Infinite Frequency Research Articles

Dispersive properties of metamaterial beams with rod-like resonators: A coupled axial-flexural analysis

This paper addresses the propagation of coupled axial-flexural waves in metamaterial beams with rod-like resonators. Utilizing an exact frequency-dependent stiffness method, based on Euler–Bernoulli beam assumption for rods and host beam, and fully accounting for axial-flexural coupling phenomena, several adimensional parametric analyses are performed for investigating the dispersive properties of the metamaterial beams. The analyses reveal novel and relevant aspects unaddressed in previous studies. Firstly, they show that certain rod configurations lead to significant interference between flexural resonance and the band gaps opened by axial resonance, whereas other configurations enable flexural resonance to open substantial band gaps without interference from axial resonance. Results are complemented by 3D finite element analyses proving evidence of the findings and validating the method. Additional analyses demonstrate that adding a tip mass to the rods, while keeping the total mass of the resonator unchanged, can significantly reduce the opening frequency of the band gaps and can attenuate or remove the interference caused by flexural resonance within the band gaps opened by axial resonance; the rotational inertia of the tip mass can also play a significant role in removing flexural resonance interference. Notably, the paper also reveals that the attenuation phenomena for the coupled problem with a single set of rods are governed by the opening of weak band gaps, rather than by traditional band gaps; this aspect is elucidated by showing Bloch mode shapes of the infinite metamaterial beam and frequency response of the corresponding finite beam. Results and proposed design prove to be useful and promising for locally resonant beams featuring rod-like resonators, both as an alternative to traditional beam-like resonators and for their applicability in the 3D printing process of locally resonant structures, where rods serve as elastic elements in constructing the resonators.

Krylov subspace model order reduction of linear dynamical systems with quadratic output

This paper presents Krylov subspace model order reduction of linear dynamical systems with quadratic output. To reach this goal, the quadratic transfer function with two variables is taken into consideration. The Krylov subspaces are established at the finite and the infinite frequency points where both the one-sided and the two-sided projection cases are discussed. The moment matching is accordingly studied and the quadratic transfer function of the reduced system resulting from the two-sided projection case can match more moments. Finally, numerical results illustrate the performance of the proposed Krylov model order reduction methodology.

Tailoring the optical properties of dye–polymer composite films based on polyvinyl alcohol doped with phenol red toward flexible optoelectronic applications

The composite films of polyvinyl alcohol (PVA) incorporating varying concentrations of phenol red (PR) dye were fabricated using the solution casting method. Structural characteristics of the prepared films were explored through XRD and FTIR spectroscopy analyses. The inclusion of PR dye within the PVA matrix induced cross-linking, enhancing the amorphous nature of the doped PVA samples, as evidenced by XRD patterns. In the presence of PR dopants, the FTIR peaks for PVA exhibited altered intensities and increased width, indicating physical interactions between the functional groups of PVA and PR dopants. The impact of PR additives on the optical properties of PVA was investigated across the spectral range of 190–2500 nm. The PVA/phenol red composite demonstrated enhanced UV blocking in the 190–400 nm wavelength range, rendering it suitable for applications such as UV notch filters, including laser blocking filters. The indirect and direct optical band-gaps of PVA polymer films were reduced from 5.20 eV and 5.78 eV to 4.30 eV and 5.28 eV, respectively, with an increase in the PR filling ratio from 0 wt% to 1.8 wt%. The dispersion region of the refractive index was analyzed using the single oscillator model (Wemple-DiDomenico). Calculation and discussion of values such as dispersion and oscillation energies (Ed and Eo), permittivity at infinite frequency (ε ∞), and lattice contribution to the dielectric function (ε L) of PVA/PR composite films were conducted. These advancements position PVA/PR composite films for potential applications in flexible optoelectronic devices, including light-emitting diodes and photodetectors.

