The Measurement of Dielectric Loss in Solid Dielectrics at Very High Frequencies Citation McRae, James Wilson (1937) The Measurement of Dielectric Loss in Solid Dielectrics at Very High Frequencies. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/hpzm-bs17. https://resolver.caltech.edu/CaltechTHESIS:02192025-191650445 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Electrical Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Electrical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 May 1937 Record Number: CaltechTHESIS:02192025-191650445 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:02192025-191650445 DOI: 10.7907/hpzm-bs17 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17009 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 21 Feb 2025 21:23 Last Modified: 21 Feb 2025 22:17 Thesis Files PDF - Final Version See Usage Policy. 39MB Repository Staff Only: item control page

The Measurement of Dielectric Loss in Solid Dielectrics at Very High Frequencies. A Thesis by James Wilson McRae Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor . of F'h ilosophy in Electrical Engineering The California Institute of Technology Pasadena, California May, 193? Table of Contents. Page 1. Object of This Investigation 1 2. Choice of the Method to be Investigated 3 a. b. c. d. 3. Desirable Characteristics of the Method 3 Review of Methods for the Measurement of Dielectric Loss 5 Preliminary Analysis of the Possibilities of a Coaxial Line 11 Description of Original Line 13 Description of Oscillator 17 a. Requirements 17 b. Description of Final Oscillator 18 4. Description of First Arrangement 20 5. Results with First Arrangement 23 a. 6. Calibration of Thermocouple and Galvanometer 23 b. Method of Taking Readings 25 c. Sample Curves 26 d. Discussion of Results 26 Description of Second Arrangement 28 a. Thermocouple Mounting 28 b. Use of Spacers to Center Inner Conductor 29 Split Center Section for Insertion of Samples 31 c. Page 7. Results with Second Arrangement 32 a. Sample Curves 32 b. Measured Values of Line Attenuation Constant 34 Tests on Samples of Dielectric 37 c. 8. Description of Third Arrangement 40 9. Results with Third Arrangement 42 10. Description of Fourth Arrangement 43 11. Results with Fourth Arrangement 45 12. Discussion of Results 46 13. Suggestions for Future Apparatus 50 14. Conclusion 51 15. Acknowledgments 53 List of Appendices A. Method Proposed by A. V. Haeff. B. Mathematical Analysis of Tuned Transmission Line and Effect of Sample. c.. Rectification of Resonance Curves. D. Best Ratio of Inner and Outer Conductor Radii. E. Effect of Frequency Drift. F. Effect of Changes in Oscillator Frequency due to Changes in Line Tuning. G. Effect of Direct Coupling Between Feeding and Measuring Circuits. H. Effect of Impedance Transferred into Tuned Line from Measuring Circuit. J~ Effect of Constant Separation between Thermocouple Loop and End of Line. K. Description of :Plate Supply Voltage Regulator. - 1 - 1. Object of This Investigation The object of the research described in this thesis has been to develop a method for the measurement of the losses in solid dielectrics at very high frequencies, particularly in the vicinity of 100 megacycles. No refer- ences to accurate work at such high frequencies could be found in the literature at the time this work was started, although some rather qualitative comparisons of different 1 kinds of solid insulation had been reported. These qualitative tests indicated roughly the relative losses in various kinds of insulation material under rather special conditions of field distribution in the insulation. However, they gave no accurate information from which it would be possible to calculate the actual amount of loss under .given conditions of field strength and frequency. Such information would be highly desirable in the design of certain types of hig~ frequency equipment in which it is impossible to avoid the use of insulation in regions where the electric field strength is quite high. A further reason for attempting to make rather precise measurements on insulation losses at high frequencies 1. A partial list of the papers published on this subject since 1933 will be found in the bibliography. - 2 - is that it is only in this way that the variation of the loss with frequency may be determined. In other words, it is desirable that it be possible to compare the results of high frequency tests with those which have been made by other observers at lower frequencies. From such com- parisons, it might be possible to justify an extrapolation of the results to still higher frequencies, thus enhancing the value of the tests. Moreover, the theory of dielectric losses in solids is not yet fully developed and additional information, obtained at high frequencies in such a way as to be directly comparable with the present knowledge, might be of aid in the further development of this theory. Because of the well known difficulties encountered in making accurate dielectric loss measurements at very high frequencies, it was felt that it would be desirable to make a rather thorough experimental and analytical investigation of the most promising method. Actual results were not considered to be of primary importance in this work, but rather the emphasis was placed on an endeavor to obtain data on which to base the design of future equipment. Con- sequently, considerable time waa spent on an investigation of various preliminary arrangements, obtaining experience with the difficulties to be encountered in the final - 3 - arrang ement. An account of this experience, together with the necessary mathematical analyses, is to be included in this thesis. The most important results to be presented here comprise those suggestions regarding the design of future equipment, and estimates of the accuracy to be realized, rather than the results of actual measurements with the present equipment. 2. Choice of the Method to be Investigated. 2a. Desirable Characteristics of the Method. At the outset, it was decided that the method a dopted should, if possible, possess the following features: 1. The high frequency equipment should be a s simple as possible. 2. It should be arranged so that it mi ght be completely shielded. 3. The loss in the s ample of insulation should be large enough in comparison with the unavoidable losses in the me a suring equipment so that it might be measured conveniently and reasonably accurately. 4. The losses inherent in the measuring equipment should be capable of independent measurement, the conditions under which such a measurement would be made being as nearly - 4 - as possible the same as those existing with a sample in place. 5. The distribution of the electric field in the sa.~ple of insulation should be calculable and, if possible, there should be negligible "edge effects". 6. It should be possible to check experimentally the magnitude of any unavoidable edge effects which would dis turb the field in the sample. 7. The actual magnitude of the electric field within the sample should be known, at least roughly. 8. The sample should be inserted into the system in such a way that it would be unnecessary to consider the residual inductance or capacitance of the conductors through which the current to the sample must flow. 9. It should be possible to make each determination depend on a great number of readings, each set of readings obeying some simple law. This would make it possible to check all the readings in each set for consistency and thus to eliminate some of the observational errors. 10. The results should be easily convertible into some standard form, such a s a statement of the power factor or "loss factor" of the material. - 5 - 2b. Review of Methods for the Measurement of Dielectric Losses A review was made of the methods of measurement which have been used successfully at lower frequencies, and careful consideration was given to a method proposed by Dr. A. V. Haeff. It was found that the various methods might be grouped under the following general headings: 1. Actual or indirect electrical measurement of the power input to the test circuit. 2. Calorimeter measurements of power loss. 3. Resistance substitution method. 4. Distuning method. 1. The method suggested at the start of this work by Dr. Haeff (see Appendix A) would come under the first heading, since it involved the indirect measurement of the increased radiation necessary to supply the power to the sample. The main advantage of the method would result from its use of a super-regenerative receiver as the voltage-indicator in the measuring equipment. By this means it was hoped that the losses in the voltage-indicator could be kept at a low value; sufficiently low so as not to over-shadow the losses in the sample. This precaution might possibly be necessary at some- what higher frequencies where the unavoidable losses in the - 6 - usual kinds of voltage indic ator become relatively large, but for measurements at 100 meg a cycles this difficulty does not arise. On the other hand, the method has certain inherent disadvantages which made it undesirable, at least for frequencies at which simpler and more direct methods may be used. Perhaps the most important of t hese disadvantages is that the entire measurement would have to be based on either calculated values or rather indirectly determined values of the losses in a "standard" tuned transmission line. Because of the scarcity of data indic ating the validity of transmission line calcul ations at high frequencies, it was considered highly desirable to apply a rather direct experimental check to such calculations. Consequently, the method finally adopted is such that calculations of the losses in tuned transmission lines do not form the basis of the results, -but are used only for the calculation of small correction factors. The proposed method would also involve the use of a great deal of rather complicated high-frequency equipment, - 7 - thus increasing the complexity of the necessary adjustments and the consequent possibility of error. Another difficulty which would have arisen is that of body-capacity effedts; it would have been practica~ly impossible to provide complete shielding. It was accordingly decided that other methods should be investigated, although for future work at higher frequencies Dr. Haeff's method certainly merits further investigation. 2. The calorimeter met hod might be quite suitable for qualitative comparisons between different kinds of dielectric material, but it would be e~tremely difficult to determine the power factor or loss factor of high-frequency insulation by such a method. This is true because the power loss in the sample of material is not measured directly as an electrical quantity. Instead, it is measured by determining the amount of heat which is developed when the sample is subjected to a high-frequency field. Before the result of such a test can be expressed in electrical terms an absolute measurement of one of the electrical quantities, either the current flowing to the sample or the electromotive force between the electrodes, must be made. A determination of either one of these - 8 - quantities would be difficult, not only because of the difficulty in calibrating suitable instruments for very high frequencies, but also because of the effect of distributed capacitance which may cause a large variation in total current along the length of a high-frequency conductor. Thus the current which is actually measured might be quite different from that which it was desired to measure. Because of this sort of difficulty it was decided that the calorimeter method would be unsuitable for ultra high frequency work. 3. The methods falling under the last two classifications depend directly on the pr?perties of resonant circuits, these resonant circuits usually being made up of a coil and variable condenser. The sample is usually inserted in a small condenser arranged so that it may be connected in parallel wit~ the main tuning condenser in the resonant circuit. Some form of indi- cator, often a thermocouple instrument, is used to indicate the magnitude of the current in the resonant circuit and the resonant circuit is coupled very loosely to a radio frequency oscillator of rather large output. In the resistance sub- stitution method a reading is first taken of the resonance current with the sample in place. Then, holding the oscillator - 9 - output constant and with the sample removed, the resonance current is adjusted by means of a series resistor in the resonant circuit until it has the same value as it had with the sample in place. Thus the effective resistance of the sample of insulation is measured in terms of a series resistance in the resonant circuit which produces the same effect on the resonance current. A simple calculation is then required to convert the result to its final form. This method possesses the advantage of simplicity but is quite unsuitable for very high frequency work because of the difficulty in the construction and calibration of suitable resistors for use at ultra-high frequencies. Another difficulty which may become quite serious at high frequencies results from the use of a variable condenser whose losses vary as its capacitance is changed. This effect is not important at low freQuencies, because of the small relative change which must be made in the setting of the variabl ·e condenser when the sample is inserted. However, at high frequencies the maximum capacitance of the condenser is, of necessity, rather small, and the change required on the insertion of the sample becomes important. In fact, it has been shown that, unless elaborate - 10 - precautions are taken, the reduction of the loss in the condenser when the sample is inserted and the circuit retuned may actually be greater than the increase in loss due to the sample. From these considerations it was co.n cluded that any method involving the use of known resistances or of coiland-condenser resonant circuits would not be sufficiently accurate for use in this investigation. 