Topics in..
.
Chemical instrumentation Edited by GALEN W . EWING, Seton Hall University, So. O r a n g e , N. J. 07079
These articles are intended to serve the readers o j ~ ~JOURNAL r s
by calling allention to new developments i n the lheoy, deeign, or availability of chemical laboratory instrumenlatia, or by presenting useful insights a n d ezplanations of topics that are o j practical impwtance lo those who use, or teach the use of, modern instrumenlation and instrumental techniques. The editor invites correspondence from prospective contributors.
1x11. Lock-in Amplifiers-Part
II
T . C. O ' H a v e r Deoortment o f Chemistry, University of Maryland, College Pork, M d . 20742
Lock-in Systems The synch~onousd~;modulatov,the heart of a lock-in system, is best understood by reviewing briefly the function and operation of demodulation in general. The purpose of the demodulator is t o convert, t h e amplified nc sigllnl into a. proportional de signal f m r e d o u t on dc-operated meters, recot.ders, etc. An ordinary (asynchronous) ac system uses a rectifier, usually full-wave, t,c, perform this st,ep. A full-wave rectifiel. is a circuit which passes uuchanged all input signal exeurxians of one polarit.y, while inucrling (reversing the pvlarity of) all signal excursionii of the opposite polarit,y. Thus t h e output of a full-wave recbifier is always of one polarit,y; i t in not., however, n pure dc signal, as i t contains many ae noise components and harmonics of the modulat,ion frequency. These ac components are removed by means of a. lowpass filter following the reebifier. A full-wave reet,ifier may be viewed ns x signal-opcrated device; its made of opers, tion (inverting or noninverting) is determined by the inst,ant,aneoos polarity of the total ac input signal (iueluding, unfortunately, noise). The problem is t h a t noise will also operate the rectifier, i.e., cause i t t o genreate a dc out,put signal. This, of course, is the origin of the noise offset discussed above. A synchronous (lock-in) demodulator, on the other hand, is a rcfercna:-opcratcd device; t h a t is, its mode (inverting as norrinverting) is determined by the polarity of a wjermea waneform which has t,he same frequency as, and a fixed phase relabionship to, the modulation signal. This phase relationship is adjusted, by means of n suitable electronic network, so that the amplifier out,put signal is passed unchanged whenever the modulation phase is such as t o cause a posilivr cxeursion of the desirable ac signal
component in t,he amplifier output signal, and t o inwrt the signal whenever the modulation causes negativc signal excursions. The result is t h a t only the fundamental modulation component will he elrectively full-wave rectified. Random noise and any other signals which are not phase-synchronized with the ~.eference waveform will pmduce no nrt dc output. brtt will prndnee only ac (noise) components which may be attenuated by means of a low pass filter. In other words, only signals which are p~.operlysynchronized ("locked in") t o the reference waveform will yield n. net dc out,put signal-hence the names syneh~.ono~rsd~modvlato~or lock-in detector. A synchronous demodulator may be pictured as a. double-throw relay which switches back and forth, a t t,he reference frequency, between two balanced (oppositely phased) outputs of an ac amplifie?. (This is shown in Fig. 1.) I n fact, such n circuit would actually he practical for low modulation frequencies. (The relay response time precludes high-f1.equency operation.) A solid-state switch would he more generally practical. A field-effect transistor used as an analog switch, in conjunction with an operational amplifier t o provide the required phase inversion, can be used t o make a lock-in detector usable t o several kHs. A lock-ill detector can also be made from an analog mukipher; the output of the ac amplifier goes int,o one multiplier input,; and the reference waveform, properly phaseshifted and converted t o a symmetrical, ac-coupled waveform with no net dc component, is fed into the other. The multiplier out,pnt, which is the product of the ac signal and the reference waveform, is law-pass filtered as usual. In effect, the ac signal is multiplied by fX, where X is the peak amplitude of the reference waveform. Thns the multiplier
acts ss a. switched inverter, similar in effect t o a, mechanical polarity-inverting switch. (In addition, the multiplier exhibits a voltage gain proportional t o X). Interestingly, the reference waveform applied t o the multiplier need not be square; a sine wave is also perfectly satisfactory. The multiplier essentially performs a. cross-correlation of the ac signal and reference waveforms. (In fact, lock-in detection is really a special case of cross-correlation.) I t is important t o realize t h a t a synchronous detector does not eliminate, or even at,tenuate, noise; i t merely does not convert i t t o a net dc signal. The output of s. lock-in detector will therefore be just as noisy as the input; hut i t will contain a net dc component due only t o the ac component st the modulation frequency. The ac (noise) components a t the output of the demodulator e m be attenuated t o any desired extent by simple low-pass filtering. Commercial lock-ins are usually provided with m e - or two-stage active filters for this purpose. Of course, dc offsets and drifts introduced into the system ajtcr the demodulator will have their expected undesirable eflects; but if the predetecbion gain (i.e., the gain of the ac amplifier) if high enough, then the dc detector outp u t will be large compared t o the dc errors in the post-detection stages. The eNeetive ac bandwidth of the synchronous detector and low-pass fdter combination is equal t o the low-pass bandwidth of the filter itself. Thus, a
I Figwe 1. Equivalent circuit of o synchronour demoduletor (lock.in detector), showing the input 3ine wove ,ignol Ei,, the witching woveform E,,,, and the synchronously rectified waveform before filtering (Ed and after filtering IEoutl. (Courtery of Princeton Applied Research Corp.)
