I
Operational Amplifiers Symposium
The following papers were ven in the Symposium on perational Amplifiers in Analytical Instrumentation, Division of Analytical Chemistry, 144th National Meeting, American Chemical Society Los Angeles, Calif., Aprd 1963.
s
Generalized Circuits for EIectroa nulytical I nstrumentution W. M. SCHWARZ and IRVING SHAIN Chemistry Department, University of Wisconsin, Madison, Wis.
b Using a generalized model of an operational amplifier, a classification of circuits with feedback stabilization for controlled potential and controlled current electrolysis experiments has been developed. The arrangement of the cell and electrodes, signal generators, and measuring devices with respect to the amplifier input and output has been considered. The interactions of these components, and the practical aspects of circuit grounding form the basis of the classification. Both single-amplifier and multiamplifier circuits are included, and the characteristics and the applicability of the circuits have been summarized. These summaries are designed to serve as guides for the selection of the most suitable circuit configuration for a particular application.
s
work by Booman (6) and DeFord (11) on the application of operational amplifiers to the control and measurement of the current-po t en t ial-t im e r e l a t i o n s of electrolysis cells, much progress has been made by considering these applications from the point of view of analog computers (23, 24). However, this approach has sometimes emphasized the novel circuitry to the extent that the cell, electrodes, and electrochemical INCE THE INITIAL
Figure 1. Four-terminal symbol for Operational amplifier Input is inverting with respect to output of opposite polarity.
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ANALYTICAL CHEMISTRY
phenomena have been overlooked as fundamental components of the instrumentation. By including these componentp in the feedback loops of an operational amplifier and applying Kirchoff’s rules, it has been possible to develop a very general classification of the circuits. From this, it was found that many additional circuit arrangements were possible, some of which possessed distinct advantages over those previously in use. The classification includes instrumentation for both controlled potential and controlled current experiments. GENERALIZED POTENTIOSTATIC CONTROL
In the past, a number of instruments (both mechanical and electronic) have been used in connection with threeelectrode cells for potential control. In every case, the instrument must be capable of performing certain basic operations. First, the potential between the working electrode and the reference electrode must be compared with an arbitrarily-adjustable external potential. Then, the instrument must be able to react to the difference between these two potentials through a negative feedback circuit-containing the counter e l e c t r o d e i n such a way as to reduce the difference to zero. In addition, these operations must be performed without drawing significant current through the reference electrode. I n the modern all-electronic instruments, these operations are commonly performed by an operational amplifier-Le., a high gain amplifier, usually of the differential type, designed to remain stable with large amounts of negative feedback from output to input. In the general sense, an operational amplifier has two inputs and two outputs and can be symbolized as
shown in Figure 1 (16). The polarity relations for the inputs and outputs are indicated. More frequently, a symbol with only three terminals is used, since in many applications, one of the outputs is the ground reference potential and is omitted. i n addition, one of the inputs is occasionally omitted, especially in applications where it also is grounded. In the general case, however, it is important to consider all four of the terminals, and the symbol of Figure 1 will be used here. The arrangement of such a fourterminal operational amplifier and the electrolysis cell in a generalized potentiostatic control circuit is shown in Figure 2. Here, the feedback path from the amplifier output through the counter electrode acts to restore the difference in potential (error signal) between the two inputs to zero. In the present discussion i t will be assumed that the characteristics of the amplifier and the feedback path permit the input error signal to be held a t zero a t all times. Obviously, the accuracy and speed of the actual operation will depend on the dynamic internal characteristics of the amplifier and its interaction with the
Figure 2. Generalized potentiostatic control circuit I I C, counter electrode +:
R, reference electrode
P : W,
working electrode
cell and other components in the feedback path. These fac1;ors have been discussed extensively by several groups (3, 4,7, 8, 9, 15, 29) with particular emphasis on the electronic design of fast-response amplifiers In this discussion, however, the errphasis is on the circuitry outside the amplifier.
