A Simple Electronic Integrator
M. Lindstrom and Helsinki U n i v e r s i t y
0. Sundholm
of
Technology
SF-021.50O t a n i e m i ,
with Digital Read-out
Finland
A
very useful device in electrochemical and electroanalytical studies is the coulometer or current integrator. An all-electronic integrator offers the same accuracy as a chemical coulometer and has the advantage of requiring practically no maintenance (1-3).
The integrator, to bc dcscribed here, has been used successfully in our laboratory, It is based on inexpensive solid-state components, works on the principle of voltage-to-frequency conversion and offers direct digital read-out. Thus the use of expensive recorders or digital voltmeters is avoided. Circuit Description
The circuit of the integrator is shown in the figure. The construction is such that thp instrument can be used either single-ended or differentially. Thr dectrolysis current, I, is converted to a voltage drop over the precision resistor R1. Amplifiers A l , A2 and A3 form a high-input impedancc differential amplifier (4),which follows the input voltage I.R1 ( I = I,, = I,,,). The output voltage, El, from this differrntial amplifier can be calculatpd in the following way. Assuming that R2,RS,RE,and R7 have been selected so that R2 = R3 = a.P and Re = RI = b.Rs = b.Ra, one can write for El (4) El
= - b(l+
2a).I.R1
By selecting b, Rs, and C as mentioned in the circuit diagram and adjusting the potentiometer P to give a value for a bctaeen 1 and 4, N can be determined so that the counter reads exactly 1, 10, and 100 mC/ count corresponding to the chosen values of R,, 100, 10, and 1 ohm. Thc final calibration is perhaps best done by substituting for R1 a known constant voltage, i.e., 1 V should correspond to N = 10 counts/s. Alternatively one can use a constant current supply. The potentiometer P is necessary, because the characteris tics of the unijunction transistor d l vary xith the selected type and specimen and the capacitor C can now be of a low tolerance, inexpensive type. The accuracy of the circuit could be further improved by making the resistor Rs adjustable, i.e., instead of a fixed resistor onc could use a series combination of a 100 I< resistor and a 50 I< trim potentiometer. Amplifier A6 has to be boostered by connecting a t,ransistor as an emitter follower, because the reed relay, RR, might draw a current of as much as 10 mA. A * 15 V stabilized power supply is needed for the circuit. The +4 V and +10 V required for the UJT and A6 mere derived from the same supply via voltage dividers. The electromechanical counter was an
(1)
Amplifier A4 serves as a constant-current generator. When R8,Rg,Rlo,and RI1are selected so that R ~ / R I= o R8/Rll = c the current output of this amplifier is 2,
=
-El/R8
(2)
The unijunction transistor, UJT, is connected as an oscillator with the frequency
I n this equation AE is a constant, its value depending on which type of UJT has been selected. Details of this oscillator circuit and of how to calculate the values for the resistors RI2and Ria are found in ( 5 ) . Amplifier A5 is a unit,y gain voltage follower and amplifier A6 is a boostered trigger (6), which drives the electromechanical counter by means of reed relay RR. The operating frequency of the trigger is f. Combining the above equations gives
b-15V
'+15V
f
Circuit diagram for an electronic intogrotor working on the principle of mltoge-to-frequency conversion. A 1 - A 6 = Analog Devices operational amplifiers, type AD741 C D 1. D 2 = Diode l N 4 0 0 6 . D 3 = diode l N 4 1 4 8 UJT = Unljunction transistor, type 2 N 4 8 7 0 R1 = Resistors 1, 10, and 1 0 0 ohms, 0. 5%. Ra, RL RI R, = 3 0 K, 1% R a . "R r . = 1 0 0 .K . ,-. 1 % ."R . = 1 2 0 K.. l % . R ..~ = 3 K . i. % ,. -. R ~ .~. = 1 2 K . 1. ~ ~,-. . R,, = 3 0 0 ohm,, 1%. Rt2 = 1 K,5%, R ~ s= 1 0 0 ohmr, 5%. Rid = 8.2 K, 5%. Rls = 1 8 0 K, 5%. R M = 1 8 0 ohmr, 5% Rn = 1 K. 5%. P = Potentiometer, 5 0 K, 5% C = C~pocitor,6. 8 pF, 10%. (Polyester dielectric) R R = Reed relay [coil re9istonco 7 5 0 ohmr.. o~eratina v o l t w e 6 V) . . PC = lnpvttoelectromechanicol pulsecounter,Elmeg typeUZ6 RA Tr = Transistor 21.13904
..
Thc number of coulombs passed is Q thc number of pulses counted will be
=
J I.dt, and
.
Volume 49, Number 12, December 7 972
/
847
Elmeg panel-mounted 6-digit counter (ElektroMechanik GIVIBH, Peine, W. Germany) with manual reset. The maximum counting rate for this counter is 40 counts/s. Similar electromechanical counters can be purchased from other companies. A counter with a rating of ahout 25 counts/s will probably be sufficient for the purpose. The integrator was built in one unit except for the power supply, which was available in our laboratory, and therefore was connected. through a cable to the integrator. The cost of the components for this integrator, excluding the * 1 5 V power supply, was about $50. Test Results
The performance of the integrator was tested by determination of the amount of copper deposited from a copper sulfate solution under potentiostatic condi- tions. The integrator was connected in series with the
848 / lourrml o f Chemical Education
poteutiostat output. The amount of copper during a run was determined by weighing after each run. The theoretical n-value for the reduction of Cu(I1) is 2.00. I t was found that the standard deviation of the determination was 0.01 equivalents/mole and the mean value for the accuracy of the determination was -0.02 equivalents/mole. This systematic error is greatly dependent on the accuracy of the resistor R1. The above test results indicate that this inexpensive integrator circuit is quite satisfactory for use both in research and undergraduate laboratories. Literature Cited (1) TORNE, E.. A N D DRIBOOLL, C. P., Anal. Chem., 35,1809 (1963). ( 2 ) BOOIAN. C. L.. AND H O L S B O OW ~.. B., Anal. Cham.. 35, 1193 (1963). H. Y.. ENLE,C. G.. AND TOREN. E. C., "Eleotronioa for (3) MALYBTADT, W. A. ~ ~I~C..M ~ ~ park, O icalif..1963, ~ P . 461. ~ scientists." ( 4 ) "Applicestions Manual for Computing Amplifiers," Philbriok Researches Inc.. 1966,p. 82. (5) "The Semioond~ctor ..Data B O O ~ . " 4th Ed., ~ ~ t ~ ~ rn o d. . 1969, a P. AN-IIJ.
(6) CLAYTON. G .
B.,wirelesswodd 384.1P69.
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