Thermal Noise Sources Research Articles

An experiment for verification of the auxiliary transmission-line method to evaluate a microwave thermal noise source

In order to verify the usefulness of the auxiliary transmission-line method, which has been proposed to evaluate the noise temperature of a microwave thermal noise source, a liquid nitrogen-cooled coaxial noise source system has been constructed and a preliminary experiment has been made. This measurement result and a result calibrated with two known references have been compared, and it was confirmed that they were in good agreement.

Phase noise and timing jitter in oscillators with colored-noise sources

Phase noise or timing jitter in oscillators is of major concern in wireless and optical communications, being a major contributor to the bit-error rate of communication systems, and creating synchronization problems in other clocked and sampled-data systems. This paper presents the theory and practical characterization of phase noise in oscillators due to colored, as opposed to white, noise sources. Shot and thermal noise sources in oscillators can be modeled as white-noise sources for all practical purposes. The characterization of phase noise in oscillators due to shot and thermal noise sources is covered by a recently developed theory of phase noise due to white-noise sources. The extension of this theory and the practical characterization techniques to noise sources in oscillators, which have a colored spectral density, e.g., 1/f noise, is crucial for practical applications. In this paper, we first derive a stochastic characterization of phase noise in oscillators due to colored-noise sources. This stochastic analysis is based on a novel nonlinear perturbation analysis for autonomous systems, and a nonlocal Fokker-Planck equation we derive. Then, we calculate the resulting spectrum of the oscillator output with phase noise as characterized. We also extend our results to the case when both white and colored-noise sources are present. Our treatment of phase noise due to colored-noise sources is general, i.e., it is not specific to a particular type of colored-noise source.

Interpreting anomalously low voltage noise in two-channel measurement systems.

In this work we 1) analyze and give a theoretical explanation for the anomalously low cross-spectral density of voltage fluctuations that is observed when two thermal noise sources with matched intensities are coupled to the inputs of two-channel phase modulation (PM) or amplitude modulation (AM) noise measurement systems (NMS), 2) empirically evaluate spectral resolutions of different types of measurement systems, and 3) discuss noise measurement techniques involving cross-correlation signal processing. Our work shows that the statistical uncertainty, which sets the ultimate spectral resolution in the thermal noise limited regime, is approximately the same for both systems. However, in practical terms, the non-stationary nature of the noise, the temporal separation of calibration and measurement, and the difficulty of reproducing the calibrations for two measurements make it extremely difficult to resolve noise that is more than 10 dB below the noise floor in a single channel NMS. In a two-channel NMS, however, the calibrations of the two channels are carried out simultaneously, and one can take full advantage of a large number of averages and make reproducible noise measurements with resolution 10 dB below the noise floor of a single channel NMS.

Additive and multiplicative noise driven systems in1+1dimensions: Waiting time extraction of nucleation rates

We study the rate of true vacuum bubble nucleation numerically for a ${\ensuremath{\varphi}}^{4}$ field system coupled to a source of thermal noise. We compare in detail the cases of additive and multiplicative noise. We pay special attention to the choice of initial field configuration, showing the advantages of a version of the quenching technique. We advocate a new method of extracting the nucleation time scale that employs the full distribution of nucleation times. Large data samples are needed to study the initial state configuration choice and to extract nucleation times to good precision. The $1+1$ dimensional models afford large statistics samples in reasonable running times. We find that for both additive and multiplicative models, nucleation time distributions are well fit by a waiting time, or gamma, distribution for all parameters studied. The nucleation rates are a factor 3 or more slower for the multiplicative compared to the additive model with the same dimensionless parameter choices. Both cases lead to high confidence level linear fits of $\mathrm{ln}\ensuremath{\tau}\mathrm{vs}{T}^{\ensuremath{-}1}$ plots, in agreement with semiclassical nucleation rate predictions.

A Simple Random Noise Generator Employing Metal-Oxide-Semiconductor-Field-Effect-Transistor Channel kT/C Noise and Low-Capacitance Loading Buffer

An eight-transistor random noise generator employing a new circuit architecture has been developed. A compact two-transistor thermal noise source comprising a complementary metal-oxide-semiconductor (CMOS) inverter is proposed as a viable alternative to the area consuming conventional resistive noise source. The total extracted noise power is increased by reducing the effective capacitance at the output of the thermal noise source through the use of a unity-gain low-capacitance loading buffer. A wide-bandwidth high-noise-power random noise generator comprising the CMOS inverter noise source, a CMOS source follower as a low-capacitance loading buffer and a cascode amplifier as a high-gain stage, was fabricated and its noise generation capability experimentally verified. It has a very simple circuit configuration and is fully compatible with current VLSI technology, thus making it a promising candidate for integration of multiple random noise generators on a chip.