(Continued on page ABlB)
Volume 49, Number 4, April 1972
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Chemical Instrumentation lock-in detector behaves very m ~ ~ like eh a sharply timed circoit which will accept only those frequencies in a narrow band on either side of the referalee (modulation) fl.equency. This narrow frequency band is equal t o the handwidth of the low-pass filter. If r is the time conslant of the filter, then its bandwidth is given by (4,)-1 or (Ur)-' for one- and t a a slage fikers, respectively, (corresponding to attenuation rates of 6 and 12 db per octave, respectively). Very small filtor bandwidths are prsctical in lock-in systems. For instance, time constants of 10-100 sec, corresponding t o two-sectiun bandwidths of 10-elU-3 IIs, are routinely used hy many workers. At a typical modulation frequency of 1 kHz, these values would eorrespoud t o Q valiles of 10Vo 106, values whirh are qnite impmctical fol. tuned ar amplifiers. The lack-in system, then, is capable of much greater frequency selectivity than any pmetienl tuned RC amplifier system. The bandwidth of the detector-filiel. section of a lock-in amplifier is generally so small that the a r amplifier bandwidth has little or no effect on the overall system bandwidth; thus, a wideband ac xmplifier may be used. In fact, same commercial lork-in systems use widebnnd ac amplifiers because they are simpler iu design and operation than tuned amplifiers. The main advantage of n widehand lock-in system is that it can "track" (i.e., keep locked in t o ) the sigrrd even if the modulation freqilewy changes. .4 sharply tuned ac amplifw, on the other hand, exhibits such n large change in phase shift ns a fnnetion of frequency that the phase co,ltlnl m w t be readjusted if the rnodnlation frequency changw even slightly. However, n wideband amplifier does have one disadvantage: becanse of its large noise bandwidth, the amplitude of lhe noise passed by the amplifier mey be gt.eat enoltgh t o ovelhad the detector or the last amplifier stage, especially if the signal-to-noise ratio of the signal is very low. This ove~.loadgexrally results in serious gain and offset, errors whirh may not be at all obvious t o the esperimenter on the basis of externally observable symptoms. Fm this reason. eommwrial lockin systems are provided with overload indicator lights which warn the operetor of a11 overload condition
Figure 2. The P.A.R. Model 124 Lock-in Amplifier hor interchongeoble preamplifier plug-ins, full-scale sensitivity to 1.0 nV, and f e w lures selectable signal-chonnel frequency response (Rot, vorioble-Q bond-pos, notch, lowporr, or high-pass). (Courtesy of Princeton Applied Research Corp.1
(Continued on page AZ14)
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Chemical Instrumentation A small disadvantage of a lock-in system is the necessity for a, reierence signal. This must be a reasonably clean (i.e., noise-free) waveform which is rigorously synchraniaed to the modulation waveform. The reference signal is usually obtained directly irom the modulator itself, but the exact details naturally depend upon the particular system. For example, in a system using a rotating-disc light-beam chopper, a reference signal may he obtained by means o i a n auxiliary lamp or photocell suitably positioned along the edge oi the disc. Or, if the modulator is a n electromechanical t,ransducer driven from an external oscillator, then the reference frequency may he obtained directly irom the oscillator. One more disadvantage, common t o all ac mebhads, is the signal power loss due t o modulation. By its nature, t h e modulation must periodically cut off or attenuate the magnitude of the physical quantity being measured (e.g., light intensity). Therefore, the total signal power a t the transducer is less than for an unmadulated dc system. This effect may be significant in a signal-limited experiment, such as, for example, a shotnoise-limited light intensity measurement or a. photon counting experiment limited hy counting st,atist,ics. Limitations So much has been written about the noisereduction capabilities of lock-in amplifiers that i t prohnhly is more valoable a t this stage to consider some oi (.heir limitations in this respect. Although it is probably true that a lock-in system is always superior t o a narmwhand asynchronous system (because of the toning problem), it may not he significantly superior t o a good dc system in every case. I n fact, a lock-in amplifier, because it is more expensive and complex than a dc system, may be a poor choice in some cases. There are two main limitations which shorild he considered; the first concerns tho frequency spectrum of the noise and the second concerns the origin of the noise. In the first place, s. lock-in is no hetter than a dc system of the same noise bandwidth for the reduction of purely white noise. In eibhor case the noise handwidth of the low-pass filter determines the
