Arrangement for and method of obtaining a first, second or following derivative of a titration curve
United States Patent [:91 r  
 Jilek 1 1 Apr. 1, 1975 [75] Inventor: Jaroml&#39;r J|&#39;1ek,Olomouc,  
 Czechoslovakia [73] Assignee: Universita Palackeho V. Olomouci,  
 Olomouc, Czechoslovakia 22 Filed: 0a. 18, 1972 21 Appl. No.: 298,614  
 [30] Foreign Application Priority Data Oct. 19, 1972 Czechoslovakia 7297-72 [56] References Cited UNITED STATES PATENTS 3/1948 Higginbotham.................,... 235/183 2/1955 235/183 3/1959 Malmstadt 23/253 R 3,333,185 7/1967 Riseman et a1. 324/30 3,512,093 5/1970 Perreault 328/127 3,546,601 12/1970 Hiltz 328/127 FOREIGN PATENTS OR APPLICATIONS 566,037 8/1957 Italy 23/253 OTHER PUBLICATIONS Kern &amp; Kern (Textbook) Electronic Analog Computers, McGraw Hill, 1956, sec. edit., p. 13.  
 Lokvenc: A Non-Inverting Differentiator, Tesla Laboratory Reports, Vol. 5, No. l, 3, 1972, pp. 26-27.  
 Primary Examiner-Felix D. Gruber [57] ABSTRACT Arrangement for and method of obtaining a first, second and following derivative of a titration curve with respect to time, particularly in automatic titration apparatus for quantitative chemical analysis. The arrangement of the invention comprises a low pass frequency filter followed by at least one derivator with an operational amplifier and the corresponding input and feedback impedances for obtaining a derivative of the titration curve with respect to time, said derivator may be connected behind an impedance converter for transfer of the input signal to the required voltage and power level. At corresponding places of the arrangement there are connected recording devices for recording the course of curves obtained and evaluation circuits for determination of the equivalent point.  
 3 Claims, 2 Drawing Figures 2,898,200 8/1959 Karr 23/253 R 3,026,480 3/1962 Usher Jr 328/127 3,073,682 l/l963 Lindsley 23/253 3,252,098 5/1966 Schlaepfer........,................. 328/127 3,252,099 5/1966 Dodd 328/127 SELEET 2 OF 2 PATENTEU P 1 97 ARRANGEMENT FOR AND METHOD OF OBTAINING A FIRST, SECOND OR FOLLOWING DERIVATIVE OF A TITRATION CURVE This invention relates to an arrangement for and a method of obtaining a first, second or following derivation of a titration curve over time, particularly for automatic titration apparatus for chemical quantitative analysis.  
 BACKGROUND OF THE INVENTION Titration is a rather frequently used working method at chemical quantitative analysis for determination of the concentration of a solution. The method consists in carrying out a reaction of a known amount of a solution of unknown concentration with a reaction agent of a known concentration and in the determination of the exact time when the reaction is completed. The amount of added re action agent of known concentration can be used for calculation of the unknown concentration of the solution. The determination of the moment when the reaction is completed can be accomplished by a couple of suitable electrodes, immersed into the titrated solution. The voltage, generated between both electrodes and registered in a record as function of the amount of added reaction agent has generally the course according to an S-shaped curve. called a potentiometric titration curve. It has been found that the inflection point of the potentiometric titration curve coincides with the final titration point, that is, the moment when the subject reaction is completed.  
  Since the titration with a potentiometric or other control or other measurement of the course of the titration curve is rather frequently used in volumetric analysis. a number of apparatuses have been designed which make titration easier and more accurate. A significant effect is produced when the supplying of the reaction agent proceeds at constant speed, by the determination of the equivalent point from the course of the first derivative of the titration curve with respect to time, which curve shows an expressed maximum at the equivalent point. Such equivalent point can be still better determined from the course of the second derivative of this curve with respect to time. such latter curve passing through zero at the equivalent point.  
  The derivation of the titration curve over time has been up to now obtained by using passive derivation RC elements only. followed by a simple electronic amplifier system. This method, due to the low sensitivity obtainable therewith. is unsatisfactory, as it requires quick additions of reaction agent, which reduces the accuracy of determination of the inflection point. The course of the derivative curve thus obtained is, in addition, only approximate.  
 SUMMARY OF THE INVENTION It is an object of this invention to eliminate these drawbacks and to provide an apparatus and a method which allow an accurate determination of the inflection point ofa titration curve under different operating conditions. According to this invention, the first, second or following derivatives of the titration curve with respect to time, particularly in automatic titration apparatus for quantitative chemical analysis, is obtained by connecting a low pass filter. followed by at least one derivator with an operational amplifier and the corresponding input and feedback impedances for forming derivatives of the titration curve with respect to time behind an impedance converter for transforming the input signal to a required voltage and power level; at corresponding places of the system there are provided recording devices for recording the course, and evaluating circuits for the determination of the equivalent point.  
