DIELECTRIC-CONSTANT MEASUREMENTS BY THE HETERODYNE-BEAT METHOD JEN-YUAN CHIEN University of Wisconsin, Madison, Wisconsin
IN
TEE determination of dipole moments the electric capacity measurements are usually made by one of beat method, three methods: or the the resonance alternating-current method, the bridge heterodynemethod.
For undergraduate laboratory work a very simple and efficient instrument of the resonance type has recently been described ( I , $ ) . It is the purpose of this paper to present a circuit illustrating the heterodyne-beat principle which has been found more suitable for student use than those previously recommended from this laboratorv " (3). ~, The general principle of the heterodyne-beat method is schematically represented in Figure 1. Two radio frequency signals of frequency joand j, generated by a fixed oscillator and by a variable oscillator, respectively, are fed into a "mixer" tube, in theoutput of which is produced a difference frequency or beat note of frequency 1 j-fol. I f f and joare nearly equal, the difference frequency will lie in the audio range. The frequency of the signal generated by the variable oscillator is given approximately by the relation j =
-12rdE
where L and c are, respectively, the inductance and capacity in its tuning circuit. Let us suppose that for a certain setting of C we have j>j,. On increasing the capacity, the frequency of the beat note will decrease, going from idaudible to audible, from high pitch to low pitch, until f anddo are exactly equal and the beat, frequency is zero. On further increase of capacity, a beat note will again arise, this time increasing in frequency with increasing capacity until it lies beyond the audible range. ~h~ critical capacity setting corresponding to zero beat is the reference point for capacity increment measurements by this method. l-he heterodyne-beat method offersthe mostaccurat,e method of capacity measurement. Since the inductante L is fixed, differentiation of the frequency equation gives 1 AC Af=
f
2 C
If the fixed o.scillator is of a frequency of 500 kilocycles and a beat frequency of two cycles per seoond can be distmguished from zero beat, then the detectable change of capacity of the circuit is one in a hundred thousand. The total capacity needed in a suitable tuning circuit for 500 kilocycles is in the order of 500 micro-microfarads, and if tlie capacity increment to be measured is
>
.
MIXER INDICATOR VARIABLE
D,aMm
c.a
FEa. osc
s~4-d ~ a ~ u ~ .
F~WI. I. P . ~ ~ c Iof ~ .the H . ~ . ~ O ~ ~ ~ . - B . .A: P P ~ . ~ ~ .
50 micro-microfarads, the precision of measurement attainable is one-hundredth of one per cent. The location of zero beat to within one cycle per second or better is possible, so it is obvious that the accuracy of capacity measurements by the heterodyne-beat method is limited in practice by the accuracy bf setting and calibration of the standard condenser employed (4) and by the stability of the variable and fixed oscillators. A heterodynebeat circuit designed from the point of view of oscillator stability with a visual beat note indicator is presented in Figure 2 and the recommendedpower supply in Figure 3. A quartz-crystal controlled oscillator is used for generation of the fixed frequency signal. The tuning circuit is assembled from a t ~ o - ~ variable a n ~ condenser, 140 micro-microfarads capacity Per section, 2nd a suitable plug in coil to permit convenikce in change of operatingfrequency. The coil connectionsare arranged SO that the two sections of the condenser are in series, 0' in parallel, or one section alone in use in order to provide suitable L/C ratios for the tuning circuit a t different frequencies. The tuning of the oscillator is mdlcated by a 0 to 5-ma. meter in its plate circuit. Starting a t full Capacity, the late current will be off scale; .on tuning down the capacity, oscillation sets in abruptly with a sharp dip in the plate current to about 1.5 ma. The capacity is then further decreased until the plate current rises to 3 ma. At this point the oscillator grid has less excitation and the oscillator is found to be more stable. The variable frequency oscillator employed here is of an unusual type, but because of its unusual frequency, stability, simplicity of construction, and ease of comprehension can be highly recommended in this application. The circuit, which is reproduced for convenience in Figure 4, makes use of the particular electrode arrangement of the GAS-type pentagrid convert,er tube which exhibits a negnt,ive t,rana~onduct.aucp(6, 6) between sig-
494
OCTOBER, 1947
F i m n 2. Circuit of th. H.t.rodm.-B..t
Ilp.u.tu.
