Johnson Noise

11 Key excerpts on "Johnson Noise"

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  The Art of Linear Electronics

  • John Linsley Hood(Author)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  All of these unwanted noise signals can, to some extent, be lessened, or made less obtrusive, by care in the circuit design and in the layout and construction of the equipment, and it is therefore desirable for the designer to keep in mind the nature of noise sources so that he can come closer to the ideal result of a noise free output signal. The physical basis of electrical noise Thermal or Johnson Noise (resistor noise) At all temperatures above absolute zero, (0°K or -273.15°C) the electrons present in any conductor are in a state of restless random movement, which leads to the statistical probability that, at any given moment, there will be more electrons present at one end of a conductor than the other, a situation which causes a fluctuating electrical voltage to be developed across the conductor. This noise voltage will increase as the Noise and Hum 275 temperature is raised, since this increases the degree of agitation of the electrons, and as the resistance of the conductor is increased - because the electrostatic attractions which tend to oppose the movement of charges away from their rest condition of uniform distribution are lessened by the isolating effect of electrical resistance - and as the bandwidth over which the noise signal is measured is increased. The mathematical relationship between these ef-fects, originally defined by Johnson - hence the term 'Johnson' noise - is usually expressed in the form e n (rms) = ^l4kT/yR (1) where e n is the mean noise voltage, normally defined as volts per VHz, k is Boltzmann's constant (1.38 x 10~ 23 ), T is the absolute temperature, in °K, /!/is the measurement bandwidth, and/? is the resistance of the conductor, in ohms. The probability that there will be an imbalance in the charge present between the two ends of the con-ductor is an essentially random one, which leads to the wideband noise characteristic of this voltage.

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  Handbook of High-Temperature Superconductor

  • Neeraj Khare(Author)
  • 2003(Publication Date)
  • CRC Press

    (Publisher)

  6Noise in High-Temperature Superconductor Josephson Junctions

  J.C.Macfarlane, L.Hao,* and C.M.Pegrum University of Strathclyde, Glasgow, Scotland

  (1 ) * Current affiliation: Centre for Basic Metrology, National Physical Laboratory, Teddington, England

  6.1 INTRODUCTION

  6.1.1 Sources of Electronic Noise

  Noise is an important problem in science and engineering because it degrades the accuracy of any measurement and the quality of electronically processed signals. To understand and minimize these effects, one must measure this noise simply and accurately. Perhaps the two most commonly encountered types of noise are thermal noise and shot noise. Thermal noise arises from the random velocity fluctuations of the charge carriers (electrons and/or holes) in a resistive material. The mechanism is sometimes said to be Brownian motion of the charge carriers due to the thermal energy in the material. Thermal noise is present when the resistive element is in thermal equilibrium with its surroundings, and it is often referred to as Johnson Noise (or Nyquist noise) in recognition of two early investigators of this phenomenon (1 , 2 ). Thermal noise is usually represented by the equation

  where k is Boltzmann’s constant (1.38×10−23 J/K), R is the resistance of the conductor, T is the absolute temperature, and Sv is the voltage noise power spectral density.

  Shot noise occurs when the current flows across a barrier. It was first discussed by Schottky (3 ). It is often found in solid-state devices when a current passes a potential barrier such as the depletion layer of a p-n junction. The stream of charge carriers fluctuates randomly about a mean level. The fluctuations (i.e., the shot noise) are due to the random, discrete nature of the tunneling process. The shot noise has a constant spectral density of

  where e is the electronic charge (1.6×10−19 C) and IDC is the average current. In both of the above cases, the noise spectral density is independent of frequency. In many devices, however, there is additional noise which varies with frequency as | f |−α , where a usually lies between 0.8 and 1.2. This is commonly known as 1/f noise or flicker noise or excess noise. For homogeneous materials, the 1/f noise can be represented by the empirical formula (4

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  Radio Systems Engineering

  • Steven W. Ellingson(Author)
  • 2016(Publication Date)
  • Cambridge University Press

    (Publisher)

