Chemical Instrumentation Edited by GALEN W. EWING, Seton Holl University, So. Orange, N. J. 07079
These articles are inladed to serue the readers o f ~ m JOURNAL s by calling attention to new developments i n the theory, design, or availability of chemical laboratory instrumentation, or by presenting useful ingights and ezplanations of topics that are of practical imporlance to those who use, or teach the use of, modern instrumentation and instrumental techniques. The editor invites correspondence from prospectiue contributors.
1x11. Lock-in Amplifiers-Part
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T. C. O'Haver. Deoortment of Chemistry, University of Maryland, Experimental scientists who are concerned with the recovery of small electrical signals from large amounts of noise probably use lock-in amplifiers for this purpose more than any other type of noise-reduction instrument. But some experimenters may be using lock-in amplifiers routinely without really thinking very much about haw or why they work or under what conditions they are better than simple de systems. Worse, there may be those who are not now using lock-ins, but whose work would profit from their use. The purpose of this paper is to exphiin how and why a lock-in amplifier works and to describe some of the special capabilities and limitations of lock-in systems. A lock-in amplifier is basically an instroment for the measurement of the amplitude of rtc signals in the presence of noise. It consists of a high-gain ae amplifier followed by a synchronous detector and low-pass filter. Tbe key to the operation of a lockin amplifier is the synchronous detector; and the best way t o understand the synchronous detector is to compare it to the somewhat simpler and more familiar asynchronous detector, or full-wave rectifier, such as that found in the common ac volt-meter. This DaDer will begin
nous and synchronous ac systems. W h y ac? A lock-in smplifier measures only ac signals, not do signals. If the experimental signal (i.e., the transducer output) is ordinarily ac t o begin with, then an ac amplifier-readout system is a natural choice. But many experiments, in their simplest forms, produce dc signals. These must somehow be converted into ac if a lock-in or other ac system is to be used. The obvious question a t this point is: if the signal is d r in the first place, why not simply use a dc amplifier-readout system, such as a dc microvoltmeter, electrometer, or picoammeter? There are two traditional answers t o this question. First, it is easier to design and bnild a stable, high-gain ac system then a. do system of
equivalent gain and stability. Secondly, the extent to which signal-to-noise ratios of experimental signals may be improved by simple low-pass filtering in dc systems is seriously limited by the presence of significant rtmounts of law-frequency noise, such as drift and "l/f" noise. For these reasons it is often advantageous to transpose the signal frequency from zero (do) up t o some ac frequency sufficiently high to maid these low-frequency noise effects, and then t o use an ac electronic system t o amplify and measure the ac signal. Modulation: From dc to ac The process of transposing the signal from de t o s c is called modulation. This is a. very important aspect of ac systems. The modulation must be performed in such a way that the desired information, which was formerly the magnitude of a de voltage, is now expressed as the amplitude of an ac ("carrier") waveform. I t is especially desirable that this ac waveform contain only the information of interest, without any extraneous information (noise). That is, it is best to modulate only that portion of the total
ezperimental signal which contains the desired information and leave all extraneous noise signals unmadulated. Then if the ac amplifier-readout is designed to select and amplify only the modulated signal component, a. significant increase in signal-to-noise ratio can be obtained. Many different kinds of modulation techniques have been used by experimental scientists; only a few can be mentioned here: Most of the following examples are drawn from the field of spectroscopy, as this field provides many opportunities for the profitable application of ao techniques. Consider a generalized experiment in which a very small dc voltage is t o be measured. The most generally applicable method of modula.tion in such a case would involve switching this dc voltage OFF and ON with an electromechanical or solid-state electronic chopper, thereby producing a square wave whose peak-topeak amplitude is equal t o the original dc voltage. Any dc signals, offsets, or drifts introduced into the system after
