Noise voltage

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. 

Randomness.—The word random is used frequently to describe erratic and apparently unpredictable variations of an observed quantity. The noise voltage measured at the terminals of a hot resistor, the amplitude of a radar signal that has been reflected from the surface of the sea, and the velocity measured at some point in a turbulent air flow are all examples of random or unpredictable phenomena. 

In any particular situation, it is usually possible to give a variety of reasons why the observed quantity behaves in an erratic manner. The observed quantity may be critically dependent on certain parameters and the observed fluctuations attributed to slight variations of these parameters. The implication here is that the observed fluctuations appear erratic only because we have not taken the trouble to make a sufficiently precise analysis of the situation to disclose the pattern the observations are following. It is also possible, in some situations, to adopt the viewpoint that certain aspects of the phenomenon being studied are inherently unknowable and that the best physical laws we can devise to explain the phenomenon will have some form of randomness or unpredictability built into them. Such is the case, for example, with thermal noise voltages, which are believed to be governed by the probabilistic laws of quantum physics. 

The thermally produced noise voltage X(t) appearing across the terminals of a hot resistor is often modeled by assuming that the probability density function for X(t) is gaussian,... 

The problem just considered can be generalized in a useful way by assuming that we want to predict the value of a time function Y at time t from our knowledge of the value of a different time function X at time t. For example, X(t) could be a noise voltage measured at some point in an electrical network and F(f) the noise voltage measured at a... 

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. 

The noise thermometer is based on the temperature dependence of the mean square noise voltage V2 developed in a thermistor (Nyquist theorem, 1928) ... 

In the past, except for the low-temperature range, the uncertainties of noise thermometry were not comparable to those of the gas thermometry due to the non-ideal performance of detection electronics. Up to now, the most successful technique is the switched input digital correlator proposed by Brixy et al. in 1992 [89], In this method, the noise voltage is fed via two separate pairs of leads to two identical amplifiers whose output signals are multiplied together, squared and time averaged (see Fig. 9.10). 

This eliminates the amplifier and transmission line noise superimposed on the thermal noise, since the respective noise voltages are uncorrelated. 

The signal supplied by cryogenic sensors is very low (in the order of jlV). The white noise voltage is proportional to the frequency bandwidth. To reduce the bandwidth, low-pass filters (carachteristographers with 0.01 Hz cut-off) or band-pass filters (lock-in) are used. The former method is more precise, but a longer time for the measurements is required. 

Optocouplers are a class of devices with input current (/ ) and output current (70) coupled optically, but isolated electrically. They are used extensively in the automation industry and in laboratory equipments where large common-mode noise/voltage or hazardous electrical shocks are present in circuits between transducers detectors and controlling equipments. The simplest optocoupler is composed of an LED (input) and a photodiode (output) as shown in Figure 1.19. 

The signal-to-noise ratio of a signal correlates to the ratio of induced voltage to noise voltage [1, 20]. It can be described as... 

It is assumed that the noise voltage n(t) is the result of a real stationary process (Davenport and Root, 1958) with zero mean. Because it can be shown that the spectral density function S(f) is the Fourier transform of the autocorrelation function of the noise, it follows that the rms noise is given by... 

If a noise current of 100 mA at 1 MHz is to find its way into the ground wire between the two devices, the noise voltage must be 2 V, which is enough to cause the devices to lose communication and perhaps even sustain damage, depending on the device sensitivity. This example is a simple situation consisting of only two devices however, hundreds and perhaps thousands of such devices or circuits might be present in an actual computer or communication data center. All these devices require a common reference from which to operate. This is accomplished by the use of the SRG. 

It is evidently insufficient to consider only the response of a detector when analysing its usefulness for a particular application. It is generally necessary to analyse both intrinsic and extrinsic noise signals and compare them with the response. The result of this comparison can be expressed in many different ways. One of the most useful is the noise-equivalent power nep which is the power of an rms signal input (in watts) required to give a response equal to the total rms noise voltage AVN. Then ... 

With these models, an order-of-magnitude estimate of the signal size is obtained. Both models require calculation of the magnetization of the nuclear spins and the noise due to the detector coil. The rms thermal noise voltage for the probe circuit resistance, R0, is (Fig. 5)... 

The noise level can be expressed in terms of the power incident on the detector necessary to give a signal equivalent to the noise. If the noise voltage is A EN then the noise equivalent power (NEP) is defined by... 

The root mean square (r.m.s.) noise voltage AFj for unit bandwidth is A/j/ Y, where A/j is the r.m.s. noise current for unit bandwidth and Y is the admittance. Therefore... 

This equation gives the mean-square value of the voltage appearing across the terminals of a capadtor filled with a dielectric of zero-frequency relative permittivity, s in terms of Co, the capacitance without a dielectric, and the absolute temperature, T. This noise voltage is caused by the thermally induced dipole-moment fluctuations which are themselves inextricably bound up with the dissipative processes. That this is so is indicated by the fact that equation (42) applied to aJ,to) leads to the relation... 

The noise, both AM and FM, of microwave oscillators used in ESR bridges is equal to or worse than in early years. There has been little improvement in tube oscillators and solid state oscillators have somewhat worse noise in our experience. It is important to recognize that both oscillator AM and FM noise are enhanced in a microwave bridge of the reference arm type. Wilmshurst [12] discusses AM noise enhancement, deriving the following equation for the noise voltage... 

However, in a magnitude of root-mean-square noise amplitude, i.e. DC noise, the SUL without the generation of spike noise takes poor level. Figure 7.3 shows a variation in DC noise voltage of the Co-Ni-Fe-B SUL with in-plane coercivity. DC noise was increased with increasing the value of coercivity [18]. Since the coercivity... 

Fig. 7.3 DC noise voltage of Co-Ni-Fe-B films as a function of in-plane coercivity [18]. 2005 IEEE...

Wang and Uhlenbeck in 1945 [10] showed how the solution procedure just outlined could be applied to the more general Fokker-Planck equation pertaining to an electric circuit having n meshes, each mesh being driven by a white noise voltage. Their form of the Fokker-Planck equation is (dropping the conditional probability bar for economy of notation)... 

Controllers for piezoelectric tube or tripod scanners require high-stability, low-noise voltage amplifiers. Since piezoelectric materials have a large... 

---