e-.(
1
L,-
By considering all possible combinations for the location of one signal generator and one current-measuring device in the basic control circuit, a total of nine different single amplifier potentiostatic circuits can be drawn. These are shown in Figure 4. I n the overall operation of these circuits, one further factor must be considered-the interaction between the current-carrying loop and the comparison loop. In every circuit, one section is common to both of these loops, and if the currenGmeasuring resistor or the signal generator is located as in Figure 4,c, j, g, h, or i, the I R drop across these components due t o the curreiit flow in the current-carrying loop can have a serious effect on the operation of the comparison loop. For example, if the signal generator is common to both loops, as in Figure 4c, the entire cell current must pass through its output impedance. I n cases where this impedance is high, or where the cell currents are large, significant I R drop can be developed in the signal generator. Since this I R drop appears in the comparison loop, it is included in the comparison signal a t the inputs to the operational amplifier, and ultimately appears as an unwanted potential between the reference electrode and the working electrode. As a result, these configurations can achieve effective potentiostatic control only when the I R drop in the signal generator is less than the error that can be tolerated in the cell potential. A similar interaction occurs when the component common to both loops is the current-measuring resistor, as in Figure
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I
1 ‘d
SINGLE AMPLIFIER PO1 ENTIOSTATS
To make the potentiostatic control circuit of Figure 2 useful as an instrument, provision must t e made for inserting a cuirent-measuring resistor (to measure the current Rowing through the cell), and a signal generritor (to provide an arbitrarily-adjustable comparison potential). The location of these elements in the external circuit affects both the operation and applicability of any instrument, and a systematic analysis of the arrangement of the components can provide a basis for the classification of operational a m p u e r circuit configurations. The external circuitry of the potentiostatic controller of Figure 2 can be analyzed by considering; the properties of the individual closed loops makiig up the whole circuit. Altogether there are four such closed loops. Two of these are negative feedback loops-Le., an external circuit path from an output to the corresponding inverting input. The upper feedback loop has been referred to above and consists of the counter electrode, reference electrode, and the upper input and output o f the amplifier. The lower feedback loop consists only of the lower input and output of the amplifier. Although i,hese feedback loops are necessary for operation of the actual instrument, i t is the remaining two loops that are of prime importance in developing the circu, t classification. The third loop in Figure 2 is the current-carrying loop, and consist of the counter electrode, working electrode, and the two low-impedance amplifier outputs. Since this loop is the only low-impedance path the cell current can take in flowing from the amplifier to the cell, any devire used t o measure the cell current must be placed somewhere in this loop. From Figure 3, it is seen that in a circuit contairing a single operational amplifier, there are three possible locations for the currentmeasuring device. The fourth loop in Figure 2 is the comparison loop, and consist of the reference electrode, working electrode, and the two high-impellance amplifier inputs. It is in this loop that the adjustable external potcritial is compared with the cell voltage. One method of carrying out this comparison is by introducing a signal generator into the loop in series with he cell. Sinre the sum of the potentials around any closed loop must be zerc, and since the
Figure 3. Possible locations for current measuring device and signal generator in generalized single-amplifier potentiostat 0: Current-measuring device
0: Signal
generator
error signal must also be zero, the potential between the working electrode and the reference electrode will be forced t o assume a: potential equal in magnitude to that of the signal generator. I n essence, this can be considered as a direct voltage-comparison method. (It is also possible to use a current-comparison method, where a bridge circuit is used to compare the two voltages. This arrangement requires at least two operational amplifiers and will be considered later.) Just a8 the currentmeasuring resistor had to be placed in the current-carrying loop, the signal generator must be placed somewhere in the comparison loop. The three locations that are possible also are shown in Figure 3. If it is desired to introduce more than one signal, more than one of these locations can be used simultaneously.
I
(91 Figure 4.
(h)
(!
1
Circuit Configurations for singie-amplifier poteiitiostafs :
Current-measuring device
@ : Signal generator
VOL. 35, NO. 12, NOVEMBER 1963
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-!-
~
l7Efi4 B -
A -
Figure 5. Grounding arrangements for potentiostatic circuits using single-ended operational amplifiers, showing types A and B grounding
4g. In these cases, however, the I R drop simultaneously must be present to obtain a current measurement. The magnitude of the I R drop which is required depends on the sensitivity of the read-out device and may range from a negligible 1 mv. for a sensitive recorder up to several hundred millivolts for an oscilloscope. Ultimately, a compromise must be made between the sensitivity of the read-out device and the permissible error in the cell potential in using these configurations as potentiostats. Up to this point, the practical problem of selecting a ground reference potential for the circuits of Figure 4 has not been considered. As drawn, these circuits imply that the operational amplifier and the power supply are floating with respect to the earth. Although floating the entire circuit gives maximum selectivity with respect to circuit grounding, it is rarely done in practice, Thus, in an actual circuit, any pointbut only one point-can be grounded in t he combined power supply-potentiastat circuit. In general, the power supply is grounded and this serve4 as the ground potential for the whole circuit. For an operational amplifier with true differential inputs and outputs, none of the four terminals necessarily corresponds to this ground potential, and such circuits can also be grounded externally a t any one additional point (16). However, most of the commercially available operational amplifiers, such as those