4. The distuning method, as used at low frequencies, employs the same sort of resonant circuit, but the equivalent resistance of the resonant circuit, with and without the sample, is measured in terms of a known change in reactance rather than in terms of a known change in resistance. This change in the reactance of the resonant circuit is usually effected by changing the cap,acitance of the tuning condenser a known amount, although the same result may be obtained by changing the inductance of the coil by a known amount or by slightly altering the frequency of the supply oscillator. In either case, the introduction of reactance into the resonant circuit causes a reduction in the resonant circuit current and the equivalent resistance of the resonant circuit may be calculated in terms of the known change in reactance and the resultant decrease in the resonant circuit current. Thus - 11 - the effect of the sample of dielectric in increasing the equivalent re$istance of the resonant circuit may be determined by the dif·flerence in two sets of readings, with and without the sample in place. Although this method does not involve the use of calibrated noninductive resistors, a coil-and-condenser resonant circuit is usually used and in this form it would not be suitable for ultra-high frequency use. However, the variation of the current in a resonant circuit as the reactance is changed is known to follow a relatively simple law. This is a distinct advantage, in that it allows the readings to be checked with the possibility that spurious effects may be detected and eliminated. Consequently it was decided that the method to be investigated should be some modification of the usual distuning method, provided that a resonant circuit could be constructed whose losses and reactance could be calculated to a reasonable degree of accuracy. 2. D. Preliminary Analysis of the Possibilities of a Coaxial Line. Fortunately, at frequencies of the order of 100 megacycles, tuned transmission lines form very desirable resonant circuits and, in addition, their behavior can be calculated quite - 12 - 2,3,4,5,6 accurately. This is particularly true of coaxial tuned lines, short~circuited at each end and approximately a half-wave length long when in resonance. For such lines, the only departure from a complet.ely-shielded simple geometrical configuration occurs at the points where the energy is introduced and the measuring current taken out. By making these necessary openings very small, their effect can be made negligible, in which case there results a resonant circuit which is practically completely shielded, has very low losses, and in addition is susceptible to reasonably accurate calculation.However, before these advantages could be realized, a suitable method had to be devised for introducing the sample 2. Schmidt, o. "Das Paralleldrahtsystem als Messinstrument in der Kurzwellentechnick". Hochfrequenztechnik und Electroakustik, 41, p.2, ·January 1933. 3. King, R. "Eine zussammenfassende Untersuchung uber stehende elektrische Drahtwellenu. Ann. der Phys. Folge 5, 1 p. 806 '30. 4. Sterba, J. and Feldman, C. B. "Transmission Lines for Short-Wave Radio Systems. 11 Proc. I.R.E. 20 p. 1163 July '32 5. Shelkunoff, s.A. "The Electromagnetic Theory of Lines and Shields". Bell Sys. Tech.Jour. P• 532, Oct. '34. 6. Terman, F. E. "Resonant Lines in Radio Circuits." Elect. Eng. 53, p. 1046, July '34 - 13 - of dielectric into the resonant circuit. Before the experi- mental work was started, it was decided that it might be possible to use a sample in the form of a ring about one or two centimeters in length and fitting tightly in the space between the line conductors. Such a sample would produce the greatest effect on the losses if placed at the voltage maximum in the line, one quarter wave length from the "sending end 1' . The relative magnituae of the resulting increase in the resonant circuit losses, according to a preliminary calculation, would, it was believed, be adequate for measurements on most of the available materials. In addition, there would be no additional leads required to carry the current to the sample, and the field in the sample should be almost entirely free from edge effects. In fact, the field in the sample should be exactly radial except for the effect of second-order propogation effects and these, it was believed, should be negl igible if the space between the line conductor surfaces were kept small. 2d. Description of Original Line In order to check some of the foregoing conclusions, it was decided that a coaxial tuned line should be built, to be operated from the output of a constant-frequency oscillator. The equivalent reactance of the line was to be altered by - 14- changing its length a measured amount, rather than by changing the oscillator frequency. The latter method would have required two high-frequency sources, one being of variable frequency and the other a fixed reference frequency of a highly stable type. In addition, the beat-note frequency would have had to be measured by means of a frequency bridge or some equivalent scheme, since the frequency variation required would have been greater than the audible range. On the other hand, the ~ixed-frequency method would require the use of only one oscillator of fixed frequency. In addition the measurement of the change in line length to an adequate degree of accuracy would be a relatively simple task, and the mathematical analysis would be simplified since the electrical length of the line between sending end and sample would be constant. However, the decision to make the line length mechanically variable introduced an important source of possible difficulty. This difficulty was that which might pe encountered in reducing, to a negligible quantity, the effects of contact resistance variations. In order to do this, the movable shorting piece was designed in a form intended to maintain the best possible contact with both the inner and outer conductors. The contacts - 15 - were arranged, as shown in fig. 1, so as to have rather long contact portions, slotted in order that they might press against the line conductors. The dimensions of the two conductors were chosen so that the radial distance between their current-carrying surfaces would be relatively small. In addition, the outer conductor was made slightly less than an inch in diameter. These dimensions (shown in fig.l) were chosen so as to reduce the importance of second and higher-order modes of propo5 gation in the line. In this way, the fundamental errors involved in the assumptions underlying the usual transmission line theory were reduced to a practical minimum. The radio frequency energy was introduced into the line by means of a "feeding circui t 't mounted at the fixed or "sending end" of the line. This feeding cirfuit consisted of a short section of two-conductor line, shorted at one end and tuned at the other by a small variable condenser. It was coupled to the oscillator by means of a twisted-pair transmission line. The shorted end of the feeding circuit was made of relatively small-diameter wire, projecting through 5. Shelkunoff, s. A. "The Electromagnetic Theory of Lines and Shields". Bell Sys. Tech. Jour. p. 532, Oct. '34. - 16 - a slot into the interior of the outer conductor of the coaxial line. This slot was parallel to the axis of the line and was immediately adjacent to the shorting piece at the fixed end of the line. Consequently, if a constant radio frequency current were flowing in the feeding circuit a voltage of constant magnitude would be introduced at this end of the line. The current at the same point in the line would then be dependent on the equivalent impedance of the line, as measured from the sending end. In Appendix B, part I, the relations between this impedance and the line losses, line length and constants of the sample are derived. The results show that a loss measurement could be made if the relative magnitude of the current at the sending end could be measured. Consequently, it was decided to mount a thermo- couple near the sending end of the line and to employ inductive coupling between line and thermocouple. Then, as the line length was varied through resonance, it would be possible to take readings of thermocouple current, plotting them in the form of a resonance curve. line losses could be obtained. From this curve the Then a similar run would be taken with a sample in place and the difference in loss, attributable to the sample, determined b1 subtraction. - 17 - 3. Description of Oscillator a. Requirements. Before the proposed line could be tested, it became necessary to obtain a suitable oscillator to act as the high-frequency source. This oscillator had to meet the following conditions: 1. It should be relatively simple to build, since the time available for developing a suitable high-frequency source was limited. 2. Its frequency should be highly stable. 3. Its power output should be relatively large, so that it might be coupled very loosely to the tuned line. 4. It should operate at a frequency of about 100 megacycles. Some consideration was given to the possibility of picking up a broadcast signal, removing its modulation, and multiplying its frequency in a number of steps, then amplifying the output to a suitable level. However, such a scheme would have required a considerable complication of equipment. The same considerations applied to the alterna- tive of a crystal oscillator, controlling the output of high-frequency amplifier by means of frequency-multiplying - 18 - .stages. Instead, it was decided to construct a simple tuned-grid, tuned-plate push-pull oscillator, controlled by a high Q, tuned line in the grid circuit. It was believed that such an arrangement, using Western Electric 304-A tubes, would provide the best compromise between absolute frequency stability and simplicity. 3b. Description of Final Oscillator Several preliminary models were built using tuned lines in both plate and grid circuits. These we re found to be rather critical in adjustment, and undesirable magnetic coupling was believed to exist between the two tuned circuits. In addition, the necessary space required for shielding was rather excessive. Consequently, a single-turn coil and a fondenser were substituted in the plate circuit, the tuned line being retained in the g rid circuit for frequency control. A schematic of the oscillat or circuit is shown in fig.2, with pictures of the actual arrangement in fi g .3. The grid line was made of two 5/8" O.D. cop per tubes, spaced 1 1/8" between axes, and mounted vertically in a heavy brass shorting block fastened below the wooden baseboard. The length of the tubing , above the shorting block, was 55.1 cm., the grid connections being approximately 16 cm. from the shorted end of the line. The plate tank circuit originally consisted of ,304A + ?SO J'OLTS TuNE.D L.INE R 9 - 401:JtJO ohms- ~ - .30 ohn,s, .304A cenrer- ro/'_peal F/6. .F,,/an,enr su,.oply C/rt::Uilsno.f Shown. a OSCILLATOR CIRCUIT SCHEMATI C Fig. 3. Oscillator. with and without shield. - 19 - a single turn, 9.7 cm in diameter, of 3/16" O.D. copper tubing, tuned by a Hammarlund type MCD-35-x variable condenser with its two sections in series. Under these conditions the oscillator gave a satisfactory output at about 2.9 meters, with 700 volts on the plates. Later the plate coil was replaced by one of about the same mean diameter but made of 3/8" O.D. copper tubing. As operated for some time, the plate voltage supply consisted of a simple mercury-vapor tube full-wave recti- . ) . . ' .fier and two-section filter. This was later improved by the addition of a vacuum tube voltage regulator, (described in Appendix K) thus reducing by a large factor the possible errors due to changes in line voltage, or modulation of the oscillator output by the ripple component of the plate voltage. In order to determine the variation in output freQuency during the warming-up period, the test recorded in fig.4 was made. In making this test, the tuned line was used to de- termine the apparent wave-length of the oscillator output. It will be evident that the freQuency beca~e practically constant at the end of a 20 minute period. 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TT L_ " ~ , .,. - 2Q - The use of a shield can around the oscillator was found to be necessary to prevent los~ of energy into the power supply leads and to prevent undesirable body capacity effects. As an additional precaution, the power supply leads to the oscillator were brought in through choke coils mounted in a separate shield can inside the main shield. 4. Description of First Arrangement. At first, an attempt was made to operate the apparatus without the use of complete shielding, but, even with the oscillator set up in an adjacent room, the stray field effects were found to be excessive. Consequently every part of the high-frequency equipment, from oscillator to galvanometer, was enclosed in metal shielding. Galvanized sheet iron boxes were found to be adequate for shielding the oscillator, galvanometer, and feeding circuit. The twisted pair line from oscillator to feeding circuit was pulled into a length of copper tubing, electrically connected to both oscillator and feeding circuit shields. In the same way, the direct current leads from thermocouple to galvanometer were run inside a copper tube, connected to the thermocouple and galvanometer shields. These precautions, together with the fact that both the feeding circuit and thermocouple Fi g . 