Determination of resistance at zero and infinite frequencies in bioimpedance spectroscopy for assessment of body composition in babies

Objective. Bioimpedance spectroscopy (BIS) is a popular technique for the assessment of body composition in children and adults but has not found extensive use in babies and infants. This due primarily to technical difficulties of measurement in these groups. Although improvements in data modelling have, in part, mitigated this issue, the problem continues to yield unacceptably high rates of poor quality data. This study investigated an alternative data modelling procedure obviating issues associated with BIS measurements in babies and infants. Approach. BIS data are conventionally analysed according to the Cole model describing the impedance response of body tissues to an applied AC current. This approach is susceptible to errors due to capacitive leakage errors of measurement at high frequency. The alternative is to model BIS data based on the resistance–frequency spectrum rather than the reactance-resistance Cole model thereby avoiding capacitive error impacts upon reactance measurements. Main results. The resistance–frequency approach allowed analysis of 100% of data files obtained from BIS measurements in 72 babies compared to 87% successful analyses with the Cole model. Resistance–frequency modelling error (percentage standard error of the estimate) was half that of the Cole method. Estimated resistances at zero and infinite frequency were used to predict body composition. Resistance-based prediction of fat-free mass (FFM) exhibited a 30% improvement in the two-standard deviation limits of agreement with reference FFM measured by air displacement plethysmography when compared to Cole model-based predictions. Significance. This study has demonstrated improvement in the analysis of BIS data based on the resistance frequency response rather than conventional Cole modelling. This approach is recommended for use where BIS data are compromised by high frequency capacitive leakage errors such as those obtained in babies and infants.

Earthquake Bond Pricing Model Involving the Inconstant Event Intensity and Maximum Strength

Traditional insurance’s earthquake contingency costs are insufficient for earthquake funding due to extreme differences from actual losses. The earthquake bond (EB) links insurance to capital market bonds, enabling higher and more sustainable earthquake funding, but challenges persist in pricing EBs. This paper presents zero-coupon and coupon-paying EB pricing models involving the inconstant event intensity and maximum strength of extreme earthquakes under the risk-neutral pricing measure. Focusing on extreme earthquakes simplifies the modeling and data processing time compared to considering infinite earthquake frequency occurring over a continuous time interval. The intensity is accommodated using the inhomogeneous Poisson process, while the maximum strength is modeled using extreme value theory (EVT). Furthermore, we conducted model experiments and variable sensitivity analyses on EB prices using earthquake data from Indonesia’s National Disaster Management Authority from 2008 to 2021. The sensitivity analysis results show that choosing inconstant intensity rather than a constant one implies significant EB price differences, and the maximum strength distribution based on EVT matches the data distribution. The presented model and its experiments can guide EB issuers in setting EB prices. Then, the variable sensitivities to EB prices can be used by investors to choose EB according to their risk tolerance.

Collisional space-charge-limited current with monoenergetic velocity: From Child–Langmuir to Mott–Gurney

All theories coupling electron emission theories ultimately approach the space-charge-limited current (SCLC) in vacuum, given by the Child–Langmuir (CL) law, for sufficiently high voltage, or the Mott–Gurney (MG) law for finite electron mobility and high (but not infinite) voltage. These analyses demonstrate the presence of an SCLC regime that cannot be described by either CL or MG. Here, we derive an exact solution for SCLC for general electron mobility and nonzero velocity. We recover the traditional CL with nonzero initial velocity at high voltage. For low mobility (or infinite collision frequency), we derive corrections to the MG law that depend on the ratio of initial velocity to the product of collision frequency and gap distance or initial velocity to drift velocity for low and high voltage, respectively. Increasing collisionality decreases the correction to SCLC for nonzero velocity, indicating that these corrections are less important for low-mobility materials (e.g., solids) than high-mobility materials (e.g., air or vacuum). For a given gap distance (collision frequency), increasing the collision frequency (gap distance) increases the voltage necessary to make the gap appear more like vacuum. These results provide a generalized SCLC for both collisionality and initial velocity when assessing the transitions between electron emission mechanisms.

Effect of sampling and computing times on a hysteresis vector controller applied to renewable distributed generation

Nowadays the use of renewable energies is increasing at a high rate, but there are limitations related to the low quality of the power sent to the utility. That is the reason why new control systems have been developed. Due to the difficulty of having adequate equipment to implement the different control systems [1] they have been simulated, but taking into account the data acquisition times. The paper considers the delay time in the switching status due to the data sampling and calculation of the parameters required for the control. The calculations used to obtain the phasors required to calculate the optimal switching and the switching time are shown. In order to obtain the results, the starting point is a predictive vector control, described in [2], where the calculation times have been applied for sampling frequencies of 100kHz and 200kHz, comparing the results with the case of having a infinite sampling frequency.

