Equivalent Circuit Research Articles

Evaluation of Corrosion Potential Stability of Stainless Steels in Dilute Electrolyte Solution for Application to a Quasi-Reference Electrode Used in Electrochemical Sensing System

To evaluate the long term corrosion potential stability of stainless steel (SS) in environmental water, the corrosion potential of SUS304, SUS316, SUS316L, and SUS430 was measured for 1 week in a solution of 0.9 mM NaHCO3 and 0.5 mM CaCl2, referred to as “sub-tap water.” The potential of the SSs upon initial immersion in sub-tap water was approximately 10 times less stable than the potentials of Fe and Cu. However, as immersion continued, the stability of the corrosion potential of the SS improved and became equivalent to those of Fe and Cu. The stability could be manipulated by pretreatment (pre-immersion) before samples were immersed in sub-tap water. The stability was increased by pre-immersion in an acidic solution but was reduced by a passivation treatment. The formation of iron oxides on the SS surface stabilized the potential, whereas surface enrichment with Cr led to instability. This behavior can also be inferred from a comparison of the polarization curves, where the passive current after the passivation treatment was the largest. This result is also speculatively attributed to the corrosion potential in sub-tap water decreasing over time after the passivation treatment. The charge transfer resistance likely contributes significantly to the potential stability, as indicated by an equivalent circuit analysis based on electrochemical impedance spectroscopy. The results showed that, when stabilizing the corrosion potential of SS, there is no need to reduce the charge transfer resistance as with existing reference electrodes. Stability is achieved when the surface thickness is such that the pseudo-capacitance in a dilute solution is less than 10 µF sα−1cm−2 and potential stability does not influence a few changes in the CPE1 value after potential stability is achieved. The results of this study show that SS can be used as a quasi-reference electrode material. We expect the findings presented herein to strongly affect the development of electrochemical sensors that can be easily used in long term continuous measurements and in situ applications.

Study on Length–Diameter Ratio of Axial–Radial Flux Hybrid Excitation Machine

To improve the flux regulation range of the Axial–Radial Flux Hybrid Excitation Machine (ARFHEM) and the utilization rate of permanent magnets (PMs), the effects of different length–diameter ratios (LDRs) on the ARFHEM performance are studied. Firstly, the principle of the flux regulation of the ARFHEM is introduced by means of the structure and equivalent magnetic circuit method. Then, based on the principle of the bypass effect, the analytical formulas of LDRs, the number of pole-pairs, and the flux regulation ability are derived, and then the restrictive relationship between the air-gap magnetic field, LDR, and the number of pole-pairs is revealed. On this basis, the influence of an electric LDR on motor performance is studied. By comparing and analyzing the air-gap magnetic density and no-load back electromotive force (EMF) of motors with different LDRs, the variation in the magnetic flux regulation ability of motors with different LDRs is obtained and its influence mechanism is revealed. In addition, the torque regulation ability and loss of motors with different LDRs are compared and analyzed, and the influence mechanism of the LDR on torque and loss is determined. Finally, the above analysis is verified by experiments.

Charge injection barrier at the pentacene thin film and electrode interface characterized by time-resolved electrostatic force microscopy

The contact resistances at the metal–organic interface often limit the performance of organic thin-film transistors. However, it is not straightforward to characterize the electrical property of the metal–organic interface of the organic thin film. This is because the conventional electrical measurement only gives the total electrical property of the metal–organic–metal system that is affected by many grain boundaries. In this study, we investigated a single pentacene grain connected to a Au electrode by time-resolved electrostatic force microscopy (tr-EFM), which can capture the time-evolving electrostatic force images at a nanometer-scale spatial resolution. Using the tr-EFM, we found the gradual and uniform potential increase in the pentacene grain following the positive step voltage applied to the Au electrode, which indicates that the resistance in the grain–electrode system is governed by the grain–electrode interfacial resistance. By assuming the equivalent circuit of the grain–electrode interface system, we reconstructed the femto-ampere-order current-to-voltage characteristic at the grain–electrode interface. The asymmetric characteristic in the hole injection regime and the ejection regime suggests the existence of a metal–organic Schottky junction at the interface.

