RC Time Constant Research Articles

A Modified Equivalent Circuit Model for High-Speed InGaAs/InAlAs Avalanche Photodiodes

In this paper, we establish a modified equivalent circuit model suitable for all bias conditions for high-speed InGaAs/InAlAs avalanche photodiodes (APDs). The model includes three mechanisms: the carrier transit time, the avalanche buildup time, and the RC time constant. The physical meaning of each component in it is elaborated in detail. Component parameters in it of the demonstrated APD are extracted by fitting the RF reflection parameters S22 and transmission parameters S21 measured at different bias voltages. To verify the accuracy and regularity of these parameters, some relevant finite element simulations and theoretical analyses are carried out. Values and regularities of these parameters are consistent with the results of finite element simulations and theoretical analyses. With the help of this model and these accurate parameters, impedance distribution and bandwidth limiting factors of the demonstrated APD are analyzed thoroughly. According to the above analysis results, the performance optimization scheme for the demonstrated APD is obtained.

Design and robustness improvement of high‐performance LNA using 0.15 μm GaN technology for X‐band applications

SummaryIn this paper, we present a highly robust GaN‐based X‐band low‐noise amplifier (LNA) showing promising small‐signal and noise performance as well as good linearity. The LNA is fabricated using in‐house 0.15 μm AlGaN/GaN on a SiC HEMT process. Owing to the optimum choice of HEMT topologies and simultaneous matching technique, LNA achieves a noise figure better than 2 dB, output power at 1 dB gain compression higher than 19 dB, input and output reflection coefficients better than −9 and −11 dB, respectively. The small‐signal gain of LNA is more than 19 dB for the whole band, and NF has a minimum of 1.74 dB at 10.2 GHz. LNA obtains an OIP3 up to 34.2 dBm and survives input power as high as 42 dBm. Survivability is investigated in terms of gain compression and forward gate current. Reverse recovery time (RRT), a crucial parameter for radar front‐ends, is explored with respect to the RC time constant and trap phenomenon. The analysis shows that the significant contribution in RRT is due to traps while the RC time constant is in the nanoseconds range. Moreover, this study also addresses the requirement and choice of a DC gate feed resistor for the subsequent stages in a multi‐stage design. The size of the designed LNA chip is 3 mm 1.2 mm only.

An Inquiry Approach to Effective Use of Instrumentation: An Example from RC Circuits

In this article, we present an intriguing experimental exercise that does not fall foul of improper use of instrumentation. The activity is designed as an electronics exercise where the role of the instruments in the measurement of the RC time constant is considered. Essentially, we study the accuracy and precision of a measurement of the RC time constant in a series circuit with an oscilloscope as a function of the value of the resistor, against the predicted linear model of τ = RC. As the value of the resistor approaches the value of the impedance of the oscilloscope, the time constant deviates from the linear model. We show how to adapt the model to account for this and create a mathematical model that agrees with the measurements. It is hoped that such an exercise will solidify a rule of effective use of oscilloscopes—that the resistance of the circuit should be much lower than the impedance of the scope—in the mind of the student.

Correlation between the transient variation in positive/negative pulse voltages and the growth of PEO coating on 7075 aluminum alloy

A bipolar pulse mode is usually used in the plasma electrolytic oxidation (PEO) process of aluminum alloys. The negative pulse can eliminate the cavity and improve the compactness of the PEO coating. However, the effect mechanism of negative pulse on the electrical signal of PEO is not clearly understood. In this study, a method of improving the compactness of PEO coating and reduce energy consumption under different transient voltages and current waveforms is established and discussed. An equivalent circuit of RC series corresponding to the coating and the electric double layer during the PEO process was proposed to analyze the effect of negative pulse on the compactness of the PEO coating. Results showed that the voltage in the T+off stage can be rapidly reduced to less than the breakdown voltage by introducing negative pulses, and the discharge of unextinguished sparks on the sample surface was inhibited, resulting in a relatively compact PEO coating. The time constants RC decreases with increased negative currents. The decline of the time constant RC indicates the rapid response of the oxidation reaction to the electric signal, which can improve the coating's compactness and reduce the energy consumption. In actual production, the energy consumption can be reduced by setting up a reasonable ratio of positive and negative pulse voltages in the PEO.

