Lumped-element Equivalent Circuit Model Research Articles

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.

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]

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.

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.

Equivalent Circuit Model Extraction for a SAW Resonator: Below and above Room Temperature.

In this work, a SAW resonator is characterized in terms of admittance (Y-) parameters in the temperature range spanning from 0 °C to 100 °C, with the aim of highlighting how its physical properties are affected by the temperature change. A lumped-element equivalent-circuit model is used to represent the device under test at the considered temperature conditions and a parameters extraction process based on a Lorentzian fitting is developed for the determination of the equivalent-circuit elements in the investigated temperature range. A very good agreement is observed between the performed measurements and the model simulations. The characterization process and the subsequent equivalent-circuit parameters extraction at different temperature values are described and discussed.

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.

Broadband Bandpass Filter for UWB Networks with Multiple In-Band Transmission Zeros

Proposed in this manuscript is a broadband bandpass filter (BPF) with dual in-band transmission zeros (TZs) and elongated stopband for application in ultra-wideband (UWB) networks. The basic structure is developed on the principle of broadside coupling of microstrip-to-coplanar waveguide (CPW). Semi-elliptical microstrips on the top are arranged in back-to-back manner and coupled to the open circuited CPW in the ground. The basic BPF is of 3rd order with good insertion/return loss. To this basic BPF structure multiple defected ground structures (DGS) in the shape of complimentary split ring resonator (CSRR) are appended to place dual Tzs within the passband and later dumbbell-shaped DGS are engraved in the CPW to widen the stopband. Also, an approximate equivalent lumped element circuit model is developed and its frequency characteristics matched against full-wave EM simulation. The proposed dual notched BPF is finally fabricated and is found to occupy a compact area of 13.6 × 6.75 mm2.

Mechanically coupled clamped circular plate resonators: modeling, design and experimental verification

Mechanically coupled resonators usually require a mechanical coupling element; this introduces additional complexity to the picture. We propose a novel modeling and design approach, followed by experimental verification, for mechanically coupled clamped circular plate resonators in which no additional coupling element is present. In our study, the flexural mode clamped circular plate resonators overlap to an extent, and their clamps at the overlap region are removed to generate a freely moving coupling boundary between the resonators. The practical measure of the overlapping is small enough to preserve the characteristics of each resonator. This result enables modeling the coupled resonators based on the clamped circular plate resonator model. A physics-based lumped element equivalent circuit model is developed where dimensions, bias voltage, and material properties are controllable variables. Each of the model parameters is expressed as the corresponding single resonator model parameter multiplied by a function of the amount of overlap. Analytical derivations and finite element method simulations are used to extract the dependency of the model parameters on the amount of overlap. Closed-form expressions for center frequency, bandwidth, and termination impedance of the coupled resonator are derived using the developed model. A design procedure is introduced to determine dimensional parameters and bias voltage. The proposed coupled-resonator offers up to 5% fractional bandwidth. For a typical design using a polysilicon plate with 100 nm gap height, the ratio of the termination impedance to the center frequency is calculated to be 158 Ω MHz−1. This result indicates that on-chip intermediate frequency filters can be implemented at center frequencies up to several 100 MHz using this type of coupled resonators. A coupled resonator is designed and realized for a proof of concept demonstration. The measurement results of the coupled resonator show good agreement with the equivalent circuit model simulations.

Electroacoustic analysis of a directional moving-coil microphone using combined lumped-parameter models and BEM

This article presents a lumped-parameter model combined with external sound pressure field simulation, based on the boundary element method (BEM) for utilization in a directional microphone. A study about microphone capsule of a typical handheld moving-coil microphone with hyper-cardioid pattern has been conducted. In the BEM simulation, a simplified 3D model of the capsule that met sound waves which radiated from a point sound source has been taken into account. The blocked average pressure at the openings of the capsule is used to drive the lumped element equivalent circuit model. Through the model, the sensitivity, directivity, and impedance of the microphone were analyzed. Hence, the proximity effect is observed and discussed. To verify our simulation, the microphone characteristics were experimentally measured by B&K devices with SoundCheck software in an anechoic chamber. The simulation data are in good agreement with the measurement data at low and medium frequencies below 13 kHz, and there were larger errors at higher frequencies, which may indicate that the lumped parameters is less applicable at higher frequencies. The proposed method gains more precise and comprehensive prediction for the microphone characteristics, which therefore could be utilized in optimizing the choice of materials and size of the microphone capsule design.

