, flame speed and flame thickness. Nevertheless, Abramzon–Sirignano model slightly overestimates the vaporization constant for lean cases. The distance traveled by the droplet after leaving the flame zone determines the average critical diameter. Accordingly, droplets larger than 18μm can cross the flame, leading to local modifications in the flame region due to heat loss and vapor diffusion from the droplet. Novelty and Significance Energy conversion in combustion should be carried out by optimizing efficiency, minimizing pollution, and preventing further climate change. The multiphase nature of spray combustion particularly adds further complexity due to the strong coupling of atomization, evaporation, mixing, turbulence, and chemical reactions. Although spray combustion involves a cloud of polydispersed droplets, it is of fundamental importance to understand the dynamics of an isolated droplet and its interactions with the flame front, which can provide indispensable information for spray combustion models. In this study, an experimental and computational framework has been developed to investigate droplet-flame interactions. The dynamics and evaporation characteristics of an isolated droplets interacting with stagnation flames have been determined by coupling several laser diagnostics, while further enhanced with Eulerian–Lagrangian simulations under flame conditions. Thereupon, the outcomes help the design of injectors of spray combustion systems and enhancement of evaporation models.

Design of Multi-Band Bandstop Filters Based on Mixed Electric and Magnetic Coupling Resonators

In this paper, multi-band bandstop filters (BSFs) based on mixed electric and magnetic coupling resonators are proposed. These proposed structures include a multimode resonator based on symmetrical open-circuit branches, including upper- and lower-branch filter circuits. Through this design, the center frequencies of the stopbands can be flexibly and autonomously adjusted. In addition, the filters proposed in this paper have excellent characteristics, such as miniature dimensions and abrupt roll-off skirts. Finally, these tri-band to sext-band bandstop filters were fabricated and the measured results agreed well with the simulated ones. The proposed structures can be applied in the fields of communication, information, and coal automation.

Design of Cross-Coupled Bandpass Filters with Flexible Coupling via Half-Mode Substrate-Integrated Waveguide

In this article, a simple approach for achievement of flexible coupling is presented based on the half-mode substrate-integrated waveguide (HMSIW). Since both electric and magnetic fields vary along the magnetic wall of the HMSIW, there exists mixed coupling between two adjacent HMSIWs. In this context, only by adjusting the width of the coupling slot at specific regions, both coupling property and strength can be conveniently controlled. Besides, as the coupling slot possesses the merits of simple structure and high flexibility, it is also expected to achieve desired couplings between multimode resonators. For demonstration, three cross-coupled bandpass filters (BPFs) with different kinds of frequency responses are constructed based on the typical cascaded trisection coupling topology by mixing one SIW and two HMSIWs, including two single-band and one dual-band designs. All measured results are highly consistent with the simulated ones, validating that the HMSIW not only has the inherent advantage of smaller size than the conventional SIW counterparts but also possesses unique feature in providing flexible coupling without extra circuit.

The photon blockade in a three-wave mixing system coupled with a quantum dot

In this paper, the photon blockade effect in a three-wave mixing coupling system with a quantum dot has been studied. By using analytical calculation and numerical analysis, we find that both the conventional photon blockade and the unconventional photon blockade effects could be realized in this system in strong-coupling regime just by one driving. Besides, compared with Jaynes–Cummings model, this hybrid system shows other obvious advantages in realizing the photon blockade, like blockading photon of more different frequencies, stronger antibunching effect. All the results may provide useful theoretical references for the single-photon devices design by using quantum dot and three-wave mixing system in future experiments and applications.

Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 2: A semi-discrete error analysis framework for assessing coupling schemes

