INSTRUMENTAL METHODS OF ANALYSIS LESSION NOTES

BT2258 -LECTURE NOTES ON INSTRUMENTAL METHODS OF ANALYSIS

BACHELOR OF TECHNOLOGY IV SEMESTER PREPARED BY Mr. K. Selvaraj B. Pharm, M. Tech DEPARTMENT OF BIOTECHNOLOGY RAJALAKSHMI ENGINEERING COLLEGE THANDALAM- 602 105

SYLLABUS SUBJECT

: INSTRUMENTAL METHODS OF ANALYSIS

SUBJECT CODE

: BT2258

YEAR / SEM

: II YEAR B.Tech (BIOTECH)/ IV SEMESTER

UNIT I

BASICS OF MEASUREMENT

Classification of methods – calibration of instrumental methods – electrical components and circuits – signal to noise ratio – signal – noise enhancement. UNIT II

OPTICAL METHODS

General design – sources of radiation – wavelength selectors – sample containers – radiation transducers – types of optical instruments – Fourier transform measurements. UNIT III

MOLECULAR SPECTROSCOPY

Measurement of transmittance and absorbance – beer's law – spectrophotometer analysis – qualitative and quantitative absorption measurements - types of spectrometers – UV – visible – IR – Raman spectroscopy – instrumentation – theory. UNIT IV

THERMAL METHODS

Thermo-gravimetric methods – differential thermal analysis – differential scanning calorimetry. UNIT V

SEPARATION METHODS

Introduction to chromatography – models – ideal separation – retention parameters – van – deemter equation – gas chromatography – stationary phases – detectors – kovats indices – HPLC – pumps – columns – detectors – ion exchange chromatography – size exclusion chromatography – supercritical chromatography – capillary electrophoresis

UNIT I

BASICS OF MEASUREMENT

Classification of methods – calibration of instrumental methods – electrical components and circuits – signal to noise ratio – signal – noise enhancement.

INTRODUCTION Analytical Chemistry deals with methods for determining the chemical composition of samples of matter. A qualitative method yields information about the identity of atomic or molecular species or the functional groups in the sample; a quantitative method, in contrast, provides numerical information as to the relative amount of one or more of these components. Analytical methods are often classified as being either classical or instrumental. This classification is largely historical with classical methods, sometimes called wet-chemical methods, preceding instrumental methods by a century or more. Classical Methods Separation of analytes by precipitation, extraction, or distillation. Qualitative analysis by reaction of analytes with reagents that yielded products that could be recognized by their colors, boiling or melting points, solubilities, optical activities, or refractive indexes. Quantitative analysis by gravimetric or by titrimetric techniques. 1. Gravimetric Methods – the mass of the analyte or some compound produced from the analyte was determined.

2. Titrimetric Methods – the volume or mass of a standard reagent required to react completely with the analyte was measured. Instrumental Methods Measurements of physical properties of analytes, such as conductivity, electrode potential, light absorption, or emission, mass to charge ratio, and fluorescence, began to be used for quantitative analysis of a variety of inorganic, organic, and biochemical analyte. Highly efficient chromatographic and electrophoretic techniques began to replace distillation, extraction, and precipitation for the separation of components of complex mixtures prior to their qualitative or quantitative determination. These newer methods for separating and determining chemical species are known collectively as instrumental methods of analysis. Instrumentation can be divided into two categories: detection and quantitation. 1. Quantitation Measurement of physical properties of analytes - such as conductivity, electrode potential, light absorption or emission, mass-to-charge ratio, and fluorescence-began to be employed for quantitative analysis of inorganic, organic, and biochemical analytes. 2. Detection Efficient chromatographic separation techniques are used for the separation of components of complex mixtures. Table 1. Classification of instrumental methods based on different analytical signals Signal Emission of radiation

Absorption of radiation

Scattering of radiation Refraction of radiation Diffraction of radiation Rotation of radiation Electrical potential Electrical charge Electrical current Electrical resistance

