Signals and noise


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Signals and noise

  2. 2. Introduction Undesired sound that is intrinsically objectionable or that interferes with other sounds being listened to. In electronics and information theory, noise refers to those random, unpredictable, and undesirable signals, or changes in signals, that mask the desired information content. In radio, this noise is called static; in television, it is called snow. White noise is a complex signal or sound covering the entire range of component frequencies, or tones, all of which possess equal intensity. In other words we can say that, noise is a random fluctuation in an electrical signal, a characteristic of all electronic circuits. Noise generated by electronic devices varies greatly, as it can be produced by several different effects. Thermal noise is unavoidable at non-zero temperature, while other types depend mostly on device type (such as shot noise, which needs steep potential barrier) or manufacturing quality and semiconductor defects, such as conductance fluctuations, including noise. In communication systems, noise is an error or undesired random disturbance of a useful information signal in a communication channel. The noise is a summation of unwanted or disturbing energy from natural and sometimes man-made sources. Noise is, however, typically distinguished from interference, (e.g. cross-talk, deliberate jamming or other unwanted electromagnetic interference from specific transmitters), for example in the signal-to-noise ratio (SNR), signal-to-interference ratio (SIR) and signal-to-noise plus interference ratio (SNIR) measures. Noise is also typically distinguished from distortion, which is an unwanted systematic alteration of the signal waveform by the communication equipment, for example in the signal- to-noise and distortion ratio (SINAD). In a carrier-modulated passband analog communication system, a certain carrier-to-noise ratio (CNR) at the radio receiver input would result in a certain signal-to-noise ratio in the detected message signal. In a digital communications system, a certain Eb/N0 (normalized signal-to-noise ratio) would result in a certain bit error rate (BER). SOURCES OF NOISE It is important for the analyst who uses a particular instrumental method to be aware of the sources of noise and the instrument components used to minimize this noise because noise determines both the accuracy and detection limits of any measurement. Noise enters a
  3. 3. measurement system from environmental sources external to the measurement system, or it appears as a result of fundamental, intrinsic properties of the system. It is usually possible to identify the sources of environmental noise and to either reduce or avoid their effects on the measurement. Such is not the case with fundamental noise because it arises from the discontinuous nature of matter and energy. Thus, fundamental noise ultimately limits accuracy, precision. and detection limits in every measurement. The major kinds of noise associated with solid-state electronic devices are thermal, shot, and flicker. Fundamental Noise Thermal Noise. Noise that originates from the thermally induced motions in charge carriers is known as thermal noise. It exists even in the absence of current flow and is represented by the formula where V., is the average voltage due to thermal noise, k is the Boltzmann constant, T is the absolute temperature. R is the resistance of the electronic device, and Af is the bandwidth of measurement frequencies, Since thermal noise is independent of the absolute values of frequencies, it is also known as "white noise." Methods for reducing thermal noise are suggested by Equation. Sensitive radiation detectors are often cooled to minimize this noise. Narrowing the frequency bandwidth of the detector is another way to reduce thermal noise, provided the frequencies important to the measurement of interest are not excluded. Sources of noise in instrumental analysis: Types of noise: Chemical: This noise arises from uncontrollable variables in the chemistry of the system such as variation in temperature, pressure, humidity, light and chemical fumes present in the room.