Table
Characteristics 1. No SG interaction 2. No R L interaction 3. S G grounding
a
A
B
Figure 6. Single-amplifier potentiostat using chopperamplifier stabilization, showing types A and B grounding P: Chopper amplifier
made by G. A. Philbrick Researches, Inc. (Boston), that have been used in electrochemical applications are constructed with single-ended outputs. That is, one of the output terminals operates a t the potential of the power supply ground. If the present discussion is restricted to the use of single-ended operational amplifiers with conventional power supply grounding, the points in the circuits of Figure 4 that may be a t ground potential can be identified as either the upper or lower amplifier output terminal. This can be shown (using Figure 4a as an example) by redrawing these two cases so that the amplifier ground is in the same location in each circuit (Figure 5 ) . Thus, when considered from the standpoint of the location of the circuit elements with respect t o ground, two distinctly different potentiostatic circuits are obtained. Otherwise, the operating chaiacteristics of the two circuits are identical. For brevity, circuits with the type of grounding shown in Figure 5 will be referred to as A and B circuits, as shown. Although corresponding members of the A and B circuits have the same operating characteristics, there are important practical differences between the two classes. These can be defined
in terms of three additional experimental considerations. First, unless the signal generator is a simple battery circuit, it may not be easy to isolate it from ground. Thus, among the nine A circuits in Figure 4, only in b, c, h, and i can the signal generator be grounded. These would be the most suitable for controlled potential experiments involving complex signal generators. On the other hand, all the B circuits require that the signal generator be isolated from ground. The second point is similar since, in many cases, it is important that one end of the current-measuring resistor be grounded so that the read-out device also can be referred to ground. When the read-out device is an oscilloscope with a differential input, grounding the current measuring resistor is less important, but strip chart recorders generally operate more satisfactorily when grounded. Thus, the A circuit of Figure 4,d, e, f , g, h, and i, would be the most suitable. For the B circuits, those equivalent to Figure 4,a, b, and c, permit grounding one end of the currentmeasuring resistor. The third important consideration results from the fact that operational amplifiers are subject to drift. Under optimum conditions, this drift rate can be small (a few millivolts per day), but
I. Interrelations of Characteristics of Single-Amplifier Potentiostats Circuit configuratione (Figure 4) Type B grounding Type A grounding b c d e f g h i a b c d e f g +
-
+
a
w
-
-
R L grounding - - 5. Stabilization + - + Notes: (+) indicates that: 1 . Signal generator (SG) is not located in the current carrying loop. 2 . Current measuring device ( R L )is not located in the comparison loop. 3. Signal generator can be referred to ground. 4. Current measuring device (and read-out device) can be referred to ground. 5 . Circuit can be stabilized. a In circuit i (type A ) , the signal generator and load resistor cannot both be grounded simultaneously.
4.
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ANALYTICAL CHEMISTRY
h
i
++ ++ +- ++ ++ +- +- +- -- - - + + + + + + " + + + - - + - + f - + - - - + - +
+ + - + + - + + +- ++ ++ -+ -+ - + - - -
P
P
6
d Figure 7.
Generalized follower
Z],Z*: Generalized impedances
without special precautions, drifts may be much larger. In electrochemical experiments lasting for long periods of time (as in coulometry) it may be necessary to reduce this drift by introducing a chopper amplifier such as the Philbrick K2-P between the inputs of t,he operational amp:.ifier (22, 23). To do this, a negativi: feedback loop which contains no components must be available. Thus, the A circuits of Figure 4,a, c, g, and i (and the corresponding B circuits) , (.an be stabilized. As an example, the stLbilized form of circuit 4a is shown in Figure 6 for both the -4and B configurations. [Att'empts also have been made to modify combination amplifiers such as the Philbrick USA-3 to obtain a chopper-stabilized amplifier with both fee'lback loops still available (19), but such circuit.s will not be considered here.] It should be noted that in t,lie A configuration, the chopper amplifier operat,es with respect to its normal ground, while in the B configuration, it must be isolated from ground ( I d ) . In these cases, however, floating the chopper amplifier is readily accomplished. The interrelations of these t,hree characteristics (and the int.eractions discussed above) are sumriarized in Table
I, and their importance in any one experimental setup depends on the specific application. Many of these configurations have been used. Among them are the Type A circuits of Figures 4a (26, 26, 28), 4b (13, 14, l 7 ) , 4d (WO), and 4e (13, l 4 ) , Among the Type R circuits R h i d l have been tliwussed are 4 n ( 6 ) , 46 (29), aiid 4e (8). Other :tpplicdons hare been reviewed by I)ePord (10) and Bard ( 2 ) . Obviously, by limiting the discussion to controlled potential circuits utilizing a single operational amplifier, certain arbitrary restrictions have been placed on the convenience and applicability of the instruments. Nevertheless, the simplicity of such single-amplifier potentiostats makes them particularly useful in experiments requiring fast response (4, 7 , 9, 69). GENERALIZED FOLLOWER