Instrumental Methods Emission spectroscopy (X-ray, UV, visible, electron, Auger); fluorescence, phosphorescence, and luminescence (X-ray, UV, and visible) Spectrophotometry and photometry (X-ray, UV, visible, IR); photoacoustic spectroscopy; nuclear magnetic resonance and electron spin resonance spectroscopy Turbidimetry; nephelometry; Raman spectroscopy Refractometry; interferometry X-Ray and electron diffraction methods Polarimetry; optical rotary dispersion; circular dichroism Potentiometry; chronopotentiometry Coulometry Polarography; amperometry Conductometry

Mass-to-charge ratio Rate of reaction Thermal properties Radioactivity

Mass spectrometry Kinetic methods Thermal conductivity and enthalpy Activation and isotope dilution methods

CALIBRATION OF INSTRUMENTAL METHODS A calibration curve is one approach to the problem of instrument calibration; other approaches may mix the standard into the unknown, giving an internal standard. The calibration curve is a plot of how the instrumental response, the so-called analytical signal, changes with the concentration of the analyte (the substance to be measured). The operator prepares a series of standards across a range of concentrations near the expected concentration of analyte in the unknown. The concentrations of the standards must lie within the working range of the technique (instrumentation) they are using (see figure). Analyzing each of these standards using the chosen technique will produce a series of measurements. For most analyses a plot of instrument response vs. analyte concentration will show a linear relationship. The operator can measure the response of the unknown and, using the calibration curve, can interpolate to find the concentration of analyte. Calibration curve

Figure 1.Limit of detection (LOD), limit of quantification (LOQ), dynamic range, and limit of linearity (LOL).

How to create a calibration curve The data - the concentrations of the analyte and the instrument response for each standard - can be fit to a straight line, using linear regression analysis. This yields a model described by the equation y = mx + c, where y is the instrument response, m represents the sensitivity, and c is a constant that describes the background. The analyte concentration (x) of unknown samples may be calculated from this equation. Many different variables can be used as the analytical signal. For instance, chromium (III) might be measured using a chemiluminescence method, in an instrument that contains a

photomultiplier tube (PMT) as the detector. The detector converts the light produced by the sample into a voltage, which increases with intensity of light. The amount of light measured is the analytical signal. Most analytical techniques use a calibration curve. There are a number of advantages to this approach. First, the calibration curve provides a reliable way to calculate the uncertainty of the concentration calculated from the calibration curve (using the statistics of the least squares line fit to the data). [1] Second, the calibration curve provides data on an empirical relationship. The mechanism for the instrument's response to the analyte may be predicted or understood according to some theoretical model, but most such models have limited value for real samples. (Instrumental response is usually highly dependent on the condition of the analyte, solvents used and impurities it may contain; it could also be affected by external factors such as pressure and temperature.) Many theoretical relationships, such as fluorescence, require the determination of an instrumental constant anyway, by analysis of one or more reference standards; a calibration curve is a convenient extension of this approach. The calibration curve for a particular analyte in a particular (type of) sample provides the empirical relationship needed for those particular measurements. The chief disadvantages are that the standards require a supply of the analyte material, preferably of high purity and in known concentration. (Some analytes - e.g., particular proteins - are extremely difficult to obtain pure in sufficient quantity.) Applications Analysis of concentration Verifying the proper functioning of an analytical instrument or a sensor device such as an ion selective electrode Determining the basic effects of a control treatment (such as a dose-survival curve in clonogenic assay) Standard addition method The method of standard addition is used in instrumental analysis to determine concentration of a substance (analyte) in an unknown sample by comparison to a set of samples of known concentration, similar to using a calibration curve. Standard addition can be applied to most analytical techniques and is used instead of a calibration curve to solve the matrix effect problem.

This graph is an example of a standard addition plot used to determine the concentration of calcium in an unknown sample by atomic absorption spectroscopy. The point at zero concentration added Ca is the reading of the unknown, the other points are the readings after adding increasing amounts ('spikes') of standard solution. The absolute value of the x-intercept is the concentration of Ca in the unknown, in this case 1.69E-6 g/mL.

Applications Standard addition is frequently used in atomic absorption spectroscopy and gas chromatography.

