LC Oscillator Research Articles

500 MHz high resolution proximity sensors with fully integrated digital counter

We report on the design and characterization of two inductive proximity sensors based on LC oscillators operating at 500 MHz. The distance from the target is obtained by measuring the oscillation frequency variation. Both sensors contain an off-chip LC resonator consisting of a two turns 4 mm diameter planar coil and a ceramic capacitor. The LC resonator is connected to integrated CMOS electronics. The first sensor output stage consists of a buffer whereas the second sensor output stage includes a co-integrated 21 bits digital frequency counter. The first sensor has frequency noise floor of 0.085 Hz/Hz above 3 kHz. At a distance of 200 μm from the coil, the resolution is 0.2 pm/Hz and the integrated resolution from 1 mHz to 1 kHz is 22 pmrms. The second sensor reaches a noise floor of 2 Hz/Hz corresponding to a resolution of 5 pm/Hz and an integrated resolution of 900 pmrms.

Closed-form and technology independent phase noise relation for LC oscillators

PurposeThe purpose of this paper is to find a closed relation for the phase noise of LC oscillators.Design/methodology/approachThe governing equation of oscillators is generally a stochastic nonlinear differential equation. In this paper, a closed relation for the phase noise of LC oscillators was obtained by approximating the I–V characteristic of the oscillator with third-degree polynomials and analyzing its differential equation.FindingsThis relation expresses phase noise directly in terms of circuit parameters, including the sizes of the transistors and the bias. Next, for evaluation, the phase noise of the cross-coupled oscillator without tail current was calculated with the proposed model. In this approach, the obtained equations are expressed independently of technology by combining the obtained phase noise relation and gm/ID method.Originality/valueA technology-independent method using the gm/ID method and the closed relationship is provided to calculate phase noise.

Dielectrophoresis-assisted 65-GHz LC-oscillator array CMOS chips for label-free and sensitive detection of microorganism cells

In this paper, we propose a miniature, sensitive, and label-free method for detecting Escherichia coli (E. coli) and Saccharomyces cerevisiae (yeast) by using a complementary metal–oxide–semiconductor (CMOS) chip with dielectrophoresis (DEP)-assisted LC-oscillator arrays. Each of the 62 × 24 arrayed sensor elements on the CMOS chip comprises a 65-GHz LC oscillator that senses the dielectric change due to the presence of the microorganisms. Given the non-uniform sensitivity of the LC oscillator, the DEP electrodes fabricated to be placed at the most sensitive position of the LC-oscillator were used to collect microorganisms and thereby enhance the measurement sensitivity. The AC electric field of DEP above 2 MHz interferes with the 65-GHz LC oscillator circuit in the designated vicinity. With appropriate DEP settings, each sensor element can achieve a limit of detection of two E. coli cells or one yeast cell. Quantitative enumeration reaches a single-cell resolution at small microorganism numbers. The results of this study confirmed that the novel approach of combining DEP technique and LC-oscillator array can perform high-sensitivity detection of microorganisms. Further, the realization of large-scale paralleled measurement makes the proposed CMOS biosensor a potential candidate as a rapid and low-cost lab-on-a-chip sensor for food inspection and clinical diagnosis.

Ultra-low noise bipolar current source for ultracold atom magnetic system.

We report the development of an ultralow-noise bipolar current source based on the configuration of H-bridge current switching. The measured relative current noise fluctuation reaches 4 × 10-9Hz-1/2, which enables an ultra-stable magnetic system for cold atom experiments. We avoid the influence of the AC leakage currents induced by the large parasitic capacitance of the H-bridge. First, the current sensor is placed as close as possible to the magnetic coils so that the systematic errors from these leakage currents are minimized. Second, the large parasitic capacitance, which parallels the magnetic coils and forms an LC oscillator, is removed from the feedback loop in our setup to maintain a large self-resonance frequency of the feedback control loop. These two improvements lead to a current source that is more precise and less noisy. Remarkably, the lowest current noise density produced by the proposed method is only 500 nA Hz-1/2 at a current of 100A, which is about ten fold smaller than the case with leakage current. To optimize the feedback control, a numerical simulation is implemented by using Matlab Simulink, and the numerical simulation results are entirely consistent with the experimental results.

Microwave LC Oscillators: Multimode Switching Techniques

The rapid development of wireless communications, software-defined radios, and ultrawideband (UWB) engenders an ever-increasing demand for clock generators that fully covers multiple frequency bands <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> , <xref ref-type="bibr" rid="ref3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[3]</xref> . As the “heartbeat” that pumps clock generators, such as phase-locked loops (PLLs), microwave oscillators with wideband frequency tuning range (TR) are thus attracting a great deal of research interest.

