Lumped-element Equivalent Circuit Research Articles

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.

Equivalent circuit technique for designing split ring resonator based metasurfaces

Metasurfaces are two-dimensional artificially engineered structures capable of manipulating the phase, direction and orientation of electromagnetic waves by exhibiting simultaneously negative values of permittivity and permeability. These unconventional properties have been tailored and explored in many applications such as in bio-sensors, waveguides and antennas. The split ring resonators are the commonly used constituent meta-atoms of metasurfaces whose design and analysis rely on commercially available numerical electromagnetic fields (EM) solvers and experimental analysis. These numerical EM solvers are based on meshing and partitioning of graphical structures into the desire grids or patches to solve Maxwell equations in discrete form. However, graphical rendering and meshing of 3D objects requires significant space-time computational resources to analyze the structure. With the cost of licenses of EM solvers being very expensive, analytical solution were explored. The use of LC resonant frequency analytical formula provides an approximate value of resonant frequency which is less accurate and does not gives information about the current characteristics induced on the constinuent meta-atom of a metasurface. This paper presents an analytical approach to the design and analysis of a doubly split double rings (DSRR) using lumped element equivalent circuit that can be solved by mesh network analysis. The resonant frequency is extracted from the induced current characteristics which agrees with simulations and experimental results. The resonant frequency errors for a single DSRR unit cell ranged from1.05% to 7%, and for two coupled DSRR unit cells, they ranged from 1.4% to 11%.

From Finite Element Simulations to Equivalent Circuit Models of Extracellular Neuronal Recording Systems Based on Planar and Mushroom Electrodes.

define a new methodology to build multi-compartment lumped-elements equivalent circuit models for neuron/electrode systems. the equivalent circuit topology is derived by careful scrutiny of accurate and validated multiphysics finite-elements method (FEM) simulations that couple ion transport in the intra- and extracellular fluids, activation of the neuron membrane ion channels, and signal acquisition by the electronic readout. robust and accurate circuit models are systematically derived, suited to represent the dynamics of the sensed extracellular signals over a wide range of geometrical/physical parameters (neuron and electrode sizes, electrolytic cleft thicknesses, readout input impedance, non-uniform ion channel distributions). FEM simulations point out phenomena that escape an accurate description by equivalent circuits; notably: steric effects in the thin electrolytic cleft and the impact of extracellular ion transport on the reversal potentials of the Hodgkin-Huxley neuron model. our multi-compartment equivalent circuits match accurately the FEM simulations. They unveil the existence of an optimum number of compartments for accurate circuit simulation. FEM simulations suggest that while steric effects are in most instances negligible, the extracellular ion transport affects the reversal potentials and consequently the recorded signal if the electrolytic cleft becomes thinner than approximately 100 nm. the proposed methodology and circuit models improve upon the existing area and point contact models. The coupling between the extracellular concentrations and reversal potential highlighted by FEM simulations emerges as a challenge for future developments in lumped-element modeling of the neuron/sensor interface.

New Complementary Resonator for Permittivity- and Thickness-Based Dielectric Characterization.

The design of high-performance complementary meta-resonators for microwave sensors featuring high sensitivity and consistent evaluation of dielectric materials is challenging. This paper presents the design and implementation of a novel complementary resonator with high sensitivity for dielectric substrate characterization based on permittivity and thickness. A complementary crossed arrow resonator (CCAR) is proposed and integrated with a fifty-ohm microstrip transmission line. The CCAR's distinct geometry, which consists of crossed arrow-shaped components, allows for the implementation of a resonator with exceptional sensitivity to changes in permittivity and thickness of the material under test (MUT). The CCAR's geometrical parameters are optimized to resonate at 15 GHz. The CCAR sensor's working principle is explained using a lumped-element equivalent circuit. The optimized CCAR sensor is fabricated using an LPKF protolaser on a 0.762-mm thick dielectric substrate AD250C. The MUTs with dielectric permittivity ranging from 2.5 to 10.2 and thickness ranging from 0.5 mm to 1.9 mm are used to investigate the properties and calibrate the proposed CCAR sensor. A two-dimensional calibration surface is developed using an inverse regression modelling approach to ensure precise and reliable measurements. The proposed CCAR sensor is distinguished by its high sensitivity of 5.74%, low fabrication cost, and enhanced performance compared to state-of-the-art designs, making it a versatile instrument for dielectric characterization.