5 . Feeding Circuit, cover off. Fig.6. Top View of Thermocoulpe Box, cover off. (at movable end of line, as in third arrangement) Fig. 6a. Bottom View of Thermocouple Box, showing toroidal choke and flexible shielded 1 ead to galvanometer. Fig. 7. Movable Bnd of Line, showing metric lead screw mechanism and thermocouple box as used in third and fourth arrangements. - 21 - boxes were clamped to the outer-conductor of the tuned line, reduced the stray fields to a . quite negligible magnitude. No attempt was made to match the impedance of the twisted-pair feeding line to the oscillator plate impedance. Instead, it was simply terminated in a rigid loop of wire mounted about six inches from the plate tank coil. However, undesirable power loss in the twisted pair' was avoided by matching its impedance to that of the feeding circuit. This was done by adjusting the position on the feeding circuit at which the twisted-pair line was connected. In this way, the oscillator was made to produce, with a relatively low input, considerable circulating current in the feeding circuit, when that circuit was adjusted to resonance. To indicate the relative magnitude of the feeding circuit current, a thermocouple galvanometer having a fullscale reading of 115 m.a. was mounted in the top of the feeding circuit box. It was coupled to the feeding circuit by the mutual inductance between a short loop 9f wire connected between its terminals and the conductors of the feeding circuit. The feeding circuit was mounted on a separate baseboard so that its coupling with the coaxial line could - 22 - be varied by moving the whole feeding circuit horizontally in a direction perpendicular to the axis of the line. As usually used, the coupling loop on the end of the feeding circuit projected only a very small distance into the coaxial line. The vacuum thermocouple was claraped to a vertical insulating panel to which was fastened the terminals carrying the coupling loop. This panel was fastened at its upper edge to a parallel pair of brass rods, arranged to slide in a direction perpendicular to the axis of the coaxial line. Thus the coupling to the thermocouple could be varied by sliding the thermocouple and its mounting back and forth. Screws were arranged to act as stops, limiting the motion of the thermocouple and its loop, and providing a means for locking it in place when properly adjusted. The thermo- couple pick-up loop was self-supporting, being of rectangular shape and made of about 24 gauge copper wire. Its length parallel to the axis of the coaxial line w~s about one and a half centimeters. The le~ds from the couple to the galvanometer were completely shielded by copper tubing and a choke of toroidal for,m was inserted near the thermocouple. This choke - 23 - consisted of two self-supporting windings, one connected in each lead and arranged to set up a magnetomotive force in the same direction around the toroid. A small shielding can was provided for this choke. Several mechanical arrangements were used in turn to adjust and measure the length of the line. At first, a simple lead screw of about 16 threads per inch was used in conjunction with a short length of metric scale. Sufficient precision could not be obtained with this simple arrangement, and a cathetometer arrangement was next employed. However, the difficulties encountered in measuring relatively large changes in line length with this apparatus were found to be too great for conveniently rapid work. Consequently, a new lead screw was constructed, having a pitch of two millimeters. It was fitted with a graduated dial, having twenty equallyspaced divisions, thus making it possible to change the line length by as little as one tenth of a millimeter at a time. 5. Results with First Arrangement a. Calibration of Thermocouple and Galvanometer The thermocouple and galvanometer arrangement was calibrated without disturbing the leads from couple to galvanometer. In fact, the calibrating arrangement was identical with that used in a ctual operation, except - 24 - that the couping loop was removed and the heater was connected in a direct current circuit. Because of the lack of suit able instruments, an alternating current calibration was not made. However, it was found that reversal of the heater current caused no detectable change in the galvanometer reading. It was therefore assuraed that the direct current calibration would also hold for alternating currents of low frequency. At very high frequencies, it was realized that the absolute calibration would no longer be valid. However, there seemed to be no reason to doubt that the form of the calibration curve would be unchanged at even the highest frequency. Of course this assumption implied that all the impedances in the thermocouple and galvanometer circuit would be constant at any particular frequency. As will be evident from the curves of fig. 8, the relation between the square of the heater current and the galvanometer deflection was found to be quite linear over the desired range. In fact, the errors in obser- vations due to drift of the zero point seemed to be much greater than any actual departure from the linear calibration. t..J • ·1 • • •t .,..,..t.._ -l~ ....... • .,,, ";"I" .......... t:i7t • .......-+..L. • :~ : . - : • ::.: :: :_-: . - . . - - - . - ... . . _._ .. { ~i~; I:> :T ii!i f¥if ~-rn rt:~ 1[ :L1 ?; :::f ?: \::: :!:: ;:r: it:::<~;~~:~\:~~ i}t ;~}; /~i-f+-L~ <~ ii~I ;;ii:\\:<: :.:: :: . I.: 1,-- -~ .. --- ~-- -+---+-----f-+--~---'--- ~ i ~ - - j ___ 1·• I l'li : j,,~ . ::: ~ -- ~ : ----~~-- l I 1 I I :i ' . . , , ! - f - - - - - + - - ' - - - t- - - _'._ __ . - ,._ _ __)_.._..: ' -- • - -- - - ' i - • ---•--- --•---- - -··--·- •·- -ii I ! I :B ' :B ---1-. i I , I . I I i : I .,. 1--'RIN\LU Ir-.. US. A - 25 - 5b. Method of Taking Readings After the oscillator and feeding circuit had been allowed to warm up for a period of an hour or more, the feeding circuit was adjusted for a maximum current, as indicated by the associated thermocouple meter. Then the line length was varied through resonance so as to make sure that the reaction of line tuning on the feeding circuit was undetectable. If any such reaction could be noted, the coupling between feeding circuit and line was reduced until the desired lack of reaction was obtained. Then the coupling between line and thermocouple was adjusted until the maximum galvanometer deflection fell in a suitable range. After making these preliminary adjustments, the thermocouple slide was locked in place and readings of the galvanometer were taken as the line length was varied. The value of the galvanometer zero reading was determined by readings taken before and after the resonance run. If the zero point had shifted during the run, it was assumed that the variation had been linear with time and corresponding values were subtracted from the galvanometer readin gs. - 5c. 26 - Sample Curves The runs made with the first lead screw and simple scale did not include sufficient points to form useful curves. However, on replacing this preliminary arrange- ment by the cathetometer set-up, much better results were obtained, which are illustrated by the sample curves shown in fig.9. When the cathetometer: set-up was replaced by the metric pitch lead screw and graduated dial, an even greater improvement was evident, as indicated by the curves of fig. 10. An inspection of these curves will show that the experimental points, taken at intervals of one·- tenth millimeter of line length, fell on the smooth curve remarkably well. One or two exceptions will be noted on curve 1 of this figure, but these merely served to indicate the presence of some mechanical backlash in the lead screw system. On locating and correcting this trouble, curves like that of curve 2 were obtained. 5d. Discussion of Results. Perhaps the most important conclusion drawn from ;:•} these curves was that the cont act resistance at the junctions of the movable shorting piece and the line conductors was relatively constant. At least it did not ,.. -1 I I i. ·- .. , I ! I ' i E-342 1 4 JO! .... I i I :~ I • 1> : · ! :) • - ~j - N0.1.1437-fJu •8-f.L]wqNJ-~7~!i ~~ - -1-:-~- -I .. I --i:_;-.--+~ I . : ... t-'ill,ll~-~· i ...... : u.s.A i - l:t PRINTEO IN U, a. A, KA I CO., N. Y. II ..... - 27 - suffer sudden changes between readings. On the other hand, the asymmetrical nature of the resonance curves was rather disturbing. According to the theoretical analysis {presented in Appendix B, part I) the curves should have been quite symmetrical. 7 The experience of other workers had shown that asymmetry of the kind observed might result from unsuspected direct coupling between the high-frequency source and the measuring {thermocouple) circuit. Consequently the analysis presented in Appendix G was made. A comparison of the observed curves with those shown in fig. G.l of that appendix will show that the observed effects are of the type to be expected on the assumption that such direct coupling actually existed. Because of the difficulty of determining whether or not the usual t ype of resonance curve was of exactly the correct shape, it was decided to plot readings in the form of "rectified" resonance curves. This type of 7 curve had been used by previous workers, although these workers had been dealing with coil-and-condenser resonant 7. Moullin, E. B. "Radio Frequency Measurements", (a book) Oxford University Press. - 28 - circuits. However, the analysis presented in Appendix C showed that the same method could be used to advantage in connection with the readings taken with the tuned line. In addition, it became evident that the slope of an ideal rectified resonance curve would yield the most accurate value for the losses in the line. If this method were used, the value for the losses would depend, not only on one or several pairs of readings, but on all the readings taken during any one run. In addition, those points obviously in error could be easily located and eliminated from the calculation of the desired re~ults. The existence of direct coupling from feeding circuit to measuring circuit would alter the shape of the rectified resonance curve as shown in fig. G.2, Appendix G., and in fig.11. Such a curve obviously would not yield the required results as rapidly nor with such probable accuracy as would a curve obtained with negligible direct coupling. In the latter case, the curve should be a straight line. 6. Description of Second Arrangement. a. Thermocouple Mounting. In order to avoid the effects of direct coupling, r .. i..;.-----+--+-~· -·- • ·1 :, I I I --+~---~--! __ i : I ·----1- --- -·--• -·- -- II E-342 (4 30) .... r'lsllNlt.U 1r-,. U. 5. A - 29 - it was de~ided to redesign the thermocouple mounting, placing the therrnocouple at the movable end of the line. The same thermocouple box was to be mounted on a short length of metal tubing, arranged to slide along the , outside of the outer line conductor. A long narrow slot was to be cut in that conductor, parallel to the axis of the line and the thermocouple loop was to project through this slot into the line. A small screw was also to fit through the same slot and to fasten the thermocouple box and supporting tube to the movable shorting piece inside the line. Thus, the thermocouple box would move with the shorting piece and the thermocouple loop would always be held at the same distance from the electrical end of the line. As shown in Appendix J, the current in the thermocouple loop would then be a constant fraction of the current at the end of the line. The necessary relations between line constants, the constants of sample, the line length and "recei v·ing end" current are derived, for this new arrangement1 in Appendix B, part II. 6b. Use of Spacers to Center Inner Conductor. During the first series of tests on the new arrangement, changes in galvanometer deflection were - 30 - noticed when a slight transverse mechanical force was applied to the outer conductor of the line. This was found to be due to a slight change in the capacitance of the center portion of the line as the axes of the conductors were displaced slightly. To overcome the possibility of erroneous results from this source, two sets of insulating spacers were installed. These were arranged as shown in fig. 12, adjustment of the centering of the inner conductor being accomplished by means of the three radial screws in each spacer assembly. Some difficulty was anticipated in determining the position of the inner conductor, since the presence of the outer conductor would make an actual measurement rather difficult. Actually, however, the anticipated difficulties did not materialize. Instead of attempting a mechani- cal measurement, the. adjustment was made by finding the position of the adjusting screws for which the length of the line at resonance was a maximum. Then the capacitance of the center section of the line was a minimum, showing that the conductors were properly centered. This method proved to be quite sensitive and was used throughout the work on this and the third arrangement of the line. , ,,,- - 6- .J2 mt7cl,ine sere>¥ //lsulcrror moun/, One o/ /'/Iese S,Pacer a-s.se/J?b/;~ moua/'ed ,.,-- - ncl'l?n md, .£ · hex oros-s /6 b " ~ a; 4.S- cm. /'rt7.m /ed end or Ji " lln~ a-oorher ..9(J c /77 l'/1:1 ?'l /'ed end .6/'crS"s /'/nfl, ax1,:TI /en9/ll /;e/d m place .by //1.ree //Jsu/q/or movnrs. SPACER AS.SE/1181,,}: ~?G. /2. Sp/d copper .secr1cn o/ cu/er conduct-or SPLIT CENTER SECTION FIG. 13. (Fu/./. ,S/ZE) - 31 - 6c. Split Center Section for Insertion of Samples. In order to avoid the necessity of taking the line apart each time a sample was inserted or removed, a short section of the outer conductor, one-~uarter wave-length from the fixed end of the line was made removable. For this purpose, a section about three inches in length was removed from the outer conductor. Then a new center section of copper was made in the form shown in fig. 13, forming two half-cylinders with inner surfaces to replace the inner surface of the removed section of the outer conductor. Threads were provided at each end on the outer surface so that two nuts fitting over rings fastened on the outside of the line could be used to clamp the new center section in place. This same center section was also used in the third and fourth arrangements, being slightly altered in the latter case so as to provide a mounting for the parallel-plate sample condenser. In the arrangement under discussion, samples were made in the form of split •rings, to the dimensions shown in fig. 14. They were inserted by removing the upper half of the center section and sliding each half of the ring into place between the inner conductor and 'fABLE I Results With Second Arrangment Sample Material R7 Xl0 2 CX.x lO 72.52 72.48 72.47 72.47 6.69 6.57 6.55 6.69 7 .16 7.29 7. 