Direct-Reading and Differential Frequency Meter for High Frequency Titrations W. J. BLAEDEL AND H. V. MALMMSTADT’ University of Wisconsin, Madison, Wis. The work described was undertaken to provide a meter such that both the beat frequency (cycles per second) from the high frequency titration apparatus and the first derivative with respect to time of the beat frequency (cycles per second per second) can be read directly from either panel or recording milliammeters. With this meter high frequency titrations can be performed easily and accurately by either the ordinary or differential technique. Schematic diagrams are presented for the complete meter circuit. Each section of the circuit is de-
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scribed according to its specific function. Response curves showing both the stability and linearity are given. Titrations with sharp end points may be carried out with error of less than 0.1% and no corrections because of instrumental lag are necessary. The possible use of the differential meter for measurement of rates of chemical reactions is being investigated in this laboratory. The differential circuit, with modifications, might greatly facilitate or improve obtaining experimental data, particularly in potentiometric and conductometric titrations.
the lag between the input and the differentiated response is not significant in titrations,
S PROCEDURES for high frequency titrations described earlier (1, B), the frequency meters were converted from war
surplus equipment, and were not particularly appropriate for their uses. In this article is described a direct-reading frequency meter with sufficient sensitivity and linearity for use in high frequency titrations, This instrument is so designed that the output from the direct-reading meter can be differentiated, giving directly a response that is proportional to the time rate of change of frequency. This instrument is advantageous in carrying out high frequency titrations differentially ( 3 ) . It may also be used to determine substancw by measurement of the rate a t which they react with standard substances under controlled conditions. Because of the intended application t o rate work, much more emphasis has been placed on linearity of response than would be necessary for titrations alone. Delahay (4) has successfully applied a differential meter system t o conductometric titrations. The meter system discussed here differs from that of Delahay in several important respects. The input to the meter is a continuous oscillation of varying frequency often obtained from the mixer unit of a high frequency instrument (1, 3). Both the frequency itself and its time rate of change may be read directly on panel milliammeters in the output circuits of the instrument, or recorded with an inexpensive recording milliammeter of the AMPLIFIER Esterline-hgus type. The reond monses of these meters are LIMITER p u t f r e q u e n c y (cycles per second) and to its time rate of change (cycles per second per second). The differentiating circuit, which is a simple RC differ-
age current a n d “ s o a k i n g effect” (6). The time constant is low enough so that
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Figure 1is a block diagram of the direct-reading and differential frequency meter. Each block has a specific function or functions and is labeled according to the use in the circuit. The input and output wave forms from each section are also roughly drawn. The first two blocks, consisting of amplifier, limiter, pulse former, and meter, form a direct-reading frequency meter. This is used for carrying out high frequency titrations by the ordinary and drop differential methods (3). The next two blocks consist of a filter and direct current amplifier, The filter converts the pulses from the pulse-former network into an average direct current voltage which is directly proportional to the input frequency. This direct current voltage is then amplified about one hundred-fold by means of a one-stage direct current amplifier. This direct current voltage is then differentiated through a simple RC differentiator, whose output is directly proportional to the time rate of change of the direct current voltage and, therefore, to the time rate of change of the input frequency. The final block represents a one-stage vacuum tube voltmeter which contains either a panel or recording milliammeter (zero a t center scale) as the differential output voltage indicator.
