Equivalent Circuit Extraction Research Articles

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.

Extraction of small-signal equivalent circuit for de-embedding of 3D vertical nanowire transistor

In this paper, we present an improved methodology to extract the small-signal electrical equivalent circuit of the parasitic elements using RF test structures for a 3D vertical nanowire transistor technology. The methodology is based on the extraction of the distributed parasitic elements from an open structure for which on-wafer S-parameter measurements were carried out up to 40 GHz. The electrical equivalent circuit of the passive device was then used for de-embedding of the transistor S-parameters for extraction of intrinsic small-signal parameters such as the gate capacitances.

Bayesian estimation of equivalent circuit parameters of photovoltaic cells

The equivalent circuit model of a photovoltaic cell is useful for understanding device loss mechanisms as well as the design and analysis of systems using photovoltaic cells. Although nonlinear least-squares methods are routinely applied for the extraction of equivalent circuit parameters using current–voltage characteristic curves, they only yield a point estimation sensitive to the initial value and do not provide an estimation error. In this study, a data-driven approach using Bayesian estimation is proposed to extract equivalent circuit parameters. Contrary to the conventional least-squares method, this method does not require tedious initial value adjustments and provides an estimation error.

Design and Analysis of Broadband Ultrathin Reflective Linear-to-Circular Polarization Converter Using Polygon-Based Anisotropic-Impedance Surface

A broadband reflective linear-to-circular polarization converter (LCPC) is designed using a polygon-based single-layer anisotropic-impedance surface on an ultrathin (thickness is 0.053λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>0</b></sub> , where λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>0</b></sub> is the wavelength corresponding to the mid operating frequency) ground-backed substrate. Using the admittance analysis of the equivalent circuit model (ECM) and extraction of the admittance through the area moment of inertia equations, simple and generalized design guidelines are presented. The proposed polarization converter produces left-handed circularly polarized (LHCP) and right-handed circularly polarized (RHCP) reflected waves, respectively, for the linearly polarized (LP) TE and TM incident waves. It offers 46% (7.62-12.16 GHz) 3 dB axial ratio bandwidth (ARBW) for normal incidences of both the TE- and TM-polarized waves. Moreover, for oblique incidences (up to 30°) of both the LP waves, the ARBW response remains quite stable. The far-field radiation characteristics, which are often not studied, are provided to show its usability as a dual-LP to dual-CP converting reflector for X-band communications. The measurement results show good agreement with the numerically simulated results.

Effective Simulation Approach for Lightning Impulse Voltage Tests of Reactor and Transformer Windings

In this paper, an effective simulation method for lightning impulse voltage tests of reactor and transformer windings is presented. The method is started from the determination of the realized equivalent circuit of the considered winding in the wide frequency range from 10 Hz to 10 MHz. From the determined equivalent circuit and with the use of the circuit simulator, the circuit parameters in the impulse generator circuit are adjusted to obtain the waveform parameters according to the standard requirement. The realized equivalent circuits of windings for impulse voltage tests have been identified. The identification approach starts from equivalent circuit determination based on a vector fitting algorithm. However, the vector fitting algorithm with the equivalent circuit extraction is not guaranteed to obtain the realized equivalent circuit. From the equivalent circuit, it is possible that there are some negative parameters of resistance, inductance, and capacitance. Using such circuit parameters from the vector fitting approach as the beginning circuit parameters, a genetic algorithm is employed for searching equivalent circuit parameters with the constraints of positive values. The realized equivalent circuits of the windings can be determined. The validity of the combined algorithm is confirmed by comparison of the simulated results by the determined circuit model and the experimental results, and good agreement is observed. The proposed approach is very useful in lightning impulse tests on the reactor and transformer windings.

Magnetic equivalent circuit modelling of coaxial magnetic gears considering non‐linear magnetising curve

It is necessary to have a model to design magnetic gear (MG) optimally and to investigate the effective parameters on its performance. This study proposed a two-dimensional (2D) model to predict the magnetic components of coaxial MG (CMG). This model is based on the mesh analysis method considering core nonlinear B-H curve. In the proposed model, the radial and tangential components of flux densities, magnetic fluxes as well as the inner/outer rotor torque are estimated by extraction of the magnetic equivalent circuit (MEC). The effect of non-linear B-H magnetising curve is considered on the MEC model and it is compared with linear core (constant probability). Furthermore, the dynamic model of CMG is presented and its torque-angle curve and consequently its pull-out torque is obtained. To validate the proposed model, the 2D MEC model results are compared with results of finite element method analysis.

