Small-signal Equivalent Circuit Research Articles

3D Smith Chart Constant Quality Factor Semi-Circles Contours for Positive and Negative Resistance Circuits

The article proves first that the constant quality factor (Q) contours for passive circuits, while represented on a 2D Smith chart, form circle arcs on a coaxal circle family. Furthermore, these circle arcs represent semi-circles families in the north hemisphere while represented on a 3D Smith chart. On the contrary we show that the constant Q contours for active circuits with negative resistance form complementary circle arcs on the same family of coaxal circles in the exterior of the 2D Smith chart. Also, we find out that these constant Q contours represent complementary semi-circles in the south hemisphere while represented on the 3D Smith chart for negative resistance circuits. The constant Q - computer aided design (CAD) implementation of the Q semi-circles on the 3D Smith chart is then successfully used to evaluate the quality factor variations of newly fabricated Vanadium dioxide inductors first, directly from their reflection coefficient, as the temperature is increased from room temperature to 50 degrees Celsius ({\deg}C). Thus, a direct multi-parameter frequency dependent analysis is proposed including Q, inductance and reflection coefficient for inductors. Then, quality factor direct analysis is used for two tunnel diode small signal equivalent circuits analysis, allowing for the first time the Q and input impedance direct analysis on Smith chart representation of a circuit, including negative resistance

The Dependence of the High-Frequency Performance of Graphene Field-Effect Transistors on Channel Transport Properties

This paper addresses the high-frequency performance limitations of graphene field-effect transistors (GFETs) caused by material imperfections. To understand these limitations, we performed a comprehensive study of the relationship between the quality of graphene and surrounding materials and the high-frequency performance of GFETs fabricated on a silicon chip. We measured the transit frequency (fT) and the maximum frequency of oscillation (fmax) for a set of GFETs across the chip, and as a measure of the material quality, we chose low-field carrier mobility. The low-field mobility varied across the chip from 600 cm2/Vs to 2000 cm2/Vs, while the fT and fmax frequencies varied from 20 GHz to 37 GHz. The relationship between these frequencies and the low-field mobility was observed experimentally and explained using a methodology based on a small-signal equivalent circuit model with parameters extracted from the drain resistance model and the charge-carrier velocity saturation model. Sensitivity analysis clarified the effects of equivalent-circuit parameters on the fT and fmax frequencies. To improve the GFET high-frequency performance, the transconductance was the most critical parameter, which could be improved by increasing the charge-carrier saturation velocity by selecting adjacent dielectric materials with optical phonon energies higher than that of SiO2.

28-nm FD-SOI CMOS RF Figures of Merit Down to 4.2 K

This work presents a detailed RF characterization of 28-nm FD-SOI nMOSFETs at cryogenic temperatures down to 4.2 K. Two main RF Figures of Merit (FoMs), i.e., current-gain cutoff frequency (f t ) and maximum oscillation frequency (f max ), as well as parasitic elements of the small-signal equivalent circuit, are extracted from the measured S-parameters. An improvement of up to ~130 GHz in f t and ~75 GHz in f max is observed for the shortest device (25 nm) at low temperature. The behavior of RF FoMs versus temperature is discussed in terms of small-signal equivalent circuit elements, both intrinsic and extrinsic (parasitics). This study suggests 28-nm FD-SOI nMOSFETs as a good candidate for future cryogenic applications down to 4.2 K and clarifies the origin and limitations of the performance.

Characteristic function approach to analytical parameter extraction, verification, and circuit calibration for small-signal equivalent circuit of field effect transistors

An analytical approach to parameter extraction and circuit calibration based on characteristic functions is proposed for small-signal equivalent circuit of field effect transistors (FETs). By using a π-topology of the original intrinsic sub-circuit to replace the conventional T-topology of a supplemental sub-circuit in the equivalent circuit, with the characteristic functions being fitted for both the intrinsic and extrinsic sub-circuits, high precision model parameters of the transistor can be extracted analytically without numerical curve fitting. The present method can serve as an effective way to verify and screen non-physical multiple solutions pertaining to conventional approaches. By comparing measured and simulated characteristic functions, series channel resistance along with channel inductance has been found critical for high frequency modeling. The validity of the present approach is demonstrated for 0.1 μm GaN HEMTs up to 65 GHz.