31 7.16 2.28 2.32 2.32 2.28 71.17 69.46 69.51 69.51 68.79 67.83 2.36 2.57 2.55 2.55 2.45 2.45 tan ~ ktan ~ lLo~~ factor) 2. 22x1O3 5. 24)(10 -3 4. 65xl 0-; 1. 81 x1 2. 5&<106. 58 xl0-~ 2.34xl 0-3 _ 5. 96.xl0 4. 93Xl0- 3 2.01 x10_ 33 5.ooxio- 3 2.04xl0 1.5 cm 67.99 4.0 7.4 ,x l0-2 2.8 1.1 X 10 Simple line II ti II II II II 1a k Victron 3/8 11 3/4t1 3/4 11 3/4t1 1" 1-1/4 11 "II II " ti Redmanol Hard rubber 3/4t1 Note s m Length 69.06 o-! -2 -I 2. 9 x 10 3.1 .x 10- 2 Calculated value of ~ for this simple line -s was 2. 08Xl0. FIG. 14 OIMEl'ISIONS CJF SPLIT SAMPLE RINGS - 32 - the lower half of the center section. Then the upper half was replaced and the center section clamped by means of the clamping nuts. Later, the inner conductor was also re-constructed, being made in two lengths arranged to be joined at the center. Then a sample in the form of a solid ring could be used, being inserted when both conductors were separated at the center. After insertion of the sample, the inner conductor was drawn together again and the split center section of the outer conductor replaced. 7. Results with Second Arrangement. a. Sample Curves. The results obtained with this arrangement seemed to indicate the complete absence of the effects caused by direct coupling from feeding circuit to thermocouple. The rectified resonance curves departed only slightly from the ideal straight line, as indicated by the sample curves of fig. 15. Furthermore, the accidental devi- ations from the correct curve were also very small; so small that the imperfections of the lead screw mechanism were clearly reproduced on the curves. This effect is demonstrated in fig. 16, where curve I is a ~ 0 . .., '" ' .. • • ,. , •·. .. , nl 1...-;,., "-f- f •· ~ : ! ~; . l • •' ~ • t 1. • ..,. •- i .. 1 1\ •~ ~ i ~1~- ;~·!·_; ~ .1 . . , • • . :·~ , . . ;. ... . : :• I'+I :i ' : . i + !;'! _:! ' l 1 1, 't 1 • . 1 , •'-1 _ i T, . 11 Cj, 1 ri I • ffiIHlffij -~::r L . :rt ji_; .. . ' r i.,1 ' . J I 1, -- - ~ , 1 _j_ , J I l. .1 - ~..................... ·:- _-_ t _ . ~-.1- 3 --17 -u. ,.:Lr t! r, 3 T -, 1 • • ,- J _ 1···· 1··-- , ···-· L: __ ·:4 ''' N ·· • 1 " •• t:t;J ... ., - . . . ,· :: L-►- = ~ ~ 111~• :,. C 7 2 1r 1 . • .. I ··-· •.• ,_;:_ ~-~...u~c.......----1-~ •••• :~= •• .. •·: • I I • I , - ~ -~ • [. 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IW: • . • 11 '1··' ···1 • -::--r-~t·_µ: ~ ~ ~ ,;,1 ·8ft 1 1 :: ~- ~ll .. , , ...• ,7..... 1, 1-. r.LJ, -l 1, , 1 ~, 1.1, 1 · ·i.:;. j.j1UV.1:.,rl .· L"'' • 1·· :·t,:. ::;.: :::: I·.· .' ,, _jT" '._:!. iI ...... i : i;. ;: . . • ,., .. • t ... I •·., rt· " . ·".•.··1 ,.. . JI=µ; ~ I- I :- .. , . . . : . ' .: ........, ,, 11_~-L t;. ... .-1 :~-i; ;·1; i : _: . •··: j. 1 • ~",j'- ! j~·w...:.· •!' T'.,j . - , + I ":i-:i;_._:, ;1 I 'Jt· , i. i . . ! j L ~ r l , ; -~-;. l,i•l:::T :. .·:1: :,:: .jJ':;t • • -1 , ... I••· 't''. . I Ii Ii. ,:; :lT -~ :'.: ·n:; .... "' ., .s ,,i ::w ,J,. . ~~ t .1 . . t l':':'t'Jir1.; Irr, 11• 1 • --!-;_-r+ i: J·i ... I .wi...: " ~~ . 1 ·q :,+ :·: l. l .. :- 1• , . 1·.• • • !:•- 1,-i.-, f ,,.:·1'•· . ,. I . .. ~. I, ~ ~ ~ ~ I- I- I- I- 0 ~ (.,) :: ~ ., '··l· r-':" -' , •w ~ ..... CT •.. . . . .• , . . . .. . . . . . . .. . .. . 1__:. · - ~\- ... . ... :~ I '' l • i . 1 - --.+i ---------+--+--+-:~: - I· -+-l j: ~- I . .. i . • :, : .. . ' ..:1.... .. ... .. . . . .. .. .. . .. . . . ... . · " .. . .. . :. I : : : :::j . ::· •• . : :~ •::' ... ' . . ... . . : . : : . ~ • . . . . •• I i. • • • . · ~• · · • . . i i i I •• I . , - --- __ ,l_ - I. -- ; :W:> .:.... :. ' : a ~""' •• " I I . --- +----'- ~ - .c,:t----r",--1~t-rJ-. · --,-,1'-· •- .+--•-_· +·1 --1,. -,: .I ~ _ ._, .. ! ~, .+---+- ...........:~ ·. --+ . _:·_• '{ i I ' ~, ~ L i ~ .¥..J~~ "°-~!4' : i. . .: •• - · .. .. • .• "J~~ \ : 1·_·--+-+---+-.·_· -_.__-_··+-·-· -+-•• . . --1 ... .• . . : :: : :: : : : . : : · :: i - : . .. . :. I . - ~- i ; ••• ••• • •• •• • .p ) -- ' .. ; .. I H1;',i I t.U Ir-.. E 342 , .. 30 U . S. A - 33 - rectified resonance curve,as plotted from a typical set of readings, and curve 2 is a calibration of the lead screw, made with the help of a metric micrometer. To obtain this calibration, the micrometer was clamped to the fixed framework so that it could be used to measure the motion of the movable nut on the lead screw. The characteristics of the resulting rectified resonance curves therefore indicated that the general mechanical arrangement of the moving portions of the line was quite satisfactory. However, difficulty was later experienced with the details of the support for the thermocouple loop. This was overcome by the addition of a piece of thin mica, provided with a narrow slot through which the thermocouple loop projected into the line. Since this piece of mica was fixed to the theYmo- couple box, it served to fix the spacing between the loop and the edges of the slot in the outer conductor of the line, thus preventing slight changes in the capacitance between loop and outer line conductor . . The observed curves also provided further evidence that the contact impedance between line conductors and movable shorting piece was relatiyely small and constant. - 34 - The fact that the curves were quite strai ght showed, at least, that this imp edance was very constant during e a ch individual run. Conse quently, the as sumption bec ame reasonable that the contact i mpedan ce could be a ssumed constant for all positions of the shorting piece. 7b. Measured Values of Line Attenuation Constant. The object of the first series of tests made with this arrangement was to determine the value of the equivalent transfer resistance Rr of the coaxial line. Then the apparent magnitude of the attenuat ion f a ctor ~ c ould be calculated and compared with the theoretical value. The equat ions which formed the ba sis of these determina tions are derived in App endix B, part II. For the case under consideration here, equations ( 27) and (28) of the derivation become: (1) and (2) But, in this cas e, (~ + la) is equal to A, whe re A is 2 the wave-length. Furthermore, t an ¢) .e Xr RT and, as is demonstrated in App endix C, the slope of t he - 35 - rectified resonance curve is proportional to the constant ratio, tant/J/xT. However, the actual recti- fied resonance curves were plotted in terms of/)~, and it therefore became necessary to substitute from equation (1) above. When this substitution was made, the slope m was given by, tan t/J _ Z~2 lf. 1 m - L\la - )\. RT or, RT.,. Z 0 21T 1 Tm ( 3) Also, 1 a= 47r )f m ( 4) Consequently, in order to determine Rrand ct. it was only necessary to measure the slope m of the curve of tan(/) vs. ~i. The value of the characteristic impedanfe Z0 could be calculated quite accurately from the dimensions of the line and A Was taken as twice the actual length of the line at resonance. This length was compared to that of a standard Lecher wire system and was found to agree with the distance between nodes on the Lecher wires to within a millimeter. The first step in determining the points on the - 36 - rectified resonance curve was to determine the galvanometer deflection 8r corresponding to the maximum point on the resonance curve. This wa s found, during the early pa rt of the work, by plotting the top portion of the a ctua l resonance curve, but later an analytical method, suggested by L. W. Baldwin, was adopted. Then, for ea ch re a ding in the s et, the value of tantp was determined from the relation tanip = Yt-1' ( 5) (see app endix C). The slope m of the resulting curve wa s measured and substituted in e qu ations (3) and (4). In a number of cases, the most prob able slope was found by the method of least squares but this refi nemen t was found to be unnecessary since the slope could be determined to within the observational error by simply fitting a straight line to the ca lculated points by eye. Some of the va lues obtained for Rr and d. in this way have been tabula ted in Table I. The va lues of OI... should be compared with the calcul ated va lue of ex. for a line of the same dimensions, on the as sump tion that the shorting pieces were of zero i mp edance. This - 37 - -5 calculated value was 2. 08 X 10 . 7.c. Tests on Samples of Dielectric. The next series of tests was made to determine the dielectric constant and power factor angle for various samples of insulation. These samples included one of redmanol, a second of hard rubber, and several of victron. The actual procedure in taking readings was essentially the same as that for the line alone. How- ever, in this group of tests, each determination was based on two sets of rea~ings, one with the line alone and the other with a sample in placeo From the first run, the value of()( was determined, in order that the losses due to the line itself could be calculated for the conditions of the second run. With the sample in place, the line eq_uations assumed the form, as given in eq_uations (27) and (28), Appendix B. Si nce the total line-length for resonance was only slightly - 38 - less than one-half wave-length, the t e rm in cot 2 rlz, .A app earing in the expre s sion f or Rr, could be neglected. Thus, in te rms of the slope m of the rectified resonance curve, R r= Z 0 2 7T . .A s in 2 lfla X 1 m or or 2 Jr Zo _ R Knowing a', . 1 A sini! 21~_12 ( 7) m ~{= t), 4, ). and m it wa s t h erefore possible to calcula te Z / R and thus to determine the 0 resi s tance R of the sample. The tang ent of the power f a ctor angle of the dielectric in a simple condenser is g iven by the wellknown expression tan~= 1 Rew where C is the capacit ance and R the effective parallel resist ance of t he condenser. Th e magnitude of R, for the p a rticula r s aiu ples employed, could be determined as outlined above. It remained to evalua te the quantity c. This was not the s ame a s t h e cap a cit an ce C app e a ring in the analysis of App endix B. In that case, C rep resented - 39 - the increase of capacitance at the voltage loop on the line, a s produced by the presence of the sample. Consequently it was only (k-1)/k as large as the capacitance required in the above expression. When using the method under discussion, therefore, the above expression should be written: tan$ = k-1 }.{ 1 RC <.il ( 8) where Chas now the same meaning as in the equations of Appendix B. The actual expression used in calcu- lations of tan~ was: tan~ = ~. 1 • k-1 R ~ ( g) In this forllli;- the first two factors were obtained respectively from (7) a bove and from the condition of resonance, when :( 10) Zo Cu:> = cot 2 1T 1a A The value of k was also determined from equation (10) under the assumption that edge effects were negligible and consequently that the following expression for the increase of capacitance due to the sample would be valid: C .,. (0.241) (k-1) Zsx.10- log I Oba 12 farads - 40 - Thus, in terms of the measured quantities, ( k-1) = cot 21rl 2 >-.. log10 bxl0 12 a ( 11 ) where b was the outer radius and a the inner radius of the sample, and l 5 was the axial length of the samp le in centimeters. Some of the results of these preliminary tests have been tabulated in Table I~ . 8. Description of Third Arrangement. In the course of the tests made with the second arrangement, it was realized that the introduction of a sample of victron produced rather a small increase in loss. As a result, the accuracy to be expected from measurements on victron could not be very high. To overcome this difficulty, it was decided to reduce the diameter of the inner conductor, while retaining the same dimensions for the sample. The analysis presented in Appendix D ha d shown tha t this should increase the sensitivity of the arrangement, provided that the ratio of conductor diarneters was not made g reater than about 9 , 2. - 41 - For mechanical reasons, this optimum ratio was not even approached. Instead, the inner conductor diameter was reduced to 5/16 inch, giving a ratio of 2.88, as compared with the former ratio of 1.44. According to the theory of Appendix D, this should have resulted in a sensitivity 5.32 times as great as that previously obtained. However, in order to realize this increase of sensititivity, it was necessary to provide means for the use of samples of the same dimensions as those previously used. A center section, made of copper to the dimensions of fig. 17 was therefore made to slip over the inner conductor. The sample was placed at approximately the mid-point of this center section, the position of the center section on the inner conductor being adjusted so that the saro.ple was at the quarter-wave point. In addition, certain improvements were made in the design of both the fixed and the movable shorting pieces. These were made of copper, rather than brass, and the thin-section contact flanges were made longer. As in the previous ·work, vaseline was used sparingly II TABLE Results With Third Arrangment Sample aterial Length Simple line " II la m R-r->< lOa 70.80 70.80 12.41 12.39 11.2 11.2 61.27 61. 27 12.58 12. 61 10. 9 10. 9 k tan $ (XX 10 5 1.23 1.23 5/8" cemter section only Victron "n 11 • " " 58.66 58.62 58.64 56.39 53.82 1/4" 1/4" 1/4" 1/2" 3/4" Note ktan ~ 3 2.53 2.53 2.53 2.45 2.49 1. 2JSX1O 1. 87J<lu-J3 1. 87xl o_ 3 1. 66.x l o_ l.64Xl0 3 Calculated value of d.., 3 3. 08Xl0 3 4. 67Xl0- 4. 