Nonlinear model and characteristic analysis of fractional-order high frequency oscillator

Recently, fractional calculus theory has been widely used in various fields, including the design of oscillators. However, there are still some issues that need to be studied in depth. Firstly, it is necessary to classify the fractional-order oscillators according to the properties of the frequency selective network components, and analyze the influence of the fractional order of components on the characteristics of different types of fractional-order oscillators. Secondly, for fractional-order oscillators with nonlinear devices such as transistors, the traditional linear models cannot describe them accurately. Thirdly, due to the complexity of fractional differential equation, it is difficult to obtain the general analytical solution of the fractional-order oscillator. For these reasons, this paper takes the fractional-order capacitive feedback LC oscillator as an example, and establishes a nonlinear model of this oscillator based on the transistor characteristic mechanism. With the help of the equivalent small parameter method, the influence of the fractional-order characteristics of the components on the output waveform is analyzed. It is revealed that for the fractional-order capacitive feedback LC oscillator, the order of capacitance C1 has the most significant effect on frequency and amplitude, followed by the order of inductance L2, and the order of the feedback capacitor C2 has very little effect on the oscillator. In addition, although the introduction of fractional order increases the oscillation frequency, it will also lead to an increase in THD in some cases. Simulation and experimental results verify the correctness of the proposed nonlinear model and characteristic analysis of fractional-order high frequency oscillator.

General analysis of LC oscillator with active and passive transconductance amplification

SummaryIn this paper, a comprehensive analysis of oscillation frequency, oscillation amplitude, and phase noise is conducted for an LC cross‐coupled oscillator with unequal inductors, active and passive transconductance amplification structure, and very low phase noise. In this study, for the first time, a complete analysis of the phase noise of this oscillator is presented using a novel method that does not require complex simulations to calculate the Impact Sensitivity Function (ISF) and phase noise, and as a result, a closed‐form equation is extracted for the phase noise. The calculated results are compared with the corresponding simulations to evaluate the validity of the extracted equations. Using the closed‐form phase noise equation as well as the oscillation frequency, designers can comprehend the design trade‐offs and design an oscillator for specific phase noise and oscillation frequency. The proposed method of calculating the ISF is also applicable and valid for other second‐order oscillators. In the following, the structure of the proposed oscillator is designed and simulated using the standard 0.18‐μm CMOS technology with a 1.8‐ power supply and 575.2‐MHz oscillation frequency to have the optimal coupling coefficient in terms of the phase noise and oscillation amplitude. The simulation results as well as the analyses performed based on the phase noise and oscillation amplitude parameters show that the structure proposed in this study provides a better performance with a much lower phase noise comparing with the structure of a conventional cross‐coupled oscillator as well as the proposed cross‐coupled oscillator with equal inductors.

Synchronization of oscillators not sharing a common ground

Networks of coupled LC oscillators that do not share a common ground node are studied. Both resistive coupling and inductive coupling are considered. For networks under resistive coupling, it is shown that the oscillator-coupler interconnection has to be bilayer if the oscillator voltages are to asymptotically synchronize. Also, for bilayer architecture (when both resistive and inductive couplers are present) a method is proposed to compute a complex-valued effective Laplacian matrix that represents the overall coupling. It is proved that the oscillators display synchronous behavior if and only if the effective Laplacian has a single eigenvalue on the imaginary axis.

Event-triggered control for second-order multi-agent systems under denial-of-service attacks and white noises

Under the influence of additive communication noises and system noises, we investigate the event-triggered control problem for second-order multi-agent systems composed of double integrators or LC oscillators under random denial-of-service (DoS) attacks. Different from the previous cases where the attackers completely interrupt communication networks, we consider that attackers interrupt the communication network with a specific probability and can attack part or all communication links randomly. Based on this, the conditions on the attack duration and attack success probability are given when the system can still achieve consensus under random DoS attacks. In addition, the consensus bounds are expressed. Finally, two types of LC oscillator systems are used to illustrate the effectiveness of results.