for Di.l.six4c-CoxL.t.nt
0 6-megohm potentiometer 1-megohm Vrwatt . . 5 'megohm Vcwatt 30.000-ohm I-watt
Candsesers C1, C2 C3. C4. C13, C18, C20 C5. C6 C7 C8 C9 C10. C17 ,211 C12 C14 C16 C16 Cl9
M.uur.m.nt
140-mmf. tw-gang vadable 0.1-mf. 600-~oltp a w r OJO-mmf. air trimmer 335-mmf. variahla 50-mmf. variable 0.W5-mf. mica 0.01-mf. 800-volt w p s r S-mf. 460-volt elwtrolytia 0 002-mf. mica 0.25-mf. 600-volt paper 4-mf. 460-volt electrolytic 10-mf. 25-volt eleotrolytic 300-mmi. mica
Tuhea. etc.
6J5 6E6 Crystal D-6 ma. meter Three position two-,?an. swltoh ~honajaok Sooket for ooaxial wire connector to dieleatrio oell Socket far coaxial vire connector toexternalstandard eondenaer ~
~
Coil data
Wrs Coil A1 B1 A2 82 A3
B3
nal grid G4 and anode grid G2. When the potential of grid G4 with respect to the cathode is decreased (negative bias increased) the current Ig2 is increased, in contrast to the usual Eg-Ip behavior. Because of this reversa1 of transconductance the changes in Egz,the patential of the anode grid, will be in phase with the changes
oops
No. 29 No. 29 No.29 No. 29 No. 22 No.22
Turne 106 96 31 28 22% 20
Winding Coil diomala. langfh inches oloaa wound 11/~ doao wound 1% 71s in. 1% 1 in. 1% 1% close wound close wound 1%
.
in Eg4, so that regenerative feedback may be obtained by condenser coupling between the two grids as indicated in Figure 4 by Cc. This action may be examined more carefully by consideration of the dynamic characteristics of Figure 5, which was obtained under conditions very close to the actual operating conditions.
-JOURNALOF CHFMICAL EDUCATION T Figur. 3. Cbcuit ef Volt.ge-R.c?"Supply 1.t.d Po-.
CI,
B't50v'
R7 V1 V2 Y3 V4 CK T 0-
ca 10-mf. 450-volt dectrolytio
R1 R2, R3 R4 RS RB
SW
condenser 20,000-ohm Cwatt resiator 0.5-megohrn l/rwatt reaistar 15.000-ohm '/,-watt resiator 25,000-ohm 1-watt reaistor 15.000-ohm wire-wound potentiometer 20,000-ohm 1-watt resistor 83V tube 2 4 3 tube BJ7 tube OC3 tube 30-henw 100-ma. choke Power transformer. M Thmdarson T13R08 6.P.S.T.adtitch
6".
6.3".
0
From the curve it is seen that there is a transconduct anoe of -275 microohms andavoltagegainof 14 between grids G4 and 62. The values of Eg2 are calculated from the obvious relation Eg2 = 100
- 50,MW) Igr
If the potential of G4 is momentarily a t - 1.3 volts, EgZ will be 60.5 volts and the condenser Cc will be charged to the same potential. If now the potential of G4 is decreased, say to -1.6volts, the potential of G2 willalso decrease to 53.5 volts and the condenser Cc will discharge through R, the battery and grid circuit, driving G4 more negative. This regenerative feedback keeps the L C circuit between the cathode and G4 in continuous oscillation. The output signals from the two oscillators are fed through two small trimming condensers to the signal grids G l and G3 of a 6SA7 mixer tube (Figure 2). The beat frequency signal produced is amplified by the W 5 , and then fed into the grid circuit of the 6 ~ indicator 5 tube, which acts as a sensitive grid-leak detector. With no signal on the grid, the plate current is high and the potential of the plate and ray control electrode is low because of the potential drop across the one megohm resistor in the plate circuit, so the shadow angle is wide. On receiving a signal, the shadow angle decreases.