A 50nV/√Hz 2‐channel time multiplexed bio‐chopper amplifier with current‐attenuated feedback resistor

This paper presents 2-channel time-multiplexed chopper instrument amplifier for better gain accuracy and mismatch. Mostly, the current-attenuated feedback resistor with a duty-cycled resistor is adopted for boosting the RC time constant. It can achieve the high pass corner frequencies between 10 Hz and 320 Hz by a 3-bit digitally controlled resistor bank of the attenuator. As a result, the instrument amplifier achieves 0.6% gain accuracy between two time-multiplexed channels, 100 dB CMRR, -40 dB crosstalk, and noise densities of 50nV/√Hz. It is implemented in a 180-nm CMOS technology. It occupies a 0.6 mm*0.6 mm chip area and consumes 1.5μA current consumption from a 1.8 V supply for each channel.

50-GHz-Bandwidth Membrane InGaAsP Electro-Absorption Modulator on Si Platform

We fabricate a membrane InP-based electro-absorption modulator (EAM), in which an InGaAsP-based multiple-quantum-well (MQW) absorption region is buried with an InP layer, on Si-waveguide circuits. By optical coupling between the MQW absorption region and Si core, a low-loss and large-absorption-length (300-μm-long) supermode waveguide is designed to suppress electric-field screening at high optical input power. The EAM is fabricated by combining direct bonding of the MQW layer and regrowth of the InP layer on a thin InP template bonded on a silicon-on-insulator wafer. The fabricated membrane EAM shows an on-chip loss of less than 4 dB at wavelengths over 1590 nm and temperatures from 25 to 50 °C. Since the membrane lateral p-i-n diode structure is beneficial for reducing the RC time constant of a lumped-electrode InP-based EAM, the EO bandwidth of the EAM is around 50 GHz without a 50-ohm termination up to fiber-input power of 10 dBm. Using the device, we demonstrate clear eye openings for 56-Gbit/s NRZ and 112-Gbit/s PAM4 signals at temperatures from 25 to 50 °C.

Android-based capacitor discharging calculator application

<span lang="IN">Nowadays, many people using smartphone to connet to her colleague. The electronic device using capacitor and transistor. The electronic device’s size recently become smaller. The capacitor can be used to the most important function that is used to store the energy and on the DC system is used to decrease the ripple from AC source. This research purpose build an apps which can calculate the charge remaining inside the capacitor. The method is using RC time constant. This research work well and can work functionally. </span>

Impedance spectroscopy of nanostructured ZnO morphologies

In this study, four nanostructured ZnO morphologies, nanoribbons, nanorods, nanoparticles, and nanoshuttles, were synthesized at annealing temperatures of 300 °C, 500 °C, and 700 °C. Structural properties were studied by Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), X-ray Diffraction Spectroscopy (XRD), and Differential Scanning Calorimetry (DSC). Optical properties were analyzed by UV–Visible Spectroscopy and Photoluminescence (PL). Electrical transport properties were studied by the Cole–Cole plot technique and electrical resistivity. From the impedance spectroscopy analysis, we extracted the carrier lifetime, the RC time constant, and grain and grain boundary parameters in each morphology. We observed that resistance decreased with increasing temperature in all samples in general, while nanorods, nanoshuttles, and nanoribbons showed well-defined semicircle profiles due to grain and grain boundaries at higher temperatures. From wettability studies, we obtained that surface with ZnO nanoparticles has hydrophobic properties, while nanorods, nanoribbons, and nanoshuttles resulted in a superhydrophobic surface. The optimum ZnO nanomorphology based on impedance studies can be used for developing electrodes for dye-sensitized solar cells.

Beam dynamics corrections to the Run-1 measurement of the muon anomalous magnetic moment at Fermilab

This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 data set of the Fermilab Muon g-2 Experiment. Two corrections to the measured muon precession frequency $\omega_a^m$ are associated with well-known effects owing to the use of electrostatic quadrupole (ESQ) vertical focusing in the storage ring. An average vertically oriented motional magnetic field is felt by relativistic muons passing transversely through the radial electric field components created by the ESQ system. The correction depends on the stored momentum distribution and the tunes of the ring, which has relatively weak vertical focusing. Vertical betatron motions imply that the muons do not orbit the ring in a plane exactly orthogonal to the vertical magnetic field direction. A correction is necessary to account for an average pitch angle associated with their trajectories. A third small correction is necessary because muons that escape the ring during the storage time are slightly biased in initial spin phase compared to the parent distribution. Finally, because two high-voltage resistors in the ESQ network had longer than designed RC time constants, the vertical and horizontal centroids and envelopes of the stored muon beam drifted slightly, but coherently, during each storage ring fill. This led to the discovery of an important phase-acceptance relationship that requires a correction. The sum of the corrections to $\omega_a^m$ is 0.50 $\pm$ 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of $\omega_a^m$.