Ring Oscillator for 60 Meter Bandwidth

The 60-meter band range is tremendously useful in telecommunication, military and governmental applications. The I. T. U. (International Telecommunication Union) required isolationism to former radio frequency services because the various frequency bands are extremely overloaded. The allocation of new frequency bands are a lengthy procedure as well as time taking. As a result, the researchers use bidirectional, amateur radio frequency communication for 60-meter band, usually the frequency slot of 5250–5450 KHz, although the entire band is not essentially obtainable for all countries. For transmission and reception of these frequencies, a local oscillator is used in the mixer unit to generate the local signal for mixing the input and reference signals. For this function different type of oscillators are used. In this paper, a three-stage ring oscillator is designed with 1 V supply. Ring oscillators (RO) is the base to explore like to identifying, specify with modelling resources in the disparity in behaviour of the circuit in terms of industrialized design and layout parameters. This type of oscillators are free from noise as inductor is not used to the circuit as in LC oscillator, Heartly oscillator, Colpitt and tuned oscillators. The present approach of circuit designing, the scaling of CMOS (Complementary Metal Oxide Semiconductor) transistor will moderate, the procedure variability. In the forthcoming article, a ring oscillator with fixed capacitor (1 pF) and with variable capacitors (1 to 100 pF) is analysed. The frequency analysis with different capacitor is performed. The total delay of 3-stage oscillator is 4.82 ns with 5.2 MHz oscillation frequency. The overall Power dissipation of the circuit is 1.852 μW at 1 V supply. The simulation analysis is performed on 45 nm CMOS technology with both transistor width are 278 and 420 nm.

Radiation-tolerant all-digital clock generators for HEP applications

The emergence of high-precision timing systems in High Energy Physics motivates new developments in the domain of clock generation and distribution. Particularly, when considering the challenges arising from adopting advanced deep-submicron CMOS technology nodes, all-digital PLL and clock and data recovery (CDR) architectures constitute a promising option for future high energy physics (HEP) experiments. Both LC oscillator and ring oscillator-based all-digital PLL/CDR blocks for front-end ASICs were studied, designed, manufactured and characterized. Their design, the hardening considerations, as well as the performance obtained with these circuits are presented in this article.

Theoretical investigation of injection-locked differential oscillator

A preliminary analysis of published works on this topic showed that at present there is no sufficiently substantiated theory of such devices, and the approximate approaches used are rough and do not always meet the requirements of practice. The proposed transition from a differential self-oscillator to an equivalent single-circuit oscillator has not received a convincing justification.&#x0D; This article presents a methodology for studying a synchronized differential oscillator using rigorous methods. A mathematical model of such oscillator is presented in the form of nonlinear differential equations obtained on the basis of Kirchhoff's laws. Their analysis made it possible to substantiate the transition to the model of a single circuit LC oscillator, equivalent to a differential one. A technique for such a transition is proposed, including the procedure for determining the nonlinear characteristics of the amplifying element of this self-oscillator, based on the nonlinear characteristics of two amplifying elements of the differential oscillator.&#x0D; The mathematical model of an equivalent oscillator is represented by a non-linear differential Van der Pol equation in a dimensionless form, it is simple and accurate. This form of representation made it possible to single out a small parameter and estimate its value. In the case of small values of the small parameter, as is known, traditional methods can be used for its analysis. Thus, the task of studying the synchronization process of a differential oscillator is reduced to the study of the synchronization process of a Van der Pol oscillator. The presented results can be useful in the development of various devices based on synchronized differential oscillators.

Balancing Method of Retired Battery Pack Based on Variable Domain Fuzzy Control

Abstract For the problem of the performance gap between individual cells in retired lithium batteries after group use, which affects the usable capacity of the battery pack, a grouping bidirectional equalization method based on variable domain fuzzy control is proposed. Equalization circuits based on a single inductor and LC oscillation circuit are respectively used for inter-cell and inter-cell group, to achieve inter-cell equalization and inter-cell group equalization. Variable domain fuzzy control strategy is used to determine the reasonable range of operating current according to state of health (SOH) of the battery, combined with the relationship between the capacity decay coefficient, and the average operational range of state of charge (SOC); the equalization current is dynamically adjusted according to its mathematical relationship with the operating current. To verify the effectiveness of this equalization method, an experimental platform was built and verification simulations were performed. The result of experiments shows, the equalization speed is increased by 25%, compared to the fixed equalization current control strategy; the capacity decay is reduced by 6% and the service life is extended after experiments of 1200 charge/discharge cycles, compared to traditional fuzzy equalization strategy.