Characterization of HTS SFQ circuits using interface-engineered Josephson junctions

We fabricated and tested high-temperature superconducting (HTS) rapid-single-flux-quantum (RSFQ) circuits using interface-engineered Josephson junction (IEJ). The characteristics of high-speed operation were examined by voltage-divider operation based on the toggle-flip-flop circuit. An operation at 155 GHz was obtained at 15 K and the proper functioning of the voltage divider was observed up to 27 K. Temperature dependence of the maximum operation speed was analyzed by circuit simulation with thermal-noise sources. To achieve higher speed operation using a Josephson junction with a higher I/sub c/R/sub n/ product, we also fabricated an RSFQ balanced comparator using IEJ; proper switching characteristics of the circuit was confirmed up to 190 GHz at 30 K. The bias condition dependencies were studied based on the circuit simulations in the relationship of the I/sub c/R/sub n/ product. The results of circuit simulation indicate that a Josephson junction with an I/sub c/R/sub n/ product of more than 0.7 mV is required for high-speed operation (100 GHz) in high-temperature range (30-40 K). We believe that the IEJ is a promising junction candidate for realizing high-speed operation in a high-temperature range.

Noise and energy resolution of X-ray microcalorimeters

Two type of sensor geometries of voltage-biased X-ray microcalorimeters with a phase-transition thermometer have been built and tested. Both devices show, in addition to the well-known noise sources of thermal fluctuation noise or phonon noise from the heatlink to the bath and Johnson noise from the thermometer resistance, also thermal fluctuation noise from the thermometer itself. In both cases however the measured energy resolution is limited by other sources. The energy resolution of the asymmetric lateral type of sensor, 12 to 15 eV @ 5.9 keV, is limited by a position dependent heatleak of the absorber to the bath. The energy resolution of the symmetric lateral sensor, 6.8+/-0.3 eV FWHM @ 5.9 keV, is limited by excess noise at frequencies below 1000 Hz. The origin of this noise component is unknown so far.

Modified quadratic congruence codes for fiber Bragg-grating-based spectral-amplitude-coding optical CDMA systems

We have constructed a series of new code families for the spectral-amplitude-coding optical code-division multiple-access (CDMA) system, and proposed new transmitter and receiver structures based on tunable chirped fiber Bragg gratings (FBGs). The proposed system has been analyzed by taking into account the effects of phase-induced intensity noise, shot noise, and thermal noise. We have also compared the performance of this system with that of a former system where a Hadamard code is used. It has been shown that the new code families can suppress the intensity noise effectively and improve the system performance significantly. When the effective power is large (i.e., >-10 dBm), the intensity noise is the main factor that limits the system performance. When the effective power is not sufficiently large, thermal and shot noise sources become the main limiting factors and the effect of thermal noise is much larger than that of shot noise.

Characterization of the Input Noise Sources of a dc SQUID

From the theory of the intrinsic noise in a dc SQUID by Tesche and Clarke, we derive the expressions of the current and voltage input noise spectral densities in a dc SQUID current amplifier operated in a flux locked mode. The expected current and voltage noises are compared, at audio frequencies, with the experimental results obtained with a low noise dc SQUID in which the input load (resonant and not) and the operating temperature (1–4 K) are changed. In order to evaluate the input voltage noise, which is directly related to the current noise around the SQUID loop and is usually neglected, we have used as the input circuit a LC resonator with a very high quality factor (≈106). Both the voltage and current input noises exceed the expected values by the same factor of about 8. This means that the modulus the optimum source impedance of the SQUID amplifier is still in agreement with the value expected from the theory, which is approximately given by the product of the input coil inductance and the angular frequency. To explain the excess noise results, we propose a model in which the voltage and current input noises are due to a thermal magnetic noise source which is present near the SQUID.

