Distributed Circuit Elements Research Articles

An operando ORP-EIS study of the copper reduction reaction supported by thiourea and chlorides as electrorefining additives

Additives are used in metal electroreduction processes to obtain a smooth and optimal metal deposit. However, the mechanism with which these additives influence the metal deposition is poorly understood. Operando odd random phase electrochemical impedance spectroscopy (ORP-EIS) experiments have been performed to study the effect of a chloride-thiourea additive mixture on the reduction of copper ions in a sulfuric acid solution. This additive mixture is crucial in the copper electrorefining process. An optimal experimental design and a well-founded methodology is applied to study this complex additive mixture. The ORP-EIS data is studied to analyze non-stationarities and non-linearities and the time-varying impedance is resolved when necessary. Two equivalent circuits are proposed to model the impedance data and the model parameters are linked to physical processes in the system. The use of the time-varying impedance when studying thiourea in a plating process and the use of distributed circuit elements in the EIS model is discussed.

Frequency response of electrolyte-gated graphene electrodes and transistors

The interface between graphene and aqueous electrolytes is of high importance for applications of graphene in the field of biosensors and bioelectronics. The graphene/electrolyte interface is governed by the low density of states of graphene that limits the capacitance near the Dirac point in graphene and the sheet resistance. While several reports have focused on studying the capacitance of graphene as a function of the gate voltage, the frequency response of graphene electrodes and electrolyte-gated transistors has not been discussed so far. Here, we report on the impedance characterization of single layer graphene electrodes and transistors, showing that due to the relatively high sheet resistance of graphene, the frequency response is governed by the distribution of resistive and capacitive circuit elements along the graphene/electrolyte interface. Based on an analytical solution for the impedance of the distributed circuit elements, we model the graphene/electrolyte interface both for the electrode and the transistor configurations. Using this model, we can extract the relevant material and device parameters such as the voltage-dependent intrinsic sheet and series resistances as well as the interfacial capacitance. The model also provides information about the frequency threshold of electrolyte-gated graphene transistors, above which the device exhibits a non-resistive response, offering an important insight into the suitable frequency range of operation of electrolyte-gated graphene devices.

Robust optimization of microwave structures using cosimulation‐based surrogate models

AbstractA robust and computationally efficient technique for design optimization of microwave structures is proposed.We exploit cosimulation‐based surrogate models with the essential couplings evaluated using electromagnetic (EM) solver and most of the designable parameters modeled by distributed circuit elements with physical dimensions corresponding to those of the structure being optimized. Good prediction capability of the surrogate model is ensured by the space mapping‐based alignment process. It is demonstrated that the proposed methodology is able to yield a satisfactory design at the computational cost corresponding to two or three EM simulations of the optimized structure. The design of two microstrip filters is presented for the sake of illustration. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:130–135, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25637

Parasitic Compensation Design Technique for a C-Band GaN HEMT Class-F Amplifier

A class-F/inverse class-F load circuit design method that includes parasitic elements such as drain-source capacitance and bonding wire inductance has been developed. For the class-F load circuit design, a reactance function which has zeros at even harmonic frequencies and poles at odd harmonic frequencies is expanded to an -ladder circuit including parasitic elements through the use of the second Cauer canonical form. For the inverse class-F load circuit design, the zero points and the poles are exchanged. One stage of the -ladder circuit can be approximately replaced to a distributed circuit element for higher frequency operation. The proposed method allows parasitic compensation up to an arbitrary harmonic order by adding zeros and poles. Additionally, if distributed circuit elements are used, the method also compensates frequency dispersive characteristics of microstrip lines. According to the proposed method, a class-F amplifier using an AlGaN-GaN HEMT has been fabricated at 5.8 GHz. The fabricated class-F amplifier delivered high efficiency characteristics, with a maximum drain efficiency of 79.9%, a maximum power-added efficiency (PAE) of 71.4%, and an output power of up to 33.4 dBm at 5.86 GHz.

Self-heating in a coupled thermo-electric circuit-device model

The self-heating of a coupled thermo-electric circuit-semiconductor system is modeled and numerically simulated. The system consists of semiconductor devices, an electric network with resistors, capacitors, inductors, and voltage sources, and a thermal network. The flow of the charge carriers is described by the energy-transport equations coupled to a heat equation for the lattice temperature. The electric circuit is modeled by the network equations from modified nodal analysis coupled to a thermal network describing the evolution of the temperatures in the lumped and distributed circuit elements. The three subsystems are coupled through thermo-electric, electric circuit-device, and thermal network-device interface conditions. The resulting system of nonlinear partial differential-algebraic equations is discretized in time by the 2-stage backward difference formula and in space by a mixed finite-element method. Numerical simulations of a one-dimensional ballistic diode and a frequency multiplier circuit containing a pn-junction diode illustrate the heating of the semiconductor device and circuit resistors.