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In the following sections each circuit represented in the block diagram is presented and described in detail. Because of the limitations imposed on the rest of the circuit by the RC differentiator, it is described first. The other circuits are described in consecutive order from the frequency input to the output differential indicator. RC DIFFERENTIATOR
The basic circuit for the differential frequency meter section is t,he simple RC differentiat.or (5) shown in Figure 2, where
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RC Differentiator
Eout = RC dE,,/dT-that is, the voltage output, Eout, is directly proportional to the time rate of change of the voltage input, E,,. Actually, the equation given in Figure 2 and above is only an approximation. E,,t lags behind dE,,/dT in a way given by the more exact equation, Eaut = RC dEl,/dT (1
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output, which is in the form of pulses whose average voltage is directly proportional to the frequency input. These pulses can either be amplified with a video pulse amplifier and then filtered to obtain an average direct current voltage, or filtered first and then the direct current voltage amplified with a direct current amplifier. Either method can be used t o obtain a large input voltage, E,,, to the RC differentiator. Both methods were tried and the direct current amplifier was adopted for the final circuit because of certain advantages over the video pulse amplifier, as described below. Again, however, high sensitivity may not be attained simply by making E,, large without limit. The maximum magnitude of E,, is limited by the value of the B power supply voltage and the maximum voltage rating of the condenser. The B supply voltage used with this instrument is 300 volts, and the condenser is rated a t 300 volts. Consequently, the maximum possible value for E,, is 300 volts. It is desirable to be able to change the sensitivity of the differentiator, for different applications require different sensitivities. There are several possible methods for changing sensitivity, and the particular application of the instrument will determine which method is most suitable. For high frequency titrations it is desirable to be able to change the sensitivity by changing the RC differentiator time constant. Consequently, when the rate of addition of titrant is increased, the time constant can be decreased so the response lag of the differentiator does not cause a significant titration error. The time constant, RC, is easily changed by a bank of resistors, R p jto R,,, as shown in the schematic diagram (Figure 5). I t is necessary that condenser C18 be of high quality
Eout i s p r o p o r t i o n a l t o dE,,/dT only when the system is a t steady state, and when dE,,/dT is not changing. However, when dE,,/dT is changing, the response Eout lags from strict proportion1 -- ality by the factor e RC. The lag is not significant in terms of titrant added, but causes the end point t o fall beyond the equivalence point by a time roughly equal to RC, which * corresponds to only about 0.01 ml. of titrating solution, as shown below. From the above equation, Figure 3. Amplifier and Limiter for a given time rate of RII. 10 K TI, TP.6SJ7 Rio. 500 K change in input voltage, the Ti. 6V6 Ri. 500K Ria. 100 K Rid. 50 K, 10 watts output, Eout,is larger, and Rs. 250K therefore the senaitivity of Ra. 5 0 0 o h m s Ria. 6 K, 10 watts Ris. R4. 250K 5 K 10 watts the instrument is greater, the Rs. 100K R I L 4 K: 10 watts Rs. 10K L I . 50-microhenry choke larger the time constant, RC. R,. 500K CI C4 Cs. 0.1-pfd. 600-volt paper Rs. 5 0 0 o h m s Cg: C6: 25-pf-3 25-volt electrolytic The time is in seconds if R Ra. 500K Cs. Ca. C7. CP.&. GI. 20-ufd.. 400-v .olt is in ohms and C is in farads. eleotrolytic Ria. 100 K Thus, for a sensitive instrument, RC should be as large so the leakage resistance is very high and the “soaking effect” as possible. However, as RC becomes larger, the response is (6) insignificant. For this purpose a condenser with a polydelayed. I n a titration, too large a value of RC would cause the styrene dielectric is suitable. Such condensers are not usually observed end point t o lag too far behind the theoretical equivalent point. Thus, in practice, there is a n optimum, or intermade with a capacitance much larger than 1 pfd. For this instrument a 1 pfd. polystyrene condenser is used and resistances mediate, value of RC which gives adequate sensitivity with a R25 to R2, are chosen for RC time constants of 0.25, 0.5, and 1 minimum lag of response. For titrations, where standard second. Any other time constants can be added by selecting solution is added a t the rate of 0.01 to 0.02 ml. per second, the time constant should be around 1 second t o reduce the error the suitable resistances. The high quality of %he condenser, Cia, is attested by the fact that constant input voltages to the due t o lag t o less than 0.01 ml. RC differentiator from zero t o 300 volts give zero output voltages I n order t o secure high sensitivity-that is, a large Eoutfor a across R25 t o R2,. This is expected, as the leakage resistance given time rate of change of input frequency-it is desirable to of the condenser is stated t o be approximately 500,000 megohms. have dE,,/dT large, according t o the above equation. This may If a condenser of poor quality is used, leakage causes a permanent be accomplished by amplifying the direct-reading frequency meter
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ANALYTICAL CHEMISTRY
deflection on the output meter, even when the input voltage is constant with time. This would be no disadvantage if the deflection were independent of the magnitude of the input voltage, but this deflection varies with input voltage and must therefore be eliminated. AMPLIFIER AND LIMITER
The schematic diagram for this circuit section is given in Figure 3. The amplifier and limiter convert a sine wave input from 0.02 to 100 volts into a square wave of constant voltage amplitude. The circuit shown in Figure 3 gives a good square wave with only slight distortion from 50 to 50,000 cycles per second. I t is possible to produce square waves with little or no distortion a t frequencies even greater than 50,000 cycles per second. Such a circuit (8) uses a multivibrator and has been used in one direct-reading frequency meter in this laboratory.
