Transcript Instrumental Chemistry

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 [y1, y2, …,
yN] can be converted to a new
array of smoothed data. The
"smoothed point" (yk)s is the
average of an odd number of
consecutive 2n+1 (n=1, 2, 3, ..)
points of the raw data yk-n, ykn+1, …, yk-1, yk, yk+1, …, yk+n-1,
yk+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
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•
•
•
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 Af 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 shotnoise 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, lee, and
the electron-phonon
scattering length lep.
Flicker noise...
• Its 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-KleinpenningVandamme 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
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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.
Grounding (cont)
Conductor Out From
Med Dynamic Range
(60 to 80 dB)
High Dynamic Range
(> 80 dB)
Low EMI
High EMI
Low EMI
High EMI
Low Dynamic Range
(< 60 dB)
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
• 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
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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
References
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http://www.cas.org
http://www.chemcenter/org
http://www.sciencemag.org
http://www.chemcenter/org
http://www.kerouac.pharm.uky.edu/asrg/wave/wav
ehp.html
• http://www.anachem.umu.se/jumpstation.htm
• http://hplc.chem.vt.edu/