Finite-data nonparametric frequency response evaluation without leakage

The existing nonparametric frequency response estimation methods suffer from leakage. Because of this, these methods do not yield the correct result in case of exact data of a linear time-invariant system. Our main contribution is a time-domain direct data-driven nonparameteric frequency response estimation method that, in case of exact data satisfying standard persistency of excitation condition, eliminates the leakage and has infinite frequency resolution. The method is derived in the behavioral setting. It requires solving a system of linear equations and has no hyper-parameters. In case of noisy data, a modification of the method with preprocessing with low-rank approximation results in a subspace-type method for frequency response estimation.

The Singlet: Direct Synthesis of Pseudo-Elliptic Inline Filters With Frequency Variant Couplings

A general and direct synthesis of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{p}$</tex-math> </inline-formula> poles pseudo-elliptic inline filters having <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{p}$</tex-math> </inline-formula> purely real and/or imaginary frequency transmission zeros is presented. Using an appropriate model of the resonators (bandpass distributed or lumped element) and shifting the reference planes at the input and output of the filter network, a novel direct synthesis and realization of filters based on frequency variant coupling (inductive or capacitive) in the distributed domain is demonstrated for accurate modeling of narrow and broadband filters. First, a complete general synthesis procedure is described that allows for flexible or mixed topologies realizing transmission zeros anywhere on the frequency plane (including complex and infinite frequencies). Furthermore, by exploiting the power of modular design, a synthesis procedure that enables simultaneous extraction of reflection zero (a pole) and a transmission zero in the form of a symmetrical and physically realizable singlet as an elementary unit is showcased. The physical dimensions of the extracted singlets are independently determined in any chosen technology, and the overall filter is obtained by directly cascading the physical singlets. To validate this novel synthesis technique, three design examples are shown: a narrowband four-pole, four transmission zeros (fully canonical) filter from literature is synthesized and physically dimensioned, a wideband three-pole, three transmission zero (fully canonical) filter, and a broadband three-pole, one transmission zero, filter. In the first two examples, each of the singlet blocks was implemented in an overmoded rectangular waveguide cavity operating at the TE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{201}$</tex-math> </inline-formula> mode coupled at the input and output to the fundamental nonresonating TE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{10}$</tex-math> </inline-formula> mode. The third example was implemented in a re-entrant coaxial resonator operating at the fundamental mode. The simulation of the electromagnetic (EM) high-frequency structure simulator (HFSS) models of the overall example filters was in excellent agreement with the synthesized models, thereby validating the effectiveness of the proposed synthesis technique. Furthermore, the measured results of the fabricated wide bandpass filter showed close agreement with synthesis and EM model.

Stochastic Modeling of Partially Stirred Reactor (PaSR) for the Investigation of the Turbulence-Chemistry Interaction for the Ammonia-Air Combustion

The Partially Stirred Reactor (PaSR) model is carried out for the ammonia-air combustion system by means of stochastic modeling, namely by solving the transport equation for the joint Probability Density Function (PDF). The turbulent mixing is accounted for by the Linear Mean-Square Estimation (LMSE) mixing model. Notwithstanding the simplified nature of the PaSR modeling, the transported-PDF method enables capturing the effect of mixing frequency on the combustion system, especially the NOx emission. Since the chemical source term is in a closed form in the transported-PDF method, it allows us to apply different chemical mechanisms to explore, whether the set of elementary reactions that are identified as important for the prediction of NOx in the PaSR model is sensitive to the choice of chemical mechanisms. Furthermore, the effect of the residence time in the PaSR model has also been studied, and compared with those in the Perfectly Stirred Reactor (PSR) model (infinite large mixing frequency). Moreover, since the ammonia under oxygen enrichment shows some similar combustion behaviors in terms of e.g. laminar burning velocity as the ammonia under hydrogen enrichment, how large the difference of thermo-kinetic states (e.g. temperature and NOx emission) predicted by PaSR models and in laminar premixed flame configuration is also investigated. A further discussion focuses on the effect of thermal radiation, where the radiative heat loss roles in the prediction of NOx for the turbulent simulation is examined. By using the optically thin approximation model, it is shown that the thermal radiation exhibits little effect on the considered combustion systems within a typical turbulent time-scale.