  4 Noise 4.1 INTRODUCTION .............................................................................................. As discussed in Chapter 1 , it is noise which ultimately limits the sensitivity of a radio system. Noise is present in a variety of forms, both internal and external to the receiver. This chapter addresses the fundamentals of noise, beginning with some basic theory ( Sections 4.2 and 4.3 ), and continuing with concepts pertaining to the characterization of internal noise ( Section 4.4 ), and external noise ( Section 4.5 ). 4.2 THERMAL NOISE .............................................................................................. The atoms and electrons comprising any material experience random displacements with an associated kinetic energy that increases with physical temperature. In an electric circuit, the combined displacement of charge-carrying particles – electrons in particular – is observed as a current. The net difference in electrical potential over some distance can be interpreted as a voltage. The voltage and current resulting from random displacement of charged particles due to temperature is known as thermal noise . This specific noise mechanism is also known as Johnson Noise or Johnson–Nyquist Noise . Because the displacements of charged particles due to temperature are random, the resulting noise voltage and current waveforms can only be described statistically. The instantaneous magnitude of noise waveforms are found to well-modeled as a Gaussian distribution with zero mean. 1 To determine the relevant characteristics of this distribution, let us consider the example of a resistor. Figure 4.1 (a) shows a Thévenin equivalent circuit 2 for a resistor, consisting of an open-circuit voltage v n in series with an ideal (noiseless) resistance R . v n represents the thermal noise generated by the resistor.

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  Microwave System Engineering Principles

  • Samuel J. Raff(Author)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  CHAPTER I THERMAL NOISE 1.1 Basic Nature and Principles Which Can Be Derived From It. The basic limitation of microwave systems is thermal noise. This is sometimes called Johnson Noise or Nyquist noise after two of the principal researchers in this field. J.B. Johnson and H. Nyquist published the two definitive articles on this subject in 1P28 (Ref.1,2). It is surprising that our understanding of thermal noise is so recent. Consider that Maxwell de-veloped the theory of the electromagnetic field in the 1870's and the Quantum theory and relativity date from the early 1900's. Thermal noise is quite as basic a phenomenon as these others and more easily understood. It is noted in References 1 and 2 that thermal noise is closely related to Brownian move-ment and its magnitude is derived from thermodynamics by considering the electrons in a conductor as particles which, like any other particle, have kinetic energy 1/2 kT per degree of freedom, (k is Boltzman's constant. See Eq.1.1) In fact, thermal noise is a modified form of the tail of the black body distribution curve. However, in what follows we shall take a more empirical approach. Suppose we were to take a resistor into a perfectly shielded room and measure the average voltage across it with a high impedance voltmeter that had at its input a very sharp skirted filter of bandwidth B. Thermal noise theory predicts that the measurement would give a root mean square average voltage. V = /4RkTB (1.1) m r.m.s. where V -root mean square average voltage measured (volts) r.m.s. R = resistance (ohms) -23 k = Boltzmann's constant (1.38 χ 10 watt-second/degree) m Τ = absolute temperature (degrees Kelvin) Β = bandwidth of the sharp skirted filter (Hertz) Notice that the noise per unit bandwidth is independent of frequency.

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  Noise in Radio-Frequency Electronics and its Measurement

  • François Fouquet(Author)
  • 2020(Publication Date)
  • Wiley-ISTE

    (Publisher)