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PULSE-FORMER AND DIRECT-READING OUTPUT CIRCUIT
The schematic diagram for this section is shown in Figure 4. The square wave input is converted into uniform pulses of constant amplitude by a simple RC network ( 7 ) .
h.0-1 milliammeter, M I , or a recording milliammeter is incorporated in the RC network in order to read the average current of the pulses, The average current of these pulses is directly proportional to the frequency. Similar types of direct-reading frequency meters are described in the literature (8). The 6H6 duo-diode, Td, is used as a half-wave rectifier, so that only one negative pulse appears a t the output for every square wave a t the input. The condensers, C12 to C I ~enable , the RC time constant to be changed so that several different frequency ranges may be selected. Frequency ranges especially desirable for use with the high frequency instruments used in this laboratory are 5000, 10,000, 25,000, and 50,000 cycles per second for full scale reading on meter MI. Any other ranges may be easily obtained by addition or substitution of other condensers for C12 to C15. Resistance R22 is used in series with MI, so that the total resistance of this branch is 1400 ohms. The resistance of an EsterlineAngus recording 0-1 milliammeter is also 1400 ohms, and it is possible to interchange the recorder and panel milliammeter and have the same frequency ranges available as on the ordinary panel milliammeter, M I . The total resistance of the RC network is Rnoplus 1400 ohms, regardless of whether the recorder or panel meter M I is in the circuit. The values of Rzo and C12 were selected to satisfy two conditions so that (1) milliammeter MIreads full scale for an input frequency of 50,000 cycles per second, and (2) milliammeter M z (Figure 5) reads full scale (from zero center) for a time rate of change of input frequency of about 150 cycles per second per second. When switch 8 1 inserts condensers C13 to C16, meter MI reads full scale for input frequencies of 25,000, 10,000, and 5000 cycles per second, and the differential meter iVl2 reads full scale (from zero center) for frequency rates of change of about 75, 30, and 15 cycles per second per second. For some applications this is a good method for changing the sensitivity of the differential meter output. By this method, an increase of differential output sensitivity reduces proportionally the total possible frequency span. Resistance R21 and switch Sa are used to introduce “pip” marks a t desired intervals in the differentiated output. This is useful for recording purposes. 5 3 has a spring contact so that Rzl is across the output only momentarily. This causes the output voltage to change rapidly by a small amount and return quickly to normal. Therefore, the momentary closing of switch Sa produces the sharp marker pips shown on one of the recorded titration curves in the followlng paper (3). Figure 6 4 , shows graphically the response of the directreading, 0-1, panel milliammeter for input frequencies of
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Puke-Former and Direct-Reading Meter Circuit 6H6 1 K , 5 watts 15 K, 5 watts 400ohms 100 K 1300 o h m s 90 micromicrofarads 180 micromicrofarads 450 micromicrofarads 900 micromicrofarads Rotary switch, 1 pole, 4 positions, shorting-type Lever switch, 1 pole, 2 positions, shorting-type Push button, spring return switch (make) Panel milliammeter, 0 to 1 ma., 4.5-inch rectangular
0 to 60,000 cycles per second when the instrument is set on the 50,000 cycles per second range (Cl* in circuit). The linearity is excellent from 0 to 45,000 cycles per second, with a slight falling off in response from 45,000 to 50,000 cycles per second. The known input frequencies were obtained from an accurately calibrated signal generator. Although the data for curve A , Figure 6, is given for the range of 50,000 cycles per second, it is also characteristic of the other frequency ranges-that is, on all ranges the linearity is excellent from zero to about nine tenths of full scale, with a slight falling off of response in the last 0.1 division. This slight deviation from linearity is of no consequence for titration purposes. For very accurate work the meter scale can either be calibrated in the last 0.1 division or data taken only from zero to nine tenths of full scale. Because this falling off occuw on the low as well as the higher frequency ranges, it is probably not caused by a high frequency effect, but results from a loading on the output power tube, Ts DIFFERENTIAL FREQUENCY METER
The entire schematic diagram for the differential frequency meter section is given in Figure 5 . The schematic is subdivided by dotted lines to indicate the function of each circuit, and the characteristics of each circuit are described below. FILTER