LAWS OF ELECTRICITY Ohm's Law For many conductors of electricity, the electric current which will flow through them is directly proportional to the voltage applied to them. When a microscopic view of Ohm's law is taken, it is found to depend upon the fact that the drift velocity of charges through the material is proportional to the electric field in the conductor. The ratio of voltage to current is called the resistance, and if the ratio is constant over a wide range of voltages, the material is said to be an "ohmic" material. If the material can be characterized by such a resistance, then the current can be predicted from the relationship:

Kirchhoff's Current Law (KCL) The current entering any junction is equal to the current leaving that junction. i1 + i4 = i2 + i3.This law is also called Kirchhoff's first law, Kirchhoff's point rule, Kirchhoff's junction rule (or nodal rule), and Kirchhoff's first rule. Power law The general form of the law is P=VI where I is the magnitude of the physical stimulus, ψ(I) is the psychophysical function relating to the subjective magnitude of the sensation evoked by the stimulus, a is an exponent that depends on the type of stimulation and k is a proportionality constant that depends on the type of stimulation and the units used.

DIRECT CURRENT CIRCUITS AND MEASUREMENTS Direct Current.(DC) Is one that flows always in the same direction. Most electronic devices need Direct Current because they require a steady flow of electrons that always head in the same direction. A battery is Direct Current. Alternating Current (AC) is changed to Direct Current (DC) with the use of Diode Rectifiers. You cannot use a transformer with Direct Current.

Series Circuit A Series circuit is one in which all components are connected in tandem. The current at every point of a series circuit stays the same. In series circuits the current remains the same but the voltage drops may vary.

Parallel Circuit Parallel circuits are those in which the components are so arranged that the current divides between them. In parallel circuits the voltage remains the same but the current may vary. The circuits in your home are wired in parallel.

MEASUREMENT OF DC

Digital voltmeters (DVM) Digital voltmeters usually employ an electronic circuit that acts as an integrator, linearly ramping output voltage when input voltage is constant (this can be easily realized with an opamp). The dual-slope integrator method applies a known reference voltage to the integrator for a fixed time to ramp the integrator's output voltage up, then the unknown voltage is applied to ramp it back down, and the time to ramp output voltage down to zero is recorded (realized in an ADC implementation). The unknown voltage being measured is the product of the voltage reference and the ramp-up time divided by the ramp-down time. The voltage reference must remain constant during the ramp-up time, which may be difficult due to supply voltage and temperature variations. Part of the problem of making an accurate voltmeter is that of calibration to check its accuracy. In laboratories, the Weston Cell is used as a standard voltage for precision work. Precision voltage references are available based on electronic circuits.Digital voltmeters, like vacuum tube voltmeters, generally exhibit a constant input resistance of 10 megohms regardless of set measurement range. ALTERNATING CURRENT CIRCUITS The amplitude or peak value of the sinusoidal variation we shall represent by Vm and Im, and we shall use V = Vm/21/2 and I = Im/21/2 without subscripts to refer to the RMS values. For an explanation of RMS values, see Power and RMS values. So for instance, we shall write: v = v(t) = Vm sin (ωt + φ) i = i(t) = Im sin (ωt). where ω is the angular frequency. ω = 2πf, where f is the ordinary or cyclic frequency. f is the number of complete oscillations per second. φ is the phase difference between the voltage and current. We shall meet this and the geometrical significance of ω later. Resistors and Ohm's law in AC circuits The voltage v across a resistor is proportional to the current i travelling through it. Further, this is true at all times: v = Ri. So, if the current in a resistor is i = Im . sin (ωt) , v = R.i = R.Im sin (ωt)

we write:

v = Vm. sin (ωt)

where

Vm = R.Im So for a resistor, the peak value of voltage is R times the peak value of current. Further, they are in phase: when the current is a maximum, the voltage is also a maximum. (Mathematically, φ = 0.) The first animation shows the voltage and current in a resistor as a function of time. Impedance and reactance Circuits in which current is proportional to voltage are called linear circuits. (As soon as one inserts diodes and transistors, circuits cease to be linear, but that's another story.) The ratio of voltage to current in a resistor is its resistance. Resistance does not depend on frequency, and in resistors the two are in phase, as we have seen in the animation. However, circuits with only resistors are not very interesting. In general, the ratio of voltage to current does depend on frequency and in general there is a phase difference. So impedance is the general name we give to the ratio of voltage to current. It has the symbol Z. Resistance is a special case of impedance. Another special case is that in which the voltage and current are out of phase by 90°: this is an important case because when this happens, no power is lost in the circuit. In this case where the voltage and current are out of phase by 90°, the ratio of voltage to current is called the reactance, and it has the symbol X. Capacitors and charging The voltage on a capacitor depends on the amount of charge you store on its plates. The current flowing onto the positive capacitor plate (equal to that flowing off the negative plate) is by definition the rate at which charge is being stored. So the charge Q on the capacitor equals the integral of the current with respect to time. From the definition of the capacitance, vC = q/C, so