Analysis of temporal noise in CMOS photodiode active pixel sensor

Temporal noise sets the fundamental limit on image sensor performance, especially under low illumination and in video applications. In a CCD image sensor, temporal noise is primarily due to the photodetector shot noise and the output amplifier thermal and 1/f noise. CMOS image sensors suffer from higher noise than CCDs due to the additional pixel and column amplifier transistor thermal and 1/f noise. Noise analysis is further complicated by the time-varying circuit models, the fact that the reset transistor operates in subthreshold during reset, and the nonlinearity of the charge to voltage conversion, which is becoming more pronounced as CMOS technology scales. The paper presents a detailed and rigorous analysis of temporal noise due to thermal and shot noise sources in CMOS active pixel sensor (APS) that takes into consideration these complicating factors. Performing time-domain analysis, instead of the more traditional frequency-domain analysis, we find that the reset noise power due to thermal noise is at most half of its commonly quoted kT/C value. This result is corroborated by several published experimental data including data presented in this paper. The lower reset noise, however, comes at the expense of image lag. We find that alternative reset methods such as overdriving the reset transistor gate or using a pMOS transistor can alleviate lag, but at the expense of doubling the reset noise power. We propose a new reset method that alleviates lag without increasing reset noise.

Noise analysis of imagers with a-Si:H pin diode pixels

We propose a comprehensive noise analysis for a-Si:H pin diode pixels in thin film on application specific integrated circuit (ASIC) image sensors. Signal-to-noise (SNR) ratio and dynamic range (DR) at the input of the pixel amplifier are calculated with shot and flicker noise of photocurrent and dark current and the thermal noise of the pin diode parallel resistance. The effect of the thermal noise of the pin diode series resistance under consideration, of the dynamic systems properties of pin diode and pixel amplifier, and of reset noise are included. The thermal noise of the series resistor is the largest source of thermal noise at the input of the pixel amplifier. The effect of the decreasing pixel area when scaling down the technology on feature sizes is discussed. The noise analysis is presented for a high resolution imager.

An Australia Telescope survey for CMB anisotropies

We have surveyed six distinct ‘empty fields’ using the Australia Telescope Compact Array (ATCA) in an ultracompact configuration with the aim of imaging, with a high brightness sensitivity, any arcminute-scale brightness-temperature anisotropies in the background radio sky. The six well-separated regions were observed at a frequency of 8.7 GHz, and the survey regions were limited by the ATCA primary beams which have a full width at half-maximum of 6 arcmin at this frequency; all fields were observed with a resolution of 2 arcmin and an rms thermal noise of 24 λJy beam−1. After subtracting foreground confusion detected in higher resolution images of the fields, residual fluctuations in Stokes I images are consistent with the expectations from thermal noise and weaker (unidentified) foreground sources; the Stokes Q and U images are consistent with expectations from thermal noise. Within the sensitivity of our observations, we have no reason to believe that there are any Sunyaev-Zeldovich holes in the microwave sky surveyed. Assuming Gaussian-form CMB anisotropy with a ‘flat’ spectrum, we derive 95 per cent confidence upper limits of Qflat<10-11 λK in polarized intensity and Qflat<25 λK in total intensity. The ATCA filter function peaks at l=4700 and has half-maximum values at l=3350 and 6050.

Preamplifier limitations on the accuracy of Johnson noise thermometers

A detailed analysis is presented of noise and input impedance in noise thermometer preamplifiers. The analysis highlights the advantages of cascode amplifiers and the disadvantages of amplifiers employing global feedback. Feedback gives rise to two significant errors, one arising from an increase in the input-noise current, the other from the modification of the amplifier input impedance. With care, the errors arising from thermal-noise sources associated with the preamplifiers can be kept below 1 mK. However the largest error associated with the preamplifiers, typically 10 mK to 30 mK and previously unnoticed, arises from the interaction of the input capacitance and the transmission line inductance. This effect negates the common practice of matching the RC time constants in noise thermometers.

Excess thermal-noise in the electrical breakdown of random resistor networks

We discuss a new type of excess noise strongly sensitive to non-homogeneous Joule heating of random resistor network and associated with local sources of thermal noise. The evolution of the network towards an electrical breakdown of conductor-insulator type is then studied by using a biased percolation model and it is analysed in terms of an excess-noise temperature. Monte Carlo simulation results show a significant increase of the excess-noise temperature over the average temperature of the network. Remarkably the excess-noise temperature scales with the resistance with an exponent of about 3. The predictivity of the model can be tested on thin film resistors where the determination of the excess noise temperature should provide a valuable indicator of the defectiveness of the film.

