Topics in
... Chemical lnstrumentation
Edifed by S. Z. LEWIN, N e w Y o r k University, N e w York 3, N. Y.
These articles, most of which are to be conlributed by guest aulhors, are intended to serue the readers of this JOURNALby calling allenlion lo new developments in the theory, design, or availability of chemical laboratory instrumen/ation, or by presenting useful insights and ezplanations of lopics that are of pradical importance to those who use, .or leach the use % modern instrumentation and instrumental techniques.
IV.
Instrumentation Based on Operational Amplifiers (Part II) .
N. Reillev. of Chemistry, University of .. De~arfmenf North Carolina C.
In Part I (81), the principles of elementary operational amplifier networks were discussed, and several qqdicatians of each type were given. This concluding part continues the coverage of elementary networks and a180 describes a few multiamplifier circuits and their application. The final portion of this part lists manufacturers of equipment of this nature and gives a hrief description of the various farms as applied in our laboratory a t
Hence, the output voltage from this circuit e m be madc, by appropriate choice of resistors R, and Rs, to equal exactly 10.00 volts even though the value uf I;' i~ 1.0182 volts. Considrrahle currwrt ran
UNC. Standard Voltage Source The circuit given in Figure 1 illustrates a slandarduollage sowce. The output from the operational amplifier is fed back into the input via a voltage source, E, which is commonly a Weston standard cell ( E = 1.0182 v). Because t,he input to the operational amplifier draws negligible current, no load is p l a r d on the Weston
Figure 2.
Standard voltage source.
a180 be drawn from this accurate standard voltage source. Circuits such as these are frequently used as v a h g e sources for t,he
Booster
Figure 1.
to estahlisll an identily: the potential at point z must h e equal to thnt of E. This idcntity is achieved by t,he output voltage, e,, being of s magnitude such that passage of current through R, and R2 rill lead t,o :m appropriate voltage drop across R., whirh is then equal to E. With K. and E constant, t,he current through the resistanre RI must also be constant, and inde~endentof the value of R?. Cin:uits has& on this principle have bee" employotl for prerise control of currents far magnets, et,c. (3, 8). An analogous rircuit useful in eonlrollrd polenfial electrolysis is shown in Figure 3 The reference electrode corresponds to the point z in Figure 2, and the working electrode is grounded. Thc auxiliary elrrtrode is connected to the point corresponding t,o ca. A current through the cell will then develop to n magnitude such thnt the potential created hetween the working and reference electrodes will be equal t,o thnt of the applied potential, E. The circuit t,hen maintains the potential between the working electrode and reference electrode a t the value of E by altering the eurrent to suit the flux of electralyzahle material arriving a t the working electrode. The advantage of this circuit is that no current is drained from the reference electrode, and the time for corrective action is very small. For current demands of higher magnitude, non-inverting boaster amplifiers may he employed as shown. The same circuit is very useful for thrre electrode polamgraphy, a technique particularly applicable for studies in soht,ion of low conductivity, such as nonaqumus media (14, 15). Here the dropping mercury electrode is grounded, and the reference and auxiliary electrodes are a ~ a i nattached as indicated in Figure 3. For best compensation of IR drop through the solut,ion, the reference electrode tip should be placed very close to the surface of th? working electrode.
Current meter
,,
I
I
, %
Standard wltoge source.
standard cell. Also since the summing point is a t virtual ground potential, the output voltage of the operational amplifier is identical in value to that of the Weston standard cell. An important feature of this circuit irr that considerabk current may be drawn from the output without altering the voltage of the output m d without causing current t o he drained through the Weston standard cell. By connecting the circuit in a someudmt different manner, as shown in Figure 2, the output voltage, e., will be: e. =
(1
+ R I I R ~X E
(1)
c
w
i
Auxiliary Elsctroda Reference Electrode n g Electrode
6 Figure 3. Controlled potential electrolysis instrument IleHI. IPotentialr between reference ond working electrodes mmintained at a value equal to E.1 Right: Alternative method d current measurement le, = R8[1 IRIIRs)] X il
+
operational amplifier instruments discussed in Part I, i.e., for generating linear voltage for polarography, etc. (17). ~h~ in ~i~~~ 2 may he sidered to operate in a manner such as
Differential Operational Amplifiers The operational amplifiers described ~ ~ e v i o u s lhad y single inputs and were
(Continued on page 4934)
Volume 39, Number 12, December 1962
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A933
Chemical instrumentation
Figure 4.