MODELING OF BANDPASS FILTERS WITH ATTENUATION POLES USING PARALLEL COUPLING CHANNELS

Background. Microwave filters are critical components in modern communication systems, playing a fundamental role in signal processing by allowing specific frequency bands to pass while attenuating unwanted frequencies. Over the years, significant advancements have been made in the design and development of various types of microwave filters, including directional, microstrip, and multi-resonator filters. These filters are widely used in radar, satellite communications, and wireless networks, where high performance and precise frequency control are essential. Objective. This paper is dedicated to reviewing various microwave filters that were constructed developed or analysed by the team, including directional filters, microstrip filters with attenuation poles, and multi-resonator filters. The studies focus on investigating their unique properties, such as the formation of attenuation poles, metamaterial characteristics, and the effects of resonator coupling on filter performance. New Python-based software realization for modelling different filters six resonators, four resonators, and two resonators were developed and frequently used. Methods. Electrodynamics simulations using software tools like CST Studio Suite, AWR Microwave Office, and LabVIEW, modelling filters using equivalent circuit models and bridge circuits. Use of microstrip lines, circular resonators, and dielectric resonators to construct and analyse different filter configurations. Analysis of energy propagation paths, resonator coupling, and transmission characteristics to optimize filter design. Results: Various structures were researched like Microwave Directional Filters, Microstrip Resonator Filters with 2, 4, 6 resonator, their structures and characteristics were analysed, New python-based software that allows modelling resonance curves using corresponding parameters for filters with 2, 4, 6 resonators. The parameters of the scattering matrix of a bridge quadrupole were expressed in an analytical form and were used for Python based program. Conclusions: the research presented across these publications contributes significantly to the development and understanding of advanced microwave filter designs. The article reveals various resonator-based filters, including directional, microstrip, and multi-resonator filters, these studies have highlighted key performance enhancements achievable through resonator coupling, metamaterial properties, and the introduction of attenuation poles. The use of advanced simulation tools, such as CST Studio Suite, AWR Microwave Office, and LabVIEW, allowed for accurate modelling and validation of theoretical designs. The introduction of Fano resonances and trapped modes in filters demonstrated improvements in selectivity and attenuation characteristics, which are critical for modern communication systems. Trapped modes manifest as attenuation poles, resulting from the interference of even and odd oscillations. This is evidenced by the presence of two independent energy pathways, along which these interfering oscillations propagate. With appropriate design parameters (such as resonator coupling coefficients and resonance frequencies), a complete energy exchange between resonators can occur at a certain frequency, in a direction perpendicular to the primary energy flow from input to output. The design and properties of directional filters based on circular resonators and dielectric resonators were described. These filters have "metamaterial" properties and are widely used in modern microwave technology. The characteristics of bandpass and rejector filters, as well as the characteristics of the filters formed by two microstrip resonators and resonators connected to each other, are given. It is important to emphasize the phenomena of "Fano resonances" observed in these filters, which arise as the interference of oscillations from individual resonators.

Review on Development and Research of Underwater Capacitive Power Transfer

Wireless power transfer (WPT) technology applied to underwater environments has the advantages of no electrical contact, high safety, and high applicability. Underwater capacitive power transfer (UCPT) technology shows great potential in the field of underwater wireless power transfer as it has more advantages compared to underwater inductive power transfer (UIPT) technology. This paper begins with the system principles of UCPT and explains the advantages of UCPT technology for underwater applications. It then reviews the coupler and equivalent circuit models currently used for UCPT in various underwater environments, which indicates the direction for the design of underwater couplers in the future. In addition, compensation networks currently applied in UCPT systems are summarized and compared. Furthermore, different application examples of UCPT are introduced, and the key factors constraining UCPT development are pointed out. Research directions for future development of UCPT technology are also investigated.