Electrical impedance spectroscopy in relation to seed viability and moisture content in snap bean (Phaseolus vulgaris L.)

A method, electrical impedance spectroscopy (EIS), is introduced to study seed viability non-destructively. Snap bean (Phaseolus vulgaris L.) seeds were studied by EIS to determine the most sensitive EIS parameter(s) and the optimal range of moisture content (MC) for separation of viable and non-viable seeds. Hydrated seeds exhibited two impedance arcs in the complex plane at the frequency range from 60 Hz to 8 MHz, and impedance spectra of viable and non-viable seeds differed. The hydrated seeds were best-modelled by an equivalent electrical circuit with two distributed circuit elements in series with a resistor (Voigt model). Moisture content and seed viability had strong effects on the EIS parameters. The most sensitive EIS parameters for detecting the differences between viable and non-viable seeds were the capacitance log(C2), the resistance R2, the resistance ratio R2/R1 and the apex ratio, which all represent specific features of the impedance spectrum. The highest differentiation in the EIS parameters between the viable and non-viable seeds occurred in partially imbibed seeds between MC of 40 and 45% (fresh weight basis).

Physics-based CAD models for the analysis of vias in parallel-plate environments

In this paper, physics-based computer-aided-design (CAD) models for through and buried vias in parallel-plate environments are presented based on radial transmission-line theory. The crosstalk power transferred by the TEM parallel-plate mode between vias is characterized, and extended to the treatment of vias in finite substrates by means of image theory. The presented CAD models can be combined with lumped and distributed circuit elements, as well as linear and nonlinear devices, providing an accurate and fast procedure for the global modeling of high-speed electronic circuits. The corresponding simulation time for representative single or multiple via configurations has been drastically reduced compared to full-wave simulations while maintaining comparable accuracy.

Design of planar circuit structures with an efficient magnetostatic-field solver

We introduce a highly efficient field solver for the calculation of the quasi-static magnetic field in order to design lossless planar circuit elements with nearly arbitrary shape. The field solver is based on a finite-difference (FD) formulation of a scalar magnetic potential, using potential partitioning surfaces (PPS's). The modeling of the quasi-static fields in distributed circuit elements leads to the development of lumped element equivalent circuits in a very fast and efficient way. For structures with sizes far below the wavelength, the equivalent circuits can be derived in a direct way. For the field modeling of larger structures, the quasi-static field solver can be used in a hybrid full-wave analysis as well. Numerical examples are presented for different planar-circuit elements.

Effects of freeze-thaw injury on parameters of distributed electrical circuits of stems and needles of Scots pine seedlings at different stages of acclimation

Frost hardening and frost injury of both the stems and needles of Scots pine (Pinus sylvestris L.) seedlings were studied by electrical impedance analysis. This impedance analysis was based on equivalent circuits with distributed circuit elements (DCE). A double-DCE model for stems and two single-DCE models for needles provided excellent fit to the experimental impedance data. However, the single-DCE model for needles which takes into account the asymmetry of the impedance arc proved more appropriate than the symmetric model. Several parameters changed in proportion to frost injury. In stems, extracellular resistance and one relaxation time decreased with increasing damage, whereas intracellular resistance remained relatively unchanged

Adaptive enhancement of timing accuracy and waveform quality in high-performance IC testers

A means of improving edge-placement accuracy and waveform quality in high-speed high-performance integrated circuit test and verification systems is being developed. Its aim is to minimize timing skew, maintain signal integrity at the device under test (DUT), and actively reduce waveform errors caused by uncertain DUT loading and transmission path imperfections. The path between the pin electronic card (PEC) and the DUT is modeled using a signal flow graph (SFG) technique. The model contains both lumped and distributed circuit elements, each of which is represented by scattering parameters. Frequency domain reflectometry (FDR) is used to measure voltage reflection coefficients of both the load (DUT) and PEC receiver ends of the transmission path. Load models are obtained through a direct search optimization algorithm. Examples of time domain compensation are presented for matched and mismatched transmission paths. >

Impedance spectroscopy: old problems and new developments

The generality, scope, and limitations of Impedance Spectroscopy (IS) are discussed, with emphasis on unsupported conditions in ionic systems. For such conditions, the maximum reaction rate which can be determined from IS data is limited. The finite-length-Warburg diffusion frequency responses of unsupported and supported situations are simplified and compared, and similarities and differences emphasized. Two types of ambiguity possibly present in fitting IS data to equivalent circuits are discussed, one intrinsic and the other associated with distributed circuit elements. Powerful new features have been added to the author's compex nonlinear least squares (CNLS) fitting program, and the results of a Monte Carlo simulation study of bias and statistical uncertainty in CNLS fitting of equivalent circuit data are discussed. The program now incorporates new variable weighting choices which can greatly minimize such bias. It also allows two unknown weighting parameters of the error variance model to be automatically estimated during the least squares fitting, thus best matching the weighting to the data and yielding most appropriate estimates of the parameters of the fitting model.