Millimeter-Wave Wide-Band Bandpass Filter in CMOS Technology Using a Two-Layered Highpass-Type Approach With Embedded Upper Stopband

An on-chip millimeter-wave (mm-wave) broad-band bandpass filter (BPF) developed in bulk CMOS technology is reported. It is based on a two-layered implementation in which the circuit structure patterned in the top layer exhibits a highpass-type filtering response, whereas an upper stopband is created by the bottom-layer cell when coupled to the top-layer one to obtain a composite overall quasi-elliptic-type wide-band BPF functionality. The locations of the transmission zeros (TZs), which confer sharp-rejection capabilities to the overall frequency response, can be flexibly adjusted with the values of the capacitors that are employed in both layers. A simplified equivalent lumped-element circuit model of the proposed wide-band BPF approach is provided and applied to multi-stage BPF arrangements for higher-selectivity designs. Furthermore, for practical-demonstration purposes, an on-chip passive-integrated single-stage broad-band BPF prototype on silicon with 34.5-GHz center frequency and 61.2% 3-dB relative bandwidth is designed, manufactured, and characterized.

A chip-sized piezoelectric receiver for low-frequency, near-field wireless power transfer: design, modeling and experimental validation

This work presents the design, modeling and characterization of a chip-sized piezoelectric receiver for low-frequency, near-field wireless power transmission. Utilizing a laser micro-machined titanium suspension, one NdFeB magnet, and two PZT-5A piezo-ceramic patches, the receiver operates at its torsion mode mechanical resonance. Two unimorph piezo-ceramic transducers are designed to maximize the power density of the receiver while maintaining a low mechanical resonant frequency for low-frequency electrodynamic wireless power transmission. An equivalent lumped-element circuit model is used to model the system performance. A prototype device is fabricated, assembled and tested, and the experimental results are compared with the system model. The 0.08 cm3 device generates a maximum of 360 μW average power at 1 cm distance from a transmitter coil operating at 724 Hz and below human head and torso exposure limits. This data corresponds to 4.2 mW cm−3 power density. Overall, this volume-efficient design offers a low-profile and compact footprint for potentially wirelessly charging wearable and bio-implantable devices.

Resonant Characteristics of Split Ring Resonator and Unit Cell for Periodic Metamaterial Devices

The resonant characteristics of single split ring resonator-based metamaterial devices with single gap are presented using the analytical formulation developed for the lumped element equivalent circuit model. The characteristics of the metamaterial resonators have been investigated for different ring sizes, gap widths and substrate permittivity. Equivalent circuit model is developed for two ring structures. The analytical, and simulation results are compared and verified. The prototype has been then built and measured. It has been observed that all the results agree. The results presented in this paper can be used to develop devices at the THz range that can operate as sensors, antennas or tuning elements.

QMSIW-Based Single and Triple Band Bandpass Filters

This brief proposes compact and planar substrate integrated waveguide (SIW)-based filters for single and triple band operations using two quarter-mode SIW (QMSIW) cavities. Two miniaturized QMSIW cavity resonators (QMSIWCRs) are capacitively coupled. Miniaturization in the QMSIWCR is achieved by adding an arc-shaped slot and a rectangular open-ended stub at the closed-end of the QMSIWCR. In the triple band bandpass filter (BPF), a capacitor is added to the open-ended side of the stub to enhance impedance matching at the higher modes. It has the centre frequencies of 2.1, 3.98 and 6.6 GHz with an insertion losses (ILs) of 0.93, 0.98, and 1.2 dB at the lower, middle and upper passband, respectively. Moreover, the measured fractional bandwidths (FBWs) are 16.97, 8.77, and 8.42% at the lower, middle and upper passband, respectively. Two rectangular slots are etched on the upper layer of the cavity to suppress the second mode and reduce coupling of the third mode; this realizes a single-band filter with an improved upper stopband response. It has the centre frequency of 2.1 GHz with a wide upper stop-band response, having a rejection level of 20 dB up to 3.19f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> . The operation of filter is additionally discussed and verified by means of a lumped element equivalent circuit model and experimental results. The proposed filters are suitable for integration with other planar radio-frequency (RF) components due to their compact sizes, low ILs, planar structures, multiple transmission zeros (TZs) and adequate bandwidths.

Miniature Electrodynamic Wireless Power Transmission Receiver Using a Micromachined Silicon Suspension

We present the design, modeling, fabrication, and experimental characterization of an electrodynamic wireless power transmission (EWPT) receiver for low-frequency (<; 1 kHz), near-field wireless power transmission. The device utilizes a bulk-micromachined silicon serpentine suspension, two NdFeB magnets and two precision-manufactured coils. The architecture of the transducer is designed to maximize the electrodynamic coupling coefficient while maintaining a low mechanical resonant frequency in order to maximize the power density for low-frequency wireless power transmission. An equivalent lumped-element circuit model is established to parameterize the system and to predict the output performance of the proposed system. A prototype device is fabricated, assembled and tested, and the results are compared with the model prediction. The 0.31 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> device generates 2.46 mW average power (7.9 mW·cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> power density) at 4 cm distance from a transmitter coil operating at 821 Hz and safely within allowable human exposure limits. This data corresponds to a normalized power density of 21.9 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> , which is 44% higher than similar reported devices. Based on these results, this device shows great suitability for wirelessly charging mobile, wearable and bio-implantable devices. [2020-0161]