When the beat frequency is high the shadow is blurred, but when the beat frequency falls below the persistence period of vision there is seen the periodic blinking of the "eye" a t the frequency of the beat note. At zero beat the "eye" remains wide open. A trouble usually met in .heterodyne-beat oscillators is the phenomenon called l'locking in" of the oscillators. -That is, when f is brought close to fo, low frequency beats cannot be observed because the more stable of the two oscillators exerts a synchronizing action on the less stable, and over a considerable range the two oscillators are locked in step with one mother and a sharp zero beat setting cannot be obtained. This rnins the accuracy of the determination completely. In this re-
OCTOBER, 1947
spect the circuit here described is entirely satisfactory, as low frequency beats d o m to one beat or so per second are easily observed, confirming the claim that this type of oscillator is capable of 'LTodmachen ohne Mitnahme," as quoted by Taylor (6). Another method of avoiding the synchronizing effect, partichlarly a t higher frequencies or in high precision work, is to tune the variable oscillator to a fixed beat frequency as determined by comparison witha constantfrequency tuning-fork oscillator (7). A modification of this method which we have found of interest employs a vibrating reed-type frequency meter. A 380 to 420cycle frequency meter was used in' the circuit given in Figure 6. The meter has nine reeds diiering successively in natural frequency by five cycles. One can then always tune the variable osdlator to give a beat frequency of 400 cycles to within one or two cycles, and in addition any drift with time in the frequencies of two oscillators is directly apparent.
497
ray oscilloscope. J3 is provided to permit use of a earphone for rough location of zero beat. The' tuning eye gives a much more sharp setting for zero beat because both the response of the amplifier-earphonesystem and the audibility drop steadily a t low frequencies, as shown, for example, in the following table (8); Frepuacy,
cycles per s e d
25 50 100 200
Relative sensitivity of null detedwn 1 5 50 5W
--,-"-
. .
14,000
2
However, we recommend the simultaneous use of both earphone and tuning eye for zero beat location, because the earphone tells you immediately whether you are tuning down or tuning up. It is found that the tuning indicator here described gives the same performance as a cathode ray oscilloscope as zero beat indicator; the response of the shadow is instantaneous. Dielectric-constant cells can be conveniently constructed from 50-micro-microfarad midget variable condensers by removing plates as required to give the capacity appropriate for the particular frequency employed. The cell should be shielded and co-axial cable used for the necessary connections. The circuit can be used with any medium giving a cell-leakage resistance greater than lo4 ohms. Details concerning the procedure of measurement, calculation of the dipole moment, and necessary precautions are available elsewhere (B, 3, 4). LITERATURE CITED
F i g u n 6. The Fnqvsney Mster DriCirmvit for Bart-Fnquenog Indioltion C1 C2 CH V P
M
2 5 m f . 2 5 v o l t electrolytic 0.5-mf. 800-volt paper Output transformer primary 676 tube
Plug to .I2 of Figure 2 380-420 Cycles per second vibrating-reed frequency meter
The three output jacks shown in Figure 2 provide versatility in beat detection. J1 can be used for injection of a constant frequency audio signal from a tuning-fork oscillator as previously mentioned. J2 can be used for feeding the beat-frequency signal into a cathode
(1) ALEXANDER, F. C., JR., Electvonic~,18,No. 4, 116 (i945). P., J. CHEM.EDUC.,23,179 (1946). (2) BENDER, (3) DANIELS, F., J. H. MATHEWS, m , J . W. WILLIAMS, "EXperimental Physical Chemistry," 3rd ed., McGraw-Hill Book Company, Inc., New York, 1941,pp. 257-59. (4) S m a , C. P., "Determination of Dipole Momenta" in Weissberger's "Physical Methods of Organic Chemistry," Vol: 11, Interscience Publishers, Inc., New York, 1946,pp. 1000-4. (5) SMITH,F. L., "The Radiotron Designer's Handbook," Radio Cornoration of America. Harrison. N. J.. 1941, . 0. . 106. A. H., Electronics, 19,NO.12,p. 142 (1946). (6) TAYLOR, B. E., AND M. E. Hosss, Rev. Soi. Instruments, 13, (7) HUDSON, 140 (1942). (8) BINNS,J. E., AND H. W. WEBB,ibid., 10,89(1939).