Direct parameter extraction method for InP heterojunction bipolar transistors based on the combination of T- and π-models up to 110 GHz

A parameter-extraction approach for determination of the small-signal equivalent circuit model for InP/InGaAs double heterojunction bipolar transistors is presented in this paper. This method combines the advantages of conventional T- and π-type equivalent-circuit topologies. All the equivalent circuit elements are only extracted analytically from S-parameter data without any numerical optimization. The agreements between the measured and the model-calculated data are excellent in the frequency range of 0.1–110 GHz.

Describing Broadband Terahertz Response of Graphene FET Detectors by a Classical Model

Direct power detectors based on field-effect transistors are becoming widely used for terahertz applications. However, accurate characterization at terahertz frequencies of such detectors is a challenging task. The high-frequency response is dominated by parasitic coupling and loss associated with contacts and overall layout of the component. Moreover, the performance of such detectors is complicated to predict since many different physical models are used to explain the high sensitivity at terahertz frequencies. This makes it hard to draw important conclusions about the underlying device physics for these detectors. For the first time, we demonstrate accurate and comprehensive characterization of graphene field-effect transistors from1 GHz to 1.1 THz, simultaneously accessing the bias dependence, the scattering parameters, and the detector voltage responsivity. Within a frequency range of more than1 THz, and over a wide bias range, we have shown that the voltage responsivity can be accurately described using a combination of a small-signal equivalent circuit model, and the second-order series expansion terms of the nonlinear dc I-V characteristics. Without bias, the measured low-frequency responsivity was 0.3 kV/W with the input signal applied to the gate, and 2 kV/W with the input signal applied to the drain. The corresponding cutoff frequencies for the two cases were 140 and 50 GHz, respectively. With a300-GHz signal applied to the gate, a voltage responsivity of 1.8 kV/W was achieved at a drain-source current of 0.2 mA. The minimum noise equivalent power was below 30 pW/ √Hz in cold mode. Our results show that detection of terahertz signals in graphene field-effect transistors can be described over a wide frequency range by the nonlinear carrier transport characteristics obtained at static electrical fields. This finding is important for explaining the mechanism of detection and for further development of terahertz detectors.

Uniformity investigation of pHEMTs small-signal parameters for pre and post multilayer fabrication in 3D MMICs

The main aim of this paper is to investigate the uniformity of pHEMTs small-signal parameters before and after multilayer fabrication in 3D MMICs. Seven samples of pre-and post-multilayer fabricated pHEMTs at different representative locations to reflect the degree of consistency. This study deals with the fabrication, measurement, simulation, and comparison of both sample in form of means and slandered deviation. On wafer scattering (S-) parameter measurement has been accomplished to investigate the small signal equivalent circuit parameters up to 50 GHz. The main finding was observed that all parameters are increased after multilayer fabrication except the transconductance and the parasitic inductances. The employment of the 3D-MMIC technology does not induce any evident extinction of the pHEMTs performance utilizing seven different samples of pre-and post-multilayer fabrication.

Small-Signal Equivalent Circuit Model of Photonic Crystal Fano Laser

We develop a new small-signal equivalent circuit model for photonic crystal Fano laser based on standard linearized equations. The results are compared with those obtained by the numerical simulation approach. This novel circuit model being a cost-effective fast tool is advantageous over solving the rate equations for designing and extending the photonic crystal Fano laser. Using this circuit model, we have investigated the laser current modulation via the conventional method and via modulating the Fano mirror. The results show that the bandwidths of the amplitude modulation of the laser through-port and the frequency modulation of its cross port are both in the range of THz. It is also shown that the larger the nanocavity detuning, the greater the relaxation oscillation frequency, increasing the possibility of widening the laser bandwidth, through which the modulation efficiency may decrease. Moreover, we show that the longer the laser active region, the narrower the modulation response bandwidth. The results show that the circuit model accurately explains the photonic crystal Fano laser small-signal modulation characteristics.