Compact Quasi-Elliptic-Type Inline Waveguide Bandpass Filters With Nonlinear Frequency-Variant Couplings

This work presents the design techniques to synthesize a class of compact inline quasi-elliptic-type waveguide cavity bandpass filters based on novel nonlinear frequency-variant couplings (NFVCs). These highly dispersive frequency-variant couplings (FVCs) are realized by means of a pair of partial-height posts that are placed at the junctions between every two cavity resonators. Each NFVC produces a transmission pole in between a pair of independently adjustable transmission zeros (TZs). Although the pole is added to the overall filtering function to augment its order, the TZs can be placed at each side of the filter passband to attain sharp rejection capability and increase the stopband attenuation levels. To synthesize these filters, two coupling-routing-diagram (CRD) approaches for the NFVC are presented that either consider: 1) an arbitrary FVC (AFVC) or 2) two resonating nodes interacting with a zero-susceptance nonresonating node through constant inverters. An equivalent lumped-element circuit model associated with both CRD approaches is provided. It is demonstrated that both CRD models can be exploited for the theoretical synthesis of this type of filter, whereas the equivalent lumped-element circuit model can provide a deeper insight into the systematic dimensioning of the posts. For experimental validation purposes, three design examples are synthesized, and 10-GHz proof-of-concept filter prototypes of two of them are EM-simulated, fabricated, and characterized. The measured results agree well with the simulations and the design theory, thus verifying the concept of inline waveguide cavity filters with TZs using NFVCs.

Development and Validation of an ANN-Based Approach for Temperature-Dependent Equivalent Circuit Modeling of SAW Resonators.

In this paper, a novel approach is proposed for modeling the temperature-dependent behavior of a surface acoustic wave (SAW) resonator, by using a combination of a lumped-element equivalent circuit model and artificial neural networks (ANNs). More specifically, the temperature dependence of the equivalent circuit parameters/elements (ECPs) is modeled using ANNs, making the equivalent circuit model temperature-dependent. The developed model is validated by using scattering parameter measurements performed on a SAW device with a nominal resonant frequency of 423.22 MHz and under different temperature conditions (i.e., from 0 °C to 100 °C). The extracted ANN-based model can be used for simulation of the SAW resonator RF characteristics in the considered temperature range without the need for further measurements or equivalent circuit extraction procedures. The accuracy of the developed ANN-based model is comparable to that of the original equivalent circuit model.

Realization of a novel dual-band bandpass filter with coupled series gaps and stepped impedance complementary split ring resonators

In this article, a bandpass filter (BPF) is proposed by etching stepped impedance complementary split ring resonators (SICSRRs) pairs in parallel with series gaps on the top side of a coplanar waveguide (CPW). The Nicolson-Ross-Weir (NRW) method is used to analyze the left-handed (LH) behavior of the filter. The effects of the resonators parameters on the left-handed BPF are studied. The parameters and number of the resonators are adjusted properly to obtain the desired filter characteristics. Split ring resonators (SRRs) are magnetically coupled to the BPF to realize a novel left-handed dual-band bandpass filter. Besides, The dual-band filter is described by means of the lumped-element equivalent circuit model. Also, the quasi-static analysis is used to obtain the equations for the resonant frequencies of the resonators. The efficient electrical size of the dual-band filter is 0.51λg × 0.42λg where λg represents the guided wavelength at the first passband center frequency. The prototype of the compact dual-band BPF is fabricated and measured. The measured results reveal low insertion loss and high return loss at the passbands along with wide upper stopband attenuation. The measured result is in a good agreement with the corresponding simulation result.

Rogowski Coil Sensors for Measuring Lightning Strike Currents on Mechanical Aircraft Joints

The study of currents flowing through the fuselage of an airplane is of vital importance from the standpoint of electromagnetic compatibility due to their potential for causing severe failures on embedded systems. Direct lightning strikes can produce extremely high currents propagating through the fuselage panels. Such high currents are critical when flowing through mechanical joints, a point of complex analysis due to the existing electrical discontinuities. Consequently, understanding the propagation of these currents is vital for protecting avionics through improved joints not only from a structural standpoint, but also from an electromagnetic perspective. In this article, we propose designing and validating a Rogowski coil sensor to measure the current flux through the mechanical joints that attach different fuselage panels. This sensor is theoretically analyzed, and a circuit model is provided. Then, a printed circuit board (PCB) Rogowski coil is designed and manufactured for measuring high-intensity pulsed currents with a bandwidth of 10 MHz. Subsequently, the probe is characterized through its S-parameters. Next, its equivalent lumped-element circuit is extracted and simulated for validating the sensor’s transient response. Finally, the Rogowski coil sensor is experimentally evaluated in the measurement of a surge current pulse that emulates a real scenario.