Acquiring and Modeling of Si Solar-Cell Transient Response to Pulsed X-Ray

We report on the acquisition and modeling of the transient response of a commercial silicon (Si) solar cell using a benchtop pulsed X-ray source. The solar-cell transient output to the X-ray pulses was acquired under the dark and steady-state light illumination to mimic the practical operation of a solar cell under different light illumination levels. A solar-cell circuit model was created to develop a fundamental understanding of the transient current/voltage response of solar cell at read-out circuit level. The model was validated by a good agreement between the simulation and experimental results. It was found that the solar-cell resistance ( R) and capacitance ( C) depend on the light illumination, and the resulting variation in RC time constant significantly affects the solar-cell transient response. Thus, the solar cell produced different transient signals under different illumination intensities in response to the same X-ray pulse. The experimental data acquired in this work proves the feasibility of using solar panels for prompt detection of nuclear detonations, which also builds a practical mode of X-ray detection using a low-cost self-powered detector.

Chemically Roughened, Sputtered Au Films with Trace-Loaded Manganese Oxide for both On-Chip and Off-Chip High Frequency Supercapacitors.

High frequency supercapacitors (HFSCs) are promising in alternating current line filtering and adaptable storage of high-frequency pulse electrical energy. Herein, we report a facile yet integrated-circuit-compatible fabrication of HFSC electrodes by combining chemical roughening of the sputtered metal (Au) films and in situ trace loading of a pseudocapacitive material (MnOx). The developed electrode fabrication route is versatile for different substrates, and is described with the application paradigms of both on-chip (with Si/SiO2 substrate) and off-chip (without Si/SiO2 substrate, with Ti substrate as an example in this study) HFSCs. With Au/MnOx films on Si/SiO2 substrates as the working electrodes, the derived on-chip HFSC displayed satisfactory performance in high frequency applications (i.e., an areal capacitance of 131.7 µF cm−2, a phase angle of −78°, and a RC time constant of 0.27 ms, at 120 Hz).

Switched-Capacitor Circuits [Education

The first publication of a switched-capacitor resistor occurred nearly 150 years ago in James Clark Maxwell’s pioneering book A Treatise on Electricity and Magnetism [1] . He pointed out that the average current through a periodically inverted capacitor C remains the same when it is replaced by a resistor of value ${R} = {T}/{2}{C}$ , where ${T}$ is the period of inversions. He used this equivalence to give a method for measuring capacitance using a circuit employing a battery and galvanometer. The next publication came nearly a century later, when D. L. Fried proposed the idea of sampled-data analog filters [2] , containing only switches, capacitors and (if necessary) amplifiers. His paper showed how to realize the equivalent of a resistor using two switches and a capacitor. A motivation for using such circuits may be found from the history of analog filters. These were developed for telephony, and used initially resistors, capacitors and inductors. Inductors were bulky and lossy, and were replaced at the earliest opportunity by alternative circuits using amplifiers. The resulting active-RC filters were realized by discrete elements: capacitors, resistors and integrated-circuit amplifiers. With the development of integrated-circuit technology, there was strong motivation to put these filters on a single-substrate IC. However, the absolute values of resistors and capacitors could only poorly be controlled by the fabrication process: errors of 20-30% were common. Since the errors of resistors and capacitors were not tracking each other, the errors of time constants given by RC products were unacceptably high. This made their frequency responses unpredictable. Trimming could be used to tune such filters, but this was expensive. When the resistors were replaced by their switched-capacitor (SC) equivalents, the RC time constants were replaced by time constants of the form ${TC}_{1}/{C}_{2}$ . Since the switching period ${T}$ can be accurately controlled, as can the ratio of on-chip capacitors, the SC filters (SCFs) could be implemented with high accuracy. The design of such filters initially was based on those of active-RC ones, but it was soon recognized that they can be more effectively designed directly in the sampled-data domain, in terms of the ${z}$ variable, similarly to digital filters. Although other design techniques exist, the most popular one constructs higher-order filters as a cascade of lower-order sections, such as biquadratic filter or “biquad” shown in Figure 1 .