In some cases the limitations of the single-amplifier circuits make them very inconvenient for electroanalytical work. For example, special restrictions must be placed on the output impedance of the signal generator or the sensitivity of the read-out device in five of the circuits of Figure 4. These restrictions can be overcome by using additional operational amplifier circuitry such as the "cathode bias" circuit of Booman (6) (for compensation of IR drop in the current-measuring resistor) or the stabilized voltage follower of DeFord (12) (to serve as an impedance-matching device for the signal generator). The analysis of these additional circuits can be carried out by a consideration of the generalized follower circuit from which both are derived. Using the previous notation for the operational amplifier, a generalized follower can be drawn as shown in Figure 7 , where z1 and 22 represent generalized impedances. Four terminals are available for coupling the follower to another circuit. However, in most applications only three of these are used at any one time, depending on
the particular function of the follower. There are two negative feedback loops and, as before, the action of the amplifier is to adjust the output volt'age so that t8he potent,ial differerrce bet.neen the amplifier inputs is zero. Since the periinrt'rr of the circuit' can br consirlerd as a closed loup, the resultiiig volt,age distrihiition arc~irridthe 100i) VMI be defined readily. 'Yhus, the magnitude ( J f the voltage ac~'oss i h c amplifier output terminal:, is equal t o tlic absolute difference of the voltages across zI and z2. The current How through the external circuit also can be defined by not'ing that the impedance between the two amplifier inputs (usually open grids) is estremely high, that the impedance between the two amplifier outputs is w r y lowv,and tha,t the impedances of t8he negative feedback paths depend on the values of 2, and zg. As with the previous operational amplifier circuits, t'he generalized follower circuit can be stabilized with a chopper amplifier if either z1 or z2 is zero-i.e., if there are no components in one of the feedback loops. Simple Voltage Follower. The conventional voltage follower can be derived from the generalized circuit in Figure 7 by setting z1 equal to zero and allowing z2 t o be a very large (ideally infinite) resistance. This follower circuit is shown in Figure 8a with a signal generator attached to the follower input terminals. By summing the potentials around the outer closed loop, it is clear that the output pot,ent.ial is equal to that of t,he signal generator. The signal generator itself works into tthe very high input impedance of the amplifier, while the follower output impedance is very low, being the order of 1 ohm for commonlyused operational amplifiers. Because of this, the follower circuit is primarily used as an impedance-matching device for coupling into low impedance d.c. circuits. Wit,h this simple voltage follower, the previous discussion of grounding is applicable, so that two distinct series of
/--------I I------I (0)
(b)
Figure 8. Simple voltlige follower, showing Types A and 6 grounding
(a)
(b)
Figure 9. Stabilized voltage followers, showing types A and B grounding VO1. 35, NO. 12, NOVEMBER 1963
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4 3
2 6 Figure 10. Current follower (cathode bias unit) Input terminals, 1 and 2 Output terminals, 1 and 3 or 3 and 4
follower circuits corresponding to the type A and type B grounding configurations can be drawn (Figures 8,a and 6 ) . Since z1 is always zero in the simple voltage follower, the circuit can always be stabilized against drift. The stabilized forms of the voltage follower, showing the two grounding arrangements, are given in Figure 9. The configuration shown in Figure 9a is identical to the stabilized follower developed by DeFord, and features a grounded signal generator and a floating chopper amplifier. If separate operational and chopper amplifiers are used (such as the Philbrick K2-X and K2-P) there is no particular problem floating the chopper amplifier (18). In some designs of composite stabilized operational amplifiers (such as the Philbrick USA-3), the chopper amplifier is permanently connected to the grounded output terminal of the operational amplifier. With such amplifiers, the arrangement shown in Figure 9b must be used, where the signal generator is isolated from ground. The problem of floating the signal generator can be avoided, however, by isolating the entire circuit and the power supply from ground. Then t,he upper output terminal can be grounded in place of that shown. This is the basis of the “grounded output” follower circuit described by Booman and Holbrook (7). Current Follower (Cathode Bias Unit). The current follower can be derived from the generalized circuit in Figure 7 by setting zz equal to zero, and letting ZI be a currentmeasuring device with a finite d.c. resistance. This circuit along with the appropriate input and output terminals is shown in Figure 10. Any current flowing into the input Terminal 1 follows the low impedance path through the current measuring device and the amplifier output to Terminal 2. Since the two input terminals are maintained a t the same potential, the effective input impedance of the current 1774
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ANALYTICAL CHEMISTRY
follower is practically zero, and the current can be measured without introducing the I R drop normally associated with a current measuring device. Because of this, the current follower is very useful for coupling out of low impedance d.c. circuits. For the case where the currentmeasuring device is an ohmic load resistance, the voltage drop across the resistor and hence, also the output voltage, is directly proportional to the current. Under these conditions the output voltage can be used as a measure of the current. Furthermore, the low impedance output of the current follower is ideal for driving conventional read-out devices.