  An advantage of the arrangement according to this invention over previously known methods for obtaining the derivation of a titration curve with respect to time is the high and adjustable sensitivity of the arrangement, allowing the use in analysis of a titration with small doses with low titration speed, and thus also for titrations wherein the respective chemical reaction proceeds at low speed. The arrangement further makes possible the use of an electrode or some other detection system having a high internal resistance, such as glass and similar electrodes, and makes it possible to follow the titration with potentiometric indication in a non-aqueousmedium, which generally has a high internal resistance.  
 DESCRIPTION OF THE DRAWINGS In the attached drawings:  
  FIG.1 is a block wiring diagram of an arrangement according to this invention; and  
  FIG.2 is a more detailed wiring diagram of the arrangement of FIG. I.  
 DESCRIPTION OF THE ILLUSTRATED PREFERRED EMBODIMENT Referring to FIG. I, an electrode system (not shown) is connected to the input 12 of an operational amplifier I. This section of the circuit constitutes an impedance converter 5. The output 6 of the impedance converter is connected by way of an active or passive filter I4 with a low pass frequency characteristic to a first derivator l5, represented by an operational amplifier 3 and by suitable impedances 31. 32 connected in its input and feedback circuit. A second derivator I6. represented by an operational amplifier 4 and suitable impedances 37, 38, connected in its input and feedback circuit, is connected to the output 8. Evaluating devices. as for instance a recording device and logic circuits may be connected to the individual terminals 6 to 9.  
  An evaluating circuit 40 for the determination of the equivalent point is connected to the terminal 9, and recording devices. of which one is shown at 41 and connected to terminal 6, may be connected to any desired one of the terminals 6 through 9, inclusive.  
 A practical embodiment is indicated in FIG. 2. An  
 operational amplifier l is used as impedance converter,  
 an electrode (not shown) with a high internal resistance being connected to terminal 10. and a reference electrode connected by a potentiometer 17 to terminal 11. The potentiometer I7 controls the voltage amplification of the impedance converter 5 so that the properties of all following circuits should be utilized to their utmost. An active filter 14 with a low pass frequency characteristic is connected behind the impedance eonverter 5, said filter 14 being represented by an operational amplifier 2 and the respective RC network I8 to 30. The filter serves to eliminate interference signals. generated especially with mixing the solution and the addition of reaction agent and its limited frequency is chosen according to the speed of feeding the reaction agent and the steepness of the titration curve so as to prevent a deformation of the course of the titration curve.  
  Derivators l5 and 16 are connected behind the filter 14. their frequency characteristic being limited by small additional resistors and capacitors 23 to 36. The transmission constant of the first derivator l5 represented by the operational amplifier 3 and the respective RC network is determined by a capacitor 31 and a resistor 32. Additional elements for limiting the frequency characteristic of the derivator are a resistor 33 and a capacitor 34. The value of these additional elements are chosen so as not to distort the measured course and to maintain a negligible phase error of the derivator 15. A similar frequency limitation is provided for the second derivator l6 represented by the operational amplifier 4 and the corresponding RC network 35 to 38 by the resistor 35 and by the capacitor 36. Its transmission constant is determined by the capacitor 37 and the resistor 38. it is possible to further increase the transmission constant of the first derivator for extremely slow titrations by changing the value of the capacitor 3] or resistor 32.  
  A device for recording the course of the potentiomet ric titration curve is connected to the output terminal 6 or 7. A device recording the course of the first deriva tion of the titration curve with respect to time is connected to the output terminal 8 and a device recording the course of the second derivation of the titration curve with respect to time, or logic circuits for the evaluation of the inflection point of the potentiometric titration curve are connected to the output terminal 9.  
  The applied operational amplifiers l to 4 have no automatic zero setting; they are provided with an electrometric input and have the following fundamental paramcters: amplification -l 0, input current l.l0&#34; A,  
 maximum width of output voltage :10 V, and maximum output current ZmA.  
  Although the invention is illustrated and described with reference to a single preferred embodiment thereof it is to be expressly understood that it is in no way limited to the disclosure of such a preferred embodiment, but is capable of numerous modifications within the scope of the appended claims.  
 What is claimed is:  
  l. A circuit arrangement for obtaining a first derivative ofa titration curve with respect to time, comprising a low pass frequency filter connected to titration moni toring means for eliminating interference signals gener ated by the addition of reaction agents. and at least one derivator with an operational amplifier for obtaining a derivation of the titration curve over time connected to the filter, and at least one recording device for recording the course of the obtained curve of the first derivative connected to the output of the said derivator.  
  2. A circuit as claimed in claim 1, comprising at least one additional derivator for obtaining at least a second derivative of the titration curve with respect to time, the additional derivator being connected to the output of the first recited derivator and the first of the said derivators being connected to the output of the low pass frequency filter, and a further evaluation circuit for the determination of the equivalent point being connected to the output of the said additional derivator.  
  3. A circuit according to claim 1, further comprising an impedance converter for transfer of the input signal to the required voltage and power level, the low pass frequency filter being connected to the impedance converter.