Dr. Thomas C. O'Haver is .\ssistmt Professor of Chemistry at the University of Maryland, College Park. He received his B.S. in Chemistry from Spring Hill College in 1963 and his Ph.D. in Analytical Chemistry from the University of Florida. in 1968. His main research interests are in the areas of analytical spectroscopy and instrumentation, with particular emphasis an the flame methods, luminescence methods, modulation techniques, and the application of signal-to-noise ratio concepts in instrumental optimization. H e has been the author of several papers in these fields. He is a coauthor of the new book "Luminescence Spectrometry in Analytical Chemistry" to be published by Wiley-Interscience in the Spring of 1972. I n 1970, Dr. O'Haver was awarded a. National Science Foundation grant for the developmentof a new course in modern solid-state electronics for chemists. is modulation step would not be pass the ac amdifier and thus would n interfere with the measurement. The only real advantage of this kind of modulation is that it is completely general; that is, it works with anu kind of dc signal. I n fact, what we would have would be nothing more than a chopper-type dc amplifier. However, this may well be a waste of the capabilities of an ac system, because there may be more advantageous ways to modulate the signal. Take, for another example, an experiment in ir spectroscopy, using a thermocouple detector (essentially a. source of low dc voltages). I t is well known that dc measurements of thermal detectors are plagued by drift due to tiny ambient temperature changes, air currents, etc. Constant, tedious re-zeroing is mandatory. These difficulties can be avoided by the proper choice of modulation technique. Chopping the electrical signal from the detector itself would not help, because the drift signals from the thermocouple would also be chapped (modulated). If, on the other hand, the beam of ir radiation falling on Lhe thermocouple were chopped by means of a rotating half-sector or (Continued on page A1481 i
Volume 49, Number 3, March 1972
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other mechmical light-beam chopper, then the ae component of the thermocouple signal would correspond only t o the intensity of the ir beam. The drift signals caused by air currents and ambient temperature changes, which are introdueed into the system after the modulation step, are not modulated by the beam chopper and thus remain a t dc, where they are not amplified by the ac system. By using this type of modulation, we can "pick out" the desired signal from the confusion of offsets and drift signals which are not related t o the light intensity being measured. In a way, this systemre-zerositself continuously, because the ae eomponent in the thermocouple signd is proportiond to the differme between the light-ON detector voltage and the light-OFFdetector voltage. But can we do even better than this? Yes! If we can modulate the signal "further up the line" away from the transducer, we may be able t o leave other undesirable signals unmodulated. The ideal situation would be to modulate the signal before any undesirable signals are added t o it, but this is not possible in general. Consider, for example, an experiment in ~ttomic flame fluorescence spectrometry using light-intensity modulation. I n this ease it is best t o modulate the light beam a t a position between the excitation source and the flame, rather than between the flame and the photodetector, because in the former case the undesirable flame background and thermal emission signals remain unmodulated and artre eliminated by the ac amplifier
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system. However, uncontrolled varis, tions in the intensity of the excitation source itself will be modulated, because sueh variations are introduced into the system before the modulation step. Thus light-intensity modulation is of no help if source instability is a major problem. Light-intensity modulrttian is not, of course, the only kind of modulation, although it is the most widely used in spectroscopic measurements. Other kinds of modulation applicable to spectroscopic measurements include wavelength modulation and sample modulation. Wavelength modulation is used when the information of interest is the difference between the spectral intensities a t two adjacent wavelengths or when the rate of change of intensity with wavelength is desired. In this modulation technique, the wavelength setting of the spectral selection device (usually a monochromator) is varied rapidly back and forth over a small spectral interval AX centered on h. The amplitude of the resulting ac eomponent in the photodetector signal is proportional to the difel-ence between the AX/2 and that spectral intensity a t h a t ho - AX/% For this reason, wavelength modulation hasbeen used as an aid in the detection of weak spectral lines superimposed on an intense continuum background; in this case the scanning interval AX is adjusted so that the monochromator scans across the line and down into the background adjacent t o the line. This results in a sort of continuous automatic background correction. Another application of wavelength modulation is