Figure 1 1 . Application of voltage follower Elimination of signol generator IR drop potentiortat-comparison loop
in
The problems of stabilizing and grounding the current follower are similar to those of the voltage follower and will not be discussed further. MULTI-AMPLIFIER POTENTIOSTATS
Voltage Comparison Circuits. By adding current and voltage followers t o a number of the single-amplifier controlled potential circuits in Figure 4, the problem of I R drop in components common t o the current carrying and the comparison loops can be eliminated. For example, in the circuit of Figure 4c, a simple voltage follower can be inserted between the signal generator and the control circuit as shown in Figure 11. This provides a low impedance path for the cell current while introducing a signal into the comparison loop identical t o that from the signal generator. Similarly, in the circuit of Figure 49, a current follower (cathode bias unit)-with the current measuring device-can be inserted into the control circuit in place of the current measuring
device alone, as shown in Figure 12. This provides an effective low impedance path for the cell current while still permitting the current to be measured. With the addition of a second operational amplifier to the potentiastat circuit, the problem of grounding becomes more complex. To use a single power supply, there must be a common grounding point for both the follower amplifier and the control amplifier. Such a common grounding point will be available in any given circuit only if the element involved-i.e., signal generator or current measuring d e v i c e w a s originally referred to ground. If the component was isolated from ground, the follower must also be isolated, using a second, floating power supply. This can be illustrated by referring to Figures 11 or 12. If type A grounding is employed in these circuits, the two amplifiers can be referred to the same reference potential. On the other hand, if type B grounding is used, the follower amplifier (and its separate power supply) must be isolated from ground. Several applications of multi-amplifier potentiostats, using either current or voltage followers as in Figures 11 and 12 have been reported (1, 6 , l l , 19, $1). Bridge Circuits. Up t o this point, the operation of all the potentiostatic circuits was based on a direct voltage comparison between the signal generator and the cell potential. It is also possible, however, t o achieve this potential comparison indirectly by measuring the current that each voltage source causes t o flow in a resistive load. This is commonly done in a simple bridge network such as the one incorporated in the potential control circuit shown in Figure 13. The four legs of the bridge are the two voltage sources (signal generator and electrolysis cell potential) and the two load re-
I Figure 12. Application of a current follower Compensation for current-measuring device IR drop in potentiostat-comparison loop
Figure 13. Potentiastatic control circuit with bridge network for potential comp a rison bridge resistor for cell; signal generator
R1,
R2,
bridge resistor for
sistors. The action (of the operational amplifier is the samt? as in the direct It voltage-comparison potentiostat. forces current through the cell so as to maintain the potentiedl difference across the amplifier inputs at zero-Le., to keep the bridge in balance. In the bridge arrangement there are several factors con3ected with the current flow within tk.e comparison loop that must be considered further. Although the bridge circuit will be considered with only one signal generator, it is possible to insert additional
voltage sources either in series with the bridge as in the direct voltage comparison circuits, or in parallel with the bridge as shown by the dotted lines in Figure 13. In the latter case the sum of the currents flowing through each signal generator load resistor is equal to the current flowing in RI. This arrangement has been analyzed in terms of an analog computer adder (11) and has the advantage that all the signal generators can be referred to the same potential. Although the circuit of Figure 13 fulfills all the operational requirements of a potentiostatic control circuit, significant current must be drawn through the reference electrode to operate the comparison bridge. This difficulty is generally avoided by using a voltage follower as an impedancematching device to couple the cell to the bridge (Figure 14). The further analysis of the bridge comparison circuits with respect to grounding and the location of the current-measuring device can be carried out following the methods used for the singleamplifier potentiostats. In this case, however, there are so many possible grounding arrangements that the discussion will be restricted to the
'5 Figure 15. Locations for current-measuring device in bridge-type potentioritat with type A grounding
Figure 14. Voltage follower used as impedance-matching device in bridgetype potentiostat
most useful case where both amplifiers and the signal generator are referred to the same ground potential. Then there are three possible locations for the current-measuring device in the current carrying loop. These are shown in Figure 15 for circuits with type A grounding, while those for type B grounding are shown in Figure 16. As before, placing the current measuring device as shown in Figures 15b and 16b introduces I& drop in the comparison loop, while the location in Figure 15c prevents stabilization of the controller amplifier. None of the type B circuits can be stabilized. These considerations (and others) are summarized in Table 11.