The filter is a single section, series inductance-input circuit. An inductance input is required rather than a condenser input to prevent a falling off of direct current output voltage for frequencies greater than a few thousand cycles per second. The filter is essentially an integrating network, giving a direct current output voltage which is directly proportional to the fiequency of the input pulses. The time constant of the filter network is only about 0.005 second, and, therefore, no appreciable response lag is introduced by this circuit. DIRECT CURRENT AMPLIFIER
The direct current amplifier consists of one half of a duo-triode, T L(9). ~ A duo-triode is used so that the other triode section may be used in the differential output circuit. Therefore, only one tube is required for the entire direct current amplifier, RC
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method is the use of an alternating current line voltage regulator with 6.3-volt output. A s a t i s f a c t o r y compensation for filament voltage variations may be obtained by any of several methods such as described by Valley and Kallman (9). However, these methods require more tubes and circuit components and add somewhat to the complexity of the circuit. The use of a video amplifier rather than a direct current amplifier eliminates the need for filament voltage compensation. This 0.05 rfd., 450 volts method, however, requires I-microfarad, 300-volt, polystyrene condenser 8 henry choke three tubes (video stage, Rotary switch, 1 pole, 3 positions. shortingtype cathode follower, and direct Lever switch, 1 pole, 2 positions, shortingc u r r e n t r e s t o r e r ) . The tvne 1.5:;olt A battery maximum possible average 22.5-volt B battery Panel milliammeter, 0.5-0-0.5 ma., 4.5-inch direct current voltage from rectangular the amplified pulses is not as large as the amplified direct current voltage from the direct current amplifier; therefore the differential frequency meter sensitivity with the video amplifier method is not so great as with the direct current amplifier. r
I N P U T , K I L O C Y C L E S PER S E C O N D
Figure 6. Direct-Reading Meter and Direct Current Amplifier Characteristics
differentiator, and meter circuit. The cathode resistance, R q is used to give about a 0.5-volt bias. This eliminates nonlinearity which is present when the initial bias voltage is zero. The small amount of ripple voltage and “noise” from the filter is amplified in the direct current amplifier stage, but this is easily eliminated by means of the small by-pass condenser, C1, in the amplifier output. Curve B , Figure 6, is a plot of output voltage of the direct current amplifier versus input frequency. This curve shows the excellent linearity of this stage. There is a slight falling off a t the high end of the scale, but this is because the voltage input t o the direct current amplifier falls off slightly as shown in curve A ( A is identical t o the direct current amplifier input voltage). With this direct current amplifier it is necessary t o have a regulated filament supply or filament compensation. This regulation or compensation may be obtained in several different wavs. Because a storage batterv is used for the filaments on the associated high frequency oscillators, it is expedient to use this same storage battery for the filament of Ts. Another possible I
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Figure 7 . Differential Output Tube Response for Equal Voltage Increments (Positive and Negative) on Grid
The output voltage from the direct current amplifier is fed directly into the RC differentiator, as shown in Figure 5 . DIFFERENTIAL OUTPUT METER CIRCUIT
The output from the RC differentiator is used t o vary the grid bias of one triode section of the duediode, Tm. A 0-1 recording milliammeter (with zero adjustable to center scale) or a 0.5-0-0.5 panel milliammeter is used in the plate circuit of this triode t o indicate the changes in plate current resulting
A N A L Y T I C A L CHEMISTRY
454 from the changes in grid voltage. This simple meter circuit is not perfectly linear-that is, equal positive and negative voltage increments applied t o the grid of the output triode do not give absolutely equal plate current increments. This is illustrated in Figure 7, which is a recorded trace from a recording milliammeter. This meter was adjusted to have zero a t center scale. Five positive voltage increments and five negative voltage increments were applied t o the triode grid in equal steps. Each voltage increment in Figure 7 is 0.095 volt. These voltage increments give nearly equal current increments of about 0.1 milliampere as shown by the current recorded trace in Figure 7 . The observed nonlinearity is from the nonlinear grid voltage-plate current characteristics of the t,riode tube. The small amount of nonlinearity, however, is of no consequence in titration procedures,
the instrument from the mixer unit of a high frequency titration apparatus. The resulting meter deflections on the outupt differential meter were plotted as points on Figure 8. The points fall very closely to the solid straight line calculated as described above. The rates of frequency change from the high frequency apparatus were obtained by adding dilute solutions of sodium chloride a t a constant flow rate to solutions of greater or less concentration. The number of seconds necessary to traverse a certain frequency interval was precisely timed and the rate of change of frequency determined. Figure 8 shows conclusively that the differential frequency instrument from frequency input to outpuh meter deflection has a linearity commensurate with the linearity of the individual circuits as shown in Figures 6 and 7 . POWER SUPPLY