Figure 3. The P.A.R. Model 220 Lock-in Amplifier ir one of o series of modules which can be arranged to perform a variety of meorurement function.. A sectored-disc light beam chopper is shown on the right. (Courtery of Princeton Applied Re9earch Corp.1
(Continued on page ABlG)
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Chemical Instrumentation extent of noise attenuation: for white noise, the output noise level is proportional to d ~ j .However, if low-frequency noiaes (such as drift or l/f noises) are significant, then a lock-in system may be superior, depending on the kind of noise. In a dc system, low-pass filtering will not reduce drift and l / j noise components significantly; in fact, the long response times resulting from low filter bandwidths may even increase the effect of theselow-frequency noises. The only kind of noise whieh an ac system can eliminate more effectively than a dc system is additive noise which enters the system. at a point belween the modulation and demodulation stages. By the term additive naise is meant a noise (random or drift) which adds to the dc level, but does not change the ac signal
Figure 4. The Keithley Model 850 Lock-in Amplifier is a relatively h p l e unit, yet has dl the boric controls. (Courtesy of Keithley Instrumenk, Inc.1
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mnplitude, of the total signal a t the amplifier input. Examples of additive noises mclude: drifts and offsets in the ac amplifier; dark current variations in the photodetector of a system using some farm of optical modulation; variations in the background continuum intensity in s wavelengthmodulation experiment; variations in the flame background and thermal emission intensity in an atomic fluorescence experiment using a chopped excitation source. A lock-in system can effectively discriminate against noises of this type, even if they contain large drift and l / j components. More precisely, a lock-in system will eliminate all additive noise frequency components falling outside of the very narrow frequency interval whieh extends one noise handwidth on either side of the modulation frequency. Multiplicative noise, on t,he other hand, multiplies i e amplitude modulates) the ac signal component, producing a. variation (noise or drift) m the amplitude of the ac signal. Some examples of multiplicative noises include: gain-variation noise in thelock-in system, either before or after the demodulat,or; variations in the sensitivity of the transducer (such as that due t o changes in the dynode voltage supply of a multiplier phototube); source intensity variations in a chopped-source fluorescence experiment or in a wavelength modulation experiment; variations in background l with a licht " emission in an o ~ t i c a svstem light beam chopper placed after the source of the background radiation; variations of
Figure 5. The Keithley Model 80 Lock-in Amplitier is a highly versotile modulor instrument. (Courtesy of Keithley Instruments, 1nc.l
flame conditions or solution Row rate in flame photometric systems using any eammon type of modulation. These noises are of two general types: ( I ) noises which are introduced into the system before the modulation step and are modulated along with the desired signal; and (2) gain-variation noises introduced a t any point in the system. A lock-in amplifier is not better than a dc system at dealing with noises of this type. Both systems must rely solely on the low-pass filtering. Therefore only those noise frequency components falling outside the narrow frequency interval (the noise bandwidth) centered about zero (dc) will he eliminated. This means that drift and l / j noises of the multiplicative type will not be effectively attenul~ted by either system. I t is at this point that the exasperated experimenter begins looking nervously (Continued on page A918)
Figure 6. The lthoco Model 353 i s on ultraverwtile modular ryrtem. A voriety of unique ~ 1 ~ g units . i ~ ir available. Shawn here i s o dual channel log system capable of meawring the lineor or log ratio of two input signals on two liner modulated at the same or different frequencies, or on the rame line modulated a t m o different frequencies. This sort of lock-in $yrtern is essential in dud-frequency doublebeam optical meowromentr [See Munroe, R., Americoo Laboratory 3.52 ( 1 971 11.
