Thermal, independent noise

In thermal detectors and especially in bolometers, the energy exchange between the sensing element and the heat sink through a thermal link of conductance G results in a thermal noise known as phonon noise. The NEP associated with this phonon noise, which is a white (frequency-independent) noise, is given by ... 

Semiconductor devices ate affected by three kinds of noise. Thermal or Johnson noise is a consequence of the equihbtium between a resistance and its surrounding radiation field. It results in a mean-square noise voltage which is proportional to resistance and temperature. Shot noise, which is the principal noise component in most semiconductor devices, is caused by the random passage of individual electrons through a semiconductor junction. Thermal and shot noise ate both called white noise since their noise power is frequency-independent at low and intermediate frequencies. This is unlike flicker or ///noise which is most troublesome at lower frequencies because its noise power is approximately proportional to /// In MOSFETs there is a strong correlation between ///noise and the charging and discharging of surface states or traps. Nevertheless, the universal nature of ///noise in various materials and at phase transitions is not well understood. 

Sums of Independent Random Variables.—Sums of statistically independent random variables play a very important role in the theory of random processes. The reason for this is twofold sums of statistically independent random variables turn out to have some rather remarkable mathematical properties and, moreover, many physical quantities, such as thermal noise voltages or measurement fluctuations, can be usefully thought of as being sums of a large number of small, presumably independent quantities. Accordingly, this section will be devoted to a brief discussion of some of the more important properties of sums of independent random variables. 

Many common infrared and near-infrared detectors are subject to phenomena that are mainly thermal in origin, and therefore the detector noise is independent of the signal level. 

For this method, the first derivative of the temperature has to be determined from process measurements with amplified noise filtered out. Since the "safe" temperature need not be specified, the independence and selectivity of this method is greater than with the temperature criterion alone. Another advantage is that a potentially unsafe condition can be identified in its early development stage. However, a number of frequently used, but low hazard thermal processes are characterized by fairly high heating rates, making the use of the first derivative ineffective. 

The thermal motion of electrons in a resistor results in noise that is independent of the nature of the resistance. The power of such thermal noise, within a frequency interval A/, is... 

Next we must consider the different types of noise which can be present in the spectrum [2,9], Detector noise is generally due to random fluctuations in the detector, such as thermal noise, and is therefore independent of the signal level. This type of noise is proportional to the square root of the amount of time a given... 

The frequency distribution of noise is characterized by a power spectrum. There a two types. First, white noise, whose noise power is independent of the frequency. This noise arises from the statistics of electrons or photons and of the thermal energy of conductors. White noise can be reduced by extending the measuring time. Second, excess low frequency noise, flicker, or 1// noise is due to fluctuations, drift and schlieren. It can be reduced by modulation. All types of noise are reduced by multiplex procedures, multichannel techniques, and multiple recording (Schrader, 1980). 

Excitable systems as considered here are many particle systems far from eqnilibrium. Hence variables as voltage drop (neurons), light intensity (lasers) or densities (chemical reactions) are always subject to noise and fluctations. Their sources might be of quite different origin, first the thermal motion of the molecules, the discreteness of chemical events and the quantum uncertainness create some unavoidable internal fluctuations. Bnt in excitable systems, more importantly, the crucial role is played by external sources of fluctuations which act always in nonequilibrium and are not counterbalanced by dissipative forces. Hence their intensity and correlation times and lengths can be considered as independent variables and, subsequently, as new control parameters of the nonlinear dynamics. 

Ionic systems, such as water solutions of NaCl, CuS04, K2Cr04, and Ca(NOs)2 and solutions of sulfuric acid in ethyl alcohol, were among the objects of Johnson s experiments (I) that led him to conclude that there exists equilibrium electrical noise of a universal nature that manifests thermal motion of charged particles in conductors on a macroscopic level. Independently of a particular conductivity mechanism, the voltage spectral density, Sv(/), of this noise can be calculated from the real part of the system... 

It is important to note that thermal noise, although dependent on the frequency bandwidth, is independent of frequency itself. I or this rea.son. it is sometimes termed whi c fwise by analogy to white light, which contains all visible frequencies. Also note that ihcrmal noise in resi.siivc circuit elemonis is independent of the physical size of the resistor. 

Infrared and near-infrared spectroph( tometcrs also exhibit Case 1 behavior. With these, the limiting random error usually arises from Johnson noise in the thermal detector. Recall (Section. 8-2) that this type of noise is independent of the magnitude of the pho-locurrcnt indeed, iluctuations arc observed even in the absertce of radiation when there is essentially zero net current. 

Figure 4. Noise spectra at various temperatures for a PS sample (4% CB) showing an 1/i type dependence of the current noise (direct current 20 pA) and a frequency independence of the thermal noise at all temperatures (even in the transition region). Bandwidth,...

The frequency distribution of the current noise was of the l// -type and was independent of temperature that is to say, it was the same inside and outside the Tg or Tm region, respectively. This constancy is illustrated in Figure 4 for the Tg region of PS. The spectrum for thermal noise was white in all the measurements carried out. The sample resistance values calculated from the observed noise spectra agreed with the resistance values obtained with the conventional resistance bridge irrespective of the temperature or time scale of the experiment. 

The spectral density of the process is constant at constant temperature, i.e., 6 co) is independent of the noise frequency the case of the so-called thermal noise. 

Because the performance of infrared detectors is limited by noise, it is important to be able to specify a signal-to-noise ratio in response to incident radiant power. An area-independent figure of merit is D ( dee-star ) defined as the rms signal-to-noise ratio in a 1 Hz bandwidth per unit rms incident radiant power per square root of detector area. D can be defined in response to a monochromatic radiation source or in response to a black body source. In the former case it is known as the spectral D, symbolized by Df X, f, 1) where A is the source wavelength,/is the modulation frequency, and 1 represents the 1 Hz bandwidth. Similarly, the black body D is symbolized by Z> (T,/1), where T is the temperature of the reference black body, usually 500 K. Unless otherwise stated, it is assumed that the detector Held of view is hemispherical 2n ster). The units of D are cm Hz Vwatt. The relationship between )J measured at the wavelength of peak response and D" (500 K) for an ideal photon detector is illustrated in Fig. 2.14. For an ideal thermal detector, Df = D (T) at all wavelengths and temperatures. 

This noise temperature may not correspond to any physical temperature, since a source of nonthermal white noise may produce far more white noise than would correspond to the thermal noise at its actual operating temperature. The fact that Equation (1.6) and Equation (1.7) are independent of resistance makes them easily extendable to transistors and diodes, which have varying resistances depending on the current they carry. Since source and load devices would be carrying the same current the formulas can be applied. 

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