Abstract. Part 1 (Wan et al., 2024) of this study discusses the motivation and empirical evaluation of a revision to the aerosol-related numerical process coupling in the atmosphere component of the Energy Exascale Earth System Model version 1 (EAMv1) to address the previously reported issue of strong sensitivity of the simulated dust aerosol lifetime and dry removal rate to the model's vertical resolution. This paper complements that empirical justification of the revised scheme with a mathematical justification leveraging a semi-discrete analysis framework for assessing the splitting error of process coupling methods. The framework distinguishes the error due to numerical splitting from the error due to the time integration method(s) used for each individual process. Such a distinction results in a framework that provides an intuitive understanding of the causes of the splitting error. The application of this framework to the dust life cycle in EAMv1 confirms (i) that the original EAMv1 scheme artificially strengthens the effect of dry removal processes and (ii) that the revised splitting reduces that artificial strengthening. While the error analysis framework is presented in the context of the dust life cycle in EAMv1, the framework can be broadly leveraged to evaluate process coupling schemes, both in other physical problems and for any number of processes. This framework will be particularly powerful when the various process implementations support a variety of time integration approaches. Whereas traditional local truncation error approaches require separate consideration of each combination of time integration methods, this framework enables evaluation of coupling schemes independent of particular time integration approaches for each process while still allowing for the incorporation of these specific time integration errors if so desired. The framework also explains how the splitting error terms result from (i) the integration of individual processes in isolation from other processes and (ii) the choices of input state and time step size for the isolated integration of processes. Such a perspective has the potential for the rapid development of alternative coupling approaches that utilize knowledge both about the desired accuracy and about the computational costs of individual processes.

Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 1: Dust budget analyses and the impacts of a revised coupling scheme

Abstract. An earlier study evaluating dust life cycle in the Energy Exascale Earth System Model (E3SM) Atmosphere Model version 1 (EAMv1) has revealed that the simulated global mean dust lifetime is substantially shorter when higher vertical resolution is used, primarily due to significant strengthening of dust dry removal in source regions. This paper demonstrates that the sequential splitting of aerosol emissions, dry removal, and turbulent mixing in the model's time integration loop, especially the calculation of dry removal after surface emissions and before turbulent mixing, is the primary reason for the vertical resolution sensitivity reported in that earlier study. Based on this reasoning, we propose a revised numerical process coupling scheme that requires the least amount of code changes, in which the surface emissions are applied before turbulent mixing instead of before dry removal. The revised scheme allows newly emitted particles to be transported aloft by turbulence before being removed from the atmosphere, and hence better resembles the dust life cycle in the real world. Sensitivity experiments show that the revised process coupling substantially weakens dry removal and strengthens vertical mixing in dust source regions. It also strengthens the large-scale transport from source to non-source regions, strengthens dry removal outside the source regions, and strengthens wet removal and activation globally. In transient simulations of the years 2000–2009 conducted using 1∘ horizontal grid spacing, 72 vertical layers, and unchanged tuning parameters of emission strength, the revised process coupling leads to a 40 % increase in the global total dust burden and an increase of dust lifetime from 1.8 to 2.5 d in terms of 10-year averages. Weakened dry removal and increased mixing ratios are also seen for other aerosol species that have substantial surface emissions, although the changes in mixing ratio are considerably smaller for the submicron species than for dust and sea salt. Numerical experiments confirm that the revised coupling scheme significantly reduces the strong and non-physical sensitivities of model results to vertical resolution in the original EAMv1. This provides a motivation for adopting the revised scheme in EAM as well as for further improvements on the simple revision presented in this paper.

A complete deterministic model of point contact mixed lubrication coupling dual-mode effects of surface fractal characteristics

For mixed lubrication under point contact, a complete model is proposed including two modes of direct effects of surface roughness on the oil film thickness and rough solid contact characteristic. A new method to describe initial oil film thickness is established based on the effects of the holistic interface roughness. The real contact area of the interface is directly obtained by the sum of all solid nodes in a discrete grid, based on which, the solid contact characteristics are calculated by the fractal method considering the surface roughness. This fills the gap in mixed lubrication where the calculation of the solid part has no basis since solid contact force is unknown. The total load balance is taken as the convergence condition, and film thickness and pressure distribution of mixed lubrication are solved ultimately. The direct influences of fractal factors on lubrication characteristics are analyzed, and a comparison between the classical statistical method and the fractal method is conducted.

Searching for ultralight dark matter conversion in solar corona using Low Frequency Array data

Ultralight dark photons and axions are well-motivated hypothetical dark matter candidates. Both dark photon dark matter and axion dark matter can resonantly convert into electromagnetic waves in the solar corona when their mass is equal to the solar plasma frequency. The resultant electromagnetic waves appear as monochromatic signals within the radio-frequency range with an energy equal to the dark matter mass, which can be detected via radio telescopes for solar observations. Here we show our search for converted monochromatic signals in the observational data collected by the high-sensitivity Low Frequency Array (LOFAR) telescope and establish an upper limit on the kinetic mixing coupling between dark photon dark matter and photon, which can reach values as low as 10−13 within the frequency range of 30 − 80 MHz. This limit represents an improvement of approximately one order of magnitude better than the existing constraint from the cosmic microwave background observation. Additionally, we derive an upper limit on the axion-photon coupling within the same frequency range, which is better than the constraints from Light-Shining-through-a-Wall experiments while not exceeding the CERN Axion Solar Telescope (CAST) experiment or other astrophysical bounds.