Circuit Simulator Compatible Model for the Ring-Dot Piezoelectric Transformer

A lumped-element equivalent circuit model for the ring-dot piezoelectric transformer (PT) is derived based on a one-dimensional analysis of the radial vibration mode. Initially, equations for the magnitudes of force, vibration velocity at the boundaries of each Section of the device are derived based on the piezoelectric constitutive equations and using Kirchhoff plate theory. Similarly, equations for the amplitudes of input and output currents are derived from the electric displacement field and Gauss’ law. From this analytical approach, an equivalent circuit model is developed and, using a Taylor expansion, approximated as the Mason equivalent circuit. A key contribution of this work is the development of a circuit simulator compatible model which can be used by electronic engineers, without in-depth knowledge of the underlying material science, to design ring-dot PTs for power conversion applications. The resulting model is verified against both COMSOL finite element simulations and experimental impedance measurements. Compared to COMSOL, the model estimates the resonant circuit elements to within 1% and the input and output capacitance are estimated to within 10%. Experimental results match the simulation to within 10% for most parameters, and 1% for resonant frequency. [2022-0154]

Modeling and analyzing coupling noise effect of Cu-carbon nanotube composite through-silicon vias interconnects using NILT based

In the modern field of microelectronics, the performance of interconnects tends to decrease as the technology node advances. Therefore, Cu-CNT composite TSV interconnects are utilized due to their favorable performance. In this article, Cu-CNT composite TSV interconnects have been studied. The objective of this work was to propose an accurate method for calculating time domain coupling noise in 3D structures based on Cu-CNT composite TSVs. The equivalent lumped element circuit, the NILT method, and the T-matrix were exploited. Throughout the study, the influence of geometric parameters, temperature, and CNT filling ratio were examined. The proposed method has been validated using PSpice results. The obtained results have shown good performance and accuracy. The average percentage error observed is less than 1 %.

Multifrequency nonlinear model of magnetic material with artificial intelligence optimization

Magnetic rings are extensively used in power products where they often operate in high frequency and high current conditions, such as for mitigation of excessive voltages in high-power switchgear equipment. We provide a general model of a magnetic ring that reproduces both frequency and current dependencies with the use of artificial intelligence (AI) optimization methods. The model has a form of a lumped element equivalent circuit that is suitable for power system transient studies. A previously published conventional (non-AI) model, which we take as a starting point, gives a good fit of parameters but uneven characteristics as a function of current, which pose numerical instabilities in transient simulations. We first enforce the Langevin function relationship to obtain smooth characteristics of parameters, which reduces the number of parameters and ensures their even characteristics, however, compromises fit quality. We then use AI metaheuristic optimization methods that give a perfect fit for the model in the whole range of frequency up to 100 MHz and current up to saturation, with smooth characteristics of its parameters. Additionally, for such fitted parameters, we show that it is feasible to find a frequency dependence for the magnetic saturation parameter of the Jiles-Atherton (JA) model, thus enabling frequency-dependent JA.

Homotopy Optimization and ANN Modeling of Millimeter-Wave SIW Cruciform Coupler

The development of millimeter-wave and terahertz (THz) passive components such as couplers and filters is an intimidating task because of underlying ultrasensitivity of electrical performances to geometric dimensions and processing tolerances. It is a common practice for us to use an integrated optimizer of commercial electromagnetic (EM) software packages for the design and optimization of such geometric parameters. However, those optimizers may fail to achieve a desired performance if initial variables are not in a range close enough to the optimal solution. In this article, we introduce an homotopy approach to optimizing the geometric parameters of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$D$ </tex-math></inline-formula> -band cruciform coupler based on substrate integrated waveguide (SIW) technique in conjunction with an artificial neural network (ANN) model. Starting from a set of initial variables, a homotopy optimization is set to search for an optimum solution. The ANN technique is adopted as the surrogate in place of a usual time-consuming EM model to accelerate the homotopy optimization process of the cruciform coupler. We propose a feed-forward computational formulation inspired by the fundamental transmission line impedance equation. Such a transmission line knowledge-based feedforward network results in a faster convergence with better accuracy than its conventional counterpart. To demonstrate the homotopy optimization method based on the ANN model, an example of multiparameterized cruciform coupler design is detailed. This cruciform coupler with optimized geometric dimensions is simulated, fabricated, and measured. Measured and simulated results validate the combined ANN model and homotopy method. An equivalent lumped-element circuit model of the cruciform coupler is also proposed in this work. An ANN model development technique is described how to extract the equivalent circuit parameters for given coupler specifications. Extracted circuit parameters in connection with the desired coupler performance are then compared with published results which verify the ANN model development algorithm.