A regulated power supply of 300 volts, 100 ma., is used for the plate supply. The schematic for this supply is not presented, but any regulated power supply is suitable (6). There are many inexpensive commercial power supplies available with the above ratings. The same power supply may be used for the plate supply voltage on the oscillator tubes of the high frequency titration apparatus. All the filaments except Ts are supplied from a 6.3-vo1t1 2-ampere transformer. The filament voltage for Ts is supplied from the same storage battery used a8 filament supply for the oscillator tubes of the high frequency titration apparatus. SUMRIARY
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Figure 8. Differential Frequency Meter Response for Various Rates of Change of Input Frequency 50,000 cycles per second range; I-second time constant
For the measurement of chemical reaction rates the scale can either be calibrated t o account for this slight nonlinearity or a more linear output circuit substituted. A meter circuit with greater linearity for use with a 0 - 1 recording milliammeter is described in the literature (9). This circuit, however, requires several tubes and greater circuit complexity. The ehange in output voltage from the direct current amplifier (which is the input voltage to the RC differentiator) is known for a given frequency change (see Figure 6, curve B). Knowing this and using the formula, E,,t = RC dEin/dT, it is possible t o calculate the output voltage from the RC differentiator for a given time constant and given time rate of change of frequency. Also, because the change in grid voltage of TSSnecessary for full scale deflection (from zero center) of the differential output meter is known, it is possible to calculate the rate of change of frequency necessary for full scale deflection. When switch & (Figure 3) is set on the 50,000 cycles per second range and switch Sa (Figure 5 ) set for a 1-second time constant, it is calculated from Figures 6 and 7 that a rate of change of frequency of about 150 cycles per second per second gives full scale deflection on the differential output meter. A plot of rate of change of frequency versus meter deflection is shown in Figure 8. The recorder chart used is divided into 25 equal divisions on either side of zero center. A straight line is drawn from the calculated value for full scale deflection through zero. Therefore, for any given meter deflection it is possible to read the calculated time rate of change of frequency from the ordinate. In order to check the complete circuit, various constant and known rates of change of frequency were fed into the input of
A direct-reading and differential frequency meter is described which is especially applicable for use with high frequency titration apparatus. Its particular application to carrying out titrations by the ordinary titration method using the direct reading frequency meter section and by the differential technique using the differential frequency section is described in the following paper ($1. The possible use of the differential meter for the measurement of rates of chemical reactions is being investigated in this laboratory. There are, of course, many other potential uses of thie differential circuit which, with modifications, ‘might greatly facilitate or improve obtaining experimental data, particularly in potentiometric or conductometric titrations. These use8 were not investigated. The direct-reading meter is also applicable to many projects where frequency measurements are best read directly from a panel meter or recorded continuously on a recording milliam-. meter. ACKNOWLEDGMENT
The authors wish t o express their thanks to John Lofstrom, Richard Lathrop, and V. C. Rideout for valuable help and suggestions with certain phases of this work. This work was supported in part by the Wisconsin Alumni Research Foundation, and in part by grants-in-aid from E. I. du Pont de Nemours & Co. and the Atomic Energy Commission. LITERATURE CITED
(1) Blaedel, W. J., and Malmstadt, H. V.. ANAL.CHEM.,22, 734 (1950). (2) Ibid., p. 1413. (3) Ibid., 24, 455 (1952). (4) Delahay, Paul, Ibid., 20, 1215 (1948). (5) Greenwood, I. A., Hoidam, J., Jr., and MacRae, Duncan, Jr., “Electronic Instruments,” Radiation Laboratories Series, MIT, Voi. 21, pp. 64,68,New York, McGraw-Hill Book Co., 1948. (6) Hoadley, J. C., Radio and Television News, 44, 47 (1950). (7) Navy Dept., Washington, D. C., Bureau of Ships,“Radar Electronic Fundamentals,” p. 180,1944. (8) Reioh, H. J., Rev. Sci. Instruments, 19, 43 (1948). (9) Valley, G.E.,Jr., and Wallman, H., “Vacuum Tube Amplifiers,” Radiation Laboratories Series, MIT, Vol. 18,pp. 437,458,480, New York, McGraw-Hill Book Co., 1948. RECEIVED for review June 16, 1951. Accepted September 25, 1951.