  1.2. Spontaneous fluctuations in electronic components 1.2.1. Introduction The different mechanisms giving rise to background noise in electronics are: – thermal noise; – shot noise; – generation / recombination noise; – excess noise. All these noises have in common a mean value of zero, but as they carry a certain power, they are characterized by their root mean square value which has the same definition for random variables as for deterministic signals. In the rest of this section, we will describe these different noises by explaining the mechanisms involved. 1.2.2. Thermal noise Thermal noise originates from the thermal agitation of free charges (conduction electrons and holes, where they exist) in metallic conductors or semiconductors. This noise is also called “Johnson Noise”, “Johnson-Nyquist noise” or “resistance noise”. The explanation of the phenomenon is the following: when a free charge – a conduction electron for example – jointly undergoes the deterministic action of an electric field ܧ ሬ Ԧ and the temperature ܶ, its velocity is ݒ ௘ି ሬ ሬ ሬ ሬ ሬ ሬ ሬ Ԧ ൌ െߤ ௡ ή ܧ ሬ Ԧ ൅ ݒ ்௛ ሬ ሬ ሬ ሬ ሬ ሬ Ԧ where ݒ ்௛ ሬ ሬ ሬ ሬ ሬ ሬ Ԧ is the thermal velocity which is randomly distribu results f is propo one fin distribu Sour – the – the R bb′ , the uted in modul from the disp ortional to th nds instanta ution of ݒ ்௛ ሬ ሬ ሬ ሬ ሬ ሬ Ԧ. Figur rces of therm e “real” resis e non-active e base access Figure 1 le and argum placement of he projection aneous fluct This phenom re 1.1. mal noise are stors; doped areas s resistance o 1.2. ment. If one i f a set of ele of ݒ ௘ି ሬ ሬ ሬ ሬ ሬ ሬ Ԧ alon tuations tha menon is sho resistors in a s of semicon of a bipolar tr Background is interested ectrons in a c ng the axis o at are relat own in Figur all their form nductor comp ransistor as s d Noise in Elect in the curren conductor an f the electric ted to the e 1.1. ms: ponents, for shown in Fig tronics 3 nt which nd which c field ܧ ሬ Ԧ , random example gure 1.2;

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  Information Security Science

  Measuring the Vulnerability to Data Compromises

  • Carl Young(Author)
  • 2016(Publication Date)
  • Syngress

    (Publisher)

  The thermal motion of atoms within the electronic components of any electronic device or sensor sets the limit on sensitivity and therefore determines the minimum signal power that is detectable by a sensor. For example, a resistor in an electronic device will produce a noise voltage and is therefore a source of noise power. Thermal noise in electronic components is also known as Johnson Noise.

  The magnitude of the thermal noise power N in any electronic component is given by the following expression:

  N = k T W

  (5.1)

  Here k is Boltzmann’s constant, which is equal to 1.37 × 10−23  J/degree, and T is the temperature of the resistor in kelvin, which is the number of degrees Celsius (Centigrade) above absolute zero.3 W is the bandwidth of the noise power.

  The implication of expression (5.1) is straightforward: the wider the bandwidth or the greater the absolute temperature, the more noise power is generated. The simplicity of this statement belies the profound consequences to information transmission and signal detection.

  Electronic receivers are rated according to the total noise the receiver adds to the signals it amplifies relative to thermal noise. The relevant rating is known as the equivalent noise temperature and it is a measure of the inherent noisiness of the receiver. Another measure of receiver noisiness that is based on the equivalent noise temperature is the Noise Figure (NF). NF is defined as the ratio of the total output noise, which consists of the thermal noise at 293 K (room temperature) at the input plus the noise produced by the receiver, relative to the thermal noise.

  The important points are that a radio receiver always adds noise to signals, and it simultaneously amplifies both the unwanted noise and the desired signal across the signal bandwidth. However, thermal noise represents the minimum noise power in electronic devices, although other sources often dominate.

  Noise is always present, and depending on the scenario, a particular source of noise will determine the limit on the minimum detectable signal power. In other words, the signal power to be measured is always referenced to noise power. Signal and noise are forever in competition, and the winner will vary depending on scenario-specific conditions. In fact, the signal-to-noise ratio is the

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  Intuitive Analog Circuit Design

  • Marc Thompson(Author)
  • 2013(Publication Date)
  • Newnes

    (Publisher)

  Thermal (a.k.a. “Johnson” or “White”) noise in resistors

  Thermal1 noise is caused by the thermal motion of charges in a conductor, akin to Brownian motion. Thermal noise, which is produced by all resistors regardless of type, is a noise signal that has zero average value, is broadband with a flat spectral density versus frequency, and the noise power increases with temperature. Since noise is a statistical, random phenomenon, we need to consider the mean-square and root-mean-square (RMS) quantities of noise voltage and noise power.