Structural Design and Electromagnetic Performance Analysis of Octupole Active Radial Magnetic Bearing.

This study addresses the challenges of magnetic circuit coupling and control complexity in active radial magnetic bearings (ARMBs) by systematically investigating the electromagnetic performance of four magnetic pole configurations (NNSS, NSNS, NNNN, and SSSS). Initially, equivalent magnetic circuit modeling and finite element analysis (FEA) were employed to analyze the magnetic circuit coupling phenomena and their effects on the magnetic flux density distribution for each configuration. Subsequently, the air gap flux density and electromagnetic force were quantified under rotor eccentricity caused by unbalanced disturbances, and the dynamic performances of the ARMBs were evaluated for eccentricity along the x-axis and at 45°. Finally, experiments measured the electromagnetic forces acting on the rotor under the NNSS and NSNS configurations during eccentric conditions. The results indicate that the NNSS configuration significantly reduces magnetic circuit coupling, improves the uniformity of electromagnetic force distribution, and offers superior stability and control efficiency under asymmetric conditions. Experimental results deviated by less than 10% from the simulations, confirming the reliability and practicality of the proposed design. These findings provide valuable insights for optimizing ARMB pole configurations and promote their application in high-speed, high-precision industrial fields such as aerospace and power engineering.

A Comprehensive Review of the Pseudo‐Two‐Dimensional (P2D) Model: Model Development, Solutions Methods, and Applications

AbstractRecently, a paradigm shift toward the tremendous use of portable and mobile consumer products is observed and it consequently increases the battery demand. Currently, lithium‐ion batteries (LIBs) are used in almost all kinds of devices, however, the increased usage of LIBs raises some safety concerns. For safe operation, it is necessary to investigate the all important chemical and physical features of LIBs. Several mathematical models are proposed such as equivalent circuit models (ECMs), physics‐based ECM and electrochemical models (EMs). Among them pseudo‐two‐dimensional (P2D) model is most famous and comprehensive physics‐based EM and used frequently to study the battery electrochemical phenomena. Hence, the focus of this review work is to summarize the reported literature on the P2D model governing laws, its simplified models, coupled models, solution techniques, parameter analysis, and its applications. The literature survey shows that the P2D and its simplified models are very helpful to analyze the important aspects of LIBs such as state of charge, state of health, recycling, battery manufacturing and design etc. Also, it can be seen that no single model can be fit to study every aspect of LIBs and design a comprehensive battery management system (BMS) but different models can be used to address the specific applications.

Gallium nitride ultra-wideband terahertz absorber based on periodic pyramidal array

Abstract Gallium nitride (GaN) has garnered significant attention due to its unique properties. Here, we present, for the first time, a polarization-independent ultra-wideband absorber in the terahertz band, consisting of a pyramidal GaN array and a GaN substrate. Numerical simulation results indicate that the designed absorber exhibits excellent absorption performance in the range of 0.39 to 1.98 THz, with a center frequency of 1.185 THz. The relative bandwidth ratio is 134.2%, and the absorption exceeds 90%. The equivalent circuit model (ECM) further illustrates the ultra-wideband strong absorption characteristics of the proposed absorber. The simulated electromagnetic field distribution indicates that the perfect absorption of the designed absorber is attributed to the excitation of electromagnetic resonance. Additionally, due to the high structural symmetry, the absorber exhibits polarization-independent properties and maintains high absorption performance at large incidence angles. In the future, this holds great promise for optical applications, including detector devices, photo detection equipment, and solar energy collection systems.