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Figure 16. Locations for current-measuring device in bridge-type potentiostat with type B grounding VOL. 35, NO. 1 2 , NOVEMBER 1963
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Of these circuits, 15b is of particular importance. By addition of a current follower as discussed above, the I R drop across the current measuring device can be eliminated. This circuit was first proposed by DeFord (11) and has been widely used as a genwal purpose potentiostat. I t should be noted, however, that for high current applications, a booster is needed for each amplifier in the currentcarrying loop (27). For example, circuit 15b, with a current follower to compensate for I R drop in the currentmeasuring resistor, would require two booster amplifiers. Circuit 15a would require only one booster amplifier, but the current measuring device cannot be referred to ground. Without grounding restrictions, an extremely large number of distinctly different circuit arrangements are possible, some of which are of practical importance (7'). However, the analysis of these configurations involves a relatively straightforward extension of the considerations applied to this point. ilnother large class of circuits, involving compensation for I R drop by additional feedback loops (11), has been omitted entirely, since these configurations usually require additional amplifiers. Thus, most of the useful potentiostat circuits have been included in these classifications.
Table II.
Interrelations of Characteristics of Bridge-Type Multi-Amplifier Potentiostats
Characteristics 1. 2. 3.
No Rr, interaction
Circuit configurations Type A grounding Type B grounding (Figure 15) (Figure 16) a b (: a b C -1-t -t
:
RL grounding f Stabilization c c Kotes: (+) indicates that: 1. Current measuring device (RL) is not located in the comparison loop. 2 . Current measuring device (and read-out device) can be referred to ground. 3. Circuit can be stabilized.
+
I
I
difference to zero. In addition, these operations must be performed without drawing significant current from the external circuit. The circuit arrangement for generalized galvanostatic control using an operational amplifier is shown in Figure 17. If this circuit is compared with Figure 2, the close analogy between the galvanostatic atid potentiostatic control is readily apparent. Thus, in a practical circuit a simple interchange of the elements in the dashed lines in these figures will convert any potentiostat circuit directly into a galvanostat. Unfortunately, the analogy with potentiostats cannot be extended to include all circuits, since in the galvanostatic case the two elements inside the dashed
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lines can be physically separated. The principal requirement is that these two elements remain in series in the current carrying loop. However, the same methods of analysis and classification as discussed before can be applied to the galvanostatic circuits. Some of these circuits have been discussed by Giersh (15),who also included other important approaches to controlled current circuitry. SINGLE AMPLIFIER GALVANOSTATS
To make the galvanostatic control circuit of Figure 17 useful as an instrument, provision must be made for measuring the potential between the reference and working electrodes, and for
GENERALIZED GALVANOSTATIC CONTROL
Circuits with feedback stabilization
for controlled current electrolysis can be developed using the same approach as outlined for controlled potential electrolysis, and can be included in a similar general classification. The basic operations performed by any galvanostat are similar to those performed by simple potentiostats. First, the I R drop across an ohmic resistor placed in series with the cell must be compared with an arbitrarily-adjustable external potential. Then the instrument must be able to react to the difference between these two potentials through a negative feedback circuit-containing the cell-in such a way as to reduce the
Figure 17. Generalized galvanostatic control circuit C: Counter electrode W: Working electrode R.: Series resistor
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(a 1 L
Figure 18. Circuit configurations for single amplifier galvanostats
-
I
I
1
N
Figure 19. follower
Application
of voltage
Elimination of signal gerierator IR drop galvonostat-comparison loop
introducing a suitable signal generator. The arrangement for measuring the working-reference elec ,rode potential is straightforward. The measuring device must be connected directly across the two electrodeb in the cdl and must be of high enough impedance to prevent current from flowing through the reference electrode. As before, the signal generator must be inserted somewhere in the currentcarrying loop. I n the galvanostatic case, however, there %refour possible locations, one being b1:tween the series resistor and the cell. These configurations are shown in Figure 18. Another result of the cell being indepmdent of the comparison loop is that the cell can be turned around in the galvanostatic circuits-thus yielding four more possible configurations as shown in Figure I&. This simple transformation often lead5 t o a better arrangement for measuring the potential between the working rind the reference electrodes. If the use of single-ended operational amplifiers is again asmmed, two different grounding arrangements, type A and type B, are possilile, analogous to the arrangements shown in Figure 5 . Including the different grounding arrangements, there are, altogether, 16 single-amplifier gal ianostat configurations. Again, thlxe are a number of desirable characteristics which a
Table
111.