Accurate Small-Signal Equivalent Circuit Modeling of Resonant Tunneling Diodes to 110 GHz

This article presents a novel, on-wafer deembedding technique for the accurate small-signal equivalent circuit modeling of resonant tunneling diodes (RTDs). The approach is applicable to stabilized RTDs, and so enables the modeling of the negative differential resistance (NDR) region of the device’s current–voltage ( $I$ – $V$ ) characteristics. Furthermore, a novel quasi-analytical procedure to determine all the equivalent circuit elements from the deembedded S-parameter data is developed. Extraction results of a $10\,\,\mu \text{m}\,\,\times 10\,\,\mu \text{m}$ stabilized, low-current density RTD at different bias points show excellent fits between modeled and measured S-parameters up to 110 GHz.

A Novel Parameter Extraction Technique of Microwave Small-Signal Model for Nanometer MOSFETS

In this letter, the MOSFET small-signal equivalent circuit models under different bias conditions are analyzed for microwave applications. A novel parameter extraction technique named multi-parameter scanning (MPS) method is proposed. Under zero-bias, the MPS technique is used to extract the extrinsic parasitics and internal capacitances without using any high-frequency or low-frequency approximations. Extrinsic series resistances and substrate network are assumed to be bias-independent or at least have weak bias dependence. Therefore, after removing the extrinsic parasitics, the intrinsic elements in the saturation region can be formulated and directly extracted through linear-fitting to the measurement data. A set of nMOS test structures fabricated on the Shanghai Huali Microelectronics Corporation (HLMC) RF CMOS process are used for the investigation and validation of the proposed technique.

Modeling and Control of Double-Sided LCC Compensation Topology with Semi-Bridgeless Active Rectifier for Inductive Power Transfer System

This paper proposes the modeling and design of a controller for an inductive power transfer (IPT) system with a semi-bridgeless active rectifier (S-BAR). This system consists of a double-sided Inductor-Capacitor-Capacitor (LCC) compensation network and an S-BAR, and maintains a constant output voltage under load variation through the operation of the rectifier switches. Accurate modeling is essential to design a controller with good performance. However, most of the researches on S-BAR have focused on the control scheme for the rectifier switches and steady-state analysis. Therefore, modeling based on the extended describing function is proposed for an accurate dynamic analysis of an IPT system with an S-BAR. Detailed mathematical analyses of the large-signal model, steady-state operating solution, and small-signal model are provided. Nonlinear large-signal equivalent circuit and linearized small-signal equivalent circuit are presented for intuitive understanding. In addition, worst case condition is selected under various load conditions and a controller design process is provided. To demonstrate the effectiveness of the proposed modeling, experimental results using a 100 W prototype are presented.

Differential Electro-Optical Equivalent Circuit Model of a Vertical-Cavity Surface-Emitting Laser for Common-Mode Rejection Ratio Estimation

Vertical-cavity surface-emitting lasers (VCSEL) can be used to achieve galvanic isolation of systems operating in environments with high levels of electromagnetic noise. A small-signal differential electro-optical equivalent circuit model of a VCSEL is presented, in contrast to the usual single-ended models. The electro-optical and opto-electrical conversion of the signal is modelled, as well as the electrical characteristics of the VCSEL chip. The circuit model is based on an approach combining Y-parameters and mixed-mode S-parameters. Compared to conventional models that are aimed at describing the internal laser dynamics, the presented model is primarily focused on modelling the asymmetric parasitics in a differential VCSEL configuration. The parasitics between the 5-lead VCSEL TOSA package and the test printed circuit board are modelled. The impact of the asymmetry of the parasitics from the laser anode and cathode towards the ground is examined. The differential VCSEL model is used to estimate the transfer coefficients for both differential-mode and common-mode input signals. The ratio between the wanted and unwanted signal is expressed as the common-mode rejection ratio (CMRR). The model covers the frequency bandwidth up to 4 GHz required for integrated circuit EMC and ESD measurements.

