LABORATORY BRIDGES' I. A Portable Audio-frequency Conductance Bridge DAVID EDELSON and RAYMOND M. PUOSS Yale University, New Haven, Connecticut
VARIOUS modifications of
the Wheatstone bridge circuit have been used for the measurement of the a.-c. conductance of electrolytic solutions. Jones2 and Shedlovsky3independently made careful studies of the bridge oircuits with the special problems of the physical chemist in mind, and most present bridges capable of high precision are based on their design.'-= Many of these are, however, rather cumbersome and tedious to balance. In our work we need a compact portable unit which could be balanced rapidly and precisely and 'Over a faidy wide range of resistance' which Interference by near-by electrical apparatus had to be minmieed. Cost was also a limiting factor. Following these general considerations, we have constructed a bridge based essentially on Shedlovsky's recommend* tions, which differ from those of Jones in so far as shielding is concerned. However, we have made use of recent developments in the design of the associated electronic equipment which lead to simplification in the operation of the bridge. Our design is suitable for any laboratory where a small, easily operated bridge is wanted; a number of the additional reinements described were made merely for convenience and are not essential. The entire bridge, exclusive of ratio box, decade resistor, and oscilloscope, can be built for less than one hundred dollam; if desired, the ratio arms can be constructed from available parts instead of being bought as a unit. The essential details of the complete circuit are shown , equations (1) in Figure 1. For Rlo, Rn, Cso, and C ~ Isee and (2); Rg4and Raaare the R of equation ( 3 ) ; Rae = R/2; C,, and (77%are the C of equation (3), CR = 2C. The part numbers refer to a list of parts given in Table 1. As indicated, the central unit of the bridge is a Leeds & Northrup No. 1553 CampbellShackelton ratio box, which contains a pair of matched ratio arms, the Wagner ground arms, and a shielded input transformer. The unit is compactly mounted and completely shielded, and is built into the bridge without alteration. A 1 Part of Project NR 054-002 of the Office of Naval Research. Paper No. 23. 1 JONES, G . , AND R. C. JOSEP~S, J. A ~ them. . SOC.,so, 1049 (1928). a SHEDLOVSKY, T., J. Am. Chem. Soe., 52,1793 (1930). DIKE,P. H., Rev. Sci. Inslrumenle, 2,379 (1931). 6 L m ~ aW. , F., J. Am. Chem. Soc., 62,89 (1940). s BENDER, P., W. J. BIERMANN, AND A. G. WINGEE, J. CEIEM. Ennc.,27,212 (1950).
shielded decade resistance box R, two 365 w j variable capacitors BC and GC, and a small variable capacitor CV (3@50 ~rtfmax.)complete the bridge proper. TABLE 1 Conductance Bridge: Parts List V-1, V-2: 1LE3
:$$-$':T4 V-6: 3g4
T-1 Audio Output Transformer, 25,000 ohm plate te 500 ohm line, sh~elded. (Stancor A33152 T-2 Audio Interstage Transformer, shielded. (Stanoor A4205) S-1, s z : DPSTOn-Off switch. 8-3: SPDT Ground-reversing Bridge-ground selector switch. 8-4: SPDT switch. switch. 8-5, 8-6, 5-7, S-8, 8.9, 8-10: Six-gang fnquenoy Number of positions equals number of desired frequencies plus One Open. Resistors. All BT 112 26 0.5Meg. 27 Meg, &;%iton 20 K variable 28 1 Meg. 14 0.47 Meg. 29 1Meg. 15 0.1 Meg. 30 10Meg. 16 Output Control 31 Meg, 32 0.5 Meg. Meg. pot. 17 5 Meg. 33 0.25 Meg. 18,19 1WK dual pota, ganged 37 500 ohms for same rotation 38 500ohms 20 lOK 39 Gain Control, 5K pot 40 Non-linear element, 4yatt, 120-v. pilot bulb, 23 1 Meg. m serm with 1000 24 2 Meg. ohms 25 1K Capacitms. dl1 4 ~ + wwking . vollage
:OFMeg,
i54g : ::!F,";: 0.05 Paper 257; oO.l !:paper gFd 58 0.01 Paper
;! ::ii3$g
62 61 0.1Papper 0.003Mica 63 1.0 Oil-filled 64 0.001 Mica 65 1.0 Oil-filled 66 1.0 Oil-filled 67 0.01 Paper 68 O.01Paper 69 0.25Paper 70 1 . 0 Oil-filled