  The physics of thermal noise was first described2 by J. B. Johnson at Bell Labs in 1928, and hence, we sometimes call thermal noise “Johnson” noise. A noisy resistor can be modeled as shown in Figure 16.1 (a) as an ideal resistor in series with a white noise-generating voltage source. A noisy resistor has a thermal noise “power spectral density” of

  (16.1)

  independent3 of frequency, with the interesting units of mean-squared volts per hertz. The thermal voltage noise spectral density is

  (16.2)

  with units of volts per root hertz. To find the total mean-square noise voltage created by the noisy resistor, we need to integrate the power density spectrum over the circuit4 bandwidth. The mean-square value of the noise voltage generator (in units of volts squared) is found by integrating the power spectral density over all frequencies, which is easy in this case because the white noise spectral density is flat versus frequency. Let us assume that we are interested in the noise over the frequency band from direct current (DC) to Δf ; the mean-square noise voltage is then (in units of volts squared):

  (16.3)

  where k is Boltzmann's constant, T is the absolute temperature (in Kelvins), R is the resistance value, and Δf is the bandwidth of interest. The noise voltage RMS amplitude is given by (now in units of volts):

  (16.4)

  FIGURE 16.1

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  Electronic Sensor Design Principles

  • Marco Tartagni(Author)
  • 2022(Publication Date)
  • Cambridge University Press

    (Publisher)

  We charac- terize here electronic thermal noise first from experimental evidence. The tested circuit is shown in Fig. 6.3, where we measure the voltage across a resistor in open-circuit conditions. No static current is flowing through the resistor, and the whole system is at thermal equilibrium. If we measure (through an instrument with sufficient accuracy with respect to our task) the voltage across the circuit biased by an ideal generator V 0 as illustrated in Fig. 6.3A, we observe the following behavior: • The output voltage V ðtÞ is affected by random fluctuations. 256 The Origin of Noise • Its experimental mean tends toward the bias value V 0 , that is, 〈V ðtÞ〉 → V 0 as the sample space increases; therefore, associating the random variable v N ðtÞ with the perturbations around the bias we have 〈V ðtÞ〉 ¼ 〈V 0 þ v N ðtÞ〉 ¼ V 0 þ 〈v N ðtÞ〉 → V 0 ; 〈v N ðtÞ〉 → 0. Therefore, we assume that the perturbation has an expected value equal to zero. 5 • v N ðtÞ is normally distributed, and its mean square 〈v 2 ðtÞ〉 ¼ σ 2 N increases proportionally to the temperature and resistance values. • The corresponding power density S N ðf Þ is uniform in a very large bandwidth. We will refer to v N ðtÞ as the random variable modeling a stochastic process called thermal or Johnson Noise since it was first observed and analyzed by Johnson in 1927. Following the previous experimental results, and assuming the ergodicity of the process, we can model the thermal noise of a noisy resistor as shown in Fig. 6.4A as a random voltage generator v N ðtÞ whose noise power is given by the mean square value v 2 N or by the spectral power density v 2 N ðf Þ and placed in series to a noiseless resistor R as shown in Fig. 6.4B. Following Norton’ s theorem, an equivalent representation of the model mentioned above is represented in Fig.

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  Strain-Engineered MOSFETs

  • C.K. Maiti, T.K. Maiti(Authors)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  6.2 Fundamental Noise Sources The total output current, I ( t ), of a device can be written as the sum of bias cur-rent ( I bias ) and the randomly fluctuating noise current ( i n ( t )) as I ( t ) = I bias + i n ( t ). The external sources that cause fluctuations in the current are not considered in this case. There are some fundamental physical processes, which act as the sources of noise, that can generate the random fluctuations in the current (or voltage) in a device. These noise sources are discussed below and described in terms of the power spectral density (PSD) of the noise current. 6.2.1 Thermal Noise Thermal noise (also known as Nyquist, Johnson, diffusion, velocity fluc-tuation, or white noise) originates from the random thermal movement of electrons, and is present at all frequencies with a flat frequency response (PSD). The phenomenon of thermal noise can be thought of as the thermal excitation of the carriers in a resistor. Due to scattering the velocity of the electron changes randomly. At a particular time instant, there could be more electrons moving in a certain direction than electrons moving in the other directions in a random manner, resulting in a small net current. This current fluctuates randomly in strength and direction, with the average over (long) time being zero. If a piece of material with resistance R and temperature T is considered, the PSD of the thermal noise current is found to be S f kT R S f k TR ( ) 4 / or ( ) 4 I V = = (6.3) where k is Boltzmann’s constant. The thermal noise exists in every physical resistor and resistive part of a device and sets a lower limit on the noise in an electric circuit. In bipolar transistors, thermal noise can be modeled as originated from base resistance and the collector impedance. In field-effect transistors, the existence of thermal noise comes from the physical channel resistance between the drain and gate (when the device is on and conducting current).