67.Kl(j3 4 .15 ><1 o- 3 4. 10,c.io- 3 for this simple - 5 line was l.14xl0. ~ f "CO/J/'l!"r /'Vb✓n9 /soldered jom/ J'vmed c"l",Per - - - - - - - 21· - - - -- Thin .s-«:lion~ slotted to press 011 .svr/'o-ce o/ S/16' • _ j-. /JIA. CENTER F&R TIIIRLJ ARRANGEMENT ,F/6. 17. l'vbe - 42 - on the movable surfaces and was found to be effective in reducing contact impedance va riations. 9. Results with Third Arrangement. Three series of tests were made with this arrange- ment. The first comprised a determina tion of the equivalent transfer resistance and attenuation factor for the simple line only. The second comprised similar tests with the 5/8" diameter center section in pl a ce, and the third included tests on various samples of victron. Some of the results are g iven in Ta ble I I The calculations involved in obtaining these results were quite simila r to those used with the second arrangement. should be noted. Only one important difference The increase of cap a citance due to the s ample had to be c alcul ated from three sets of reading s, r ather than two. The second series of tests, on the application of equation (1 0 ) above, gave the increased cap a cit ance due to the copper center section. Then the third series gave the increase due to both center section and s ample, and, on subtra ction of the result of the second series, t he contribution of the sample itself was dete rmined. This was then substitut ed - 43 - in equa tions of the form of equations (9) and (11) above, thus obtaining the power factor and dieledtric constant of the sarnple. 10. Description of Fourth Arrangement. In order to check the results obtained with the ring S8.Ii1.ples, it was decided to construct a shielded, parallel-plate sample condenser. One terminal of this condenser was to be grounded to the outer conductor and shield, while the other was to be connected to the inner line conductor at the quarter-wave point. By the use of this arrangement, it was hoped that it would be possible to avoid at least one of the possible errors inherent in all the previous arrangements. This particular error might have arisen from the necessity of calculating the actual line losses during a test on a sample from measurements made when the line length was slightly greater than with the sample in place. In the new arrangement, it would be possible to so adjust the spacing between th~ condenser pl ates that the line length for resonance would be the same, with and without the sample. Then the current distri- bution and consequently the inherent conductor losses - 44 - would be almost exactly the same, whether or not the s ample was in pl a ce. The actual construction of the sample conde nser and its mounting is illustrated by the cross-section of fi g .18 and the picture sho~m in fi g .19. As will be evident from those fi gures, the cylindrical shiel d for the condenser wa s made of two snugly-fitted coaxial bra ss cylinders. Each of these cylinders was provided with a l ar g e opening so that t h e s ample (a fl at ci r cul ar disc) could be inserted when t he outer cylinder wa s rot ated un til the openings coinci ded. Then t he outer cylinder could be r ot a ted until the opening was completely closed, when ex cellent shielding was obt a ined. Both electrodes of the s ample condenser were made in the form of circul a r discs 1 1/2 " in diameter with their plane faces p a rallel and horizontal. The upp er disc was mounted on a vertical threaded spindle, whi ch rot ated in a threaded bearing mounted on the top of the shield box. On the other hand, the lower disc was mounted on a fi xed spindle, connected to the inner line _ n clrd/J 1nsub//1J11 ,,,,.--v,o,,o<!'/' lfg// dr s,,old cenl'er sec//on ~ J ~ e r /;;,;:::::::::r $$ 5 i S 555 SS SS lll\li\11111111111'111\IC\,_ . ii <s I ii SP i I I Si\ q SS \$\Si\\ \\ \I \ i $$ i I I Si I I i i i I IP ii ii "--- •- ou~l!"r /in'° condut:Nr '5'ECTION TIIROt/611 SAMPLE CtJN/JENSER F/6. 18. (Fv/1 S-i.?~, .rome mim,r ~mens/on.s ay,pn,.J(.) Fig . 19 . Sample CondenE-er in Place on Line . - 45 - conductor and solidly supported by a small victron insulating piece. 11. Results vri th Fourth .Arrangement. The tests and calculations made with this arrange- ment were quite similar to those made with the third arrangement. The first curve in each set vvas taken with the sample in place. Then the sample was removed and the sample condenser adjusted so that resonance occurred a.t the same line length setting as with the sample in place. In order to check the value of the dielectric constant, some curves were taken with the sample condenser set so that the separation between the plates was the same as the thickness of the sample. Because of the new procedure made possible by this arrangement, the calculations were somewhat simplified. Equation (?),above, could be re-½Titten as: ( 12) where m, and m2 are the slope of the rectified resonance curves obtained :respectively with and without the sample. The capacitance of the sample could be calculated by TABLE III Results with Fourth Arrangment The followings results were obtained from tests made on a single disc sample of victron, 0.995" dia. and 0.066" thick. lz m, k tan ~ 48.54 48.48 48.26 46.92 10. 55 10. 61 10. 35 10. 50 2.51 2.48 l.5V<l0_3 l.3? .Xl0_ l.41 .x10_33 1.3?~10 ktan -3 -3 3. ?8 xl0_3 3. 43xl 0 3. 53,<1 0-: 3. 43 Xl(J l i .] Fig. 20. Final Line Assembly. a - 46 - the well-known simple formula for the capacitance of a parallel plate condenser, neglecting edge effects. This was made possible by the use of a thin sample somewhat smaller in diameter than the electrodes. In addition, the tests made to check the value of the dielectric constant vrere found to confirm these calcul ations. 12. Discussion of Results. The tests made on the victron samples with the second arrangement indicated that the loss in the sai lple ·was only a small fraction ( about 7% for three 1/4" ring s) of the line conductor loss. Measurements of such small changes in total loss obviously could not be expected to yield results of sufficient precision. To overcome this disadvantag e, the smaller inner conductor of· the third arrangement was adopted and the loss in the sample was increased to about 27% of that in the line conductors, for three 1/4" victron rings. The fourth or final arrangement was actually not quite as satisfactory in this respect a s the third arrangement, although the relative loss in the san~le could have been increased from its observed value of about 20% by the use of a larger diameter or thinner sample. - 47 - However, several possible sources of error existed in the preliminary arrang ements which must have been eliminated, or greatly reduced, in the final arrangement. The first of these has already been mentioned. By ad- justing the sample condenser so that resonance occurred at the same line length, with or without the sample, the distribution of current in the line conductors should have been kept the sarne for each set of reading s. Thus any change in actual line conductor losses arising from the insertion of the sample should have been eliminated. In addition, the necessity of calculating the conductor loss from transmission line theory and a measurement without the sample no longer existed. One of the probable effects of the ring samples, as used in the first three arrangements, on the distribution of current in the line conductors is suggested by a comparison of the results obtained with the different arrang ements. It will be noticed that these results gave a lower value for the apparent loss factor of the material in each successive arrangement.· This may be explained, at least qualitatively, on the hypothesis that the higher apparent loss in the first - 48 - arrangements was partially due to increased line conductor losses with the sample in place. Such an in- crease could have resulted from a re-distribution of current over the surfaces of the conductors, caused by incomplete contact between conductors and sample. It was found to be an exceedingly difficult task to machine the samples accurately enough to ensure a tight fit with both conductors. Consequently there is no doubt that some re-distribution of conductor currents must have taken place. Some confirmation of this hypothesis is provided by the lower apparent loss factor obtained in the tests made on the third arrang ement. There, the greater spacing between the line conductors reduced the effect of errors in centering the inner conductor. Also the use of a removable center section ma de it possible to fit th_e solid ring samples much more accurately. Both these changes should have reduced toe effect of the s ample on the distribution of current around the surface of the line conductors. In the final arra ng ement, this effect must have been still further reduced. In that case, the insertion - 49 - of the sample could only affect the distribution of current, and consequently the loss, in the faces of the electrodes. For.this reason, and for the reasons already discussed, the values obtained with the final arrangement are considered to be the most nearly correct values so far obtained by this method. The deviation of individual results from the mean was still rather high, however. Undoubtedly, the use of a movable thermocouple pick-up loop and the consequent necessity for a long slot in the outer conductor were partially responsible for these discrepancies. The cutting of the slot reduced the rigidity of the outer tube to such an extent that the clamping pieces, visible in the photographs of the line, were required to bring the outer conductor back to its correct diameter. These could not be placed sufficiently close to the movable shorting piece to prevent small variations in outer conductor diameter over the range of motion of the shorting piece, even for a single set of readings. Furthermore, the thermocouple and galvanometer arrangement was somewhat unse.tisfactory. Very slight - 50 - changes in room temperature caused rather considerable changes in calibration factor and zero reading. It would therefore be desirable to adopt some more stable form of current or voltage indicator. 13. Suggestions for Future Apparatus. The desirability of the following changes in the design of the equipment was suggested by the experience outlined above. 1. The radii of the line conductors should be increased by, say, a factor of two. This would reduce the line losses by the same factor, while maintaining the same characteristic impedance. Thus the sensitivity of the arrangement would be increased, while maintaining the same resonant line length. The mechanical rigidity of the line would also be improved, and an increase in the length of the contact flanges on the shorting pieces would be made practicable. The ratio of line spacing to line length would still be small enough to prevent serious effects of second and higher order modes of propogation. 2. The lower plate of the sample condenser should be supported on more rigid insulation than the present - 51 - victron. Probably some low-loss ceramic insulation could be used to advantage. In addition, the contact surfaces of the electrodes should be ground plane and parallel, and the samples should be ground to fit accurately between them. 3. The possibilities of a peak voltmeter, using a tube of the "acorn" type1 to replace the thermocouple and galvanometer, should be investigated. Such a voltmeter could be arranged in a small shielded box at the same point on the line as the sample condenser, and could be coupled to the inner line conductor, or lower condenser plate, by a small capacitance. All the high- frequency portions of an arrangement of this kind could be mechanically rigid, thus avoiding the mechanical difficulties encountered with the use of a movable pick-up loop. Furthermore, the calibration and zero- reading of this type of voltmeter should be quite constant. Of course, the line equations would have to be re-written in terms of the voltage at the quarterwave point. 14. Conclusion. The results presented above indicate that the transmission line method under consideration could be - 52 - used for measurements on materials having power factors as low as 2 x 10-4 • The final arrangement, modified according to the suggestions in the preceding section would certainly fulfill all the conditions set up in Section 2a, with the possible exception of conditions 6 and 7. However, the use of disc samples has long been established as standard practise in measurements of this kind. Consequently, the influence of edge- s effects has been investigated rather thoroughly. The only other condition which might not be met completely by this method is that concerned with the determination of the magnitude of the field in the sample. With the thermocouple and galvanometer as a current indicator, an approximate determination of this field strength might be made by calibrating the pick-up arrangement at broadcast frequencies. Then only a simple calculation would be required to convert the galvanometer readings into the corresponding values for the voltage at the sample. However, if a peak voltmeter were substituted for the thermocouple and galvanometer, the voltage at the sample would be See, for example, Hartshorn, L. and Ward, W. H., "The Measurement of the Permittivity and Power Factor of Dielectrics at Frequencies from 10 4 to 108 Cycles per Second". J.I.E.E • .?g , p.597, Nov. '36. So - 53 - given directly_ by the meter readings. Experience with such voltmeters has shown that their calibration is sufficiently accurate even at frequencies of 2xl08 cycles per second. 