Solving CNLS problems using Levenberg-Marquardt algorithm: A new fitting strategy combining limits and a symbolic Jacobian matrix

The Levenberg-Marquardt algorithm (LMA) is generally used to solve diverse complex nonlinear least square (CNLS) problems and is one of the most used algorithms to extract equivalent electrochemical circuit (EEC) parameters from electrochemical impedance spectroscopy (EIS) data. It is a well-known fact that the convergence properties of the algorithm can be boosted by applying limits on EEC parameter values. However, when EEC parameter values are low (i.e., of the order of magnitude of 10−4 or smaller), the applied limits increase the first derivatives approximation errors which occur when using a numerical Jacobian matrix. In this work, we discuss the importance of the Jacobian matrix in LMA and propose a design of a new EIS fitting engine. The new engine is based on a novel fitting scheme using limits and a symbolic Jacobian matrix instead of the numerical one, i.e. a strategy that has not yet been reported in any EIS study. We show that using a symbolic Jacobian matrix the algorithm convergence is superior to the one with a numerical Jacobian matrix. We also investigate how to improve poor convergence properties when we still have to use a numerical Jacobian matrix when analytic derivatives are not available.

Equivalent circuit parameter extraction of low‐capacitance high‐damping PTs

Existing equivalent circuit extraction techniques are inaccurate for piezoelectric transformers (PTs) with low-input capacitance or high damping. A new method is presented, offering improved accuracy in both damping resistance and resonant frequency extraction compared with state-of-the-art methods. Effectiveness is evaluated on two sample PTs, with the proposed method achieving up to 84% decrease in error compared with previous methods.

Study of Excitation Characteristics of Traction Machine/Drive Systems

In order to accurately evaluate the performance of a traction machine/drive system, it is necessary to have an accurate excitation source which considers current harmonics. In this paper, four machine/drive systems with different excitation sources have been modeled, simulated, and studied to evaluate the effects on permanent magnet synchronous machines (PMSMs) from different perspectives. In Model I, the excitation is an ideal sinusoidal current source with no harmonics. Model II is excited by an ideal sinusoidal voltage source regardless of the pulse width modification’s (PWM’s) influence. Model III takes into account the influence of current harmonics under space vector pulse width modulation (SVPWM) control. Model IV is based on the equivalent circuit extraction (ECE) model (a look-up table motor model). We simulate these four models and study the characteristics of the excitation sources, based on the observations of current harmonics, torque, electromagnetic force, computation time, and efficiency. Experiments are also conducted to show that Model III allows the most precise study of the considered system. Model IV is a good substitution, providing similar results with a shorter running time.

Analytical Equivalent Circuit Extraction Procedure for Broadband Scalable Modeling of Three-Port Center-Tapped Symmetric On-Chip Inductors

This paper presents a new, almost fully analytical methodology for component value extraction of a double- ${\pi }$ equivalent circuit model for three-port on-chip inductors from a given S-parameter dataset. The compact model provides an accurate fit over a wide frequency range from dc to beyond the self-resonance frequency (SRF) to a tabular input ${S}$ -parameter model describing a symmetric center-tapped on-chip inductor. The input dataset may be obtained from a measurement or from an electromagnetic field solver simulation. Using a passive broadband equivalent circuit instead of the original ${S}$ -parameters’ description is advantageous for circuit design, as it facilitates the convergence of transient simulations. The proposed approach carefully considers center-tap parasitics. Hence, the obtained equivalent circuit model fits the input inductor characteristics accurately not only for differential excitation but also in the common-mode and single-ended operation. Due to the fact that the proposed extraction approach is based on physical assumptions and analytical circuit decomposition, the obtained component values are physically meaningful and relate to geometry. Thus, this approach is suitable for the generation of scalable compact models, which can be used to speed-up inductor optimization during the RF circuit design. The proposed methodology has been verified on a three-port inductor realized in a 28-nm CMOS technology and measured up to 60 GHz. The extracted equivalent circuit model exhibits an accurate fit to the measured data over the entire frequency range in all operation modes. Finally, field-solver models are used to verify the scalability.