Synchronization of Turing patterns in complex networks of reaction–diffusion systems set in distinct domains

We present an innovative complex network of reaction–diffusion systems set in distinct domains, with boundary couplings. The complex network models the evolution of interacting populations living in a heterogeneous and fragmented habitat, whose biological individuals migrate from one patch to another. In our model, the displacements of individuals are described by mixed boundary couplings, involving both the Neumann and Robin boundary conditions, which improve the modeling of migrations by point-wise couplings. We investigate the cases of diffusion in isotropic and anisotropic habitats and establish original sufficient conditions of synchronization in this complex network model, for complete graphs, cyclic graphs and rings of nearest neighbors. In parallel, we apply our theoretical framework to a nonlinear predator–prey model with Leslie–Gower-type functional response and explore numerically the emergence of synchronization on heterogeneous Turing patterns.

Seasonal Variations in Eddy-Induced Atmospheric Perturbations in the South China Sea

Abstract This study investigates the impact of eddy-induced sea surface temperature (SST) anomalies on the overlying atmosphere in the South China Sea, utilizing observational and reanalysis datasets. The results reveal that SST anomalies caused by anticyclonic or cyclonic eddies have a significant impact on the acceleration or deceleration of surface winds, with a stronger response in summer compared to winter. Moreover, atmospheric responses, such as heat flux, precipitation, and marine atmospheric boundary layer (MABL) depth above anticyclonic or cyclonic eddies, exhibit in-phase seasonal variations as surface winds. The study also explores the mechanisms leading to atmospheric response, pointing toward the vertical mixing mechanism as the dominant cause, supported by both the in-phase relationship between SST and surface wind anomalies and the linear relationship between the wind stress divergence anomaly and downwind SST gradient anomaly. Seasonal variations in coupling intensity are attributed to varying background atmospheric conditions, with more effective vertical turbulence mixing and stronger coupling intensity caused by more unstable MABL and enhanced large-scale vertical wind shear during summer than winter. Besides, the atmosphere above eddies is under a quasi-equilibrium condition, in which the surface wind stress increases monotonically with the depth of MABL. Given that the MABL depth response to eddy-induced SST anomaly is stronger in summer than in winter, it is reasonable to expect a more intense wind response during this season. Thus, the MABL depth coupling works together with the vertical mixing mechanism to explain the proportional relationship between SST and wind anomalies, and why the atmospheric response is stronger in summer than in winter. Significance Statement The atmosphere exerts a significant influence on the ocean, with strong winds cooling the sea surface temperature on a large scale (more than 1000 km). Conversely, the ocean tends to drive the atmosphere at a mesoscale level (10–1000 km), whereby a warm sea surface temperature causes surface wind to accelerate. This study aims to better understand how mesoscale eddies in the South China Sea influence the overlying atmosphere in different seasons. Our research explores factors that control mesoscale air–sea coupling, and highlights the importance of stability and depth change of marine atmospheric boundary layer. These results will establish a foundation for future research examining how the atmospheric perturbations caused by mesoscale eddies can in turn impact both ocean circulation and eddies.

Transmission line bandpass filters with multiple attenuation poles and small number of resonators

This article considers an alternative way to generate attenuation poles (AP) in bandpass filter (BPF) with parallel type resonators and admittance inverters. It consists in using special transmission line resonators, in which one or two antiresonant frequencies ωp1, ωp2 are placed next to the main resonant frequency ω0. These frequencies ωp1, ωp2 are the poles of the input admittance Y(jω). Four new resonators are synthesized in the article. Two resonators generate one AP, and other two resonators generate two APs located near the passband of the BPFs. If we use mixed couplings between proposed adjacent resonators in BPF, then the total number of APs will become quite large. This is because each mixed coupling adds one AP. N-order BPF without cross coupling can has (3 N – 1) APs. The increased number of APs improves the BPF selectivity, including the one-sided one. With APs, the filter can provide increased attenuation in certain frequency bands and effectively suppress unwanted signals. A microstrip second order BPF with center frequency f0 = 1 GHz and bandwidth BW = 70 MHz, which has five APs, is designed. It is compared with third order BPFs with two APs.