The bridge is connected for separate terminal balancing to ground; that is, the ratio arms and unknown arms are alternately balanced against the Wagner ground which thus serves as an auxiliary reference set of ratio arms. This procedure has the slight disadvantage that the unknown arms are not balanced directly against the ratio arms; therefore, the ground arms must be balanced with a t least as great c recision as the unknown arms. It has, however, the advantage that one side of
NOVEMBER, 1950 the detector is always a t ground potential, thereby making for much simplified coupling between the bridge and the detector-amplifier; the need for an isolating transformer a t this point is thus eliminated. L4Uconnections in the bridge proper are made with shielded cable; the shields are grounded. The switches 8-3 and 8-4 are enclosed in metal cans in order to shield them; it is usually not necessary, however, to shield the variable capacitors in this manner, provided they are mounted behind a metal panel in a shielded cabinet.' A Wien-bridge type oscillators was chosen for the source of alternating current for the bridge. This os. cillator gives excellent waveform and is exceptionally stable; in addition, it possesses the advantage of having no inductive components which might set up stray fields and lead to pickup by the bridge. A set of fixed R-C ratios was chosen to give the desired frequencies in accordance with equations (1) and (2) : f
=
I ~ ( z ~ R ~ ~ R , ~ c ~ c ~ , ) (1) R&o = RnCs, (2)
The frequencies were chosen to give a reasonable spread on a ll-\/jscale, since this is the quantity against which the data are plotted to eliminate polarization ern)rs;9 the llsr of fixrd frequenvies is morc ronwnirnt thau a (:ontinuouelv variable oscillator in this resnect., since in actual practice only a few frequencies are used. An external variable oscillator may he used if desired, by connecting it directly to the oscillator input terminals on the ratio box. Standard radio parts are used for the tuned R-C circuits, although if stability is desired a t the higher frequencies, low temperature coe5cient components are to he preferred. It is also advisable to have a small variable component in each set, e . g., 30 ppf trimmer across the capacitors; this will permit more exact tuning of the oscillator. The resistors in the tuned circuits should be of the order of 0.01-0.1 megahm. The variable resistor RB is a regeneration control, which is adjusted for optimum waveform; this adjustment need he made only at rare i n t e ~ a l sand , therefore it is well to mount the resistor where it is not likely to he accidentally disturbed, because its setting is rather critical. R ~ is O a nonlinear control element consisting of a 4-watt, 120-volt Mazda lamp; some improvement in performance may he obtained by connecting a resistance of about 1000 ohms in series with it, hut this is best determined with the apparatus in actual operation. The oscillator together with its output amplifier is
.
' Most commercially available variable condensers are designed to be mounted with the rotor grounded to the chassis. Completely insulated condensers (insulated shaft and mounting), if obtainable, should be used for BC and CV, since neither side of theae capacitors is grounded; otherwise it will be necessary to mount the condensers so that insulated extension shafts mav be used. TER~N F.,E., R. R. Buss, W. R. HENLETP,AND F. C. CAHILL, PTOC.I. R. E.,27,649 (1939). JONES,G., AND S. M. CHRISTIAN, J. Am. Chem-Sot:; 57,!272 (1935).
coupled to the bridge through a plate-to-lme audio transformer. The transformer should he of high,quality and completely shielded; the leads to the bridge
JOURNAL OF CHEMICAL EDUCATION
612
likewise should be shielded. Switch 5-4 alternately grounds one side and then the other of the oscillator input; readings are taken with the switch in each position and averaged. This operation corrects for unsymmetrical stray capacities to ground through the input transformer. If the bridge is carefully constructed, the two readings should not differ by more than 0.05 per cent.