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  Radio Frequency Circuit Design

  • W. Alan Davis(Author)
  • 2011(Publication Date)
  • Wiley-IEEE Press

    (Publisher)

  CHAPTER SEVEN Noise in RF Amplifiers

  7.1 SOURCES OF NOISE

  The dynamic range of a communication transmitter or receiver circuit is usually limited at the high-power point by nonlinearities and at the low-power point by noise. Noise is the random fluctuation of electrical power that interferes with the desired signal. There can be interference with the desired signal by other unwanted deterministic signals, but at this point only the interference caused by random fluctuations will be considered. There are a variety of physical mechanisms that account for noise, but probably the most common source is thermal (also referred to as Johnson Noise or Nyquist noise ). This can be illustrated by simply examining the voltage across an open-circuited resistor (Fig. 7.1 ). The resulting voltage is not zero! The average voltage is zero but not the instantaneous voltage. At any temperature above absolute 0 K the Brownian motion of the electrons will produce random instantaneous currents. These currents will produce random instantaneous voltages, and this leads to noise power.

  FIGURE 7.1 Voltage across open-circuit resistor.

  Noise arising in electron tubes, semiconductor diodes, bipolar transistors, or field-effect transistors come from a variety of mechanisms. For example, for tubes, these include random times of emission of electrons from a cathode (called shot noise ), random electron velocities in the vacuum, nonuniform emission energy over the surface of the cathode, and secondary emission from the anode. Similarly for diodes, a random emission of electrons and holes produces noise. In a bipolar transistor, in addition to the diode noise there is partition noise. This represents the fluctuation in the path that charge carriers take through the base to the collector after leaving the emitter. There is in addition 1/f or flicker noise (where f is frequency), which is probably caused by surface recombination of base minority carriers at the base–emitter junction [1]. Clearly, as the frequency approaches dc, the flicker noise increases dramatically. As a consequence, intermediate-frequency amplifier stages in transceivers are designed to operate well above the frequency where 1/f noise is a significant contributor to the total noise. Typically, the 1/f noise is significant in the frequency ranges from 100 Hz to 10 kHz. In a field-effect transistor, there is thermal noise arising from channel resistance, 1/f

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  VLSI Technology

  • Wai-Kai Chen(Author)
  • 2003(Publication Date)
  • CRC Press

    (Publisher)

  The next level deals with the noise properties of active devices and passive compo-nents. Three classes of active devices are chosen for illustration: bipolar junction transistors (BJTs), field effect transistors (FETs), and two terminal junction devices (diodes). Although the treatment of these device classes implies silicon-based technologies (Si-BJT, Si-MOSFET, Si-diode), it can generally be applied to other device classes as well (HBT, MESFET, etc.). Finally, the chip level noise is presented in terms of the major contributions being amplifier noise, oscillator noise, timing jitter, and intercon-nect noise. The evolution of VLSI technologies into the deep-sub-micron regime has significant implications for the treatment of fundamental noise mechanisms, which are briefly outlined in the last section of the chapter. Samuel S. Martin Thad Gabara Kwok Ng Bell Laboratories Lucent Technologies 9-2 VLSI Technology 9.2 Microscopic Noise Thermal Noise Thermal noise is, in general, associated with random motion of particles in a force-free environment. Since the mean available energy per degree of freedom is proportional to temperature, the resulting noise is referred to as thermal noise. Specifically, carrier transport in semiconductors is treated by considering energy distribution functions, such as the Fermi–Dirac distribution. The effect of local fields and scat-tering of carriers in position and momentum space is described by a change in the distribution function. This is expressed by the Boltzmann transport equation. Noise is a stochastic process and is characterized in terms of time-averaged quantities, as the instantaneous value cannot be predicted. The fundamental origins of thermal noise in semiconductors are microscopic velocity fluctuations. Velocity fluctuations occur due to various mechanisms, such as electron-phonon scattering, electron-electron scattering, etc.

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