A Cryo-CMOS Oscillator With an Automatic Common-Mode Resonance Calibration for Quantum Computing Applications

This article presents a 4-to-5GHz LC oscillator operating at 4.2K for quantum computing applications. The phase noise (PN) specification of the oscillator is derived based on the control fidelity for a single-qubit operation. To reveal the substantial gap between the theoretical predictions and measurement results at cryogenic temperatures, a new PN expression for an oscillator is derived by considering the shot-noise effect. To reach the optimum performance of an LC oscillator, a common-mode (CM) resonance technique is implemented. Additionally, this work presents a digital calibration loop to adjust the CM frequency automatically at 4.2K, reducing the oscillator’s PN and thus improving the control fidelity. The calibration technique reduces the flicker corner of the oscillator over a wide temperature range (10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> and 8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> reduction at 300K and 4.2K, respectively). At 4.2K, our 0.15-mm2 oscillator consumes a 5-mW power and achieves a PN of −153.8dBc/Hz at a 10MHz offset, corresponding to a 200-dB FOM. The calibration circuits consume only a 0.4-mW power and 0.01-mm2 area.

On-Demand Parity-Time Symmetry in a Lone Oscillator through Complex Synthetic Gauge Fields

What is the fate of an oscillator when its inductance and capacitance are varied while its frequency is kept constant? Inspired by this question, we propose a protocol to implement parity-time (PT) symmetry in a lone oscillator. Different forms of constrained variations lead to static, periodic, or arbitrary balanced gain and loss profiles, that can be interpreted as purely imaginary gauge fields. With a state-of-the-art, dynamically tunable LC oscillator comprising synthetic circuit elements, we demonstrate static and Floquet PT breaking transitions, including those at vanishingly small gain and loss, by tracking the circuit energy. Concurrently, we derive and observe conserved quantities in this open, balanced gain-loss system, both in the static and Floquet cases. Lastly, by measuring the circuit energy, we unveil a giant dynamical asymmetry along exceptional point (EP) contours that emerge symmetrically from the Hermitian degeneracies at Floquet resonances. Distinct from material or parametric gain and loss mechanisms, our protocol enables on-demand parity-time symmetry in a minimal classical system -- a single oscillator -- and may be ported to other realizations including metamaterials and optomechanical systems.

Magnetostriction Generator as Acoustic Wave Generator for Underwater Applications

At this time the research related to the effect of magnetostriction for underwater applications is still limited. Acoustic or sound waves are more easily propagated underwater than electromagnetic waves or light. An acoustic wave or sound can be generated by utilizing the magnetostriction effect, where this effect occurs when a rod of ferromagnetic material such as iron or nickel is magnetized and interacts with another magnetic field, resulting in vibration of the metal rod. This research aims to design and realize a magnetostriction generator as an acoustic wave generator at a frequency of 1 to 10 kHz for underwater applications, consisting of: a tuned LC oscillator circuit, and a ferromagnetic metal rod which is magnetized using a dc voltage. The results of measurements and testing of the magnetostriction generator show: (1) if it is equipped with a membrane, can work to emit an acoustic wave or sound at a frequency of ± 8.62 kHz in the air up to a distance of 15 cm without distortion with an average amplitude decrease of ± 0.648 dB for each the distance increased by 1 cm, and (2) if equipped with a membrane and enclosed in a waterproof casing, capable of transmitting the acoustic waves at a frequency of ± 8.31 kHz underwater up to a distance of 7 cm without distortion with an average amplitude decrease of ± 4.217 dB for each the distance up 1 cm. Overall the magnetostriction generator designed can work to generate and transmit the acoustic waves or sound underwater, as expected.

A 4.5-mW 22-nm CMOS Label-Free Frequency-Shift 3 × 3 × 2 3-D Biosensor Array Using Vertically Stacked 60-GHz LC Oscillators

In this brief, a label-free <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {3\times 3\times 2}$ </tex-math></inline-formula> three-dimensional frequency-shift biosensor array with vertically-stacked 60-GHz on-chip LC oscillators is presented. The 60-GHz LC oscillators function as sensor front-end since the frequency downward shifts due to dielectric derived from biomedical sensing targets. The proposed array element consists of the two vertically-stacked LC oscillators and 15-stage dividers necessary for extracting high-frequency output signals with a long distance. The proposed circuit was designed with Spectre RF simulation and the test chip was fabricated in 22-nm CMOS technology. The whole and element chip size is 0.04 mm2 and 0.0035 mm2 respectively. The measurement with thick and thin silicon resin samples successfully demonstrated their vertical and horizontal detection on the same chip while the prior works only achieved two-dimensional detection. The 22-nm CMOS prototype also showed high spatial resolution <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$60 ~\mu {\mathrm{ m}} \times 60 ~\mu {\mathrm{ m}} \times 4 ~\mu {\mathrm{ m}}$ </tex-math></inline-formula> and high fill factor 73% while consuming 4.5 mW under 1.2 V per the single-element.