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in derivative spectroscopy. I t can be shown that if the modulation interval AX is made small, the amplitude of the ae signal becomes proportional to the wavelength derivative a t wavelength Xo. A derivative spectrum may be obtained by recording the amplitude of the ac signal as a function of h. Tbis technique bas been used t o increase the apparent resolution of shoulders and ot,her minor spectral features a n poarly-resolved molecular spectra. Sample modulation is used when it is desired t o determine the difference between two chemical samples. Tbis type of modulation is performed by causing the instrument to measure the two samples alternately. Tbis can be done, for instance, by stream-saitching liquid samples in a flow system or by optical beam switching between the two light beams tramsmitted by, emitted by, or reflected from the two samples. In this way the ac signal component a t the switching (modulation) frequency is a measure of the optical diffemerence between the two samples. I n quantitabive analyticd experiments, the two samples are mast often chosen to be the "analytical sample," which contains the snalyte along with a solvent and/or various matrix eomponents, and the "blank," which contains everything in the analytical sample ezcept the analyte. The difference signal obtained for two sueh samples is obviously due only to the analyte. The familiar double-beam absorption spectrophotam eter is essentidy a sample-modulation (Catinued on page A1S4)
system using optical beem-switching between two sample cells. The above modulation methods, although they differ in many details, have two things in common. First, they are all chosen t o modulate the desirable part of the signal and yet leave unmodulated a t least some of the undesirable offsets, drifts, and noises. Second, they all produce an ac signal component a t the modulation frequency which is a. measure of the diferenee between two states of a system, i.e., switch-o~/switch-om, light-o~/lightOFF, ?.L/XP,sample/blank, etc.
Demodulation: Back to dc The next step is to measure the ac signal component resulting from modulation. This is done by amplifying the rtc signal in an rtc-coupled amplifier (which rejects dc signals) and then canverting the amplified sc signal back into dc, by means of a demodulator circuit, so that the signal can be read out on a dcoperated device such as a meter, chart recorder, or digital voltmeter. The various types of ac systems differ from one another in the frequency response bandwidth of their rtc amplifiers (wideband or narrowband) and in the type of demodulator (synchronousor asynchronous). The simplest ac measurement system would be a wideband ac amplifier followed by an ordinary full-wave rectifier and a low-pass filter. This system would be similar t o the familiar general-purpose ac millivoltmeter. However, a system of this type would not be useful in practical cases in which the ac signal is buried in noise, for the simple reason that a wideband amolifier will amolifv " all of the sc components in the signal, including random noise, 60 and 120 Hz straypiokup, and any other extraneous ac signals falling within the amplifier's bandpass. These amplified noise signals would be rectified and filtered and would produce a large dc offset ("noise offset") a t the output. In principle, such an offset could be subtracted out electrically; but we would still have to contend with variations in the noise offset as a function of time, temperature, signal level, etc. As a result, widehand asynchronous systems are not practical for the measurement of ac signals buried innaise. One way to reduce the noise offset problem would be t o limit the bandwidth of the ac amplifier so that i t will pass only the rtc component at the modulalwn frcpuemy and reject d l other frequencies. Replacing the wideband amplifier with a narrowband or "tuned" amplifier of sufficiently narrow bandwidth will greatly reduce the noise offset (and, more important, the variations in the noise offset). This 'nd of system ib in fact practical in some cases, but i t is not without drawbacks. The most serious problem is that it is difficult t o build stable, high-gain tuned amplifiers of sufficiently narrow bandwidth for many ~pplications;and i t is even more difficult to keep them in tune, particularly if the modulation frequency is prone to drift slightly. These difficulties can b e overcome by the use of an arnulifier of wide or intermediabe band~ u.id!ll iull.~\redI,! il o v n r h ~ o n o urlrm,,dulomr. Thi., w esenr+, a Iwk-iu :v-ten>. T o (re ronr./?.,ld 272 A p r i l )
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