The Measurement of Dielectric Losses at a Frequency of One Hundred Megacycles per Second Citation Oliver, Bernard More (1940) The Measurement of Dielectric Losses at a Frequency of One Hundred Megacycles per Second. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/TW6X-AB09. https://resolver.caltech.edu/CaltechETD:etd-06182004-135230 Abstract No Abstract Submitted. 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 1940 Record Number: CaltechETD:etd-06182004-135230 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-06182004-135230 DOI: 10.7907/TW6X-AB09 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 2637 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 21 Jun 2004 Last Modified: 17 Aug 2023 00:11 Thesis Files Preview PDF (Oliver_bm_1940.pdf) - Final Version See Usage Policy. 6MB Repository Staff Only: item control page

THE MEASUREMENT OF DIELECTRIC LOSSES .AT A FREQUENCY OF ONE HUNDRED MEGACYCLES PER SECOND A Thesis by Bernard M. Oliver Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Electrical Engineering California Institute of Technology May 1240 1. TABLE OF CONTENTS INTRODUCT ION 2. THE METHOD 2.1 Fundamental Principles of all Methods 2.2 The Present Method 2.3 Summary of Theory of Method 2.4 Sensitivity of Method 2.5 Sources of Error 8.51 Sources of Detectable Errors £2.52 Sources of Non-detectable Errors 3. DESCRIPTION OF THE APPARATUS 4. 5.1 The Resonant Line 5.2 The Sample Holding Condenser 5ec The Diode Detector 3.4 The Input Coupling Circuit 5.5 The Frequency Source 4.01 The Oscillator 3.08 The Power Supply and Regulator PRELIMINARY TESTS AND ADJUSTMENTS 4.1 Tests of Components 4.2 Resonance Tests OBSERVATION, RECORDING, AND CONVERSION OF DATA 5.1 Method of Taking Readings 5.2 Sample Data Sheet PAGE Oo f be co 15 19 20 24 28 28 él oO 34 36 36 37 53 og PAGE 5.2 Conversion of Data - Example 45 5.41 Estimation of Resonance Reading 45 5.38 Computation of Eguivalent Resistance of Sample 45 5.45 Computation of sample Capacity 48 5.64 Results for Cast Lucite 49 6. TABULATION OF RESULTS 51 6.1 Dielectric Characteristics at 100 Megacycles and 25° C, 51 6.2 Classification of Dielectrics as to their Dissipation Factors at 100 Megacycles 54 7. DISCUSSION OF RESULTS 56 7.1 Low-loss Materials 56 7.2 Anomalies and Interesting Features in the Results 58 7.6 Comparison of Results 59 8. SUGGESTED MODIFICATIONS, IMPROVEMENTS, AND FUTURE RESEARCH USES 61 8.1 Comparison of Actual and Theoretical Sensitivity 61 8.2 Localization of Other Losses 62 8.2 Origin, Magnitude, and Reduction of Loss in the Diode 63 8.4 Suggestions for Further Investigations 66 9. CONCLUSION AND SUMMARY : 68 10. ACKNOWLEDGEMENT 68 PAGE APPENDIX I Sending End to Midpoint Transfer Constant 70 APPENDIX IT Conversion of Bata 80 APPENDIX III Development of Sample Capacity Formulae BS APPENDIX IV Basic Sensitivity of the Method 87 «APPENDIX V Galculation of Line Constants 91 APPENDIX VI Method Used by Miller and Salzberg 94 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 Fig. 10 Fig.11i Fig.12 Fig.13 Fig.14 Fig.15 Fig.16 Fig.17 Fig.18 Fig. 19 Fig. 20 LIST OF ILLUSTRATIONS TITLE Block Diagram of Entire Apparatus Showing Arrangement Short Circuiting Annulus in Place in Line Short Circuiting Ring Mounted on Draw Tube Lead Screw in Cradle Complete Line Section Through Sample Holding Condenser Components of Sample Condenser Sample Condenser and Voltmeter Schematic Diagram of Vacuum Tube Voltmeter a) Schematic Diagram of Input Circuit b) Showing Coupling Action of Loop Feeding Circuit With Lid Removed Schematic Diagram of Oscillator Complete Oscillator With Shield Removed Schematic of Power Sugply and Voltage Regulator Sample Resonance Run Controlled Test of Anomaly at Low Resonance Voltage Effective Misreading Voltage at Resonance Test of Cast Lucite Diode Construction and Representation of its Loss Equivalent Diagram of Resonant Line FOLLOWING PAGE 55 Ba o4 54 36 ov 68 40 & & 63 70 DEFINITORY NOTE The term "Dissipstion Factor" hes been here used thron hout to denote that quantity which, when multiplied oy the current drarm by e given sample capacity zives the or loss, component of the totel current. It is thus the tensent of the "loss angle" and for small losses is therefore equsl to the cower factor of the dielectric. It has been czlled to the author's attention that this definition is not in accord with senerel usaze. ™o obtain the quantity which is usuelly called the "vissip- atidn Factor", the quanti ty here used should, in each cese, be maltiplied bs the dielectric constant of the mm teriel te whieh the siven disti» “tom factor perteirs., ‘L. INTRODUCTION The growth of the radio art today is principally in the direction of the utilization of higher and higher frequencies. The cry of "Lebensraum" long familiar in the communication world is heard as often today as ever be~ fore, Room for more communication channels! Room for higher fidelity transmission by wide band frequency modu-# lation: Room for high definition television - the monster whose frequency spectrum extends from zero to many mega~ cycles per second! Room for these, and for many other radio uses: room to be found only in the ultra high fre« quencies, for above 100 megacycles the air is literally free. This expansion into the shorter wavelengths has already gone far, Limited to frequencies below the high~ est then in common use, radio of 1925 could have found room on the air for but one modern television channel, and if that, then nothing else, By 1930 this number would have rismto three, Today four regular channels (each six mega= cycles wide} and many more experimental channels have been set aside for television and the "space" they take is not seriously missed, However, the end is by no means yet in sight. Today's dreams are of thousands of megacycles: centimeter waves guided like fluid in pipes, or radiated into space with optical directivity, as desired. At the high frequencies even now in use, effects negligible at low frequencies may dominate design. One such effect which becomes of engineering importance is the *loss" present in all dielectrics. At very low frequen» cies a dielectric may be described in terms of its break= down strength, dielectric constant, and leakage resistiv= ity. At high frequencies the apparent resistivity may be much less than at low frequencies. The difference is not due to increased conductivity, but arises from the energy lost by the rapid rotations of the dielectric