High-fidelity quantum information transmission using a room-temperature nonrefrigerated lossy microwave waveguide

Quantum microwave transmission is key to realizing modular superconducting quantum computers and distributed quantum networks. A large number of incoherent photons are thermally generated within the microwave frequency spectrum. The closeness of the transmitted quantum state to the source-generated quantum state at the input of the transmission link (measured by the transmission fidelity) degrades due to the presence of the incoherent photons. Hence, high-fidelity quantum microwave transmission has long been considered to be infeasible without refrigeration. In this study, we propose a novel method for high-fidelity quantum microwave transmission using a room-temperature lossy waveguide. The proposed scheme consists of connecting two cryogenic nodes (i.e., a transmitter and a receiver) by the room-temperature lossy microwave waveguide. First, cryogenic preamplification is implemented prior to transmission. Second, at the receiver side, a cryogenic loop antenna is placed inside the output port of the waveguide and coupled to an LC harmonic oscillator located outside the waveguide. The loop antenna converts quantum microwave fields to a quantum voltage across the coupled LC harmonic oscillator. Noise photons are induced across the LC oscillator including the source generated noise, the preamplification noise, the thermal occupation of the waveguide, and the fluctuation-dissipation noise. The loop antenna detector at the receiver is designed to extensively suppress the induced photons across the LC oscillator. The signal transmittance is maintained intact by providing significant preamplification gain. Our calculations show that high-fidelity quantum transmission (i.e., more than 95%) is realized based on the proposed scheme for transmission distances reaching 100 m.

Inductively Powered Sensornode Transmitter Based on the Interconnection of a Colpitts and a Parallel Resonant LC Oscillator

An inductively powered passive transmitter architecture for wireless sensornodes is presented in this paper. The intended applications are inductively powered internally illuminated photoreactors. The application range of photoreactors is wide. They are used, e.g., for microalgae cultivation or for photochemistry, just to name two important fields of use. The inductive powering system used to transmit energy to the wireless internal illumination system is to be additionally used to supply the here presented transmitter. The aim of expanding the named internal illuminated photoreactors with wireless sensors is to obtain a better insight into the processes inside it. This will be achieved by measuring essential parameters such as, e.g., the temperature, pH value, or gas concentrations of the medium inside the reactor, which for algal cultivation would be water. Due to the passive architecture of the transmitter electronics, there is no need for batteries, and therefore, no temporal limitations in their operational cycle are given. The data transmission is also implemented using the inductive layer in the low frequency range. The data transmitting coil and the energy receive coil are implemented as one and the same coil in order to avoid interference and unwanted couplings between them, and in order to save weight and space. Additionally, the transmitter works in a two-step alternating cycle: the energy harvesting step, followed by the data transmission step. The measured values are sent using on-off keying. Therefore, a Colpitts oscillator is switched on and off. The circuit is simulated using SPICE simulations and consequentially implemented as a prototype in order to perform practical analyses and measurements. The feasibility of our transmitter is therefore shown with the performed circuit simulations, and practically, by testing our prototype on an internal illuminated laboratory scaled photoreactor.

High‐Efficiency Energy Management Circuit Combining Synchronized Switch Harvesting on Inductor Rectifier and Impedance Matching for Impact‐Type Piezoelectric Energy Harvester

To improve the output power of impact‐type piezoelectric energy harvesters (IPEHs), a high‐efficiency energy management circuit combining a self‐powered synchronized switch harvesting on inductor (SP‐SSHI) rectifier and an alternative impedance matching circuit is proposed. The SP‐SSHI rectifier eliminates the effect of inherent capacitance of IPEH through LC oscillation and enhances the output power. The alternative impedance matching circuit provides two optimal load resistances for different periods of IPEHs to increase the harvested power. Furthermore, to decrease the power dissipation, the proposed circuit is activated only when the output power of IPEH is sufficiently high and the SSHI is active. A control chip of the proposed circuit is designed and fabricated in a 0.18 μm complementary metal‐oxide semiconductor process. The proposed circuit is applied for a microwind IPEH, and the peak figure of merit and efficiency are 3.68 and 90.4%, at the wind speed of 1.46 m s−1, respectively. The results indicate a significant improvement in output power and harvesting efficiency of the proposed IPEH‐specialized circuit. When a flame sensor (USEQFSEA22L80) is powered by the microwind energy harvesting system, the proposed circuit increases operating time of the sensor as 4.6 times, as compared with the traditional impedance matching circuit.