for another kind of noise-reduction instrument. Fortunately some of these problems can be solved, in some kinds of experiments, by the use of a multichannel signal nalaverager, sometimes called an ensemble auerager or a compute? of average transients. For example, an instrument of this type would allow one to obtain a good spectrum from a weak and unstable (noisy and drifty) light source, whereas an ordinary dc or lack-in system would produce a spectrum full of extraneous peaks and dips which are due to murce intensity fluctuations rather bhan to genuine spectral features. Further discussion of this topic is outside the scope of this paper. The interested reader is referred t o the extensive literature on the subject ( 1 2 ) .
Commercial Instruments Lock-in amplifier systems are manufactured by several firms (1-4). All of the commercial instruments are provided with a variable-gain ac amplifier, coarse and fine phase controls, and an output filter time-constant switch. Most are provided with variable output offset ("zero suppress"), and variable frequency pro-
Figure 7. The new lthaeo Model 391 Lock-in Amplifier user o unique heterodyne principle to provide o tracking pre-detection fllter which "drips off harmonics ond interference early in the instrument. This approach solves the noireoverload and harmonic regponre problem of the widebond front end while avoiding the phaseshift problems of a tuned front end.
(Continued a page AB?0)
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Chemicallnstrumenfat;on "Digital" vision. The specifications and features of several commercial models are summarised in Table 1.
Table 1.
Lock-in Systems
The lock-in principle is not restricted to the analog domain; it has also been applied to digital SYStemS. A good example of such an application is the "synchronous single-photon counting" sys-
Summary of Specification o f Some Commercial Lock-In Amplifiers
Manufacturer
Princeton Applied Research Corp. 120 122 5 Hz5 Hz50 kHz 150 kHz (fixed) 100 pV 100 NV
124 2 He210 Hz
RIM-220 1 Hz110 Hz
100 nV (Note 3)
1 mV
10 MR
(Note 3)
1M a
Tuned
Tuned
Wideband
10-turn/10O0 quad snitch 15'
*45O quad switch 110"
f45O quad switch
1ms100 seo (Note 5) X 10 F.S. 10-turn +O.l% per day
1 m100 sec (Note 5) X 10 F.S. 10-turn +O.l% per day
I ms30 sec
1ms30 sec
X1 F S 10-turn i0.2% per day
X 1 F.S. 10-turn 10.2% per day
NA
NA
NA
NA
Tuned or Wideband 10-turn/10O0 quad switch &20 2Hz-21 kHz 1 ms300 sec (Note 5) X 10 F.S. 10-turn 15-1000 ppm per O C (Note 7) Yes (Variable)
...
...
...
..
Yes
Yes
2350
1950
925
1200
2800 (Note 8)
1075 (Note 9)
Model Frequency range
HR8 1.5 Hz150 kHz
121 1.5 He150 kHz
Max. sensitivity (Note 1) Input Z
100 nV (Note 2)
10 #V
10 M a (Note 2) Tuned
10 M a
10 Mn
Tuned
10-turn/lOOO quad switch +5-
Signal bandwidth Phase adjust (Note 4) Phase . accuracy Time constant Zero suppress Zero stability Highor lowpass filter Second harmonic Price, $
(Note 2)
Manufacturer
Max. sensitivity (Note 1) Input Z Signal bandwidth Phase adjust (Note 4) Phase accuracy Time constant Zero suppress Zero stsbilitg Highor lowpass filter Second hmmonio Price. S
850 1 Hz50 kHz
/
80 10 Hz100 kHz
353 1 He200 kHz 1#V
300 MO
so
1 ms30 sec XI0 F.S. 10-turn +0.1% per day
...
4 kn @1 nV Tuned
Wideband
Wideband
Wideband
Wideband
1-turn/100" qusd switch
*so
1-turn/10O0 quad switch *7-
1-turn/180° quad switch 5'=
*SOD quad switch
3 ms100 sec
10 ms100 sec X5 F.S. 10-turn (uncal.) 0.1% per C
1 ms300 sec (Note 5) X 10 F.S. 1C-turn
0.01-100 sec
X 100 F.S. 10-turn (Note 6) 0.25% per OC {Note 6) Optional
10-turn/lOOO quad switch *2% 10-300 kHz 100 ms10 sec (Note 5) X 10 F.S. lC-turn 0.005% per "C
O.l%/day 0.05'%/"C
Yes
Yes
Low-cut
Yes
Yes
Yes
Yes
...