(b)
in
grounding
practical single-amplifier galvanostat should possess. First there should be a minimum interaction between the current-carrying loop and the comparison loop. That is, the circuit should be arranged so that I R drop is not developed in the comparison loop as a result of current passing through the signal generator. Second, a negative feedback loop containing no components should be available, so that the operational amplifier can be stabilized with respect to drift. Third, there should be provision for directly grounding one end of the signal generator. Fourth, the arrangement should allow one end of the potential measuring device to be referred t o ground potential. This latter condition is satisfied either if the working electrode is grounded directly or if it is only being held a t a virtual ground potential by the circuit without direct grounding. h summary of the circuits in terms of these considerations is given in Table 111. Several general points can be derived from Table 111. For example, none of the circuits possesses all four of the desirable characteristics simultaneously. A number of the circuits, however, are
useful for conventional chronopotentiometry where the signal generator is usually a battery-operated low voltage power supply which can be isolated from ground easily. For applications using complex signal generators, circuit 18b is the only configuration in which both the signal generator and the potential measuring device can be grounded simultaneously. However, the signal generator is located in both the comparison loop and the current-carrying loop. Therefore, the same restrictions (regarding I R drop in the signal generator and control accuracy) are applicable as with the analogous potentiostatic circuits. MULTI-AMPLIFIER GALVANOSTATS
Voltage Comparison Circuits. The effect of I R drop in the signal generator can be minimized in several of the single-amplifier circuits by coupling the signal generator to the comparison loop through a voltage follower. The general arrangement is shown in Figure 19 using Figure 186 as an example. I n this case the follower and the operational amplifier can be referred to the same ground
Interrelations of Characteristics of Single-Amplifier Galvanostats
Circuit configuration (Figure 18) Type A grounding
Characteristics a b c d e f g 1. No S G interaction 2. Stabilization 3. SGgrounding 4. M grounding Notes: (+) indicates that: 1. Signal generator (,SG)is not located in the current currying loop. 2 . Circuit can be stabilized. 3. Signal generator ( S G ) can be referred t o ground. 4. Read-out device (.W) can be referred to ground.
+- +++ +
h
a
b
c
Type B grounding d e f
g
h
++ +- +- +- ++ +- +- +- ++ -+ +- +- ++ -+ - + - + - + - - - -- -- - - - - - + + + +
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potential. Introducing a follower into a circuit such as 18a, however, would require floating either the follower or the controller amplifier. Bridge Circuits. So far, all of the galvanostatic circuits that have been considered are of the direct voltagecomparison type. It is aho possible t o use a bridge-type voltage comparison network similar to that shown in Figure 13, where, for galvanostatic circuits, the controlled region of the cell is replaced by an ohmic resistor. Otherwise the operation is identical to the potentiostatic bridge circuits. In classifying the bridge-type galvanostats the same assumptions will be made with respect to common grounding of the control amplifier, follower amplifier, and signal generator as were made for potentiostatic bridge circuits. Then the galvanostatic circuits corresponding to Figure 15 (A-type grounding) and Figure 16 (B-type grounding) can be drawn. These are shown in Figure 20a and 206, respectively. The analogous cases with the cell turned around are also indicated. Analysis of these four configurations in terms of the desirable galvanostatic circuit characteristics shows that the control ampliier can be stabilized only with type A grounding (Figure 20a) while one of the cell arrangements of Figure 20b with type B grounding is the only circuit in which the potentialmeasuring device can be referred to ground. The use of operational amplifier circuits for controlled current electrolysis has not been as extensive as for potentiostatic studies, Nevertheless, the ap-
plications that have been reported (11, 18, 24.4.)indicate that this approach to the instrumentation offers distinct advantages. The general classification of the circuits presented here can serve as a useful guide in selecting the most applicable circuit configurations. ACKNOWLEDGMENT
Thanks are due to G. L. Booman, who made available a copy of Reference 6 prior to it,spublication. LITERATURE CITED
(1) Alden, J. R., Chambers, J. Q., Adams, R. N., J . Electroamal. Chem. 5 , 152
(1963).
