Instrumental Chemistry CHAPTER 5 SIGNALS AND NOISE

The Signal to Noise Ratio: (S/N) The signal to noise ratio is a representative marker it that is used in describing the quality of an analytical method or the performance of an instrument. For a dc signal, S/N = mean / standard deviation = x/s where s is the standard deviation of the measured signal strength and x is the mean of the measurement -x/s is the reciprocal of the relative standard deviation (RSD) S/N=I/RSD

The Signal to Noise Ratio The purpose of this Mathcad document is to allow the student to gain a familiarity with the concepts of signal-to-noise ratios and to explore the advantages of ensemble averaging and digital filtering analytical signals. Simulated noisy signals are used to guide the student through a series of individual exercises.

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: Weight determinations made in synthesis and color comparisons made in chemical content determinations

Signal Smoothing Algorithms The signal-to-noise ratio (SNR) of a signal can be enhanced by either hardware or software techniques. The wide use of personal computers in chemical instrumentation and their inherent programming flexibility make software signal smoothing (or filtering) techniques especially attractive. Some of the more common signal smoothing algorithms described below.

Signal Smoothing Algorithms The simpler software technique for smoothing signals consisting of equidistant points is the moving average. An array of raw (noisy) data [y 1, y 2, …, y N ] can be converted to a new array of smoothed data. The "smoothed point" (y k ) s is the average of an odd number of consecutive 2n+1 (n=1, 2, 3,..) points of the raw data y k-n, y k- n+1, …, y k-1, y k, y k+1, …, y k+n-1, y k+n, i.e.

Ensemble Average In ensemble average successive sets of data are collected and summed point by point. Therefore, a prerequisite for the application of this method is the ability to reproduce the signal as many times as possible starting always from the same data point, contrary to the previous two algorithms which operate exclusively on a single data set.

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. 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 High Pass Filters Band Pass Filters

Low Pass Filter Schematic and Graph

High Pass Filter Schematic and Graph

Band Pass Filter Schematic and Graphs

Boxcar Averaging...

Ensemble Averaging...

Moving Average Smooth...

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. 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.

Categories of Instrumental Noise Thermal or Johnson Shot Noise Flicker Noise Environmental 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. Since thermal noise is independent of the absolute values of frequencies, it is also known as "white noise."

Thermal Noise (cont) 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 A f is the bandwidth of measurement frequencies

Shot Noise 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.

Shot Noise (cont) The sub-Poissonian shot- noise power, S, of a metallic resistor as a function of its length, L, as predicted by theory. Indicated are the elastic mean-free path, l, the electron-electron scattering length, l ee, and the electron-phonon scattering length l ep.

Flicker noise... I ts magnitude is inversely proportional to frequency of signal 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 (cont) 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.

Flicker Noise (cont) Change in electrical flicker noise power in hot carrier semiconductors can be explained by fluctuations in the intensity of impurity scattering, which contradicts the Hooge-Kleinpenning- Vandamme hypothesis, which relates flicker conduction noise to lattice scattering. It has been shown that such noise can be caused by fluctuations in the effective number of neutral scattering centers within the semiconductor volume. This source modulates carrier mobility, i.e., mobility fluctuations are a secondary effect.

Environmental Noise Environmental noise is due to a composite of noises from different sources in the environment surrounding the instrument. 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.

Environmental Noise (cont)

Types of Hardware Grounding- 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) Shielding- shielding consists of surrounding a circuit, or some of the wires in a circuit with a conducting material that is attached to earth ground

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.

Conductor Out From Low Dynamic Range (< 60 dB) Med Dynamic Range (60 to 80 dB) High Dynamic Range (> 80 dB) Low EMIHigh EMILow EMIHigh EMI Ground Electrode Master Bus Local Bus141212* 10* Maximum resistance for any cable (W) * 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. Grounding (cont)

Difference Amplifiers 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 non-inverting inputs of the amplifier and is largely subtracted out by the circuit so that the noise at its output is diminished substantially.

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

Analog Filtering 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.

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

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

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