15. Acknowledgments. A vecy grateful acknowledgment is due to all the members of the Staff in the Department of Electrical Engineering, for their encouragement and assistance during the progress of this work. In addition, much of the experimental work was done by G. Grimm, Bo Tu'.L . Oliver and L. W. Baldwin, who were associated successively with this research while carrying on their graduate studies. Mr. J. Millen, of the National Company, Malden, Mass., also assisted by supplying samples of victron for test. Appendix A. p.l. Appendix A. Method Proposed by A. V. Haeff. The essentials of the proposed method will be evident from the schematic diagram of fig. A.l. A modulated oscillator of constant frequency and percentage modulation, but of variable output, was to be arranged to supply energy to the antenna A 1 , a portion of the resulting radiation being picked up by antenna A~ and applied to a tuned line resonant circuit L,. At the voltage maximum on this line, there was to be conne cted another tuned line Lz, together with a superregenerative detector and audio amplifier, the latter provided with an audio frequency output meter M,. This meter was to be used only to ensure that the maximum voltage on the line L 1 should remain con:tant during each set of readings. The actual determination of dielectric loss was to depend on the readings of the thermocouple meter Ma in the auxiliary antenna A 3 , together with the calculated value of the loss in a "standard" transmission line. The standard line was first to be connected in the position indicated by Le and readings taken of the meters M , and Mz- Then the standard line was to be replaced by Appendix A. p .2 a line containing the sample of insulation, and the reading of M1 returned to its previous value by increasing the transmitter output. The ratio of the loss in the line containing the sample and that in the standard line would then have been given by the two readings of the meter M2 . Knowing the calculated value of the loss in the standard line, the total loss in the line containing the sample could then have been found by use of the observed power ratio. It would only remain to calcu- late the residual loss in the line containing the sample and thus to determine the loss in the s ample itself. Avo10 AMPL/r!ER AMPI.ITIIOE SuPER-REG. Co1YTHO£ I Moovl.ATOR - O.sc11.1.A ro.ll RECEIYE~ -- SCHEMATIC _ /JIAGRAM TO ILL U..5TRA TE MET/-100 /'ROPtJ:!cO BY A. V. flA£FF FIG. A.1. App endix B. p.l App endix B. Mathematical Analysis of Tuned Transmission Line and Effect of Sample. Part I - Input Impedance of Half- V\iave Line. a. Without a Sample. 4 ~ --------------------/ ~ The g eneral equations for a four-terminal network may be written Es - A ER..+B IR Is =- C ER +D Ift. ( 1) In the case of a transmission line, the constants A, B, C and D may be expressed in terms of the transmission line constants as follows: A ... cosh 0 ( 2) C= 1 sinh 0 Zo D = cosh 0 App. B. p. 2 where B= ~l' the electrical angle of the line I= a. + j(3, the propogation constant <X is the attenuation constant fd is the phase constant l is the physical length of the line z 0 is the characteristic impedance . When the line is short-circuited at the receiving end, E~ becomes zero and equations (1) become Es = B IR. I 5 = D IR Consequently, the sending end impedance is Es _ B _ Z 0 tanh 0 I 3 ( 3) D - On substitution from the above definitions this becomes Z5 = Z0 tanh(cx. + jf3) 1 = Z 0 sinh (cd + j /31) cosh (txl-j(3l ) cosh (al 1-jf3l) • cos h (Cl Z - j (31 ) =z -= 0 sinh ( 2a.l) cosh ( 2ctl} -1~ z sinh 2al 0 cosh 2tX.l sinh 2 l) cosh ~ j2(37 j sin 2,l.3Z cos 2pll -I- Now, in the line under consideration here,~ is -s- very small, being of order 10 . AlsoI 3 order 102., hence al is of- order 10Typical values are _, a=1.2x10 l = 145 cm 3 al = 1. 74 ,1( 10- . I is of ( 4) App. B. p.3 Hence sinh2<U may be set equal to 20!.l with an error of less than one in 100,000. Similarly cosh 2«l =1 within one in 10000. Making these 6 approximations and simplifying; Zs ::: Zo ( al cos'(.1Z -r jtan 131) (5) Now let R~ = Zoal cos 2 Xe -= \ Z5 /3l Z 0 tan j3l I =fR; -t- X~ ( 6) Near resonance, l= A+tJ, and, since at high 2 frequencies /3= 27Twith negligible error, ~may be >- written Xe =- -Z 0 tan 211" llZ ~ ( 7) where A is the wave-length and ~lis the difference between the actual line length and one half wavelength. If Al is sufficiently small: ( 8) In other words, Xeis directly proportional to l:!l. As the length of the line is va ried a round the resonant length, there is evidently a small variation in R~. To determine the magnitude of such v ariation, the expression for R@ may be differentiated with respect to /. App. B. p. 4. dRe dL = Z 9 (J. cos 2 /32 ~ Zo al + 2Z 0 ct lpsin(3l co's o/3z' ( 9) rrf1 213 tanj3llJ -1- cos 2 j3l therefore at resonance, where tanj9Z = 0 Consequently, if the total line length l is approximately 145 cm and if LJl=±. 3cm., the percentag e change in ~throughout the rang e of variation of cannot be greater than 0.2%. Within these limits, Re can evidently be regarded as a constant. The input impedance of the line, near resonance, can therefore be regarded as a simple series combination of a practically constant resistance and a reactance which is directly proportional to d, the difference between the actual length of the line and a half wave-length. If the sending end voltage is held constant, the sending end current will therefore vary according to the familiar resonance curve as J/is taken from its negative to its positive maximum. The interpretation of this resonance curve in terms of the line losses is discussed in Appendix C. b. With a Sample. It will be assumed that the sample is inserted in App. B. p.5 such a way that it may be represented as a lumped capacitance and pa·r allel resistance connected across the line one-quarter wave-length from the sending end. Then the complete resonant system may be con- sidered as two lines connected as shown in fig. B.2.. ~_ - _______z_~-_Il_:--_2_~----ol -----2,---- Tne first line is of length I,= A, while the second 4 is of variable length receiving end. la and is shorted at its The two lines are connected through the network representing the impedance of the sample. The impedance Za, looking into the second line, will be z2 = Zot anh Ba ( 10 .) Looking into the sending-end terminals of the network representing the sample, the i mpedance Z3 will be given by l_,.jCw+l R Za = Z2 + R + j Cw Z2 R RZ 2 App. B. p. 6 or R RZg (11) R +l+jCt.c>R Z2 To find the sending end impedance of the complete circuit, it will be necessary to consider the input impedance of a Quarter-wave transmission line terminated by the impedance z3 • This can best be found by con- sidering the general eQuations for a transmission line, as follows: or =- A, Z 3 +B, C, Z3 -t-D, = Z 3 cosh 0, + Z9 sinh 8, Z 3 sinh + cosh e, e, (12) Zo In this particular case, 0, = (a -t- j~) ~ or 4 e = al, + j..:!!._. 2 ConseQuently the following simpli- 1 fications may be introduced: cosh e, = cosh ( al, + j 7T) = cosh a.1, cos Tr+ j sinhd. l, sinll 2 2 _ jsinhlX-1, : sinh 0, ::: sinh (al,+ j-1!:._) = sinh 2 jtxl, -.z, cos.1I_ +j coshctL, sinlf 2 =- j cosh G(.1, 2 .. 2 j App. B. p.7 Therefore (13) (14) In order to justify this last approximation it will be necessary to estimate the relative magnitudes of z 0 al, and Z3 . The former is approximately, for the line under consideration, -~ 63.5Xl.2xl0 x73 = 5.6Xl0-a ohms. In the case of the same line, at resonance, R + 1 t- jCt.i)R H. Z 0 tanh8~ - R - 1 + R coth 82 + j C@R Zo = l+ R al2 (15) sinr(3la Now ale will always be much less than unity, sin >;8(2 . hence at resonance Z3 may be considered simply eQual to App. B. p. 8. R. Depending on the particular sample under test, R will lie between 1000 and 20000 ohms. ConseQuently the error introduced into the denominator of expression (13) for Z 1 by neglect of Z 0 {){l, could never amount to more than say, one part in 10,000. Hence it is sufficiently accurate to write Zs = Z 0 Ci..~ -t- z; Z3 = Z 0 al, -;- z! {R + 1 -;- j ~RJ R • zo[al, +- Z2 ~1 + Z o +j(zocw-cot(JlJl 'J sin ;3Ze R Here the line losses are represented by the terms a.( ale , both of which will remain practically constant as 4 is varied over the range necessary to and sin )1Za obtain a satisfactory resonance curve. The manner in which the reactance term in this input impedance will vary as the line length is varied near the resonance length may be found by considering the Taylor's series for cotfJ4 of !9~. a bout various values This series may be written cot/(4. +LJl;) = cot,;94 - ft A4 -t- (fltll) 2 cot/1~ sin a13zi! r -.? sinj(Ile App. B . p. 9 ( 17) The coefficients~, aaand a3 , together with the actual magnitude of the corresponding terms of the series for ~~ = 0.4 cm are given in Table B.I. In the case of the final transmission line, the values of ~4 necessary to obtain a satisfactory resonance curve were much less than this, usually being less than ±0.2 cm. Thus the values given in the t a ble are definitely pessimistic. However, it will be observed tha t the deviation from a linear relationship between reactance and ,1fe is still negligibly small for a value of ,.1/2 as great as O. 4cm, and even for relatively small va lues of /3~· OonseQuently a sufficiently accurate exp ression for the reactance part of Z5 is (18) , .App . B. p • 10 Table B. I. (Values in the last three columns are for .84; 0. 4 cm. ) g a, (p'A4) aa ( /J Lllz)~ a 3 ( ,BLl4) a, ;.?la. aa a3 -3 ..1£ 2 1 0 .333 8.8 X 10 I 1.34 .666 .889 -S" -~ 11.7 xlO 5 .1 ..>< 10 .E 4- 2.0 1.414 2.66 17. 5 X 10 ..7f 4.0 3 .46 13.34 3 ,; -3 2. 2 X 10-l 0 -5 6.0.xl0-7 10.3xl0 17 .8 X 10-7 -3 -s89 X 10-? 35.0 xlO 26 . 6 xlO p.11 Appendix B Part II Sending End-Receiving End Transfer Impedance of a Halt-·wave Line, With a Sample Because of the difficulty of avoiding direct coupling between feeding circuit and thermocouple loop, it was found to be necessary to place the thermo✓ couple loop at the receiving end of the line. Thus it became necessary to determine the relation between sending end voltage and receiving end current. The following analysis was therefore made for the transfer impedance Z7 16 Es, ( 19) I The numerical suficripts refer to the two transmission lines of fig. B.2. For this arrangement, And, since t -he receiving end of line 2 is shortcircuited, E~z = 0 and Es~= B2 I~ I.s~ =- Ik I"a ( 20) App. B. p.12 Making use of the A, B, C, D line constants, Es, = A, E...e-, + B, IR, = A, B2 I,efB, { Isa+ Esa ( ~ + j cw)} =-fA,B2 + B, Dz.+ B, Ba ( ~ -,..jCw )} I~~ (21) Hence Now since line 1 is one-quarter wave-length long, A, = cosh 0, .' j ct.l, Therefore Z T = j a Z, Z sinh4 +- jZ cosh~ -t- j~ sinh4-z! C<cJ sinh Ba ~ 0 0 ( 22; ~ =a4rj fSla And, since sinh <9.a = sinh «4 cosh j;6'~ r cosh a~ sinh jfSla =# alz. cos(Jl2 + jsin p'/2 cosh ~ = cosh ot..l2 cosh j /3?_-1- sinh ct Z2 sinh j ;SZ2 : cos~li? + j a l 2 sin,,.S4 Substituting these approximations, z 7 1, = - ·z 0 ct sinp'4 -1- j z; Cw a '2cos,l-9/z - ~! sin1322 - z. tx~ sin.,/-"~ {(z a.t?llz + ~; a~ r z )cos;67l.? - z~ C wsinj3l.?} 0 0 : j(ef l, rl,(z.c,,,cot,62 t-1} +- ~f fotft?-z.c,jz.. s1~/3~~ 2 In the latter expression, the terms Z 0 tXc/,i; and Z~ al c R have been neglected in comparison to Z0 • This App. B. p .13 approximation may be justified by considering a typical case for the transmission line actually used. In that case, a =- 1. 2 x 10- 'S l:: ?2 cm. = ?O cm. z.=- 63.5 ohms. R = 1000 ohms l2. alt/,?.= ?.25.x 10-7 and Zo ak Then ~ 5.35,ic 10-5' R both of which are to be compared with unity. Con- sequently the above approximation is exceedingly good. In order to put this expression in a more convenient form for calculation, it will be desirable to write Zr= R 7 t-/XT where R 7 :: f~[l, + le(Z Cf4)cot_,4~ -I- l'ij + 0 ~oJ Z0 sin/3la and ( 24) The negative sign in front of the real part of expression (23) is disregarded since it merely implies a reversal in phase, with which this analysis is not concerned. The reactance component Xr may be expanded about its zero value as follows: 3 -z 0 f {flAl,.) t - ~ -t- VJ LJY,}s-+ .... .j(sin;Slz + Z0 C~cos /322,) I' "· s. For this value of le., Z Cwis equal to cot fSle and X7 =: 0 substituting this value in (25), ( 25) App. B. p.14 J((J~l )-1- ~}3 + (s~Zz)or,.,, ·} Xr =- -z~ Slllf9l.~ / l ~ ..3. (26) S/ 2 Since ,t'JA/e has a maximum value less than 10- , the second and succeeding terms in the series are quite negligible in comparison with the first. Con- sequently the value of X7 is given to a sufficiently accurate degree of approximation by = - Zo A'Alz XT (27) sin f3lz. Similarly RT may be expressed approximately by /a I1, j 'ju. + ii} t- '4f/ z./s1n13z. + ygLI/,, ) co sf' /).Z.t-. . == Z0sinl3l~ (1 +(JLJlz cotf3le )(a[z, r Zz(cot1/Jli! + 1!J f- ~ 1/ ( 28) . RT - t- 4{cot From this expression, the variation in Rr as a resonance Typical values of ,13A4 aJfjSl, curve is taken may be estimated. -e assuming that jSLJl2 :. 10 and for various values of f3la are given in table B.II. Table B.II. 4Alacot,t9l2 - f3lz cotj3Za JI. a 0 0 0 ..,J£ .577 6 xl0- 3 1.2 1 ;,( 10- 2 2 J£ 1.0 L 1.732 4 G Rrazax -2 1. 