Circuit Topology and Small Signal Modeling of Variable Duty Cycle Controlled Three-Level LLC Converter

With a view to regulate the output voltage with fixed frequency, without using any additional component or complex modulation technique, a topology of a variable duty controlled three-level LLC converter is proposed and an equivalent small signal model for Electric Vehicle (EV) charger applications is deduced in this paper. The steady state equations of each operating region are derived in time domain. Based on an Extended Describing Function (EDF) approach, a small signal equivalent circuit is modeled which includes both frequency and duty controlled terms. The equivalent circuit is further simplified to derive a transfer function of duty control to output voltage. The transfer function is verified through simulation software. Analyzing the transfer function, a voltage controller is designed and implemented with a PI compensator. The simulation results of the proposed control schemes are illustrated and discussed. The topology is compared to a conventional frequency control topology and the merits of the proposed topology are presented.

An improved current mode logic latch for high‐speed applications

SummaryIn this paper, an improved current mode logic (CML) latch design is proposed for high‐speed on‐chip applications. Transceivers use various methods in fast data transmission in wireless/wire‐line application. For an asynchronous transceiver, the improved CML latch is designed using additional NMOS transistors in conventional CML latch which helps to boost the output voltage swing. The proposed low‐power CML latch‐based frequency divider is compatible for higher operating frequency (16 GHz). Next, the delay model is also developed based on small signal equivalent circuit for the analysis of the proposed latch. The output voltage behavior of the proposed latch is analyzed using 180‐nm standard CMOS technology.

Small-signal equivalent circuit for double quantum dots at low-frequencies

Due to the quantum nature of current flow in single-electron devices, new physical phenomena can manifest when probed at finite frequencies. Here, we present a semiclassical small-signal model approach to replace complex single-electron devices by parametric circuit components that could be readily used in analog circuit simulators. Our approach is based on weakly driven quantum two-level systems, and here, we use it to calculate the low frequency impedance of a single-electron double quantum dot (DQD). We find that the total impedance is composed of three elements that were previously considered separately: a dissipative term, corresponding to the Sisyphus resistance, and two dispersive terms, composed of the quantum and tunneling capacitance. Finally, we combine the parametric terms to understand the interaction of the DQD with a slow classical electrical oscillator which finds applications in nonresonant state readout of quantum bits and parametric amplification.

Multi-Channel AlGaN/GaN Lateral Schottky Barrier Diodes on Low-Resistivity Silicon for Sub-THz Integrated Circuits Applications

This paper presents novel multi-channel RF lateral Schottky-barrier diodes (SBDs) based on AlGaN/GaN on low resistivity (LR) ( ${\sigma }={0.02}\,\,{\Omega }$ .cm) silicon substrates. The developed technology offers a reduction of 37 % in onset voltage, $\text{V}_{{{ON}}}$ (from 1.34 to 0.84 V), and 36 % in ON-resistance, $\text{R}_{{{ON}}}$ (1.52 to 0.97 to ${\Omega }$ .mm) as a result of lowering the Schottky barrier height, ${\Phi }_{\text {n}}$ , when compared to conventional lateral SBDs. No compromise in reverse-breakdown voltage and reverse-bias leakage current performance was observed as both multi-channel and conventional technologies exhibited $\text{V}_{{{BV}}}$ of ( $\text{V}_{{ {BV}}}>{30}$ V) and $\text{I}_{\text {R}}$ of ( $\text{I}_{{R}} /mm), respectively. Furthermore, a precise small-signal equivalent circuit model was developed and verified for frequencies up to 110 GHz. The fabricated devices exhibited cut-off frequencies of up to 0.6 THz, demonstrating the potential use of lateral AlGaN/GaN SBDs on LR silicon for high-efficiency, high-frequency integrated circuits applications.