Differential ompliner.
e" = - R?' R,' I?>'
+
p +]) I?
?
-
by suhstitnt,ing the appropri:tte values inbo rqunt,ion 2 or, n a w simply, i n m t l l ~ ~nrlirrst,:~lrmentthnt surh rirruita opwltr
Figure 5.
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Journal of Chemical Education
Voltage follower
Chemical Instrumentation
fer funrtions of each circuit. Figure 6
Thus, for
has an extrrmely low output i~npctlnnee, i P.. mrrmt, can he drawn from its outnut without altering seriously thc voltage, eo. Hence, this specialized circuit, whose output and input voltages me equal, can he considered as an impedance matching denice, drawing as little as srnp from the a n m e t o which it is connected and yet capahlo c~idrlivering nhout. I V 3 amp s t its output (6, 7, 924). With the input of a differential nmplifier grounded, the resulting operational amplifier is inverting and equivalent to those shown in Figures 1-3, 6-8 and in Part I ( 2 1 ) .
I n the analysis of rireuit,s emt,aining several operational amplifiers, t,he use of operational nutntiuu is advantageous hrcanse the rnathemntiei solution Kenerally requires only simple algebraic steps such as multiplication and arlrlit,inn.
Consecutive Circuits
Solution of Equations
In Figwe 6 is shown a circuit consisting of one integrator followed by another. In circuits such a.a this, the over-all response is given by the p r o d t ~ lof the trrtnc
The primary purpose of iq,erntiunal amplifiers is for analogue eompntatim of the solution to dzflrrrnlinl and nlqehroie (Continued on page A938)
.
+
which is equivalent t,o
Volume 39, Number 12, December 1962
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A937
Chemical instrumentation equations, and an :hrndanrr of l i k r a t ~ l ~ e exists on thi8 suhjwt ( 5 , !I, 11-16 lfi, 18, 14, #?. 86). Only t,wn simple rases are prrsprltrd here; t h first ~ involves s d n t i m to a s r t < t i slgrbraic ~ p : ~ t i r mand s the srrcmd tr, a difl'rrt.ntin1 rquat.ioa.
Figwe 7. Computer for solving rontinuouriy the following 3imultoneour equation3 for X and Y:
The rirruit i r ~Figure i may I,? usrd fctr sdving rmtinuooal\- the iollm~-ingpail. ui sio~ultm?ca~s :dgrlrnir equntims:
A , = ",X A? = aJ
/,,I++ b?l.