we have a sinusoidal current i = Im . sin (ωt), so integration gives

(The constant of integration has been set to zero so that the average charge on the capacitor is 0). Now we define the capacitive reactance XC as the ratio of the magnitude of the voltage to magnitude of the current in a capacitor. From the equation above, we see that X C = 1/ωC. Now we can rewrite the equation above to make it look like Ohm's law. The voltage is proportional to the current, and the peak voltage and current are related by Vm = XC.Im. RC Series combinations When we connect components together, Kirchoff's laws apply at any instant. So the voltage v(t) across a resistor and capacitor in series is just vseries(t) = vR(t) + vC(t) However the addition is complicated because the two are not in phase. The next animation makes this clear: they add to give a new sinusoidal voltage, but the amplitude is less than VmR(t) + VmC(t). Similarly, the AC voltages (amplitude times 21/2) do not add up. This may seem confusing, so it's worth repeating: vseries = vR + vC

but

Vseries > VR + VC. This should be clear on the animation and the still graphic below: check that the voltages v(t) do add up, and then look at the magnitudes. The amplitudes and the RMS voltages V do not add up in a simple arithmetical way. Here's where phasor diagrams are going to save us a lot of work. Play the animation again (click play), and look at the projections on the vertical axis. Because we have sinusoidal variation in time, the vertical component (magnitude times the sine of the angle it makes with the x axis) gives us v(t). But the y components of different vectors, and therefore phasors, add up simply: if rtotal = r1 + r2, ry total = ry1 + ry2.

then

So v(t), the sum of the y projections of the component phasors, is just the y projection of the sum of the component phasors. So we can represent the three sinusoidal voltages by their phasors. (While you're looking at it, check the phases. You'll see that the series voltage is behind the current in phase, but the relative phase is somewhere between 0 and 90°, the exact value depending on the size of VR and VC. All of the variables (i, vR, vC, vseries) have the same frequency f and the same angular frequency ω, so their phasors rotate together, with the same relative phases. In this series circuit, the current is common. (In a parallel circuit, the voltage is common, so I would make the voltage the horizontal axis.)

The phasor diagram below shows us a simple way to calculate the series voltage. The components are in series, so the current is the same in both. The voltage phasors (brown for resistor, blue for capacitor in the convention we've been using) add according to vector or phasor addition, to give the series voltage (the red arrow).

From Pythagoras' theorem: V2mRC = V2mR + V2mC If we divide this equation by two, and remembering that the RMS value V = Vm/21/2, we also get:

Now this looks like Ohm's law again: V is proportional to I. Their ratio is the series impedance, Zseries and so for this series circuit,

Note the frequency dependence of the series impedance ZRC: at low frequencies, the impedance is very large; because the capacitive reactance 1/ωC is large (the capacitor is open circuit for DC). At high frequencies, the capacitive reactance goes to zero (the capacitor doesn't have time to charge up) so the series impedance goes to R. At the angular frequency ω = ωo = 1/RC, the capacitive reactance 1/ωC equals the resistance R. We shall show this characteristic frequency on all graphs on this page. Remember how, for two resistors in series, you could just add the resistances: Rseries = R1 + R2 to get the resistance of the series combination. That simple result comes about because the two voltages are both in phase with the current, so their phasors are parallel. Because the phasors for reactances are 90° out of phase with the current, the series impedance of a resistor R and a reactance X are given by Pythagoras' law: Zseries2 = R2 + X2 Ohm's law in AC We can rearrange the equations above to obtain the current flowing in this circuit. Alternatively we can simply use the Ohm's Law analogy and say that I = V source/ZRC. Either way we get

where the current goes to zero at DC (capacitor is open circuit) and to V/R at high frequencies (no time to charge the capacitor).