(2) Bard, A. J., ANAL. CHEM.34, 57R
(1962). (3) Bewick, A., Bewick, A., Fleischmann, M., Liler, M., Electrochim. Acta 1, 83 I 1 4.59). (4) Be&ck, A,, Fleischmann, M., Zbid., \-_--
8, 89 (1963). (5) , , Booman. G. L., ANAL. CHEM. 29. 213 (1957j. (6) Booman, G. L., Phillips Petroleum Co., Idaho Falls, Idaho, private communication (1960). (7) Booman, G. L., Holbrook, W. B., ANAL.CHEM.35, 1793 (1963). (8) Breiter, M., Will, F. G., Z. Elektrochem. 61, 1177 (1957). (9) Brinkmann Instruments, Inc., Great Neck, New York, “Wenking Potentiostat,” 1961. (10) DeFord, D. D., ANAL. CHEM.32, 31R (1960). (11) DeFord D. D., Division of Anal tcial dhemktry, 133rd National d e t i n g , ACS, San Francisco, Calif., April, 1958. (12) DeFord, D. D., “Stabilized Follower Am Mer,” Applications Bulletin, G. A. PhiPbrick Researches, Inc., Boston, Mass.
(13) Gerischer, H., Proc. Intern. Comm. Electrochem. Thermodymm. Kinet, 9th
Meeting, 1957, p. 213, Butterworths, London. ~195% (14) Gerischer, H., Staubach, K-E., Z. Elektrochem. 61,789 (1957). (15) Gierst, L., Proc. Intern. Comm. I
Electrochem. Thernzodunam. Kinet., 7th
Meeting, 1955, p. 49, Butterworths, London, 1957. (16) Hansen, P. D., “Operational Amplifier Techniques in Process Control,” p. 3, G. A. Philbrick Researches, Inc., Boston, Mass, (1963). (17) Harrar, J. E., Stephens, F. B., Pechacek. R. E., ANAL. CEEM. 34, 1036 (1962). (18) Hurwitz, H., Gierst, L., J. Electroanal. Chem. 2, 128 (1961). (19) Kelley, M. T., Fisher, D. J., Jones, H.c.,AUL. CHEM. 32, 1262 (1960). (20) Kelley, M. T., Jones, H. C., Fisher, D. J., Ibid., 31, 488 (1959). (21) Ibid., p. 1475. (22) Malmstadt, H. V., Enke, C . .G., Toren, E. C., “Hectronics for Scientists,,’ p. 360, W. A. Benjamin, Inc, New York, 1962. (23) G. A. Philbrick Researches, Inc., Boston, Mms., “Applications Manual for Philbrick Octal Plug-in Computing Amplifiers,” 1956. (24) Reilley, C. E.,J . Chem. Educ. 39, A853, A933 (1962). (25) Schoen, J., Staubach, K-E., Regelungstechnik 7, 1.57 (1954). (26) Schwurz, W., Chem. Inq. Tech. 28, 423 (1956). (27) Underkofler, W.L., Shain, I., ANAL. CHEM.35, 1778 (1963). (28) Vielstich, W., Gerischer, H., Z. Physik. Chem. Frankfurt 4, 10 (1955). (29) Will, F. G., Z. Elektrochem. 63, 454, 689 (1959). RECEIVEDfor review June 12, 1963. Accepted August 15, 1963. Presented in part at the Division of Analytical Chemistry, 144th Xational Meeting, ACS, Los Angeles, Calif., April 1963. The work was supported in part by funds received from the National Science Foundation under Grant No. G 15741.
A Multipurpose Operational Amplifier Instrument for Electroanalytical Studies WILLIAM L. UNDERKOFLER
and IRVING SHAlN
Department of Chemistry, University of Wisconsin, Madison, Wis.
b A multipurpose instrument based on operational amplifiers has been constructed. It is useful for polarography, stationary-electrodepolarography, a.c. polarography, chronopotentiometry, cyclic triangular-wave voltammetry, step functional controlled potential electrolysis, and coulometry, and it is capable of extension to other techniques. Prewired plug-in units are employed to convert the instrument to a form suitable for each experimental technique, and to provide the operating controls. The use of plugin units makes the instrument highly versatile yet easy to operate. Signal generators suitable for each of the experimental techniques are described.
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in electroanalytical research has emphasized that many of the newer instrumental methods complement each other in providing information about an electrochemical system. Thus, there has been considerable interest in developing equipment which can be readily adapted for use in several of these methods interchangeably. The only really successful approach has involved instrumentation based on operational amplifiers, with the moddar construction used by DeFord (6). This approach provides the necessary versatility, since the individual followers, adders, integrators, etc., can be interwired as necessary to produce the required functions. HowECENT WORK
ever, such instruments are relatively inconvenient to use because of the extensive rearrangements needed to change from one experimental method to another. Furthermore, the many cables are sources of noise and erratic contacts. Thus it appeared useful to consider alternate designs for a multipurpose instrument based on operational amplifiers. T o avoid the problems associated with extensive interwiring, modular construction was not used. However, development of a single chassis instrument using switching to convert from one experimental technique to another was not practical. In such designs, versatility is limited, the switching is