Enhancement of the structural, optical, and dispersion performance of polyvinyl alcohol via coronene additive for optoelectronic applications

Composite films made of polyvinyl alcohol (PVA) filled with various coronene concentrations were fabricated via the solution casting method. Several characterization techniques were used to examine the prepared samples. The x-ray diffraction study shows decreasing semi-crystalline properties in PVA/coronene composites with increasing coronene levels, thereby improving charge carrier mobility and enhancing conductivity. The alterations in the chemical functional groups of the PVA/coronene composites were explored using Fourier-transform infrared spectroscopy (FTIR). The impact of coronene molecules on the optical characteristics of PVA was investigated in the spectral ranges of 190-2500 nm. PVA/coronene composite exhibits higher UV blocking in the 190-400 nm wavelength range, suitable for UV notch filters like laser blocking filters. By increasing the coronene filling ratio from 0 wt% to 3 wt%, both the indirect and direct optical band-gap of PVA films decreased from 5.19 eV and 5.77 eV to 3.85 eV and 5.18 eV, respectively. The single oscillator model (Wemple-DiDomenico) was used to explain the refractive index dispersion region. The extracted values of dispersion energy (Ed), oscillator energy (Eo), dielectric constant at infinite frequency (ε ∞), and lattice dielectric constant (ε L) of PVA/coronene composite samples increased from 0.78 eV, 2.41 eV, 1.32 and 1.41 to 13.44 eV, 12.22 eV 2.10 and 2.13, respectively. These changes in dispersion parameters are due to cross-linking between the PVA polymeric matrix and the coronene. As a result of these improvements, PVA/coronene films could be applied to flexible packaging applications and optoelectronic devices like solar cells or light-emitting diodes.

Quantum phase transitions in the anti-Jaynes-Cummings triangle model

We carefully investigate the comprehensive impact of atom-cavity interaction and artificial magnetic fields on quantum phase transitions of anti-Jaynes-Cummings triangle model in the infinite frequency limit. We discover that ground states of the optical field can be a gapped normal phase (NP) or three kinds of gapless superradiant phases with infinite degeneracy. When the atom-cavity coupling is weak, the optical field is in a NP, which is a vacuum with no photons. Otherwise, it will stay at one of the superradiant phases: a normal superradiant phase without photon currents and another two chiral superradiant phases with opposite photon currents. The former only breaks the continuous U(1) symmetry and its gapless excitations are normal Goldstone modes. Nevertheless, the latter, mainly induced by an external synthetic gauge field, break both the continuous U(1) symmetry and chiral symmetry, thereby corresponding gapless excitations are chiral Goldstone modes. In addition, we also propose a detecting scheme to distinguish these superradiant phases.

Development and validation of the in-house hydrodynamics code and the DNV software for TALOS wave energy converter

The Lancaster in-house code is a time-domain analysis code, developed especially for the TALOS wave energy converter, a novel wave energy conversion technology. The TALOS wave energy converter is a point absorber-like wave energy converter, but with a unique power take-off (PTO) system. The whole PTO system is fully enclosed within the structure, hence no moving parts are exposed to the harsh marine environments.&#x0D; The PTO of the TALOS WEC consists of a mass ball within the structure, with a number of springs and dampers (for instance, direct drives or hydraulic systems) connecting between the mass ball and the structure. Such an arrangement of the PTOs would make the PTO essentially non-linear, regardless whether the actual PTO dampers are linear or nonlinear as well as the linear springs. Therefore, a time domain analysis must be established for the TALOS WEC. Towards the goal, an in-house time-domain model has been developed at Lancaster University, and now it is to be validated via the delicated numerical models built using well-established commercial software (and in the future via experimental data). Within this framework, the present paper presents an effort for validation using the DNV SESAM commercial hydrodynamic and structural analysis software. &#x0D; To build a numerical model for TALOS WEC, the Lancaster in-house time domain code is based on the hybrid frequency-time domain approach. That is, the basic hydrodynamic parameters are analysed using the panel methods (WAMIT, HAMS, NEMOH), and then the relevant parameters are transformed for the Cummins’ time-domain equation, such as the added mass at infinite frequency, and the memory effect (the convolution terms). This work is an extension of the comparison between the in-house code and the DNV SESAM software, and the comparisons would include the relevant hydrodynamic analyses, the time-domain analyses with and without the TALOS PTO system, with the aims towards developing the validated tools of both the in-house code and the commercial software.