Analysis, modeling and design of piezoelectric-capacitive hybrid micromachined ultrasonic transducer

Abstract This paper proposes a spring-mass-damper model for a piezoelectric-capacitive hybrid micromechanical ultrasonic transducer (HMUT) in immersion. Based on this model, a dual-force actuation mode is identified, where piezoelectric micromachined ultrasonic transducer (PMUT) and capacitive micromachined ultrasonic transducer (CMUT) are strongly coupled to achieve enhanced sensitivity. In order to design HMUT efficiently, an electro-mechanical-acoustical equivalent circuit model (ECM) is constructed and then the round-trip gain is calculated to demonstrate its pulse-echo response. The ECM calculations results align with those of finite element model (FEM) simulations, showing a relative deviation less than 4%. In the design cases, the transmit sensitivity of HMUT is twice that of PMUT and more than five times that of CMUT. The receive sensitivity of HMUT is 1% lower than that of CMUT, but an order of magnitude larger than that of PMUT. The round-trip gain of the HMUT is at least 24.9 dB higher than that of PMUT and 14.1 dB higher than that of CMUT. These results demonstrate the potential of HMUT in surpassing bulk piezoelectric ultrasonic transducers in pulse-echo imaging. Furthermore, the impact of cell pitch on the pulse-echo response of HMUT arrays is characterize.

A novel dual-band absorber for millimeter-wave RADAR applications

Abstract A linearly polarized dual-resonant millimeter-wave absorber for Radio Detection And Ranging (RADAR)applications is presented in this paper. The frequency-selective absorber (FSA) is composed of solitarily using the distributed elements. The proposed FSA achieves a dual-band resonance characteristic utilizing the mutual coupling between concentric square loops, the second harmonic mode of the Jerusalem cross, and the corrugated cross grids. The proposed dual-band FSA operates from 25.5 to 26.5 GHz (1 GHz) (fL) and 31.8 GHz–32.5 GHz (0.7 GHz) (fH) with minimum absorptivity of 96% and 92%, respectively. The desired frequency response of the proposed unit cell is demonstrated by an equivalent circuit model. The FSA prototype is fabricated and the simulated results are validated using experimental measurements. The proposed FSA is a suitable candidate for stealth application in defense and military systems.

Comparative Analysis of Computational Times of Lithium-Ion Battery Management Solvers and Battery Models Under Different Programming Languages and Computing Architectures

With the global rise in consumer electronics, electric vehicles, and renewable energy, the demand for lithium-ion batteries (LIBs) is expected to grow. LIBs present a significant challenge for state estimations due to their complex non-linear electrochemical behavior. Currently, commercial battery management systems (BMSs) commonly use easier-to-implement and faster equivalent circuit models (ECMs) than their counterpart continuum-scale physics-based models (PBMs). However, despite processing more mathematical and computational complexity, PBMs are attractive due to their higher accuracy, higher fidelity, and ease of integration with thermal and degradation models. Various reduced-order PBM battery models and their computationally efficient numerical schemes have been proposed in the literature. However, there is limited data on the performance and feasibility of these models in practical embedded and cloud systems using standard programming languages. This study compares the computational performance of a single particle model (SPM), an enhanced single particle model (ESPM), and a reduced-order pseudo-two-dimensional (ROM-P2D) model under various battery cycles on embedded and cloud systems using Python and C++. The results show that reduced-order solvers can achieve a 100-fold reduction in solution times compared to full-order models, while ESPM with electrolyte dynamics is about 1.5 times slower than SPM. Adding thermal models and Kalman filters increases solution times by approximately 20% and 100%, respectively. C++ provides at least a 10-fold speed increase over Python, varying by cycle steps. Although embedded systems take longer than cloud and personal computers, they can still run reduced-order models effectively in Python, making them suitable for embedded applications.