Frequency reconfigurable dielectric lens antenna with graphene nano-antenna feed for THz applications

This paper proposes a frequency reconfigurable dielectric lens antenna (DLA) to compensate high attenuation due to atmospheric losses in the THz region. An aperture coupled graphene plasmonic nanoantenna has been designed and used to feed DLA. Frequency tuning has been introduced by varying the chemical potential of graphene. A lumped elements equivalent circuit for graphene-based feed antenna has also been proposed. The values of the lumped elements are obtained using the vector fitting algorithm. The proposed DLA has high gain, narrow beamwidth, broadside radiation pattern and stable input impedance. Directivity achieved through simulation is up to 7.3 dBi with radiation efficiency of 70 % and 21.2 dBi with radiation efficiency of 65 % for feed antenna and DLA respectively. The performance of DLA has also been studied as the function of feed element, relative permittivity of lens material, radius of lens and off-axis displacement tolerances.

Analysis of a Dual-Transduction Receiver for Electrodynamic Wireless Power Transfer

In this article, we present the characterization and an experimentally validated electromechanical model of a dual-transduction receiver for electrodynamic wireless power transfer (EWPT) system. This dual-transduction EWPT receiver contains two unimorph-type, series-connected piezoelectric transducers and an electrodynamic transducer within a compact footprint and low-profile design. The receiver makes simultaneous use of both piezoelectric and electrodynamic transducers to generate electrical power while operating at its torsion mode mechanical resonance at ∼744 Hz. The electromechanical system behavior and output performance under low-frequency, magnetic near-fields are analyzed by establishing an equivalent lumped-element equivalent electrical circuit model. A prototype device is fabricated, assembled, characterized, and the experimental results are compared with the model predictions under various excitation and loading conditions. A maximum of 49 μW average power is generated by the prototype under 120 μT <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rms</sub> , which corresponds to 0.54 mW·cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">–3</sup> power density and 37 mW·cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">–3</sup> ·mT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">–2</sup> normalized power density. This chip-sized (0.09 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) design offers an innovative and volume-efficient architecture for application in wirelessly charging wearable and implantable medical devices.

Wideband Microstrip Filtering Power Divider Designed by Direct Synthesis Technique (DST)

In this letter, a wideband microstrip filtering power divider (FPD) with a fifth-order bandpass response is discussed. Its even- and odd-mode models are obtained, which separately determine the transmission property and the isolation of the FPD. At the first, the distributed-element to lumped-element equivalence is applied to derive its lumped-element equivalent circuit of the even-mode model, so that its physical mechanism is clearly revealed, such as how the resonances are generated and coupled. Then, the direct synthesis technique (DST) we recently proposed is applied to determine the initial electric parameters of the FPD. Further, the initial values of the isolation resistors are calculated by letting the odd- and even-mode reflection coefficients be equal. Based on these initial values, the performance of the FPD can be easily optimized. For demonstration, an FPD example was designed, fabricated, and measured, whose 3-dB fractional bandwidth is as wide as 65.4% and isolation is 22.5 dB over the passband. Compared with other ones, the FPD is featured by a wide band, good selectivity, compact size, and so on.

Quantum Based Particle Swarm Optimization for Equivalent Circuit Design of Terminal Antenna Impedance

AbstractIn this paper, an improved quantum‐behaved particle swarm optimization (QPSO) approach for modeling antenna impedance is illustrated. In the proposed study, the enhanced weighted quantum particles swarm optimization (EWQPSO) is introduced with the aim to achieve local convergence acting on a reduced number of free parameters. To verify the performance of the proposed EWQPSO, several tests involving Ipersphere, Alpine, De Jong, Zakharov, Salomon functions were carried out. The obtained results demonstrated that the convergence is achieved more quickly by the EWPSO than other optimization algorithms based on QPSO. A lumped element equivalent circuit was designed to model the terminal impedance of a broadband planar sinuous antenna in the frequency range from 1 to 3 GHz. The developed EWQPSO algorithm is then used to recover all the parameters characterizing the equivalent circuit. The resulting circuit exhibited a good impedance fidelity over the whole frequency range.