(5)
F:quntions of t,his Lrrm are enronntrrrd in t,hr sperlrcq~lrc,tc,metricanalysis uf t,w-o romponrnt m i ~ t u r r swhrrr A rorrrspmds to the measor~d :hsr,rhnnc~,a tr, thr m h r al,surptivity v i solmt:mce S, and b to the sul,st,anre Y, at bwc, navrlrngths d m o t d by the suhsrriptu 1 nnd 2. S and 1. rcrrrspr,nd to blw aun~w~trations ( l i the t~wr spwies. AS SWII frum th? figur*, the i n c h itl,sorptivitirs are plnrrd int,o the computer 1,y the values ui thrir rrspwtive rsistors; thrn the v a l ~ ~ rois ahsorbwnrr at the two navelmgths n1.e inserted st thr. t,no input p,,ints ( I I O ~t Ph ~ c ~ p p ~ s~iitg~n ) . 'l'h~ ~rpwitt,e 01ltput voltages, corresperhtiunsl amplifier through resist:mcrs of q~proprintrvalue surh that thc output cd the s ~ c o n dstage will he kbz kaB cqml to the quantity, k.z . This qosntity, except for its sign, is now id~nticalto the right-hand side of equation 7. Thus, this quantity is now i d through an inverting amplifier of
+
+
gain, 1 , to yield the dcsircd relatim and correct sign. Now by connecting the output of this inverter to the original inpxt, we establish the idenbity stated in equation 7. In practice, the initial concmlsations of R and A are inserted s t the pnint marked on tho diagram as uollages. $3 the initial ronrentr~tionof z is scrc,, (Conlinmd on page A942)
Chemical Instrumentation wr establish this condition by closing the switch across the capacitor C, which has t,lx effect of yielding zero voltage a t the rnltput of bhe first amplifier. Now t o commence the computation: the switch is simply aponed, and the voltage a t the point, -z (or r if the inverter is employed a s shown) is measured. As can be seen from the recorded curve, equilibrium eventually is reached, and the concentration uf z no longer changes. If one wished, the
cmeentration of B nr ;I nr bchh r d d n o r be suddenly chrtnged and t,he resstablishmont of equilibrium rould he ohserved. I t is also obvious that, the k, and k s d c t e r m i n i n g resistors and repeating the solution a t various wttings of the resistors until tho dads oht,ained matched t h a t found experimcntdy. More than one circuit configuration m > q he employed for determining the sdution of equations. Thus, some thought s h w l d be given t o the initial configuration t o see if R simpler circuit nil1 prrforn~the
same t,ask. Fur example, thr rircuit shoxn in Figure 8 may he simplified by ronnecting the circuit as shown hy the dnt,ted line, and the two inverting amplifiers in the loop thereh? eliminet,ed. Furthermow, if the initial voltage mrrespnnding to 1.41 and [BI are introduced wit,h polarities opposite tr, those shown in Figure 8, the third inverter amplifier may also he eliminakd. The values selected in Figure fi \\-ere chosen to represent real tinw solutions, i.e., one serond computer time equals one second real time. Also one volt equals m e mole l x r lit,er since this is t,he normal a.2y of expressing roncentratian in chemirul kinetics. The computer time can, hwwrver, he made a dpfinibe frnrtion of real life-time so t h a t computer solutions ran be obtained in a very short time (lime scaling). I n this way thc solution to a kinetic equation which rrquires m e hour in real time ran he sralrd so that t,he solution ran he obtained in one hundredths of a. necond. In ordcr t o utilize the opt.imum voltage range of the amplifiers, i t may also he desirable t,n have one volt corrpspond t o 0.001 molar (an~plilude scaling). The methods of nvromplishing n m p l i t u d ~and time scaling arc given in the literature eitcd (9, 11-13, 16, 19, 25, 3.5, 26). Analogue computers may also be employed for solving kinetir rquat,ions for second-order chemical reactions. I n this rase, multipliers are necessary, and they are available from several companies. The simple principles outlined here are, however! still applicable ( 1 8 ) . It, is important t o note t h a t certain ecmplex second-order equation?, ahich d ~ f inber gration by mathematical methods, e m he set. up ior analogue romputntion and their corresponding rate emst,nnts ohtained by iterative methods.
Other Operdions Operational amplifiers may alsu hr smployed t o perform a. number of nonlinear functions such as multivibrating, flipping, flopping, Sehmitt-triggering, clipping, gating, etc. The Philbrirk applications manual ( I ) contains numcrons hints and ideas. Other circuits permit rq~erstion as frequency-selective amplifiers ( 2 0 , Sf?), phase d~tectors,memory units (2, 4 ) , and in prerision bridges ( 1 0 ) .