In-plane and out-of-plane gigahertz sound velocities of saturated and unsaturated phospholipid bilayers from cryogenic to room temperatures

Here, we examined the gigahertz sound velocities of hydrated multibilayers of saturated (1,2-dimyristoyl-sn-glycero-3-phosphocholine, DMPC) and unsaturated (1,2-dioleoyl-sn-glycero-3-phosphocholine, DOPC) phospholipids by Brillouin spectroscopy. Out-of-plane and in-plane (lateral) phonons were studied independently of each other. Similar strong temperature dependences of the sound velocities were found for phonons of both types. The sound velocities in the low-temperature limit were two-fold higher than that at physiological temperatures; a significant part of the changes in sound velocity occurs in the solid-like gel phase. The factors that may be involved in the peculiar behavior of sound velocity include changes in the chain conformational state, relaxation susceptibility, changes in the elastic modulus at infinite frequencies, and lateral packing of molecules.

Wave Conversion, Decay, and Heating in a Partially Ionized Two-fluid Magneto-atmosphere

A ray-theoretic phase-space description of linear waves in a two-fluid (charges and neutrals) magnetized plasma is used to calculate analytic decay rates and mode transmission and conversion coefficients between fast and slow waves in two dimensions due to finite ion–neutral collision frequencies at an arbitrary ionization fraction. This is relevant to partially ionized astrophysical plasmas, in particular solar and stellar atmospheres. The most important parameter governing collisional effects is the ratio of the wave frequency to the neutral–charges collision frequency, ϵ = ω/ν nc, with secondary dependence on ionization fraction and wave attack angle. Comparison is made to the one-fluid magnetohydrodynamic case, and it is found that acoustic-to-acoustic and magnetic-to-magnetic transmission through the Alfvén-acoustic equipartition layer is decreased by a term of relative to one-fluid (infinite collision frequency), and correspondingly acoustic-to-magnetic and magnetic-to-acoustic conversion is increased. The neutral-acoustic mode is shown to dissipate rapidly as ν nc → ∞. Away from the mode conversion region, dissipative decay along the remaining magneto-acoustic rays scales as and is found to be much more effective on magnetically dominated rays compared to acoustically dominated rays. This produces a steep jump in dissipation in mode conversion regions, where the rays change character, and can produce localized heating there and beyond. Applications to the solar chromosphere are discussed.

Density of states effects on emission and scattering of photons in plasmas

Plasma supports electromagnetic waves propagation for frequencies higher than plasma frequency but features dielectric permittivity less than 1. This property leads to photon density of states (DOS) lower than in vacuum and should result in subnatural spectral linewidths, sub-Planckian spectrum of thermal radiation, and sub-Rayleigh scattering as well as in lower inelastic photon scattering including Raman scattering. Lamb shift will be altered as well though the decisive contribution from high-energy modes in this case makes the photon DOS effect rather small since plasma DOS converges with the vacuum one in the limit of infinite frequencies. We emphasize the basic character of all these phenomena though absolute values of corrections in many real experiments may appear to be small as compared to other factors. We found that dissipative losses make possible DOS effects smaller though not vanishing and additionally bring about indefinite growth of DOS in the low-frequency limit.

Probabilistic Optimal Power Flow for Balanced Islanded Microgrids

This paper presents a Probabilistic Optimal Power Flow (POPF) for losses minimization in balanced islanded microgrids considering load uncertainties following a normal distribution. The peculiarities of the islanded operation, like the absence of infinite bus and frequency variation in the face of load and loss variations, are adequately considered. The constraints deal with the power balancing, angular reference, droop control mode of generators (P-f e Q-V), and the probability of satisfying the limits of microgrid frequency, nodal voltages, and power generation. As the main contribution, the Differential Evolution method and the Unscented Transformation solve the POPF, reducing the computational time and providing accurate results compared with the Monte Carlo Simulation. The proposed approach is evaluated using a 33-bus islanded microgrid.