S parameters: a practical education

The course on radiofrequency amplifier design by the technique of S-parameters offered at Virginia Polytechnic Institute and State University is described with some emphasis on the associated laboratory portion of the course. The course begins with microstrip amplifier construction and the modeling of both lumped and distributed circuit elements. Attention is then given to the design of a transistor amplifier in the UHF spectrum. Biasing and parameter measurement are first considered. Matching networks are then designed and installed, followed by the measurement of several amplifier specifications. In five years of running the laboratory course there has never been a case of a student failing to end the course with a working amplifier. Typical amplifiers (900 MHz) have gains of 12 and 13 dB, input and output reflection coefficients below 0.05, third-order intercept points of 0-10 dBm (input), and noise figures near 5 dB. >

Some small-signal relaxation response models and their limiting responses

This paper is concerned with the small-signal time and frequency response of anomalous dispersion and distributed circuit elements in either conductive or dielectric systems. In the course of responding to recently published comments and criticisms of Dissado and Hill, a detailed discussion is presented of high and low frequency limiting response possibilities, with a special consideration of such response for a single broad dispersion region. For such a region the Dissado-Hill criticisms are shown to be either incorrect, inappropriate or irrelevant. The usefulness of distribution of relaxation and distribution of activation energy approaches is demonstrated and the response of a general exponential-distribution-of-activation-energies model is compared with that of a relaxation response function which was derived by Dissado and Hill in two different ways, with the two approaches based on different physical assumptions. It is concluded that the Dissado-Hill response function does not lead to the necessary low and high frequency limiting response for a single broad dispersion region, is essentially limited to dielectric materials and cannot describe intrinsically conductive ones which can pass DC, and is severely limited in its temperature dependence possibilities. By comparison, these limitations and restrictions do not apply to the distribution of activation energy model, one which has been shown capable of fitting a great variety of conductive and dielectric system experimental data for thermally activated situations.

A flexible procedure for analyzing impedance spectroscopy results: Description and illustrations

General considerations in nonlinear least squares fitting of small-signal ac frequency response data (conductive or dielectric systems) are first discussed. A very general and flexible complex nonlinear least squares fitting (CNLS) program (LOMFP) is described which runs on microcomputers of the PC and AT type. Advantages and disadvantages of LOMFP are discussed and compared to those of a recent CNLS program developed by Boukamp. LOMFP incorporates many thousands of equivalent circuits fitting possibilities and ten different distributed circuit elements which can be used in these circuits. Its fitting is both speedy and accurate, and it provides considerable insurance against confusing local minima fits with true least squares fits. It is optimized for fitting real, imaginary, or complex data of either partly conducting or purely dielectric character, and it incorporates great flexibility in handling and fitting data in different forms (different immittance levels and rectangular or polar representation). Seven different data weighting choices are provided. Exact synthetic data were generated from a typical Impedance Spectroscopy equivalent circuit, and the effects on CNLS fitting were investigated of rounding the exact data to 4, 3, and 2 decimal places. We present the results of an extensive study of the effects of transforming exact data to different immittance levels and representations and then rounding to two places or of transforming rounded 2-place data directly. We conclude that real data should not be transformed from its original measured form before carrying out CNLS fitting. Finally, the effects were investigated of various kinds of weightings on CNLS fitting of 2-place data, leading to the conclusion that in spite of its advocacy and use by Zoltowski and Boukamp, modulus weighting generally yields misleading and appreciably worse CNLS fitting results than does proportional weighting. The LOMFP program (source and executable files) is available from the first author.