Effects of Gate-Length Scaling on Microwave MOSFET Performance

This paper focuses on the extraction of an accurate small-signal equivalent circuit for metal-oxide-semiconductor field-effect transistors (MOSFETs). An analytical modeling approach was developed and successfully validated through the comparison between measured and simulated scattering parameters. The extraction of the equivalent circuit elements allowed for the estimation of the intrinsic unity current-gain cutoff frequency, which is a crucial figure of merit for assessing the high-frequency performance. The experimental data show that the cutoff frequency of the tested devices exhibits a nearly ideal scaling behavior with decreasing gate length.

Planar ACS Fed Dual Band Antenna With DGS for Wireless Applications

A novel Asymmetric Coplanar Strip (ACS) fed antenna with Defected Ground Structure (DGS) suitable for dual application is presented. The Method of Moments (MoM) based mentor graphics IE3D electromagnetic solver has been used for this design. Dual band operation has been obtained by modifying the ground plane of the proposed design with spur-slots. It has been fabricated and tested with the overall size of 21x15x1.6 mm3 . The measured results indicate that the proposed antenna yields <-10dB impedance bandwidth of 13.13% and 9.86% which meets the requirement of 3.5GHz and 5.5GHz Wireless Local Area Network (WLAN) and World Wide Interoperability Microwave Access (WiMAX) applications. The approximate lumped equivalent circuit extraction for the proposed DGS fed dual band antenna has been discussed in detail. Because of its stable radiation patterns with low cross polarization,miniature size, high average antenna gain of 2.5dBi and good electromagnetic characteristics, the proposed antenna is a promising candidate for dual mode wireless communication devices.

On‐wafer characterization setup for model extraction and validation of high‐power GaN HEMT switches

SummaryAn ad hoc setup for complete on‐chip large‐signal characterization of both series and parallel high‐power GaN high‐electron‐mobility transistor switches has been developed. Thanks to its characteristics, arbitrary loads at both switch terminals (i.e., drain and source) for power levels up to tens of watts can be applied. The setup is suitable for extraction and validation of equivalent circuit and behavioral models. The potentiality of the presented solution is demonstrated by model validation and measurements of series and shunt C‐band high‐power GaN high‐electron‐mobility transistor switches from two commercial foundries. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Simulation and Measurement of Lightning-Impulse Voltage Distributions Over Transformer Windings

This paper presents: 1) a novel method for accurate high-frequency modeling of dry-type transformer windings based on magnetic and electric field simulations for parameter extraction of the detailed equivalent circuit of the entire winding system; 2) a method for fast and accurate transient solution of the circuit differential equations that describe the voltage distribution over the winding system; 3) an efficient, cheap, and nondestructive low-voltage measurement system based on a self-developed lightning-impulse generator; and 4) verification of the simulation results by comparison with measurement.

A High Frequency Equivalent Circuit and Parameter Extraction Procedure for Common Mode Choke in the EMI Filter

Power converters with high switching frequency generate conducted electromagnetic interference (EMI) noise. EMI filters are thus widely used to reduce these conducted noises for the compliance with electromagnetic compatibility standards. In this paper, a high-frequency (HF) equivalent circuit model for common mode (CM) chokes used in EMI filters is proposed together with its parameter extraction procedure. This procedure is based on impedance measurements and it incorporates an iterative rational function approximation fitting algorithm to extract the parameters in the model. The proposed model and procedure is applied to a planar CM choke which is used to realize an EMI filter. The simulated results of the filter show good agreement with the experimental ones. This extraction procedure is quite general and it can also be extended to identify the HF model of other passive components.