1395
1895
3455
1590
...
journal o f Chemicol Educafian
f
131 0.5 Hz10 kHz (fixed) 1 nV
10 Mn
*
l&turn/lOOD quad switch
Brower Laboratories
11 M a
Notes: 1. Full-scale, rms volts sine wave. 2. With type A pream&ifier. 3. Depends on preamplifier. 4. Quad switch changes phase in increments of 90, 5. Selectable roll-off rate 6 or 12 dh per octave. 6. On X l multiplier p o s h n . 7. Depends on function switch position. 8. Plus preamplifier. 9. Lock-in module only.
A220
+loo
Ithaco
Keithlev Instruments Inc. 840 0.5 Hz15 kHz
Model Frequency range
tem for low light-levcl measurements proposed by Arecchi, Gatti and Sans in 1966 (13). This is a. photoelectron counting system employing a mechanical lightbeam chopper and bidirectional (up-down) counter. The counting direction is determined by a, synchronous reference signal
...
+100% of full-scare ...
and
(Continued a page A H 8 )
Chemical Instrumentation in such a way that the light-ON signal is counted UP and the lightrom signal counted DOWN. In this way the phototube dark current pulses, as well as any other stray signals or background light pulses, are continuously subtracted from the light pulse count, so that the counter accumulates only the net light pulse count. In effect, this system is the digit d counterpart of an analog system consisting of a loek-in detector followed by a. dc integrator. Some commercial photoncounting systems use this lock-in principle.
Conclusion Much more could be said about lock-in systems, of course. Little has been said here about the design and operational facilities of commercial lock-in amplifiers; but these aspects are very well treated in the manufacturer's literature (1-4). I n fact, some manufacturers distribute, free of charge, very good instructional material in addition to the usual descriptive product brochures. Some of this material is listed in the references (5-12). These articles and pamphlets include useful discussions of lock-in amplifiers (5, 6, 11),as well as other noise-reduction instruments such as hox-car integrators (7), correlators ( 9 ) , and signal averagers (12).
References (1) Princeton Applied Reaearoh Corp.. P. 0. Boa 565, Princeton. N. I. 08540. (2) Brower Laboratories, Ino.. 241 Crescent St.. Waltham. Masa. 02154. (3) Ithaco. Inc., 735 W. Clinton St., Ithacs, N. Y. 14850. (4) Ksithley Instruments, Inc.. 28715 Aurora Rd.. Cleveland, Ohio44139. (5) .'A Practical Guide t o Measurement of Weak Signals Buried in Noise," Brewer Laboratories, 1968. (0) "How the Look-in Amplifier Works," Brower Laboratories, undated. (7) Frsnen, J. C., "Look in the Devil, Educe him. or Take him for a Last Ride in a Boxcar?" Tek Talk, 6 (1). Princeton Applied Researoh Corp. (8) CrrAr~owssr.0. C., AND MOORS, R. D.. Reaaoich/DmrlopmenI, April, 1968, p. 32; Princeton Applied Research Corn., Technical Note T-196. (9) Nmrsonen, C. A,, "Modern Bignal Processing Techniques for Overcoming Noise;' Elceti. Insf. Digeat, Sept.-Oot., 1968: Princeton Applied Researoh Cow. Technical Note T-200. (10) Coon, T.,"Signal-tc-Noise 0ptimim.tion in Precision Measurement Systems." J. CHBM. EDUC..45, A533. A583 (1988); reprinted in "Topics in Chemical Instrumentation" ( ~ d i t o r : G. W. EwrNa. Chem. Edua. Publ. Co.. Eaaton.Pa.. 1971. p. 249. (11) "The Use of a Lock-in Amplifier for the Detection and Measurement of Light Signals," Sipnol Nolea, 1, 1 (1967); Princeton Applied Rerearoh Corp. (12) NITTROUER,C. A,, "Signal Avaragars." Princeton Applied Research Corp., Techniod Note T-162A (1968). (13) A B E C C ~F. I . T., Gawr. E., n w Son*. A., RN. Sci. Instrum.. 37,942 (1900).
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