  4. 4. Instrumental : Noise that arises due to the instrumentation itself. It could come from any of the following components- source, input transducer all signal processing elements, and the output transducer. This noise has many types and can arise from several sources. There are four main categories of instrumental noise: Thermal or Johnson, Shot, Flicker, and Environmental. Thermal noise or Johnson noise: arises from thermal agitation of electrons or other charged carriers in resistors, capacitors, radiation detectors, electrochemical cells and other resistive elements in the instrument. this agitation is random and can create charge variations that create voltage fluctuations that we view as noise the magnitude of thermal noise is given by: vrms = (4kTR f)1/2 where vrms = root mean square noise voltage, f = frequency bandwidth, k = l.38 x 10-27 J/K (Boltzman Constant), T = temperature in Kelvin, R = resistance in ohms of the resistive element the bandwidth is inversely proportional to the rise time (t), (response time in seconds to an abrupt change in input) f = 1/3tr rise time is taken as the time required for the output to increase from 10% to 90 of the final value narrowing bandwidth can decrease thermal noise but it will also slow the rate of the machine therefor increasing time required to make a reliable measurement can also be lowered by lowering temperature or electrical resistance dependent upon frequency bandwidth but independent of frequency Shot Noise: Shot noise is encountered whenever electrons and other charged particles cross a junction. In typical electronic circuits, these junctions are found at pn interfaces. The shot noise in arises when current involves the movement of electrons or charged particles across a junction these junctions are typically found at pn interfaces; in photocells and vacuum tubes. shot noises are random and their rate of occurrence is subject to statistical fluctuations which are defined as follows: irms. = (2I f)1/2 where irms = root mean sq. current fluctuation associated with average direct current (I), e = l.60 x 10-19 C, f = bandwidth of frequencies shot noise can be minimized only by reducing bandwidth
  5. 5. Shot noise refers to the random fluctuations of the electric current in an electrical conductor, which are caused by the fact that the current is carried by discrete charges (electrons). The strength of this noise increases for growing magnitude of the average current flowing through the conductor. Shot noise is to be distinguished from current fluctuations in equilibrium, which happen without any applied voltage and without any average current flowing. These equilibrium current fluctuations are known as Johnson-Nyquist noise. Flicker noise: its magnitude is inversely proportional to frequency of signal causes of flicker noise not understood but recognized by frequency dependence can be significant at frequencies lower than 100 Hz causes long term drift in de amplifiers, meters, and galvanometers can be reduced significantly by using wire-wound or metallic film resistors rather than composition type Flicker Noise is associated with crystal surface defects in semiconductors and is also found in vacuum tubes. The noise power is proportional to the bias current, and, unlike thermal and shot noise, flicker noise decreases with frequency. An exact mathematical model does not exist for flicker noise because it is so device-specific. However, the inverse proportionality with frequency is almost exactly 1/f for low frequencies, whereas for frequencies above a few kilohertz, the noise power is weak but essentially flat. Flicker noise is essentially random, but because its frequency spectrum is not flat, it is not a white noise. It is often referred to as pink noise because most of the power is concentrated at the lower end of the frequency spectrum. Environmental noise: Environmental noise is due to a composite of noises from different sources in the environment surrounding the instrument. Figure 5-3 shows some common sources of environmental noise. Much environmental noise occurs because each conductor in an instrument is potentially an antenna capable of picking up electromagnetic radiation and converting it to an electrical signal. There are numerous sources of electromagnetic radiation in the environment including ac power lines, radio and TV stations, gasoline engine ignition systems, arcing switches, brushes in electrical motors, lightening, and ionospheric disturbances. HARDWARE TECHNIQUES FOR SIGNAL- TO-NOISE ENHANCEMENT To avoid losing data, the signal from the input transducer (see Section 1.4) should be sampled at a rate twice that of the highest frequency component of the signal according to the Nyquist
  6. 6. sampling theorem (see Section 2.6). Adherence to this theorem is important to obtain reliable results from either hardware or software S enhancement methods. The rise of time of an instrument is its response time in seconds to an abrupt change in input and normally is taken as the time required for the output to increase from 10% to 90% of its final value. If the rise time is 0.01s, the bandwidth is 33Hz. It is important to note that thermal noise can also be reduced by lowering the electrical resistance of instrument circuits and by lowering the temperature of instrument components. Cooling often reduces the thermal noise in transducers. It is important to note that thermal noise, while dependent on the frequency bandwidth is independent of frequency itself, thus it is sometimes termed white noise by analogy to white light, which contains all visible frequencies. Thermal noise in resistive circuit elements is independent of the physical size of the resistor. Filtering Although amplitude and the phase relationship of input and output signals can be used to discriminate between meaningful signals and noise, frequency is the property most commonly used. As discussed in the previous section, white noise can be reduced by narrowing the range of measured frequencies, environmental noise can be eliminated by selecting the proper frequency. Three kinds of electronic filters are used to select the band of measured frequencies: low-pass filters that allow the passage of all si2nals below a predetermined cutoff frequency, high-pass filters that transmit all frequencies above a given cutoff point, and band pass filters that combine the properties of the other two filters to pass only a narrow band of frequencies. The simplest filters are composed of passive circuit elements (resistors, R, capacitors, C. and inductance coils, L) with the transmitted frequencies determined by values of the individual circuit components.