Impedance spectroscopy and its use in analyzing the steady-state AC response of solid and liquid electrolytes

Impedance spectroscopy is defined and some of its applications illustrated for both liquid and solid electrolyte situations. Particular emphasis is placed on complex least squares fitting of small-signal frequency response data at various immittance levels. Most such response data must be fit to an equivalent electrical circuit since a detailed microscopic model of the response is usually lacking. It is found for most ionic response data, as well as that from purely dielectric systems, that one usually must include in the equivalent circuit one or more distributed circuit elements in addition to the usual ideal elements, such as resistors and capacitors. Important distributed circuit elements useful in equivalent circuits are described. A number of actual equivalent circuits used in the past for both liquid and solid electrolytes are presented and compared. Equivalent circuits following from detailed continuum models of the electrical response of blocking and partly conducting systems are compared, and it is shown that some of the same circuits may be used even in the presence of dc bias which usually makes the charge distribution in the system very inhomogeneous. Because frequency response data have often been inadequately analyzed, the author's general and powerful complex nonlinear least squares fitting program is now available for use by others.

Distributed circuit elements in impedance spectroscopy: A unified treatment of conductive and dielectric systems

Distributed elements have a long-established position in the field of impedance spectroscopy (IS). Presented here is a survey of a number of the more common elements, including the new distribution-of-activation-energies element. A unified treatment of the different IS levels (impedance, admittance, complex modulus, and complex dielectric constant) is proposed, enabling standard distributed elements to be used in the fitting of data taken from either conductive or dielectric materials. Various distributed elements are discussed and their responses are shown graphically and compared to one another in both 2-D complex plane projections and 3-D perspective plots.

Some simple equivalent circuits for ionic conductors

Some equivalent circuits which involve one or two distributed circuit elements are discussed. These circuits are useful in fitting small-signal frequency response data for solids and liquids. A fitting circuit recently proposed by Bruce to represent distributed bulk effects in conducting materials is shown to be closely related to earlier work. Although Bruce demonstrated that his circuit fitted certain data better than a simple alternative circuit, it is not physically realistic in the high frequency region. We investigate how well the response of the Bruce circuit (which involves one distributed circuit element and three ideal elements) can be simulated by that of simpler circuits, ones which involve a single unified distributed element, possibly in parallel with a single ideal capacitor. The usefulness of several different distributed elements, most of which have been widely used for data fitting in the past , is compared. Complex nonlinear least squares fitting results suggest that several of the simpler circuits considered are preferable to the proposed Bruce circuit for fitting of most ionic-conductor frequency response data. Finally, two structurally different equivalent circuits which involve two distributed elements each, so they can represent distributed interface as well as bulk effects, are compared and found to be able to simulate each other quite well under certain conditions. Problems which thus arise in choosing the best equivalent circuit for data fitting are discussed.

When is a device passive?

AbstractPassivity is perhaps the most basic concept in circuit theory. Unfortunately, the existing definitions of passivity are too restrictive and often contradict one another. In this paper, a new passivity definition is proposed which is applicable to all n‐port and (n + 1)‐terminal devices—including time‐varying, non‐linear, and distributed circuit elements. This definition generalizes and reconciles several recent conflicting definitions.

GaAs monolithic Lange and Wilkinson couplers

An important part of monolithic microwave integrated circuits are the passive distributed circuit elements which divide and combine RF signals. This paper describes the design and performance of a monolithic GaAs X-band three-port Wilkinson coupler [1] and a monolithic GaAs X-band four-port interdigitated Lange coupler [2], [3]. These couplers are useful both as power dividers and power combiners. In the Wilkinson, the input power is split equally between the output ports with zero differential phase shift. For the Lange, there is a phase difference of 90° between the outputs. All ports are well matched and the output ports are highly isolated. The transmission mode chosen for these couplers is microstrip on semi-insulating GaAs with conductor-to-ground plane spacing of 0.1 mm. This low-loss, high permittivity medium is compatible with the present monolithic GaAs FET technology which thus allows combining more complicated monolithic microwave integrated circuits on a single chip. The fabrication process takes advantage of the technology developed for proeessfng GaAs FET's. For example, connecting the coupling conductors for the Lange coupler requires RF crossovers. To minimize crossover capacitance, an air-bridge interconnection technique is used. Calculated coupling, isolation, and VSWR data for the Wilkinson and Lange couplers are compared with actual measured performance showing good agreement with expected results. Measured loss, minus fixture contributions, shows 0.25 dB for the Wilkinson and 0.75 dB for the Lange.

A circuit technique for broadbanding the electronic tuning range of Gunn oscillators

A circuit technique is described whereby the electronic tuning range obtained by varactor tuning solid-state oscillators, such as Gunn oscillators, can be improved. The principle of the technique has been demonstrated by doubling the tuning range obtained from a coaxial X-band Gunn oscillator using distributed circuit elements. An analytical expression for the improved tuning range is presented and predictions for the improvement in an existing microstrip X-band oscillator using chip devices given.