Multi-objective optimization of an electrical injector in Urea-SCR system

Electrical injector is mainly used in non-air-assisted urea dosing systems to atomize and inject urea water solution. It consists of solenoid switch valve and injector. A good performance of the electrical injector can improve dosing precision of urea dosing system. To investigate dynamic characteristics of the electrical injector, an equivalent magnetic circuit model of the solenoid valve was established and magnetic field of the solenoid valve was also simulated using a three-dimensional finite element model. The results show that the calculation error of the two models is 6%, demonstrating that the equivalent magnetic circuit model can effectively predict the magnetic characteristics of the solenoid. Taking opening time, closing time, and coil area of the electrical injector as objective functions, a multi-objective optimization algorithm was used to optimize the design parameters of the electrical injector. Opening and closing processes of the optimized electrical injector under different pressures and driving voltages were measured through laser triangulation sensor. The experimental results showed that calculation results of the proposed theoretical model were close to the measurement results. The opening time of the optimized injector has been reduced by 11%, the response of the injector has significantly improved.

Broadband tunable multi-functional polarization converter based on a graphene metasurface

In this paper, a tunable multi-functional polarization converter based on a graphene metasurface has been designed. For the chemical potential of 1 eV, the structure has a polarization conversion ratio higher than 0.9 in the frequency range of 8.08 to 8.29 THz and also in the wide frequency range of 10.28 to 12.56 THz. Therefore, broadband linear to linear polarization conversion has been obtained. Also, in four frequency ranges, linear to circular polarization conversion has been realized. In addition to linear to linear and linear to circular functions, the structure also has circular to linear and circular to circular polarization conversion capabilities. The effects of chemical potential, geometrical parameters, and incident and polarization angles on the polarization conversion performance have been investigated. By changing the chemical potential, the reflected wave switches between different polarizations. Moreover, the results show that polarization conversion is insensitive to the incident angle up to 40°. The physical mechanism and analytical methods of multiple interference theory and equivalent circuit model for the suggested polarization converter have been presented. The presented structure with appropriate features such as different polarization conversions, adjustability, switching capability between different polarizations, broad bandwidth, good incident angle stability, and simple construction has many applications in communication, biological detection, imaging, and sensing.

DEVELOPING ELECTRICAL MODELS TO SIMULATE THE CONVERSION OF SOLAR RADIATION INTO ELECTRICAL AND THERMAL ENERGY

This article focuses on developing electrical models to investigate the conversion of solar radiation into both electrical and thermal energy. Our findings indicate that semiconductor converters are unable to harness the entire electromagnetic spectrum emitted by the sun. A substantial portion of solar radiation is transformed into heat. To achieve these results, we employed a corpuscular model to represent the solar radiation flow and a quantum mechanical framework to describe the energy associated with electromagnetic radiation and thermal processes within the crystal. To derive electrical modeling parameters, this study leveraged the principle of electrical and electrothermal analogies. We established a direct equivalence between the flow of solar photons and the flow of charge carriers represented by the electric current. Additionally, we demonstrated that the energy carried by photons is analogous to the voltage generated across the photovoltaic device. When modeling thermal energy using electrical circuits, we found that the electric current can be used to represent the flow of phonons, quasiparticles associated with thermal vibrations in the crystal, while the voltage corresponds to the energy of phonons. This study developed electrical models to simulate the conversion of solar radiation into both electrical and thermal energy. Current and voltage sources were employed to represent the energy conversion processes. It is shown that the internal resistances of energy sources in electrical models simulate the losses during the generation of electrical and thermal energy. It is noted that the proposed electrical model of a photovoltaic power source corresponds to the traditional equivalent circuit with a diode. The paper concludes by discussing the potential applications of the proposed modeling framework.