Bandpass filters based on integrated aperture‐ and gap‐coupled discontinuities

An electromagnetic coupling mechanism is discussed for distributed-element aperture- and gap-coupled discontinuities based on rigorous lumped-element equivalent circuit analysis. The two discontinuities are analysed in terms of their transmission poles and transmission zeros for the selectivity enhancement of microwave and or millimetre-wave components. The integration of these two discontinuities is put forward for bandpass filter design. A frequency-dependent lumped-element equivalent circuit is employed to study the behaviour of the two distributed-element discontinuities in the transverse direction. Bandpass filters are characterised based on the dual aperture- and gap-coupled discontinuities integrated within substrate integrated waveguide structures. It is shown that multiple transmission zeros close to transmission poles are realised due to the magnetic and electric field cancelation in the gap-coupled discontinuity, while the aperture-coupled discontinuity contributes to a resonator with a higher quality factor. The integration of both aperture- and gap-coupled discontinuities shows the priority of this kind of microwave resonator in terms of selectivity, size, and upper stopband in comparison with the conventional aperture-coupled one.

Equivalent Circuit Approximation to the Connector-Line Transition at High Frequencies using Two Microstrip Lines and Data Fitting

This article presents a method of obtaining an equivalent lumped element circuit to model the electrical connector-line transitions in the ultra-high frequency (UHF) band. First, the scattering matrices of two microstrip transmission lines that are otherwise identical but have the physical lengths of dd and 2d2⁢d are measured. Next, the theoretical model of the lines cascaded with the connector-line transitions modeled as lumped element circuits is established. The selection of the line lengths to be dd and 2d2⁢d results in an over determined system of equations that links the circuit component values to the two-port network parameters of the cascaded system. Finally, the least-squares data fitting procedure yields the best-fit component values. The results show that in our tested scenario, 3-component reactive circuit models well the transitions. Compared with the previous methods, the proposed approach does not require knowledge of the dielectric properties of the substrate of the measured transmission lines. This property integrates the method with our previous work on estimating a microstrip line substrate’s relative permittivity and loss tangent. The obtained transition circuit model is also validated through the testing of two quarter-wave transformers. The lines and transformers are implemented on a textile substrate to highlight the method’s applicability to wearable textile-based electronics.

A W-Band Compact Substrate Integrated Waveguide Bandpass Filter With Defected Ground Structure in CMOS Technology

This brief proposes the first on-chip bandpass filter (BPF) based on substrate integrated waveguide (SIW) for W-band applications. Slot-loaded, folded ridge and quarter mode technology is used to reduce the cavity size. The coupling characteristic of two folded ridged quarter mode substrate integrated waveguide (QMSIW) cavities implemented in CMOS technology is investigated. A simplified equivalent lumped-element circuit model of the proposed wide-band BPF approach is provided and applied to study the coupling characteristic of slot-loaded folded ridged QMSIW cavity. Then, a novel coupling method using a defected ground structure is proposed to realize a proper coupling intensity for BPF design. Finally, the proposed BPF design is implemented in a commercial complementary metal-oxide-semiconductor (CMOS) technology, fabricated, and measured. The active size of the proposed cavity resonator is only 405 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}\,\,\times185\,\,\mu \text{m}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.22{\lambda }_{\mathrm{ g}} \times 0.1 \lambda _{\mathrm {g}}$ </tex-math></inline-formula> ), and the measured insertion loss ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert|\text{S}_{21}~\vert|$ </tex-math></inline-formula> ) is 3.15 dB with a central frequency of 85.5 GHz.

A tunable bandpass filter with extended passband bandwitdh

AbstractAn Nth-order tunable bandpass filter (BPF) structure with extended passband bandwidth has been proposed in this paper based on the novel tunable resonator and coupling structure. The designed tunable resonator is composed of two coupled lines and one varactor diode, while the presented tunable coupling structure is constructed by two cascaded transmission lines and one short-circuited varactor diode. Moreover, the even-(odd-) method and lumped-element equivalent circuit are employed to analyze the operating mechanisms of the designed Nth-order tunable BPF. Specifically, the frequency tuning range is determined by the characteristic impedance and electrical length of coupled line when the varactor diode is within the fixed tuning range. Then, the design procedure for the Nth-order tunable BPFs is proposed. To demonstrate the presented idea, the second- and third-order fully tunable BPFs have been designed and simulated. Finally, a second-order tunable BPF with the compact size of 0.03λg × 0.13λg has been fabricated and measured, and the measured center frequencies are ranging from 0.91 to 1.46 GHz with the passband bandwidths wider than 11.2%.