The detector is a three-stage resistance-coupled amplifier which uses super-control pentodes in the first two stages; miniature 7-pin tubes were used because they are less subject to microphonics than other types. Gain rontrol is accomplished by varying the grid bias on the first two stages. The output stage has a parallel-T shunt filter designed to by-pass low- and high-frequency noise; the romponents are chosen such that These filters are ganged with the oscillator networks so t,hat one switch selects both the oscillator and amplifier frequencies. The output of the amplifier is fed through a blocking condenser to the vertical input of an oscilloscope; a jack may be provided if desired so that highimpedance earphones may be used as well. The bridge is coupled to the detector through a bloclcing condenser and a frequency-selective network which shunts high-frequency noise and harmonics to ground. Care should be taken to shield completely all leads to the first grid of the detector; the input network may be effectively shielded for this purpose by mounting it beneath the amplifier chassis. An oscilloscope is preferred as a balance instrument; it obviously requires no soundproofing, and is more sensitive than earphones. The scope may be used merely as a voltmeter for this purpose, balance being indicated by minimum amplitude of the wave pattern;
however, we have found it more convenient to balance by the use of Lissajous figures.lo In this method, a small portion of the bridge input signal is fed to the horizontal plates of the scope through a suitable phaseshifting network, while the voltage from the bridge midpoints is fed to the vertical plates. When the two signals are properly phased, resistance and capacitance balance are indicated separately, one hy the opening and closing of the loou, - . and the other by the tilt of the loo^ from horizontal. The correct pha'e shift is best detelymined by trial inasmuch as it is a rather complicated function of the bridge impedances and may change slightly with widely differing unknowns; it is therefore essential to provide a complete range of variability. The adjustment is made by first balancing the bridge on a "known unknown," using the scope as a voltmeter. The reference signal is then applied to the horizontal plates, and either the resistance or capacitance of the test "unlmown" is thrown off balance; this will generally result in a tilted loop appearing on the screen. The phase shift is then adjusted to either close the loop or to bring it to horizontal, as the operator prefers. The phase shift also depends on frequency and readjustment is necessary for each frequency; since this is a rather tedious operation, we have provided our bridge with a separate variable element in the phase shift network for each frequency. These are preset as described above and connected automatically during a measurement by being ganged on the frequency selector switch. A small isolating transformer should be used to couple out the reference signal, since one side of the scope input is generally grounded. The bridge is powered by batteries; in this way, we need no power packs and elaborate filters, nor shielding devices, to prevent introduction of 60-cycle hum into the bridge and coupling between oscillator and amplifier through the power supply. Separate B and C hatteries are used for the oscillator and amplifier. The potentials given, especially the screen voltages, may be varied slightly for optimum performance by the individual worker; the values listed are merely a guide in this respect. A 1.4-volt air cell is used for the filament supply because of its extremely long life; a separate small battery is used to power the oscillator stage because a different cathode potential is necessary. It should be noted that the on-off switch is in the grounded side of the filament supply; it also disconnects the amplifier bias battery, which otherwise would slowly discharge through the gain control. The entire bridge, including oscillator, amplifier, and batteries, is contained in a standard 17.5- X 19-inch cabinet rack, and is therefore completely portable (Figure 2). Connections to the unknown are made directly from the C and SI+ terminals on the ratio box, through a shielded two-conductor cable. The unknown should, of course, be shielded by being placed in a metal thermostat or similar apparatus; all shields should be connected to the bridge cabinet, which in ~
p~
lo
LAMSON, H. W., Reu. Sei. Insl., 9,272 (1938).
NOVEMBER, 1950
turn should be connected to a suitable external ground, such as a water pipe. The amplifier tubes are mounted in shielded sockets with metal cans which fit over them; this is not necessary for the oscillator tubes, since these are of the lock-pin type and are shielded internally. Calibration. The resistors R are calibrated against resistance standards on direct current. A source of d. c. (2-6 volts, from batteries) is connected to terminals A and C, and a galvanometer is connected between D and B, thus utilizing the apparatus as a d.-c. bridge. In this way lead resistances within the bridge are taken into account by the calibration. Operation. The bridge is first balanced by measuring the unknown arms against the ground arms (switch S 3 to position D). Resistance balance is made first, then capacitance, followed by a fineradjustment of resistance, etc. The ground is then balanced (S-3 to position B) in a similar manner. Alternate balance of unknown and ground is continued until both are in balance simultaoeously. This procedure is repeated for each setting of 8-4, and the results averaged. Occasionally, it may be found that more capacitance is needed in arm AD to balance the bridge; this is inserted by connecting an auxiliary shielded capacitor across the decade box. It may also be found that there
613
is insufficient variability in the ground arms to balance them. m e n this occurs, the resistance may be adjusted by connecting a high resistance shunt, of the order of a megohm, between either A or C and ground. Results. As a test of the precision of the bridge, some solutions of potassium chloride in water were measured and the results compared with those given by Shedlovsky." A set of measurements was made to calibrate the cell, and the average cell constant used to recalculate the data to equivalent conductances. The data are given in Table 2. TABLE 2 Conductances of Aqueous Potassium Chloride C X 104
7.3412 20.674 44.985 128.01
-Equivalent ShedLousky 147.40 145.78 143.99 140.46
Caductance---. (This Work) 147.31 145.76 144.00 140.48
The aid of V. F. H. Chu in calibrating the bridge and making the conductance measurements is gratefully acknowledged.