Identification of self-discharge mechanisms of ionic liquid electrolyte based supercapacitor under high-temperature operation

Ionic liquids (ILs) are promising electrolytes for supercapacitors (SCs) aimed for high-temperature applications, where increased ionic conductivity results in superior capacitive performance compared to room temperature (RT) performance. However, an increased temperature also accelerates the self-discharge rate that adversely affects energy retention and restricts the usage of SCs in standalone applications. In this study, a detailed electrochemical investigation on the self-discharge behaviour of carbon-based SCs containing an IL, 1-Ethyl-3-methylimidazolium acetate (EMIM Ac), has been carried out in the temperature range RT - 60 °C, and the underlying self-discharge mechanisms are identified. The results reveal that at a high voltage of 1.5 V, the self-discharge is characterized by a combination of charge redistribution and diffusion at both RT and 60 °C. At 60 °C, the diffusion-controlled mechanism dominates at lower voltages over the charge redistribution effect, while at RT both mechanisms contribute to a similar extent. The observed difference in the self-discharge mechanism between RT and 60 °C is explained in terms of a decreased RC time constant (τRC) at elevated temperature, and the same conclusions are potentially applicable to other IL-containing SCs as well.

Universal Model of Pulsed Alternators Using LTspice

The high power and energy density of synchronous machines turn them into reliable sources of energy for pulsed power applications. In this article, two mathematical models using both actual and normalized (per-unit) parameters have been developed and simulated in LTspice, which is a powerful and a free tool to simulate electrical/electronic circuits. In this article, an efficient solver based on the flux and current equations is presented. The model has been validated against published results with both actual and per-unit parameters. It has been observed that for models with normalized parameters, the simulation time is significantly reduced. The validated model of the machine has been used to show the effects of nonlinear loads on the voltages and currents, in particular the reaction currents in the damper winding inside of the generator. In addition, the model has been used to study the effect of the RC time constant of the load on the peak power provided by a synchronous machine used to store energy for pulsed power applications.

A 33-ppm/°C 240-nW 40-nm CMOS Wakeup Timer Based on a Bang-Bang Digital-Intensive Frequency-Locked-Loop for IoT Applications

This paper presents a wakeup timer in 40-nm CMOS for Internet-of-Things (IoT) applications based on a bang-bang Digital-intensive Frequency-Locked Loop (DFLL). A self-biased $\Sigma \Delta $ Digitally Controlled Oscillator (DCO) is locked to an RC time constant via a feedback loop consisting of a single-bit chopped comparator and a digital loop filter, thus maximizing the use of digital circuits while keeping only the RC network and the comparator as the sole analog blocks. Analysis and behavior level simulations of the DFLL have been carried out to guide the optimization of the long-term stability and frequency accuracy of the timer. High frequency accuracy and a $10\times $ enhancement of long-term stability is achieved by the adoption of chopping to reduce the effect of comparator offset and 1/f noise and by the use of $\Sigma \Delta $ modulation to improve the DCO resolution. Such highly digitized architecture fully exploits the advantages of advanced CMOS processes, thus enabling operation down to 0.7 V and a small area (0.07 mm2). The proposed timer achieves the excellent energy efficiency (0.57 pJ/cycle at 417 kHz at 0.8-V supply) over prior art while keeping excellent on-par long-term stability (Allan deviation floor < 20 ppm) and temperature stability (33 ppm°Cat 0.8-V supply).

A low power trimming-free CMOS relaxation oscillator with process and temperature compensation

The design of a 22 KHz 358 nW CMOS relaxation oscillator with a process and temperature compensation scheme is presented. Instead of the commonly used RC time constant, the oscillation period of the proposed circuit is determined by the resistance ratio of several resistors, which is insensitive to process and temperature variations. The on-chip relaxation oscillator is simulated in a 0.18 [Formula: see text]m CMOS process. Without any calibration or off-chip components, the frequency variation of the proposed oscillator is ±[Formula: see text]3.24% across [Formula: see text] to 100[Formula: see text]C temperature range and 5 different process corners. Compared to the conventional relaxation oscillator, the frequency variation of this circuit is reduced by 89%. The simulated temperature coefficient is 111 ppm/[Formula: see text]C, and the frequency variation over the supply voltage from 1.2 V to 1.7 V is 2.1%/V. The typical power consumption of the proposed circuit is 358 nW.