7 .x 10 RT R 7:a?ia. X /tJtJ/4 3.4 App. B. p.15 The values given in the table are quite pessimistic since, for the final line, j.9A~had a maximum value of less than one-half that assumed here. Consequently it was permissible to consider Rr as a constant for each resonance curve. The equivalent circuit of the arrange- ment therefore reduced to a simple series circuit includi ng the constant resistance Rr and the reactance Xr. Appendix C. p. 1. Appendix C. Rectification of Resonance Curves The magnitude of the current flowing in a simple series resonant circuit may be written I = E In terms of the current Ir, the resonance current, this becomes Thus, if a thermocouple galvanometer is used to measure the current, its readings will be given by fl - Ra Br rf+x2 or _fl = cose/ Br where{!) is the power-factor angle of the cir:fuit corresponding to the galvanometer deflection 6? sequently the value of Con- /J may be determined directly from the ratio of the corresponding galvanometer deflection to the maximum deflection. Then it becomes possible to obtain the value of tanj) ,which may be expressed as tanf = X R App. C. p. 2. Evidently, if the resistance in the circuit is constant, there will be a linear relation between tanf!' and the react4nce. The slope of the curve tan/J vs. X will g ive the resistance of the circuit, while deviations from the expected linear relationship will be extremely easy to detect. Also the value of resistance so ob- tained will depend on a large number of readings which obey a rather simple law. This is very much more satisfactory than the usual method of plotting a resonance curve and using three points (the maximum and the two 0.707 maximum points) to determine the effective resistance of the circuit. In the case of the tuned transmission line it has been shown (see app. B) tha t the equivalent react ance may be taken as directly proportional to the devi ation of line length from its resonant value. Also the equivalent resistance was shown·to be practically constant over the range covered by the usual resonance curve. Consequently the above method is applicable to the case of the transmission lines used in this work. Actually, the calculations were made in the f ol lowing manner: Since 8/6',. -= cosa/, B,./tl = seccj!J d/?4 App. C. p. 3. tl,./IJ-1 = tan 2 ¢, the value of tan/) was found by evaluating i l),.IB-1' Then this value of tanj?} was plotted against the line length and Rr was found by measuring the slope, m, of the resultant straight line and substitutihg in an equation of the form where K is the factor relating the reactance X to the corresponding deviation t14 of the line length from its resonant value. For example, for the arrangement treated in Appendix B, Par t II, K = 2;,/3 sinJSle as given by equation (27) of that appendix. Appendix D. p.l Appendix D. Best Ratio of Inner and Outer Conductor Radii. As given in equation (28) Appendix B, the value of the equivalent resistance of the line, with the sample in place, is R7 = Z O sin,,Bl2 ( 1 +-/Ji:Jl,, cot /JI,, l{a.[l, r l.,( cot j1l2 + i]+ ~ •} where R is the resistance of the sample. Thus, i.n order that the sample should have a maximum effect on the equivalent resistance of the line, the quantity Zo d- should be a maximum. In terms of the constants of the line, where R1 is the loop resistance of the line in ohms per cm., bis the outer conductor radius and a is the inner conductor radius. If bis fixed, Zo may be maximized (t. with respect to a, as follows: let b = x -a log x { 2 ~ l og x/ :i+ l X X +if which is zero when x log x - 2(x+l)-=- 0 Solving this equation with the help of Newton's method, there results, App. D. p. 2. b = . 9 2 for a maximum value of Zo. a ~ 0 This is the same result as that previously obtained 6 by Terman as the condition for the maximum sending- end impedance of a coaxial line. In addition, he has b a plotted the quantity {10g as a function of b. The a) b a +l a resultant curve shows a rather broad maximum, having a value of about 0.88 at b : 5, as compared with a value a of 1. 00 at b =- 9 . 2. Thus an increa se, from the optimum a value, in the relative size of the inner conductor is not accompanied by a very rapid decrease in the value of z •. A larger inner conductor, desirable for Ci. mechanical reasons, may therefore be used without an app reciable loss in the sensitivity of the line arrangement. 6. F.E. Terman. Resonant Lines in Radio Circuits, Elect. Eng. 53 , p. 1046, July '34. App endi x E. p. l Appendix E. Effect of Frequency Drift. The effect of a drift in frequency during the time required to obtain a complete resonance curve may be obtained by .considering the effect on line reactance caused by such a drift. The effect on the equivalent resistance will be too small to have any serious effect. The e quiva lent reactance of the line, with a sample in place, is given by equation (27) App . B. It is X, = cosp'(lz -r Llla) - Z C4}sinj1(l2. + Ll4_ ) 0 Now if the frequency ( or wave-length) and ~ both vary in a linear fashion with time, then Ala =- k, t and A : - ),. +ka t or A= Ao+ ka Lll :: ,\,+ k Ala 0 k, where t i s the time measured from the instant of resonance and A is the wave-length at resonance. Hence 0 X T ,.. App. E. p. 2 Approximately, this becomes an error in the value of X1 will Since RT= produce a proportional error in RT. Consequently the quantity l-k l1, must be equal t o unity within the required >-a If ~ is, say, Ao then in order that 8 the error in RT be less than 1.0%, k must have a value limits of error. less than 0.08. In a typical case, the corresp onding change in wave-length during the taking of a res onance curve would be 2k.Llle -= 2 X .08 X .2 == . 032 cm. = O. 32mm. It is believed that deviations of frequency of this order of magnitude did not exist in the wave-length of the final oscillator (which was equipped with a regulated plate supply) at least after the expiration of the warm-up period. In addition, it should be noticed that only a linear variation of wave-length with line length would give an undetectable error of App. E. p. 3 the kind treated here. For any other kind of variation, curvature would be introduced into the rectified resonance curve, which could be immediately detected and the cause eliminated. Appendix F . p . 1. Appendix F. Effect of Changes in Ocsillator Fre quency Due to Changes in Line Tuning. Sinc e this method of measuring resistance depends on calculated changes of reactance, it is essential that means be available for checking the constancy of the oscill a tor frequency. It has already been shown that a steady drift in oscillator frequency cannot be detected by an inspection of any one of the rectified resonance curves. On the other hand, it will now be shown that changes in frequency produced by changes in line tuning can only cause easily detectable changes in the shap e of the curves. If such changes become apparent, it is then only necess a ry to reduce the coupling of the feeding circuit to the line until the proper rectified resonance curves are obtained. As the line is tuned over the rang e necessary to obt a in a resonance curve, the transferred reactan ce and resist ance in the feeding circuit will vary through a certain rang e of values. This va ri ation is given by the following equations = - M,:alx , --=-'----'- Re,+ ~x a I App. F. p. 2. M"12. R, x, are the resistance and reactance transferred from the tuned line to the feeding circuit. is the mutual inductance between the two circuits. is the angular velocity corresponding to the applied frequency. is the sending end resistance of the tuned . line. is the sending end reactance of the tuned line. Since the (;of the feeding circuit is very much smaller than that of the tuned line, the resistance reflected back into the feeding circuit from the line must be very small compared with the actual feeding circuit resistance and will produce only a negligible effect. On the other hand, since the reactance of the feeding circuit is normally adjusted to zero, the possible effects of the transferred reactance must be investigated. To do this, it will be convenient to rewrite the above expression for the transferred reactance in the following form: = - App. F. p.3 where,;6 is the power factor angle of the sending-end impedance of the line. Since tanl is the only variable in this expression, the manner in which the transferred reactance varies with the line tuning can be expressed as a simple function of tan/. plotted as fig. F.l. This function has been The significant portion of the curve, at least for this work, is that lying between tan¢=t-2.5 and tan/= -2.5, since most of the readings taken lie in this range. Next, it becomes necessary to consider the effect of reflection of reactance from the feeding circuit into the plate tank circuit. Since the coupling between these two circuits is also a mutual inductance, the same relations will hold as for the case already considered. However, because of the small coupling between line and feeding circuit, the total variation in feeding circuit reactance will be very small. In fact, the coupling was purposely made so small that a thermocouple galvanometer, coupled to the feeding circuit, showed no detectable change in reading as the line was tuned through resonance. It follows that the power factor angle of the feeding circuit impedance I I. I I II I ' I I . i 1-- t • ! .: j . . .-~ -, . r :: ~ _:j .J . . ~ ;) . . . :) ~ • i I ..' (l )s: :•. ) • . ~ i,.: ; \p ::i . (:i, I, . t .. 1, Ii : II, ! ·- \ ·,· I . II ! ! .! 1- I . I i : ; ' \ \ ! ! - i 1•• • - i ! I l • i l--t--l--.+,l-+----,-11--+----+-:--+--t--t---!-,l--t---,·-- i I I I l I 1 - -,----~I-·• r--:--rl - - - - -i--i· -I ; ____ .J......._ _ _ ..._1_+---+i-~--+--+----r- I -r-:- I · I .. : : ~-i' I. I 1 -~J_I __ ,_ --!--+--;.. i -+----t--:-r-r.1I:---11 .. n11 f. .•.-J. " r 1-<INll:.U IN U.S. A E-342 14 30) - L App. E' . p. 4 varies only very slightly and the reactance transferred back into the ~late circuit may be taken as diredtly proportional to the reactance transferred into the feeding circuit. It should be noted, however, that there is' a change in the sign of the reactance at each transfer. Thus the additional reactance appearing in the oscillator tank circuit inductance will be of the same sign as that of the line reactance. Also, as noted above, it will vary with the reactance of the line according to the curve of fig. F. 1. The resultant increase or decrease of the equivalent inductance of the plate tank coil will evidently tend to produce a change in oscillator frequency. An attempt was made to minimize such variations by the use of a high-Q grid circuit, loosely coupled to the oscillator grids. Because of this precaution, and bedause the transferred reactance was kept small by the use of very loose coupling, the changes in frequency should be extremely small and may be assumed to be inversely proportional to the transferred reactance appearing in the plate tank coil. The same curve, fig. F. 1, may therefore be used to show roughly the App. F. p.5. drift in wave-length as the line length is altered. From the results obtained in appendix E, the effect on the shape of the rectified resonance curve may then be deduced. At the points tan~=±l, the slope of the latter curve should be equal to the correct value, since the rate of drift in the wave-length is zero. However, as the line length is increased near resonance, the wavelength will be decreasing at a nearly constant rate • .Again referring to Appendix E, this means that the indicated values of reactance will be changing more rapidly than the values calculated from equation 27, appendix B. The slope of the rectified resonance curve at the origin will therefore be greater than its correct value. As a check on this conclusion, the condition when tan p= rl may be considered. Then the reactance trans- ferred hack into the plate tank coil will be a maximum and the wave-length will be higher than when the line is at resonance. Thus the line length to give tanj?*r/ will be slightly greater than the desired value. For very large positive or negative values of App . F. p . 6 . tan ~ , the experimental curve will be asymptotic to the straight line. The actual curve, as affected by reaction on the oscillator frequency, should therefore have the shape indicated in fig. F.2. Any curvature of this kind would be easily detected on the experimental curves. However, on a simple resonance curve this cause of error would be difficult to detect and would be likely to lead to an unduly low value for the equivalent resistance of the line. This would be particularly true if the customary 0.707 I r points were used for a calculation of the equivalent resistance. .. I - •• 1 ,,,. . ... ·, .. 1 · · : r-:-:..~-.:... •'t:-:-·---t--:-t-:-+~F+~+-:. :.·. . :·-+:----i..:..........·.:-i1. :.~:. :;.t· . h ~_j.;..:.:..:..t..:..:.:.....!._:._:_:_~;: ,,. ! • _·] 1·•- :_:_:_...;_;_·_ ·.:_ ~:.:,;L:1>:. ,•. -:~ i;~ [:~; t: !L •• ~i ~::: L~ -~~ _ __ I.: r; ;j -~ ,. . :I ... i 1 •. 1- .. ·-1--:-· .-,- --•·-·• ·-t--:-· 1 • 'I - ...... ' - •- ..._ -• 1' I ' - • -- - ! ._,_ . • . '. .:....i l • • ---L . , :_- - J_ : ~:= .=-·_t~_: •➔ !=~ .. ~=- ,__:._I--!.._:::--=: .-_ .,.J_ r.:.:l. 1-- f-,.j ___ ;___ - .. , :. -i- --- r:_ ., . ..:L : ~ ~i- __: • : . ,. I '1' " . . \.. • - I ·-+---+--+l -+--~+--1----- .__ · - ~---1----,f----,f---l----l l I · I j'~i---•➔-~+--+-,1--l--+l-+---+---l--•e----+--l I I t--t---t-+-':_.+- £-342 (4.30) T_ _ - •·--··-- I - ----+-..........+-.+---1-.....:._j--+---l--_:__i...--11 . _j ' .PHINlt.~> IN U . 