From simple trigonometry, the angle by which the current leads the voltage is tan-1 (VC/VR) = tan-1 (IXC/IR) = tan-1 (1/ωRC) = tan-1 (1/2πfRC). However, we shall refer to the angle φ by which the voltage leads the current. The voltage is behind the current because the capacitor takes time to charge up, so φ is negative, ie

φ = tan-1 (1/ωRC) = tan-1 (1/2πfRC). At low frequencies, the impedance of the series RC circuit is dominated by the capacitor, so the voltage is 90° behind the current. At high frequencies, the impedance approaches R and the phase difference approaches zero. The frequency dependence of Z and φ are important in the applications of RC circuits. The voltage is mainly across the capacitor at low frequencies, and mainly across the resistor at high frequencies. Of course the two voltages must add up to give the voltage of the source, but they add up as vectors. V2RC = V2R + V2C. At the frequency ω = ωo = 1/RC, the phase φ = 45° and the voltage fractions are V R/VRC = VC/VRC = 1/2V1/2 = 0.71.

So, by chosing to look at the voltage across the resistor, you select mainly the high frequencies, across the capacitor, you select low frequencies. This brings us to one of the very important applications of RC circuits, and one which merits its own page: filters, integrators and differentiators where we use sound files as examples of RC filtering. RL Series combinations In an RL series circuit, the voltage across the inductor is aheadof the current by 90°, and the inductive reactance, as we saw before, is XL = ωL. The resulting v(t) plots and phasor diagram look like this.

RLC Series combinations Now let's put a resistor, capacitor and inductor in series. At any given time, the voltage across the three components in series, vseries(t), is the sum of these: vseries(t) = vR(t) + vL(t) + vC(t), The current i(t) we shall keep sinusoidal, as before. The voltage across the resistor, v R(t), is in phase with the current. That across the inductor, vL(t), is 90° ahead and that across the capacitor, vC(t), is 90° behind. Once again, the time-dependent voltages v(t) add up at any time, but the RMS voltages V do not simply add up. Once again they can be added by phasors representing the three sinusoidal voltages. Again, let's 'freeze' it in time for the purposes of the addition, which we do in the graphic below. Once more, be careful to distinguish v and V.

Look at the phasor diagram: The voltage across the ideal inductor is antiparallel to that of the capacitor, so the total reactive voltage (the voltage which is 90° ahead of the current) is V L VC, so Pythagoras now gives us: V2series = V2R + (VL - VC)2 Now VR = IR, VL = IXL = ωL and VC = IXC= 1/ωC. Substituting and taking the common factor I gives:

where Zseries is the series impedance: the ratio of the voltage to current in an RLC series ciruit. Note that, once again, reactances and resistances add according to Pythagoras' law: Zseries2

=

R2

+

Xtotal2

= R2 + (XL  XC)2. Remember that the inductive and capacitive phasors are 180° out of phase, so their reactances tend to cancel. Now let's look at the relative phase. The angle by which the voltage leads the current is φ = tan-1 ((VL - VC)/VR). Substiting VR = IR, VL = IXL = ωL and VC = IXC= 1/ωC gives:

The dependence of Zseries and φ on the angular frequency ω is shown in the next figure. The angular frequency ω is given in terms of a particular value ωo, the resonant frequency (ωo2 = 1/LC), which we meet below.

The next graph shows us the special case where the frequency is such that VL = VC.

Because vL(t) and vC are 180° out of phase, this means that vL(t) =  vC(t), so the two reactive voltages cancel out, and the series voltage is just equal to that across the resistor. This case is called series resonance. SIGNAL-TO-NOISE RATIO The signal is what you are measuring that is the result of the presence of your analyte. Noise is extraneous information that can interfere with or alter the signal. It can not be completely eliminated, but hopefully reduced. True Noise is considered random. Signal-to-noise ratio (often abbreviated SNR or S/N) is an electrical engineering concept, also used in other fields (such as scientific measurements, biological cell signaling), defined as the ratio of a signal power to the noise power corrupting the signal. In less technical terms, signal-to-noise ratio compares the level of a desired signal (such as music) to the level of background noise. The higher the ratio, the less obtrusive the background noise is.