Efficient Optical Modulation With High Data-Rate in Silicon Based Laterally Split Vertical p-n Junction

Efficient optical modulation along with high data rate is a prerequisite for the realization of high-performance optical modulator. Optical modulation in silicon with high data-rate and high modulation efficiency is proposed by a laterally separated vertical p-n junction. Two independent but synchronized p-n junctions that supports the common optical mode are created by forming a slot waveguide structure. It provides a prominent way to enhance the light-material interaction necessarily to achieve low V π L along with the low RC time constant which is crucial for the high-speed operation. The proposed device shows a high modulation efficiency of 0.74 V-cm for 1.2 mm long device. The calculated intrinsic 3-dB bandwidth reaches up to ≈ 58 GHz at a reverse bias of 6 V. We show high speed operation up to 25 Gbit/s for the device length of 600 μm with a simple lumped electrode configuration. The Traveling-wave electrodes as a coplanar waveguide is employed to further improve the speed performance of the device. By taking the advantage of excellent velocity matching between optical group index and RF effective index, high data rate performance up to 100 Gbit/s is obtained with an extinction ratio of 2.4 dB. The proposed device opens new avenues for high speed optical interconnect on an SOI platform.

A 5-bit 400-MS/s time domain flash ADC in 0.18-μm CMOS

A 5-bit 400-MHz time-domain analog-to-digital converter (ADC) was implemented in 0.18-μm CMOS technology. The proposed design is composed of a voltage-to-time-difference converter, a flash-type time-to-digital converter, and some error correction logic. Input voltage-type signals are converted to time-difference signals by a voltage-to-time-difference converter. Its rising- and falling-edge outputs contain delay information; they can then be converted by two time-to-digital converters operating at interleaving clock phases. Because of the transparent delayed signal without a sample-and-hold circuit, the subsequent time-to-digital converter structure is of the flash type. By using a distinct RC time constant of the time comparator, the time-difference signals can be converted to the relevant 1-of-n code. Because this conversion is almost entirely digital in nature, little static current is consumed. The measured signal to noise and distortion ratio and spurious-free dynamic range of the ADC are 26.1 dB and 31.5 dB, respectively, at a 400-MHz sampling frequency for a 100-MHz input signal.

Thermal Stability Analysis of Graphene Nano-ribbon Interconnect and Applicability for Terahertz Frequency

In this paper, we have studied the thermal stability of GNR and Cu interconnects for terahertz frequency range. The top-contact (TC) and side-contact (SC) GNR interconnects are analyzed for stability, RC-delay, and power consumption at different interconnect lengths ($$10\,{\upmu }\hbox {m}$$, $$50\,{\upmu }\hbox {m}$$ and $$100\,{\upmu }\hbox {m}$$) and different chip operating temperatures (233 K, 300 K and 378 K). The RC-delay and power consumption are analyzed with the help of transmission line model (TLM) using 16nm PTM-HP standard CMOS model. In our analysis, we have shown that the RC-time constant for SC-GNR is $$\sim (3{-}7)\times $$ and $$\sim (2{-}6)\times $$ less than that of TC-GNR and Cu interconnects. Similarly, we have shown that the power consumption for SC-GNR is $$\sim (4{-}7)\times $$ and $$\sim (2{-}5)\times $$ less than that of TC-GNR and Cu. In terms of stability, SC-GNR interconnect is more stable at higher frequency range ($$>10^{12}$$ Hz) compared with TC-GNR and Cu for $$10\,{\upmu }\hbox {m}$$ interconnect length and three different chip operating temperatures.

Dynamic impedance spectroscopy of LiMn2O4 thin films made by multi-layer pulsed laser deposition

The kinetics of the reversible insertion of lithium ions assisted by aqueous environment into LiMn2O4 thin film fabricated by multi-layer pulsed laser deposition is studied using dynamic multi-frequency analysis (DMFA). This method allowed us to acquire time resolved impedance spectra in the range of 210 kHz to 11.5 Hz during cyclic voltammetry. The impedance spectra obtained comprises of two RC time constants (semi-circles) indicating that the reversible insertion process of lithium ions in LiMn2O4 thin films in aqueous media follows a two-stage intercalation process with the first stage as the (de)solvation step of the lithium ions and the second stage as a (de)insertion process with a concurrent change in the oxidation state of manganese. The temporal development of the kinetic parameters with the state of charge during the voltage sweep was investigated and reported in this work.