  7. 7. Signal to noise enhancement: for some measurements only minimal efforts are required for maintaining a good signal to noise ratio because the signals are relatively strong and the requirements for precision and accuracy are low Examples: o weight determinations made in synthesis and color comparisons made in chemical content determinations o when precision is important the signal to noise ratio can become the limiting factor and must be improved, there are two ways to approach this: Hardware: noise is reduced by incorporating into the instrument components such as filters, choppers, shields, modulators, and synchronous detectors these will remove or attenuate noise without affecting the analytical signal significantly Types of Hardware: Grounding and shielding: Shielding, grounding, and minimizing the lengths of conductors with the instrumental system can often substantially reduce noise that arises from environmentally generated electromagnetic radiation. shielding consists of surrounding a circuit, or some of the wires in a circuit with a conducting material that is attached to earth ground this allows electromagnetic radiation to be absorbed by the shield thus avoiding noise generation in the instrument circuit -important when using high-impedance transducers (i.e. glass electrodes)
  8. 8. This is the first line of defense against outside noise caused by high-frequency electrical field and magnetic field coupling as well as electromagnetic radiation. The theory is that the shielding wire, foil or conduit will prevent the bulk of the noise coming in from the outside. It works by relying on two properties 1. Reflection back to the outside world where it can't do any harm... (and, to a small extent, re-reflection within the shield, but this is a VERY small extent) 2. Absorption - where the energy is absorbed by the shield and sent to ground. The effectiveness of the shield is dependent on its: 1. Thickness - the thinner the shield the less effective. This is particularly true of low- frequency noise... Aluminum foil shield works well at rejecting up to 90 dB at frequencies above 30 MHz, but it's inadequate at fending off low-frequency magnetic fields (in fact it's practically transparent below 1 kHz), We rely on balancing and differential amplifiers to get rid of these. 2. Conductivity - the shield must be able to sink all stray currents to the ground plane more easily than anything else. 3. Continuity - we cannot break the shield. It must be continuous around the signal paths, otherwise the noise will leak in like water into a hole in a boat. Don't forget that the holes in your equipment for cooling, potentiometers and so on are breaks in the continuity. General guideline: keep the diameter of your holes at less than 1/20 of the wavelength of the highest frequency you're worried about to ensure at least 20 dB of attenuation. Most high-frequency noise problems are caused by openings in the shield material. Grounding The grounding of audio equipment is there for one primary purpose: to keep you alive. If something goes horribly wrong inside one of those devices and winds up connecting the 120 V AC from the wall to the box (chassis) itself, and you come along and touch the front panel while standing in a pool of water, YOU are the path to ground. This is bad. So, the manufacturers put a third pin on their AC cables which is connected to the chassis on the equipment end, and the third pin in the wall socket. This third pin in the wall socket is called the ground bus and is connected to the electrical breaker box somewhere in the facility. All of the ground busses connect to a primary ground point somewhere in the building. This is the point at which the building makes contact with the earth through a spike or piling called the grounding electrode. The wires which connect these grounds together MUST be heavy-gauge (and therefore very low impedance) in order to ensure that they have a MUCH lower impedance than you when you and it are a parallel connection to ground. The lower this impedance, the less current will flow through you if something goes wrong.
  9. 9. An added benefit to this ground is that we use it as a huge sink where all of the noise on our shielding is routed. Conductor Out From Low Dynamic Range (< 60 dB) Med Dynamic Range (60 to 80 dB) High Dynamic Range (> 80 dB) Low EMI High EMI Low EMI High EMI Ground Electrode 6 2 00 00 0000 Master Bus 10 8 6 4 0 Local Bus 14 12 12* 12* 10* Maximum resistance for any cable (W) 0.5 0.1 0.01 0.001 0.0001 * Do not share ground conductors - run individual branch grounds. In all cases the ground conductor must not be smaller than the neutral conductor of the panel it services. Difference amplifiers: used to attenuate noise generated in the transducer ac signal induced in the transducer circuit generally appears in phase at both the inverting and non-inverting terminals; cancellation then occurs at output Any noise generated in the transducer circuit is particularly critical because it usually appears in an amplified form in the instrument read out. To attenuate this type of noise, most instruments employ a difference amplifier for the first stage of amplification. Common mode noise in the transducer circuit generally appears in the phase at both the inverting and noninverting inputs of the amplifier and is largely subtracted out by the circuit so that the noise at its output is diminished substantially. Instrumentation amplifiers are composed of three op amps. Op amp A and op amp B make up the input stage of the instrumentation amplifier in which the two op amps are cross coupled through three resistors. The second stage of the module is the difference amplifier of op amp C. The overall gain of the circuit is given by: o = K(2a + 1)( 2 - 1) Analog filtering: one of the most common methods to improve S/N ratio is the use of a low-pass analog filter -is effective at removing many high frequency components such as thermal or shot noise because majority of analyte signals are dc with bandwidths that extend over only a few Hz -high-pass signals used in systems where the analyte signal is ac and the filter