In analog and digital communications, signal-to-noise ratio, often written S/N or SNR, is a measure of signal strength relative to background noise. The ratio is usually measured in decibels (dB).If the incoming signal strength in microvolts is Vs, and the noise level, also in microvolts, is Vn, then the signal-to-noise ratio, S/N, in decibels is given by the formula S/N = 20 log10(Vs/Vn) If Vs = Vn, then S/N = 0. In this situation, the signal borders on unreadable, because the noise level severely competes with it. In digital communications, this will probably cause a reduction in data speed because of frequent errors that require the source (transmitting) computer or terminal to resend some packets of data. Ideally, Vs is greater than Vn, so S/N is positive. As an example, suppose that V s = 10.0 microvolts and Vn = 1.00 microvolt. Then S/N = 20 log10(10.0) = 20.0 dB which results in the signal being clearly readable. If the signal is much weaker but still above the noise -- say 1.30 microvolts -- then S/N = 20 log10(1.30) = 2.28 dB which is a marginal situation. There might be some reduction in data speed under these conditions. If Vs is less than Vn, then S/N is negative. In this type of situation, reliable communication is generally not possible unless steps are taken to increase the signal level and/or decrease the noise level at the destination (receiving) computer or terminal. Communications engineers always strive to maximize the S/N ratio. Traditionally, this has been done by using the narrowest possible receiving-system bandwidth consistent with the data speed desired. However, there are other methods. In some cases, spread spectrum techniques can improve system performance. The S/N ratio can be increased by providing the source with a higher level of signal output power if necessary. In some high-level systems such as radio telescopes, internal noise is minimized by lowering the temperature of the receiving circuitry to near absolute zero (-273 degrees Celsius or -459 degrees Fahrenheit). In wireless systems, it is always important to optimize the performance of the transmitting and receiving antennas. Types of Noise 

Chemical Noise 

Chemical reactions



Reaction/technique/instrument specific



Instrumental Noise 

Germane to all types of instruments



Can often be controlled physically (e.g. temp) or electronically (software

averaging) Instrumental Noise 

Thermal (Johnson) Noise: 

Thermal agitation of electrons affects their “smooth” flow.



Due to different velocities and movement of electrons in electrical

components. 

Upon both temperature and the range of frequencies (frequency bandwidths)

being utilized. 

Can be reduced by reducing temperature of electrical components.



Eliminated at “absolute” zero.



Considered “white noise” because it is independent of frequency (but

dependent on frequency bandwidth or the range of frequencies being measured).



Shot Noise: 

Occurs when electrons or charged particles cross junctions (different

materials, vacuums, etc.) 

Considered “white noise” because it is independent of frequency.



It is the same at any frequency but also dependent on frequency bandwidth



Due to the statistical variation of the flow of electrons (current) across some

junction





Some of the electrons jump across the junction right away



Some of the electrons take their time jumping across the junction

Flicker Noise 

Frequency dependent



Significant at frequencies less than 100 Hz



Magnitude is inversely proportional to frequency



Results in long-term drift in electronic components



Can be controlled by using special wire resistors instead of the less expensive

carbon type.



Environmental Noise 

Unlimited possible sources



Can often be eliminated by eliminating the source



Other noise sources can not be eliminated!!!!!!



Methods of eliminating it…



Moving the instrument somewhere else



Isolating /conditioning the instruments power source



Controlling temperature in the room



Control expansion/contraction of components in instrument



Eliminating interferences



Stray light from open windows, panels on instrument



Turning off radios, TV’s, other instruments

SIGNAL-NOISE ENHANCEMENT HARDWARE METHODS Lock-in amplifier A lock-in amplifier (also known as a phase-sensitive detector) is a type of amplifier that can extract a signal with a known carrier wave from extremely noisy environment (S/N