Infinite Frequency Oscillations in a Class of Discontinuous Equations with a Variable Delay

Infinite Frequency Oscillations in a Class of Discontinuous Equations with a Variable Delay

In English

The goal of this study is unraveling the specific features of non-stationary surface concentration distribution of electroactive and inactive species in a model electrochemical process with a preceding homogeneous first-order chemical reaction (CE mechanism). For this purpose, the exact analytical expressions for the non-stationary concentration distributions of electroactive and inactive species in the thin layer attached to a planar electrode are analyzed. The both cases of equal and unequal diffusion coefficients of species taking part in the preceding chemical reaction are considered. In the former case, the exact analytical expressions for the concentration distributions of electroactive and inactive species on a planar electrode are obtained. The peculiarities of the limiting cases of zero and infinite frequency of an applied alternating current for the both cases of equal and unequal diffusion coefficients of species are discussed. It is shown that there is a phase shift between AC and the surface concentration of species that changes under the action of this current. At low frequencies, the phase angle tends to p/2, whereas at high frequencies it decreases to p/4. The phase angle is the function of the two important measures, namely, the ratio of the Nernst diffusion layer thickness to the oscillation diffusion layer thickness, and the ratio of the Nernst diffusion layer thickness to the reaction layer one. It is shown that the phase angle depends on the diffusion coefficient of species in different manner for low and high values of the rate constants of the chemical reaction. At low values of these parameters, the phase angle shifts slightly to the range of high frequencies with an increase of diffusion coefficient. At the high rate constants, the phase angle decreases with frequency more slowly, and its dependence on diffusion coefficient is observed only at middle frequencies. The surface concentration of electroactive and inactive species decreases with an increase of frequency, but for the inactive species this process is faster than that for the electroactive species. The influence of the inactive species on the surface concentration of electroactive species decreases at high frequencies and at low rate constants of the preceding chemical reaction. The results obtained shed the light on complex dynamics at an electrode/electrolyte interface under non-stationary conditions.

Calculation of Band-Pass Filters with Fixed Frequencies of Infinite Attenuation

Introduction. When calculating band-pass filters (BPF) with infinite attenuation frequencies using the frequency conversion method, the parameters of the prototype – an inverse or quasi-elliptic low-pass filter (LPF) – are recalculated into BPF parameters according to conventional formulas. Using the selected low-pass filter cutoff frequency and the Q-factor of the band-pass filter, one can select at their discretion only one infinite attenuation frequency (attenuation pole). In order to suppress a pair of concrete frequencies in the attenuation band, the synthesis of BPF should initially fix the frequencies of maximum attenuation and the central frequency of the filter. The reverse transition toward the frequency response parameters of a low-frequency prototype is carried out using frequency conversion formulas.Aim. To develop of a method for calculating band-pass filters with fixed attenuation poles.Materials and methods. Odd-order filters with an additional capacitor in the transverse branch of the П-link and an inductance in the longitudinal branch of the Т-link were used as low-frequency prototypes of the BPF with attenuation poles. Approximation of the frequency response of a low-frequency prototype (inverse or quasi-elliptical LPF) was performed by methods based on solving systems of nonlinear equations.Results. A realizable transfer function (TF) of an n-th order LPF with attenuation poles was written as the ratio of the product of binomials and a polynomial of power n with real coefficients. Systems of equations were derived to determine amplitude-frequency response coefficients with a given frequency of maximum attenuation interference for both types of filters. Analytical expressions for the TF of the low frequency prototypes of 3th and 5th orders were recorded through the capacitances of the BPF circuits tuned to the central and suppressed frequencies, thus allowing the desired capacitances to be directly calculated. The BPF inductances were determined by formulas expressing the dependences of the BPF central frequency on the circuits parameters, taking into account the relationships given in the article. An example of calculating a 10th order quasi-elliptic BPF was provided.Conclusion. The proposed method can be used to determine the BPF parameters directly, without an intermediate calculation and subsequent transformation of the LPF prototype parameters. The given analytical expressions for the frequency response of the П- and Т-shaped BPFs of the 6th and 10th orders make it possible to verify the performed calculations and to correct the frequency response using inductances, when replacing the calculated capacitance values with their standard values.