  10. 10. can reduce drift and flicker noise -to attenuate noise we use narrow band electronic filters because magnitude of fundamental noise is directly proportional to the sq. rt. of the frequency bandwidth signal. significant noise reduction occurs if input signal is restricted to a narrow band and then an amplifier tuned to this band is used. The band past by the filter must be wide enough to carry all information carried by the signal. First order analog filters depend on one of two things: an inductor or a capicitor. Although we did not actually use these particular components, as much as Sam wanted to, it is these components that make analog filters work. We decided on active rather than passive filters because they give better results. Schematics and Graphs Lowpass Filter: Highpass Filter:
  11. 11. To give those not familiar with analog circuits (or maybe its just been a really long time) an idea of what we wired together we have included some pictures of our breadboard with our first order lowpass filters. Analog Second Order Filters By going to second order filters we were able to shorten the transision band providing greater attenuation of the noise. We were also able to make a bandpass filter using second order design. Also note that compared to first order filters these circuits only require the addition of one capacitor. Schematics and Graphs Lowpass Filter: Highpass Filter:
  12. 12. Bandpass Filter:
  13. 13. Modulation: amplifier drift and flicker noise often interfere with the amplification of a low frequency or dc signal and 1/f noise is often much larger than noises that predominate at larger frequencies therefore modulators are used to convert these to a higher frequency where 1/f is less troublesome the modulated signal is amplified then filtered with a high-pass filter to remove the amplifier 1/f noise the signal is then demodulated and filtered with a low-pass filter in order to provide an amplified dc signal to the readout device noise is a concern because source intensity and detector sensitivity are low which result 'in a small electrical signal from transducer IR transducers are heat detectors, this adds environmental noise due to the thermal radiation of their surroundings -a slotted rotating disk placed in the beam path produces a radiant signal that fluctuates between zero and some max. -signal is converted by transducer to a sq. wave ac electrical signal whose frequency depends upon size of slots and rate of rotation in IR, environmental noise is usually dc and can be reduced with a high-pass filter before amplification -(refer to figure 4-6 on next page) This is a chopper amplifier that uses a solid state switch to shot the input or output signal to the ground appearance of signal at certain stages 0) input a 6-mV dc signal a) switch converts to approx. sq. wave signal of amplitude 6mV b) amplification to ac signal amplitude 6V c) shorted to ground periodically which results in d) reduced amplitude to 3V e) RC filter serves to smooth signal and produce 1.5V dc output Lock-in amplifiers: permit recovery of signals even when S/N is unity or less generally requires a reference signal at same frequency and phase (must have fixed phase relationship) as signal to be amplified Software: based on digital computer algorithms that permit extraction of signal from noisy environment requires some hardware to condition output and convert it to digital form computer and readout system are also needed common software are generally applicable to non-periodic or irregular wave forms, such as absorption spec. or signals having no synchronizing or reference wave Ensemble averaging: successive sets of data (arrays) are collected and summed point by point (often called coaddition)
  14. 14. then data for each point is averaged signal to noise ratio for signal average: points must be measured at a frequency at least 2x that of the highest frequency component of the wave form, much greater frequencies will include more noise but no additional information -wave form reproducibility is important, generally accomplished through synchronizing pulse derived from the wave form -can result in dramatic improvements. Boxcar averaging: digital procedure for smoothing irregularities, that arise from noise, in a wave form assumed analog signal varies slowly with time and that the average of a small number of adjacent points is better than any one individual point usually done by a computer as data is being collected (real time) -limitations include loss of detail, application to only complex signals that change rapidly as a function of time - for square wave or repetitive pulsed outputs where only ave. amplitude is important, it is very important -moving window averaging means point I is the ave. of 1, 2 and 3, point 2 is an ave. of points 2, 3 and 4 etc. here only the first and last points are lost Digital Filtering: moving-window boxcar method is a kind of linear filtering where it assumed that there is an approximate linear relationship among points being sampled -more complex polynomial relationships derive a center point for each window can also be carried out by Fourier transform procedure where the original signal which varies as a function of time (time domain signal) is converted to a frequency domain signal where the independent variable is frequency not time -accomplished mathematically on a computer by a Fourier transform procedure then frequency signal is multiplied by the frequency response of a digital filter which removes a certain frequency region of the transformed signal the filtered time domain signal is retrieved by an inverse Fourier transform