Symmetric white noise can induce directed current in ratchets

Symmetric white noise can induce directed current in periodic potentials that lack reflection symmetry (termed ratchets). The requirement for this to occur is that the white noise possesses non-Gaussian statistical properties with all its odd numbered cumulant correlation averages vanishing identically. The fluctuation-induced current is elucidated for three types of white noise: (i) symmetric white Poissonian shot noise with exponentially distributed amplitudes, (ii) two-state diffusion noise being composed of two thermal Nyquist noise sources that successively are switched on and off by dichotomic noise, and (iii) randomly flashing Gaussian white noise. Because the latter two noise sources are not composed of independent increments, the resulting ratchet dynamics $x(t)$ is non-Markovian. The current versus white-noise intensity typically exhibits a nonmonotonic dependence with a maximum assumed at a suitably tuned noise level.

Multi-mode noise analysis of cantilevers for scanning probe microscopy

A multi-mode analysis of micro-cantilever dynamics is presented. We derive the power spectral density of the cantilever displacement due to a thermal noise source and predict the cantilevers’s fundamental resonant frequency and higher harmonics. The first mode in the multi-mode model is equivalent to the traditional single-mode model. Experimental results obtained with a silicon nitride cantilever at 300 K are in excellent qualitative agreement with the multi-mode model. The multi-mode model may be used to obtain accurate values of the cantilever properties such as the elastic modulus, effective mass, thickness and moment of inertia.

Video-rate simulated annealing for stochastic artificial retinas

We describe a massively parallel system that uses speckle patterns projected onto a dedicated integrated circuit to carry out simulated annealing computations at video-rate on a locally interconnected mesh of binary state variables. The integrated circuit is composed of a 24 × 24 array of processing elements, with two photodetectors for speckle detection on each element. The time-varying speckle patterns incident on the circuit act as thermal noise sources responsible for simulating the thermal equilibrium. This system is a first step towards the realization of more complex systems for performing stochastic computations in early vision.

Accounting thermal noise in mathematical models of quasi-homogeneous regions in silicon devices

This work proposes stochastic generalizations of semiconductor fluid-dynamic and the Shockley equation systems for thermal-noise modeling in quasi-homogeneous regions of silicon devices. These stochastic systems include thermal-noise terms derived from the Langevin-equation theory. The Shockley-like stochastic model performs thermal-noise sources in drift-diffusion expressions in the form of the steady-state solution of the Langevin equation, rather than in the white-noise form. Differences from the previous drift-diffusion thermal-noise modeling and the relevant physical aspects are discussed. A quasi-stationary approximation for the Shockley-like stochastic system is considered and theoretically tested for resistor and p-n junction. The corresponding results agree with the expressions for spectral densities by H. Nyquist (1928) and M. Gupta (1982), and present a generalization in the latter case. The proposed models can be used in analytical techniques for device/circuit research/design or incorporated into CAE/CAD software and open for methods of stochastic-differential-equation theory to be applied to thermal-noise analysis within fluid-dynamic and drift-diffusion approaches. >

Evaluation of Uncertainties of the Null-Balanced Total-Power Radiometer System NCS1.

Standard uncertainties are evaluated for the null-balanced, total-power, heterodyned radiometer system with a switched input that was recently developed at NIST to calibrate thermal noise sources. Eight significant sources of uncertainty due to systematic effects are identified, two attributable to the two noise standards, and one each to connectors, the input mismatch, the input switch asymmetry, the isolator, the broadband mismatch and the attenuator. The combined standard uncertainty of a typical coaxial noise source calibration at a representative frequency of 2 GHz is about 1%, A strategy for reducing uncertainties is discussed.

Low temperature properties of soft magnetic materials: Magnetic viscosity and 1/f thermal noise

We study the magnetic properties of soft ferromagnetic cores in the low field linear regime at low temperature (T≤4.2 K) in view of their use in connection with superconducting quantum interference device magnetometers. We have tested several amorphous and polycrystalline alloys in the form of strip-wound toroidal cores. Both high and near zero magnetostrictive alloys are studied. All samples are found out to be the source of thermal magnetic noise of 1/f spectral density in agreement with the fluctuation dissipation theorem. This type of thermal noise comes from a frequency independent imaginary permeability. This feature is equivalently described in terms of the magnetic viscosity effect or by considering the constant (residual) term in the classical Legg’s equation of magnetic losses at low fields. Measurements on a few Co-based amorphous alloys show that the magnetic viscosity is independent of temperature. Explanations in terms of thermal activation processes and quantum tunneling are discussed.