Equipment Sevoral companies manufacture operational amplifiers and analogue eomlluters (gee Table 1). As t h e author's practical experience has been limited t o the various operational amplifiers n~anufacturedby Philbrick Researches, Inc., the comments and model numbers below refer t o those of this company. Aa the ideal choice of operational amplifiers depends upon the t,ask t o be accomplished, the following brief discussion is intended to reflect simply the modus ope~andiin one lahorstory. The Philbriek PZ ($227) oper;ttional amplifier, which requires only four 7'/2 volt mercurv batteries for nower (90 hr,urs), is particularly u s ~ f u l fur small portable instruments needing only a
(Continued on page A944)
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Journal o f Chemical Education
Chemical lnstrumentation single amplifier and whom thc & I 0 V, 1 ma. smplifier output is suitahlo. Because of its differential nature and low current input (10-'L10-12 amperes), i t can be connected as a. voltage follonw and located very dose t o high impedance sources (glass electrodes, etc.), thus minimizing induction of ar hum and noise. I t also serves as a relatively inexpensive unit far precise integration, differentiation, i.e., for gas ch~omatography,etc., since a line operated power srpp1.y is not needed for this single kind of op~ration. Where two or three op~rationnlamplifiers with great flexibility in types of response function are desired, the use of the required number of U P A 3 (5149) operational amplifiers and a R-100B ($205) power supply housed in s singlo rack cabinet has been found quite suitable. The various networks (integrators, differentiators, constant current circuits, inverters, gates, etc.) can be wired into U1 ($13.75) plug-in boxes which can be rapidly inserted into or removed from the operntianal amplifiers. Once a collection of such "function" boxes has been secured, the performance of s. wide numbcr of tasks is quickly achieved by plugging in the appropriate boxes and interconnecting them with stacking-type pnbeh cords (Pomona Electronics Co., Inr., Pomnna, California). For rather specialired uses, such as s. multi-purpose electrorhemicnl research apparatus, the excellent modular i n 8 t ~ mentation of DeFord (7), using Ii2-W (822) and K2-PA (KLZ) operational amplifiers is employed and pawerod by tho R-lO0B power supply. In this instrument a specific task (such as integration, inverting, ete.) is assigned to each aperational amplifier, and, while rarh resulting module is designed t o pcrform its task with optimum nccurac,v, the "bard' operational amplifier itself is not aeeessihle for a dotally difierent function. Where a large number nf accessible operational amplifiers are needed and flrxibiliby is of great importance, a Iii-A10 (81365) operational amplifier manifold powered by s. R-300 ($445) supply is employed. This manifold contains ten operationrtl amplifiers of characteristics identical t o those a1 the UPAS. Again the passive networks are wired into plug-in boxes of the U2 (513.i5) or the larger U1 types; the lildter must be turned !lo0 so aa t o fit the space required. If greater output current is needed, booster smplifiers (SKZ-B, S36) or transistors (3, 8) may be conneeted t,o the out,pot of the opwational amplifier and t h ~ i r out,pot thrn fed hack t o the summing point of t,he operational amplifier. The capacitors employed in the operational amplifier instrumentation, and particularly for integration circuitry, must be of high quality (low lealiagp and low retentiveness); pol,vstyrene types suitable for this purpose are available (Southern Electronics Corp., 230 W. Orange Grove Avenue, Burbank, California; Condenser Products, Kew Havcn Cluck and Watch
(Continued on page A94fi)
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Journal of Chemical Education
Chemical Instrumentation Co., 140 Hamilton Street, Krw Havnn 1, Connecticut; Industrial Condenser Corp., 3243 N. California Avenue, Chiengu I X . Illinois). Mylar capacitors ran sometimes be substituted where the olx?ration is not critical. T o minimize tcrnp~rature fluctuations, precision wire-wound manganin resistors are empluyed. For the plug-in t ~ p operational e amplifiers (UPA2) and rnanifolds(Ki-AlO), t h r immediate
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lournol of Chemical Education
external circuitry can often be "patched up" using a/, in. dual banana-plugs on which components such as resistors and condensers are mounted. Such component plugs are also commercially available (Pomona Electronics Company, Inc.; Donner Scientific Company)
Acknowledgment The author nishes t o acknowledge the assistance of the Xatimal Scienre Foundation, uhose grant (G-1770'2) supported part oi this work on operational amplifi~re.
Chemical lnstrumentation Literature Cited
(1) "Appliration Manual for Philbrick Octal Plug-in Computing Amplifiers." (;mrge A. Philhrirk Rramrches, Boston, Mass. (21 AUERBA,H,C., FINSTON, H. L., I