Mechanisms of Current Transport and Resistive Switching in Capacitors with Yttria-Stabilized Hafnia Layers

The peculiarities of resistive switching in capacitors with yttria-stabilized hafnia layers were studied. The characteristics of current transport in the initial state and after electroforming and resistive switching at different temperatures were examined. The parameters of a small-signal equivalent circuit of a capacitor were determined for switching into low- and high-resistance states. These parameters suggest that the resistance of filaments changes after each successive switching. This provides an opportunity to use such measurements to determine the nature of resistive switching and verify the reproducibility of its parameters. The contribution of electron traps to switching was revealed. Ion migration polarization was observed at temperatures above 500 K, and the activation energy of ion migration and the ion concentration were determined. The effect of resistive switching under the influence of temperature was observed and interpreted for the first time.

Analysis of Modular DCM Flyback Converters in Input Parallel Connections with Parametric Mismatches

This paper analyzes the effects of parameter mismatches in the balance mechanism of modular DC-DC Flyback converters operating in discontinuous conduction mode. The natural current and voltage distributions among modules are evaluated when mismatches on duty cycles, transformer magnetizing inductances and transform turns ratios are present. From these results, the critical values of inductances and duty cycles that assure the discontinuous operation are equated. The small-signal equivalent circuit for Input-Parallel-Output-Series and Input-Parallel-Output-Parallel connections are found, followed by a simple control strategy. The theoretical analysis is verified by experimental results obtained with a prototype composed of three 200 W Flyback modules, with a rated power of 600 W and maximum efficiency of 95.5%. Results corroborate the proposed equations for the steady state balance and dynamic behavior of both connections, highlighting the modular characteristic of the converter.

Dynamic modeling and analysis of the bidirectional DC-DC boost-buck converter for renewable energy applications

This paper focuses on the modeling, dynamic analysis, and simulation of the bidirectional DC-DC boost-buck power converter. The switching sequence applies different duty cycles in the input and output stages, resulting in full regulation of the system variables. By using this strategy, the input stage can be regulated disregarding perturbations in the output leg, as well as the output stage can be controlled independently of the effects of disturbances in the input part; which gives significant robustness to the converter. Based on the switching actions, the state-space average equations are derived, accomplishing the base to obtain the small-signal equations and equivalent small-signal circuits. The open-loop transfer functions are developed, besides the input and output impedance, and the audio susceptibility. Simulation results indicate that the proposed model can predict the dynamic behavior of the system in a wide range of the frequency spectrum, and the results in the time domain are in perfect agreement with the model predictions under disturbances of the control variables, variations of the value of the supply voltage and load changes.

Modeling a Dual-Mode Controller Design for a Quasi-Resonant Flyback Converter

The proposed system can overcome the disadvantage of a high peak current in quasi-resonant fly-back (QRF) converters when operated under heavy load conditions. The operating mode and control scheme of a QRF converter with dual-mode control were established and analyzed. The dual-mode control scheme not only enabled a valley-switching detection technique that satisfied the zero-voltage switching condition but also provided a constant frequency mechanism to reduce the conduction loss in QRF converters when operated in a continuous conduction mode and under heavy load conditions. The small-signal equivalent circuit model of QRF converter circuits was constructed using an average approximation method. The technological advancement of a QRF converter with a dual-mode controller was presented in this study. The circuit simulation result of the proposed QRF converter with a mix control scheme proved that the derived circuit component parameters meet the requirements of the converter.