State preparation by shallow circuits using feed forward

Fault tolerant quantum computers repetitively apply a four-step procedure: First, perform a few one and two-qubit quantum gates. Second, perform a syndrome measurement on a subset of the qubits. Third, perform fast classical computations to establish if and where errors occurred. And, fourth, correct the errors with a correction step. The next iteration applies the same procedure with new one and two-qubit gates. Even though current error-rates prohibit this procedure to work and fault tolerant quantum computing remains a distant goal, the same procedure can already prove useful today. In this work we make use of this four-step scheme not to carry out fault-tolerant computations, but to enhance short, constant-depth, quantum circuits that perform 1 qubit gates and nearest−neighbor 2 qubit gates.We introduce a new computational model called Local Alternating Quantum Classical Computations(LAQCC). In this model, qubits are placed in a grid and they can only interact with their direct neighbors; the quantum circuits are of constant depth with intermediate measurements; a classical controller can perform log-depth computations on these intermediate measurement outcomes and control future quantum operations based on the outcome. This model fits naturally between quantum algorithms in the NISQ era and full-fledged fault-tolerant quantum computation. We first prove that any Clifford circuit has an equivalent LAQCC circuit, and that any LAQCC circuit can be simulated by a QNC1circuit. Next, we conjecture the non-simulatability of LAQCC by showing that LAQCC contains the class of Instantaneous Quantum Polynomial-time circuits. We also show that any LAQCC circuit with polynomial-sized quantum circuits and unbounded classical computations is contained in the class of quantum circuits equipped with post-selection gates with respect to the task of state preparation. We continue by presenting LAQCC implementations of different subroutines, including OR-gates, quantum Fourier transforms and Threshold gates. These subroutines prove vital in constructing three state preparation routines in the main part of this work. Preparing a uniform superposition uses constant-depth arithmetic gates, combined with an exact Grover implementation by Long. For the W-state, we employ a compress-uncompress method to switch between a binary and one-hot encoding. This method extends to the more generalized Dicke-states, the superposition of n-bit strings of Hamming weight k, for k=O(n), but fails for higher k due to the birthday paradox. We extend this protocol to a protocol that prepares many-body scar states, highly excited states with low entanglement and longer coherence times than states with the same energy density. We present a circuit for preparing Dicke-states for larger k requiring log-depth circuits that maps between the factoradic number system and the combinatorial number system.

Enhancing transformer windings monitoring: An approach using longitudinal branch‐circuit conductance analysis

AbstractThe operating environment of transformers is getting more complex with the emergence of new energy sources and power electronic devices. This complexity can cause minor internal faults in transformer windings. Under the cumulative effect, minor faults gradually develop into serious faults, resulting in transformer damage. Conventional differential protection systems may have difficulty detecting these glitches and require avoiding the problem of protection false activation caused by inrush currents. This paper proposes a new online monitoring method for transformer windings based on longitudinal branch‐circuit conductance to address this issue. First, a unified transformer equivalent circuit is proposed to represent transformers under normal conditions, inrush currents, and internal faults. Then, an online transformer monitoring method based on branch conductance is proposed, which is immune to inrush currents. This method aims to prevent delayed detection of faults during inrush currents, improving sensitivity and response speed, especially for minor turn‐to‐turn faults hidden in inrush currents. The proposed method also provides higher sensitivity to minor turn‐to‐turn faults and larger protection margins. Simulation and experimental results validate the effectiveness of this method.

Assessment of Non-Linear Modeling of Ladle Furnace Transformer Using Finite Element Analysis

This paper assesses a non-linear model of a three-phase Ladle Furnace Transformer, on slow front transients under no-load conditions. The model is designed to maintain accuracy and reduce complexity in estimating equivalent circuit parameters using three methods: analytical calculations, finite element analysis, and test measurement. The results reveal that analytical and finite element methods show discrepancies lower than 1%. Tests measurement, on the other hand, shows discrepancies higher than 5%, when compared to ones obtained from analytical and finite elements methods. Such discrepancy is particularly high in the estimation of leakage inductances and capacitances, and it is attributed mainly to differences between the transformer design and its actual assembly. Additionally, there are inherent inaccuracies in test procedures and instrumentation errors. The proposed model does not require difficult-to-obtain parameters and incorporates the non-linearity of magnetizing inductance, contributing to more accurate simulations. This simplified model is suitable for analyzing slow front transients and can be integrated into future studies addressing vacuum circuit breaker switching in electric arc furnace power systems, contributing to performance improvements in industrial applications. Additionally, the methodology for parameter determination can be applied to conventional power transformers, highlighting its versatility.