ratio can be as low as -60 dB or even less . It is essentially a homodyne with an extremely low pass filter (making it very narrow band). Lock-in amplifiers use mixing, through a frequency mixer, to convert the signal's phase and amplitude to a DC—actually a time-varying lowfrequency—voltage signal. Basic principles Operation of a lock-in amplifier relies on the orthogonality of sinusoidal functions. Specifically, when a sinusoidal function of frequency ν is multiplied by another sinusoidal function of frequency μ not equal to ν and integrated over a time much longer than the period of the two functions, the result is zero. In the case when μ is equal to ν, and the two functions are in phase, the average value is equal to half of the product of the amplitudes. In essence, a lock-in amplifier takes the input signal, multiplies it by the reference signal (either provided from the internal oscillator or an external source), and integrates it over a specified time, usually on the order of milliseconds to a few seconds. The resulting signal is an essentially DC signal, where the contribution from any signal that is not at the same frequency as the reference signal is attenuated essentially to zero, as well as the out-ofphase component of the signal that has the same frequency as the reference signal (because sine functions are orthogonal to the cosine functions of the same frequency), and this is also why a lock-in is a phase sensitive detector. More basic principles Lock-in amplifiers are used to measure the amplitude and phase of signals buried in noise. They achieve this by acting as a narrow bandpass filter which removes much of the unwanted noise while allowing through the signal which is to be measured. The frequency of the signal to be measured and hence the passband region of the filter is set by a reference signal, which has to be supplied to the lock-in amplifier along with the unknown signal. The reference signal must be at the same frequency as the modulation of the signal to be measured. A basic lock-in amplifier can be split into 4 stages: an input gain stage, the reference circuit, a demodulator and a low pass filter. Input Gain Stage: The variable gain input stage pre-processes the signal by amplifying it to a level suitable for the demodulator. Nothing complicated here, but high performance amplifiers are required. Reference Circuit: The reference circuit allows the reference signal to be phase shifted.

Demodulator: The demodulator is a multiplier. It takes the input signal and the reference and multiplies them together. When you multiply two waveforms together you get the sum and difference frequencies as the result. As the input signal to be measured and the reference signal are of the same frequency, the difference frequency is zero and you get a DC output which is proportional to the amplitude of the input signal and the cosine of the phase difference between the signals. By adjusting the phase of the reference signal using the reference circuit, the phase difference between the input signal and the reference can be brought to zero and hence the DC output level from the multiplier is proportional to the input signal. The noise signals will still be present at the output of the demodulator and may have amplitudes 1000 times as large as the DC offset. Low Pass Filter: As the various noise components on the input signal are at different frequencies to the reference signal, the sum and difference frequencies will be non zero and will not contribute to the DC level of the output signal. This DC level (which is proportional to the input signal) can now be recovered by passing the output from the demodulator through a low pass filter. The above gives an idea of how a basic lock-in amplifier works. Actual lock-in amplifiers are more complicated, as there are instrument offsets that need to be removed, but the basic principle of operation is the same. Application to signal measurements in a noisy environment The essential idea in signal recovery is that noise tends to be spread over a wider spectrum, often much wider than the signal. In the simplest case of white noise, even if the root mean square of noise is 106 times as large as the signal to be recovered, if the bandwidth of the measurement instrument can be reduced by a factor much greater than 106 around the signal frequency, then the equipment can be relatively insensitive to the noise. In a typical 100 MHz bandwidth (e.g. an oscilloscope), a bandpass filter with width much narrower than 100 Hz would accomplish this. In summary, even when noise and signal is indistinguishable in time domain, if signal has a definite frequency band and there is no large noise peak within that band, noise and signal can be separated sufficiently in the frequency domain.If the signal is either slowly varying or otherwise constant (essentially a DC signal), then 1/f noise typically overwhelms the signal. It may then be necessary to use external means to modulate the signal. For example, in the case of detection of small light signal against a bright background, the signal can be modulated either by a chopper wheel, acousto-optical modulator, photoelastic