Highly Sensitive ELC Resonator Based Differential Sensor

A highly sensitive electric LC resonator-derived differential sensor is proposed in this work, with the major focus on detecting the purity of any reference dielectric material. The proposed sensor is designed with two identical electric-LC (ELC) resonators being loaded on either side of a 50- $\Omega $ microstrip line such that the magnetic wall of the microstrip line is perfectly aligned with that of the resonators. The fabricated unloaded sensor is operating at a resonance frequency of 3.385 GHz, falling between the two ISM bands, exhibiting a peak electric field intensity at the capacitive gap. The working principle of the sensor is analyzed through a lumped element equivalent circuit model. Experimental validation is performed via the fabricated prototype of the developed sensor on Taconic TLY-5 substrate for various standard and unknown dielectric samples. For the accurate testing of various samples using the proposed sensor, an empirical relationship is developed relating the difference in the resonance frequencies of the unloaded and loaded resonators, and the sample thickness. Furthermore, a novel error modeling technique is also incorporated to take into consideration the effect of fabrication tolerance and any possible air gap between the sensor region and the test specimen. The proposed differential sensor possess a substantially higher normalized sensitivity of 4.915% (165 MHz in terms of absolute sensitivity), which is quite useful for applications requiring detection of purity of a product. Its applicability is validated here by detecting the presence of termite infestation in wood sample.

On the Modeling of Microstrip Lines Loaded With Dumbbell Defect-Ground-Structure (DB-DGS) and Folded DB-DGS Resonators

This paper presents a lumped-element equivalent circuit model of microstrip lines loaded with dumbbell defect-ground-structure (DB-DGS) resonators, etched in the ground plane. The model is valid for ordinary (i.e., unfolded) DB-DGSs, as well as for folded DB-DGSs with an arbitrary aperture angle and relative orientation between the line and the resonator. It is shown that in folded, or partially folded, DB-DGS resonators both magnetic and electric coupling between the line and the resonator should be considered, except for a particular DB-DGS orientation, namely, the one where the symmetry plane of the particle (a magnetic wall) is orthogonal to the line axis. In this case, the particle is exclusively excited by the electric field generated by the line. It is also shown that the circuit model of a microstrip line loaded with an unfolded DB-DGS resonator transversally oriented to the line can be derived from the general model by considering the effects of opening the particle, i.e., a reduction of the electric coupling. In the extreme situation where the DB-DGS is completely opened (unfolded), the electric coupling vanishes, and the particle is exclusively driven by the magnetic field generated by the line. This effect is taken into account in the model by considering that the capacitance between the line and the inner metallic region of the folded, or partially folded, DB-DGS depends on the aperture angle of the particle, and it is null when the particle is unfolded. The models are validated by parameter extraction and comparison of the circuit responses with the responses inferred by electromagnetic simulation and measurement.

An Improved Transistor Modeling Methodology Exploiting the Quasi-Static Approximation

In this paper, a new modeling technique is proposed for extracting small-signal lumped-element equivalent-circuit models for microwave transistors. The proposed procedure is based on using an optimization approach that is improved by targeting a quasi-static behavior as additional objective function rather than only minimizing the error between the simulated and measured scattering parameters. The validity of the developed modeling methodology is successfully demonstrated by considering a 0.25x1000 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> gallium nitride (GaN) high-electron-mobility transistor (HEMT) as a case study.

Polarization Insensitive and Transparent Frequency Selective Surface for Dual Band GSM Shielding

This article proposes a single-layer, dual-band, optically transparent frequency-selective surface (FSS) for GSM shielding. The design evolves from a fractal cross dipole to achieve dual-band response, polarization insensitivity, and wide angle of incidence stability with a miniaturized size. A two-axis symmetric structure helps to provide a stable frequency response for incident waves with different polarization angles up to 60°. Capacitive loading further reduces the unit size and extends the maximum stable incident angle. The working mechanism of the design has been explained through an equivalent lumped element circuit model (ECM), which provides a generic approach to retune or optimize the design for another frequency band. Both the full-wave EM and circuit simulations are in good agreement. A prototype has been realized by screen printing a custom silver nanowire (Ag NW)-based transparent ink on a flexible polymer substrate. A decent reflection performance has been achieved from 0.71 to 1.25 GHz and from 1.73 to 2.16 GHz in measurements, which are consistent with the simulations. Optical measurements reveal a transparency of 81.6%. Printed FSS is completely flexible, and the performance does not deteriorate after bent or rolled up conditions. Field testing on a glass box demonstrates decent shielding from the incoming GSM signals. The highly transparent and flexible nature of the FSS structure makes it suitable for mounting on glass windows of cars or home environments for EM shielding purposes.