Measuring kinetic inductance and superfluid stiffness of two-dimensional superconductors using high-quality transmission-line resonators

The discovery of van der Waals superconductors in recent years has generated a lot of excitement for their potentially novel pairing mechanisms. However, their typical atomic-scale thickness and micrometer-scale lateral dimensions impose severe challenges to investigations of pairing symmetry by conventional methods. We demonstrate an improved technique that employs high-quality-factor superconducting resonators to measure the kinetic inductance—up to one part per million—and loss of a van der Waals superconductor. We analyze the equivalent circuit model to extract the kinetic inductance, superfluid stiffness, penetration depth, and ratio of imaginary and real parts of the complex conductivity. We validate the technique by measuring aluminum and finding excellent agreement in both the zero-temperature superconducting gap as well as the complex conductivity data when compared with BCS theory. We then demonstrate the utility of the technique by measuring the kinetic inductance of multilayered niobium diselenide and discuss the limits to the accuracy of our technique when the transition temperature of the sample, NbSe2 at 7.06 K, approaches our Nb probe resonator at 8.59 K. Our method will be useful for practitioners in the growing fields of superconducting physics, materials science, and quantum sensing, as a means of characterizing superconducting circuit components and studying pairing mechanisms of the novel superconducting states which arise in layered two-dimensional materials and heterostructures. Published by the American Physical Society 2024

Enhancement of Harmonic Heating by Magnetized Plasma Series Resonance in Capacitive Radio Frequency Discharges.

We present a novel resonance mode in capacitive radio frequency (rf) discharges in the presence of an oblique magnetic field at low pressures. We observe the self-excitation of high-frequency harmonics of the current in magnetized capacitive rf discharges through the magnetized plasma series resonance (MPSR) induced by applying a low-frequency power. Utilizing an equivalent circuit model, we reveal that these harmonics arise from the hybrid combination of the magnetic gyration of electrons and the PSR. When the MPSR occurs, the impedance of the series resonator system is at a minimum, resulting in the amplitude of higher harmonics being comparable to that of the fundamental frequency. The high-frequency harmonics with large amplitude cause strong oscillations in the electron heating rate, ultimately enhancing the total power dissipation. The presence of harmonics is suppressed by increasing the pressure due to collisional damping.

Mathematical modeling development and synthesis of tapered transmission line resonators and filters

Abstract Tapered transmission line resonators can be used to achieve specific frequency responses and enhance the performance of microwave devices and impedance transformers. To develop a mathematical model (transfer function) of such a wideband resonator will facilitate the construction of an equivalent circuit and the synthesis of resonators of this type. This study discusses the system modeling of tapered transmission line (TTL) resonators using the singularity expansion method (SEM). The transfer function is analytically established for two types of wideband TTL resonators: exponential tapered transmission lines (ETTL) and linear tapered transmission lines (LTTL). The analytical transfer function is derived for the general tapered ratio (k/β). The physical poles of the structures are identified using the pole-energy matrix pencil (MP) approach. The transfer function expression is then utilized to develop an accurate equivalent lumped-element circuit for the TTL resonator. This study’s simplified approach for estimating the transfer function and associated poles and zeros from the S-parameters is the main contribution, whereas it is known that the transfer function becomes complicated for wideband frequency response. A direct synthesis approach is presented to develop two-stage and four-stage ultra-wideband (UWB) bandpass filters. The agreement between the frequency response data and the derived transfer function of the system model of the synthesized TTL filters demonstrates the reliability of the presented method. The proposed system modeling and synthesis methodology can be applied to more sophisticated filter TTL architectures.