modulator at a large enough frequency so that 1/f noise drops off significantly, and the lockin amplifier is referenced to the operating frequency of the modulator. In the case of an atomic force microscope, in order to achieve nanometer and piconewton resolution, the cantilever position is modulated at a high frequency, to which lock-in amplifier is again referenced. When the lock-in technique is applied, care must be taken in calibration of signal, because lock-in amplifiers generally detect only the root-mean-square signal of the operating frequency only. For a sinusoidal modulation, this would introduce a factor of between the lock-in amplifier output and the peak amplitude of the signal, and a different factor for a modulation of different shape. In fact, in the case of extremely nonlinear systems, it may be advantageous to use a higher harmonic of reference frequency because of frequency-doubling that take place in a nonlinear medium. Chopper amplifiers One classic use for a chopper circuit and where the term is still in use is in chopper amplifiers. These are DC amplifiers. Some types of signal that need amplifying can be so small that an incredibly high gain is required, but very high gain DC amplifiers are much harder to build with low offset and 1/f noise, and reasonable stability and bandwidth. It's much easier to build an AC amplifier instead. A chopper circuit is used to break up the input signal so that it can be processed as if it were an AC signal, then integrated back to a DC signal at the output. In this way, extremely small DC signals can be amplified. This approach is often used in electronic instrumentation where stability and accuracy are essential; for example, it is possible using these techniques to construct pico-voltmeters and Hall sensors. SOFTWARE METHODS Signal Averaging (one way of controlling noise) 

Ensemble Averaging  Collect Multiple Signals Over The Same Time Or Wavelength (For Example) Domain  Easily Done With Computers  Calculate The Mean Signal At Each Point In The Domain

 Re-Plot The Averaged Signal  Since Noise Is Random (Some +/ Some -), This Helps Reduce The Overall Noise By Cancellation.



Boxcar Averaging  Take an average of 2 or more signals in some domain  Plot these points as the average signal in the same domain  Can be done with just one set of data  You lose some detail in the overall signal

Polynomial Smoothing  Like Boxcar Averaging  Multipoint digital data averaging  Results in loss of some data at the beginning and the end of the data set.

UNIT II OPTICAL METHODS

GENERAL DESIGNS OF OPTICAL INSTRUMENTS SAMPLE

ELECTROMAGNETIC

ELECTRICAL

RADIATION

CURRENT

Optical Domain

Electrical Domain

Chemical, Physical Domain POWER SAMPLE

WAVELENGTH

SOURCE CELL

DISPERSER

PHOTODETECTOR

NUMBER Digital Domain READOUT

Power Source: spectrochemical encoding system Sample: must be in form suitable for analysis, may involve a separation or speciation Sample cell: cuvette for UV-VIS, flame for atomic spectroscopy Wavelength Disperser: an information sorting system, spreads light out spatially according to its wavelength Photodetector: radiation transducer changing optical info into electrical info Readout: digital (ADC), meter, strip chart recorder SOURCES OF RADIATION Continuum Sources Ar Lamp Xe Lmp H2 or D2 Lamp Tungsten Lamp

VAC UV VAC UV, UV-VIS UV UV-Near IR

Nernst Glower Nichrome Wire Globar Hollow Cathode Lamp Lasers

UV-VIS-Near IR-IR Near IR-Far IR Near IR-Far IR UV-VIS UV-VIS-Near IR

Radiation Sources Sources may be continuous or pulsed in time Continuum sources -

Continuum sources are preferred for spectroscopy because of their relatively flat radiance versus wavelength curves

-

Nernst glower (b) W filament (c) D2 lamp (d) arc (e) arc plus reflector

-

produce broad, featureless range of wavelengths

-

black and gray bodies, high pressure arc lamps

Line sources -

produce relatively narrow bands at specific wavelengths generating structured emission spectrum

-

lasers, low pressure arc lamps, hollow cathode lamps

Line plus continuum sources -

contain lines superimposed on continuum background

-

medium pressure arc lamps, D2 lamp

Black body sources  Nernst glowers (ZrO2, YO2), Globars (SiC)  1000-1500 K in air - max lies in IR  relatively fragile  low spectral radiance (B~10-4 W·cm-2·nm-1·sr-1) Arc sources  Hg, Xe, D2 lamps  AC or DC discharge through gas or metal vapor -

20-70 V, 10 mA-20 A

Line sources  Generally not much use for molecular spectroscopy

 useful for luminescence excitation, photochemistry experiments  where high radiant intensity at one q required Arc lamps  Low pressure (