Parameter extraction of MEMS comb-drive near-resonance equivalent circuit: physically-based technique for a unique solution

A new extraction approach for MEMS comb-drive equivalent circuit parameters is presented. The proposed method eliminates the need for fitting and optimization by direct extraction from the measured data and, thus, avoids the nonuniqueness problem associated with fitting algorithms. A silicon-on-insulator-based MEMS comb-drive actuator is designed, fabricated, and measured, and its equivalent circuit is obtained by the proposed procedure. Analytical estimation for the uncertainty in the extracted values due to the discrete nature of the measurement frequency resolution is carried out. Uncertainty in the extracted values of the equivalent motional parameters is well below 0.6% when a 0.1-Hz frequency resolution is used. The method has been used to extract the resonator quality factor at both atmospheric and vacuum operations and can be extended to other types of resonators.

Closed-Form Design Formulas for the Equivalent Circuit Characterization of Ferrite Inductors

Miniature inductors, consisting of thin-wire solenoidal or toroidal coils wound on a high-permeability soft ferrite core, find wide application in the filtering of noise or electromagnetic interference at RF. An understanding of the high-frequency parasitic and packaging effects of the inductor, such as stray capacitance, magnetic losses, self-resonance, etc., can be gained from an equivalent circuit characterization of the inductor. In this paper, we present a rigorous experimental method to fully characterize the RF behavior of ferrite inductors. The equivalent circuit parameters of the inductor, namely, series inductance, loss resistance, and stray capacitance, as well as the effective permeability of the core, are extracted in closed form from an accurate measurement of the RF impedance, without recourse to cumbersome optimization procedures usually followed in equivalent circuit extraction from measured data. We derive design equations for the equivalent circuit elements based on the proposed measurement-based model, and rigorously validate the model using inductors wound on commercial toroidal and rod-type Ni-Zn ferrite cores.

DC and RF Performance of AlN/GaN MOS-HEMTs

This paper reports the DC and RF characteristics of AlN/GaN MOS-HEMTs passivated with thin Al2O3 formed by thermal oxidation of evaporated aluminium. Extraction of the small-signal equivalent circuit is also described. Device fabrication involved wet etching of evaporated Al from the Ohmic contact regions prior to metal deposition. This approach yielded an average contact resistance of ∼0.76Ω.mm extracted from transmission line method (TLM) characterisation. Fabricated two-finger AlN/GaN MOS-HEMTs with 0.2µm gate length and 100µm gate width showed good gate control of drain currents up to a gate bias of 3V and achieved a maximum drain current, IDSmax of ∼1460mA/mm. The peak extrinsic transconductance, Gmax, of the device was ∼303mS/mm at VDS =4V. Current-gain cut-off frequency, fT, and maximum oscillation frequency, fMAX, of 50GHz and 40GHz, respectively, were extracted from S-parameter measurements. For longer gate length, LG =0.5µm, fT and fMAX were 20GHz and 30GHz, respectively. These results demonstrate the potential of AlN/GaN MOS-HEMTs for high power and high frequency applications.

A Novel Time Domain Method to Extract Equivalent Circuit Model of Patterned Ground Structures

A novel and efficient time-domain method is proposed to extract the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> equivalent circuit model of the patterned ground structure. Based on time domain reflection analysis and Laplace transform, two analytical equations are derived to compute the corresponding <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> values. The non-ideal effect of the excitation source and nonzero rising time in time domain reflectometry (TDR) measurement and analysis is also considered. The equivalent <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> due to the conductor loss of the slot is obtained by the steady state DC level in TDR waveform. Two test samples are fabricated on a Duroid substrate and a FR4 board to verify the accuracy of the extracting method. The extracted <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> models for these two cases have a good agreement with the full-wave simulation and measurement results both in the time domain and frequency domain.

Extraction of SOS MOSFET RF equivalent circuit elements by LCR meter measurements

Two methods for the extraction of the small-signal equivalent circuit of high frequency silicon on sapphire (SOS) MOSFETs are compared. One technique employs microwave vector network analyser measurements in the 0.2-24GHz range, while the other uses a low frequency LCR meter at 100kHz to determine the circuit element values. Results presented show excellent agreement between the two methods. It is concluded that the low frequency method can be successfully used to extract high frequency circuit-model elements and reasons for this are offered. © 2010 The Institution of Engineering and Technology.