5. A. Ap pe ndix G. p .l Appendix G. Effect of Direct Coupling Between Feeding and Measuring Circuits. In order to make use of the relations derived in the preceding appendices, it is essential that it be possible to measure the relative magnitude of the current flowing in the tuned line while a constant voltage is applied at the sending end. Obviously, this me a surement will not be possible if there exists app reci aJ) le direct coupling between the feeding circuit (o r the oscilla tor itself) and the mea suring device. Similar difficulties may arise in the case of measurements made on any resonant circuit, whet her or not it be a tuned transmission line. Consequently the following analysis will be applicable to any similar resonant circuit me a surements. It is fairly well-known that direct coupling of the kind under consideration usually results in asymmetry of the resulting resonance curve. Consequently it is easy to detect the existence of such coupling , but the errors which may result therefrom require some consideration. It is the purpose of the following analysis to demonstrate the reason for the a syrnmetry found experimentally and to indicate the nature of the App. G. p. 2. resulting errors. The arrangement to be considered consists of three circuits, each pair being coupled by a corresponding mutual inductance. The equations will first be written in the following general form, subscript 1 applying to the resonant circuit, subscript 2 to the feeding circuit and subscript 3 to the measuring circuit: ( 1) ( 2) Eliminating I 2 , ( 3) This expression is rather formidable, particularly since z1 is a complex quantity, but it may be simplified by neglecting the second term in the denominator. The effect of this term on the resonant circuit current is discussed in appendix H. To justify this assumption, it should be noted that ~ 3 is large compared to M, 8 ~ (see App. H) and that M1a is purposely made very large compared to M23 • Physically, the neglect of this term implies that the voltag e induced in circuit 1 by the App. G. p.3 current in circuit 3 is negligible compared with the voltage induced by the current in circuit 2. In the present case, circuit 1 is the tuned line or other resonant circuit, circuit 2 is the feeding circuit, and circuit 3 is the thermocouple pick-up circuit or measuring circuit. Thus it has been assumed that the reaction of the thermocouple current on the current in the resonant circuit is negligible. Such an assumption has been amply justified by the experience of many workers. Written in the simplified fo,;rm, equation ( 3) becomes, I _3 I, = ( 4) Since M,3<.u is a constant, the ratio between the Z3 resonant circuit current I, and the measuring current is 1-j (R, + j X ,) M a3 ( 5) M,2 Squaring both sides, and simplifying, ~l 1 -t-( l,~R,,a,1 k ;a3 2 + X, R, JJl ( 6) App. G. p.4 In order to demonstrate the effect of this variable ratio between I 3 and I,, mutually consistent values were dSSVmecl foundAfor ka and k 3 • Then the value of the ratio was determined for various values of tan¢ and the resulting ratios applied to an ordinary resonance curve. The ideal resonance curve, together with the curve which would have been observed if ka and k~ were to have the assigned values, is plotted in fig. G.l. It will be noticed that, even though the maximum value of the observed curve is only slightly greater than that of the actual curve, the shape is considerably different. A definite asymmetry has been introduced. This asymmetry arises from the fact that the current induced in the measuring circuit by direct coupling is not in phase with the current in the feeding ' circuit. Perhaps the reactance of the measuring circuit might be neutralized by series resonance, thus putting its current in phase with the voltage induced in it by the feeding circuit. Then the current in the resonant circuit and in the measuring circuit would be in phase when the resonant circuit was set at resonance. However, the resonance curve, while symmmetrical, would still not be of the correct shape, since the current in the measuring circuit would consist of two components, one ·l· •• .: .1: :. -+--·~1--+-·-··+1_:_: ~-- : • :! •• ➔: r.:-.-:-:.i-~1-'---+-·:_.-1!f--,. :. ,..:..:~~-.:.....:i..:..:.w;:...:.:.:...:!:.i:..:..:: :. :+---:-:-i : r-;-'--1;_'.+-!_:.;__: -:..:..;:......j:: .....:..:... ..... ......:....:...:. •• , ·:. .... .... •• ·•·· ;:: . . 1:· ,,. .... . J:~ : ;:. :: i_: !::! f :~ ··1 .. , ::! •. : ' •• : • • • 1· -r,-:-t--;--t-~:-+-:-~~+~~.:..;-j,~-r ...:....j·.~--fl~~JJ _ . , ~.._.:..:_J_:..._ ,..: -~ +-·- ~ --.: '--..• , . . ' ;;: :·/: ;!:. j ... •.. · _:_ "';,,.; ., .. i.~ ~: • 1 ·, - :I -• I _:• ______,___........_..,____, . I. '· • ' i . ,._- : ·1 l I I ' :i ~) :1 .. '-:: .. • t.:"' • r . -...."'. ... i:I .. ····1 i • • . I .. I l I ..·- : I ! l I i .. : i ·-. .,II I I .... -- --t----,,----+- - - - -+- 4. ·- -,~ - --- -··· -··- --- .. - ._ r\ -- - .. - I. ll,I II i i ., 1.. : 1 .I - \ ..__ i .I i------t---:'~t-:-:-t-1~+---ti -t--+-+--4!-+-+-+......:.....:+--1--+~+--l----+-I----L\ I t , • -~ 1 t-\-:-··- ; ! -\-1,-4--\-,-+i-.J-.--+-~-:J. : 1----J •. • : : . '--~- --+-j--+---r!_--·+-+-I_-+_---+--➔--!--+-.._J__J:-_:_+-_---1_-,'-._--+--L-~----l _ _.__I-~'\- ~ " . .I ~_l--:-:-t--ti-t--J---+-:-+1-:--+:-+.--+-il---:-:-+-+:-:-=+~~+..:..+-+...:.._+-+-+-'! -t-j_-i--1-_j.f--_.,..-l-_____jl---..L-lll I . . .. I ..• I. : ~:: •• • • ; T - - - -i--t-1-+--+---if---f:-+--+-+--+-~-+---+=----·.+.:,--+--d-+--+-',__ +-+--+---+-+ !.-:-. ·t E-342 (4.30) l ~,- .1. .:J • .. ! :l. T· • . r-- ,-, .( • --1---1---tl-··_-... , ' •• • • f-'HIN 1 !;..!..J IN _ . • ~- U. ·s. A - ! App. G. p.5 of constant phase and another whose phase would depend on the phase of the current in the resonant circuit. Of course, these components could not be separated by simple subtraction from the ordinates of the resonance curve. Some more complicated method for separating the two effects would have to be developed. The "observedt' curve shown in fig.G.l would yield a rectified resonance curve as shown in fig. G.2. The errors in measurement which would result from excessive direct coupling to the measuring circuit will be evident from these curves. The apparent resonance point is shifted from its actual position, a fact which may be important in measurements of wave-length by the use of lecher wires or measurements of dielectric constant by determining the point of resonance with and without the sample. Obviously, the use of such curves for the determination of resonant circuit losses might lead to a different value for every pair of points chosen. If, for instance, the width of the curve at the "halfcurrent sq_uared" points were to be used to calculate the losses, a value somewhat higher than the correct value would be obtained. If the width at some lower value of current were used, the value obtained for the losses would be still higher. -----, I' ' i! jl ' I' I' I! I' --- r .. I' ' ... 11; . '!-- ·, . ' 1· I : . : ',~ .. ' ' ' .• 1 .... , . ,. ..l :• I I I I I· , I • .. I I . J . ·,I ! ' .-r .. • 1- ..l ...' ! .. I 1... -j~ I I I l .. --~ -342 (4 30) -. l .... ' • t .. • ~ • ' Appendix H. p.l Effect of Impedance Transferred Into Tuned Line From Measuring Circuit. Denoting the resonant circuit (the tuned line) by the subscript 1 and the measuring circuit (thermocouple loop) by the subscript 3, the following equations may be written: I, Z,=-E, - jc,)M,:, I 3 ( 1) I 3 Z3=- jwM, 3 I, ( 2) Eliminating I, , I.,. = -jE,wM,a ., 1 Z o Z I ' wa vJ.' il /3 ..L ( 3) The factor - jE1wM,3 represents the multiplying factor Z3 necessary to convert the resonant circuit current into the thermocouple current. The remainder of the expression represents the actual resonant circuit impedance together with the resistance and reactance transferred into the resonant circuit from the measuring circuit. Evidently, the presence of the measuring circuit increases the measured resistance by the quantity a RI w2 Mir . Also the reactance is reduced by the R3 + X3 quantity X½td~Mf~ R3 -t-X3 . Consequently it becomes necessary App. H. p. 2 to estimate the approximate magnitudes of these two quantities. Because of the simplicity of the g eometrical arrangement, the approximate calculation of ~1/3 is not difficult. Fig. 1. shows the a ctual dimensions. The coupling between line and therrnocouple loop is obtained by the magnetic flux passing through the wire loop - the area shown lightly cross-hatched. This flux is given by: /2 r =l.143 dr = 0.741I, j = l.i~; 5 r ... 0.893 Hence the mutual inductance is: -9 M13 = o. ?41 x 10 and e _2. w M,a = 2. 36 J< 10 henri e s -, Now R is more than 1000 ohms, hence, even if X~is neglected, a a R\w M~ R3 + X 3 -4- 2. 36;<. 10 For the line under consideration, the resistance R is, approximately, 0.11 ohms. Consequently, the error in the measurement of R introduced by the reaction of the measuring loop is only 2. 36)(10-4 1.1 X /0 - I App. H. p. 3 Furthermore, this additional resistance is a constant quantity and will be eliminated in the subtraction of losses to determine those present in the sample. The reactance component is similarly very small and can only cause the resonance point to be shifted very slightly. To sum up, both components of transferred impedance will be very small and in any case will not affect the final result. Appendix J". p .1 Appendix J". Effect of Constant Separation between Thermocouple Loop and End of Line. Throughout the preceding analyses, it was assumed that the current affecting the measuring circuit was actually the current in the shorting piece at the end of the line. However, mechanical requirements made it necessary to mount the thermocouple loop a short distance from the actual end of the line. Furthermore, the thermocouple loop itself extended for about 1.5cm. along the length of the line. Consequently, it becomes necessary to consider the kind of relationship to be expected between the current in the thermocouple loop and that at the end of . the line. In order to determine this relationship, it will first be assumed that the flux at any point in the line, and near its end, will be directly proportional to the line current at that point. This current must obey the usual relations for a four-terminal network, which are: Ex..,. ~ ER.+B" IR. Ix. r C:,eE~+D.x:.IR. App. J. p. 2 where Ex and Ix.are the voltage and current at a distance X. from the shorted end of the line. Because of the shorted termination, E~ must be zero and thus Iz = Dx:.I,e In this expression, Dx. is a constant, dependent only on the electrical distance .X to the end of the line. Thus, no matter what the total length of the line, the current and flux at a given distance from the shorted end of the line will always be the same fraction of I~. Integrating Ix:. from one end of the thermocouple loop to the other will therefore yield a quantity directly proportional to IR. The only possibility for deviation from this simple relationship lies in the possibility of relative motion . between the thermocouple loop and the shorting piece. However, small accidental movements of this kind will produce only a small effect, since Dx.. = cos 2 1T X. >.. and in this case Xwas very small compared to A. In fact, the minimum value of Dx: would occur at the far end of the thermocouple loop, about 2 cm from the end of the line. For this value of X, Dx would still be approximately 0.9990. Consequently, the assumption App. J. p . 3 that the thermocouple loop current would be directly proportional to the line receiving end current is amply justified. Appendix K. p. - 1 Appendix K Description of Plate Supply Voltage Regulator. The operation of this device was very similar to that of various commercial plate power supply regulators. However, the voltage reference was obtained from a 90 volt ncn battery, rather than from the more customary glow tube. Furthermore, the required voltage output was higher than that usually handled by tubes of the type usedo Both of these departures from the usual design were made possible by the particular use for which the regulator was built. It was believed that practically constant supervision would prevent operation with a run-down battery, while the relatively fixed output voltage and current requirements would allow the various tubes to operate within a safe range of currents and voltages. The method of operation will be evident from the circuit diag ram, fig. ko lo If the output voltage tends to rise, the grid of the 57 type control tube will become more positive, and permit more current to flow in the 2 megohm pl ate resistor. The grids of the 2A3's will consequently be driven to a more negative / 8 5 0 + - - - -... ~ii. ;trqns. .St:>COl'l<YO'"'f ;:;Jli,,-,--....,--- f- 7.SO OUTPUT /IV.PUT IIE/ITE~ 0/r" J7 IVOT SHOWA/ FIG. K.1. SIMPLIFIED SCHEMATIC OF J/tJLTAGE /i'EGULATCJR (PROTECT/Ve CIRCVITS NOT SHOWN) App. K. p. 2 potential, wit~ respect to the anodes, and the total voltage across these series tubes will increase. Because of the high available amplification obtained from the grid of the 57 to the grids of the 2A3's, only a small change in the output voltage will be required to produce a large change in the voltage drop through the 2A3's. Large changes in input voltage or output current will therefore produce very small changes in output voltage. In addition, a very great reduct-ion in the ripple component of the output volt ag e was obtainedo This resulted from the use of the 1 mfd. condenser from the high-volta ge terminal to the potentiometer arn1. The entire ripple voltage was applied in this way to the grid of the control tube and thereby almost completely eliminated. A ripple voltage of about 3.5 volts peak on the 900 volt output of the rectifier and filter was reduced in this way to such an extent that it could no lo ng er be measured with the availa ble oscilloscope. Bibliography 1. Some recent papers reporting the results of dielectric loss measurements at frequencie s in the vicinity of 10 8 cycles per second are: a. Rhode, L. und Schlegelmilch, W. E .T.Z. 54, 24, p. 580, 1933. b. "Stand der Isolierstuff-Forschung" E.T.Z. 54, 23, p. 569, 1933. c. Tu1uller, E. und Zinke, O. Hochfrequenztechnik und Elektroakusti k , 43, p. 145, 1934. d. Rhode, L. und Schwartz, H. Hochfrequenztechnik und Elektroal(ustik, 43, p. 156, 1934. e. Rhode, L. Zeitschrift fur Techni s che Physik. 12, p. 637, 1935. f. Race, H. H. and Leonard, s . C. Elect. Eng., 55, 12, p . 1347, 1936. g. Hartshorn, L. and Ward, VV .H. - J.I.E.E., 79, p. 597, Nov. 1936. 2. Schmidt, O. "Das Paralleldrhtsystem als Messinstrument in der Kurzwellentechnik". Hochfrequenztechnik und Elektroakustik, 41, p. 2, Jan. 1933. 3. King, R. "Eine zussammenfassende Untersuchung uber stehende elektrische Drahtwellen." Folge 5, p. 806, 1930. Ann. der Ph ., 7, - 4. Sterba, J. and Feldman, C.B. ''Transmission Lines for Short-Wave Radio Systems." Proc. I.R.E., 20, p. 1163, July, 1932. 5. Shelkunoff, S.A. "The Electromagnetic Theory of Lines and Shields~ Bell Sys. Tech. Journ. p. 532, Oct. '34. 6. Terman, F.E. "Resonant Lines in Radio Circuits", Elect. Eng., 53, p. 1046, July, 1934. 7. Moullin, E.B. "Radio Frequency Measurements", (a book), Oxford University Press. 8. Hartshorn, L. and Ward, W.R. "The Measurement of the Permittivity and Power Eactor of Dielectrics at Frequencies from 10 4 to 10 Cycles per Second". J.I.E.E. 79, p. 597, Nov. 1936.