molecules in the polarizing field. The measurement of this dielectric loss at a very high frequency and in many dielectrics has been the object of the investigation to be here described. This investigation of dielectric losses at a frequency of one hundred megacycles per second was begun py Mc Rae"). in 1935e36, at which time the author assisted with some of the work and became familiar with the problem. Mc Rae was successful in establishing the feasibility of the basic method employed here, but very few actual re= sults were obtained. The project was then abandoned, and when the author returned to the California Institute of Technology in 1937, it was his intention to investigate as a research subject the propagation of 41 megacycle radiation over the Mount Palomar = Pasadena path and to correlate these observations with atmospheric conditions, This work was carried on with Doll in 1937=38, and the results have been described by him®), However, by the end of 1938, it was apparent that no significant developments could be expected from a continuation of the measurements, and it was decided to return to the original problem of dielectric loss measurement: to bring this project to some degree of completion. This was done during the spring and summer of 1939, Many refinements of the original method em~ ployed by Mc Rae were introduced, and the mechanical ac» curacy of the apparatus used was brought to a point where accurate determinations of the losses in the newer ultra- low-loss dielectrics were possible. 2¢ THE METHOD 2.1 Fundamental Principles of all Methods In all the many ways by which dielectric losses can be measured, but two fundamental principles are em~« ployed: either the energy lost in the dielectric is mea- sured directly, or else the effect of this energy drain on some associated electrical circuit is determined. Methods by which the energy loss is measured dix rectly usually involve calorimetric determinations of the rate of production of heat in the sample, and have been employed successfully by Debye, and others?) » using liquid samples. Because the liquid in this case may serve as its own thermometer, the method is particularly applicable, However, since in all dielectrics, the losses increase very nearly as the square of the polarizing field, it is ap» parent that if anything more than mere relative values of loss are desired, it is necessary to know accurately the polarizing field present with this method. This fact, plus the difficulty of making accurate calorimetric measurements in the case of solid dielectrics and particularly those for which the loss is small, make the method impractical for measuring just those materials which are of engineering im portance. In the second class of methods: those in which the effect of the loss on an associated electric circuit is measured, the fact that the loss in the dielectric in» creases with the square of the polarizing field merely means that at any given frequency this loss may be repre» sented as a resistance independent of the applied voltage, and either in shunt or in series with the capacitance of the dielectric, depending upon which is more convenient. The loss thus simply introduces another circuit element in the form of a resistance. At audio and low radio frequencies this equiva- lent loss resistance associated with the dielectric may be rather accurately measured by bridge methods. With ine creasing frequency, however, the difficulties of making ac~ curate bridge measurements become greater and greater until at frequencies well below 100 megacycles the method becomes hopeless. Another method which suggests itself of measure ing the equivalent resistance is to let this resistance be as nearly as possible the only loss present in a resonant circuit of some form. Since the sharpness of the resonance curve of any form of singly resonant circuit is determined solely and uniquely by the ratio of the resistance to ree actance in the circuit, it is evident that by measuring the shape of the resonance curve of a given circuit with and without the sample present, a very direct indication of the loss in the sample may be obtained. This is essen= tially the method which has been used in the present work. It avoids the serious drawbacks of the heating method with its heat losses and the necessity for accurate voltage de- termination, and of the bridge methods with their uncon» trollable effects of stray capacity and shielding defects, without having, as far as the author has been able to de~ termine, any serious fundamental limitations of its own. 2.28 The Present Method Briefly the method may be described as follows. A transmission line consisting of two coaxial conductors is short circuited at both ends, one of the shorting rings being movable and the other fixed. The line is supplied with a constant voltage at the desired high frequency by a very slight electromagnetic coupling at the fixed end. At a point one quarter wavelength down the line from this fixed end, the sample is introduced in such a fashion that it bridges the gap between the inner and outer conductors and thus has applied to it the entire line voltage, which is a maximum at that point. The length of the remaining section of line is then adjusted by means of the movable short circuiting ring until the Line is brought into resonance, as indicated by some detector designed to read either the voltage appear~ ing at the center of the line or the current at the movable ende | The short circuited transmission line is thus the resonant circuit of this method and has the advantages of having very low losses, and of being self shielding. Fure thermore, except for the sample and sample holder capacity and loss it is entirely a distributed constant system and is treated as such in the analysis, whereas any coil«con= denser system would, although treated as a lumped constant circuit, actually have distributed constants of indeter- minable magnitude as well. Since variation of the frequency in order to cover the resonance range would require a calibrated oscil~ lator of fantastic precision, the oscillator was allowed to stabilize itself at some fixed frequency and the line length was varied to pass through resonance. In the pre+ sent arrangement the detector device was arranged to read the voltage at the center of the line, and this quantity was recorded as a function of the line length. This repre~ sents a departure from Mc Rae's method in which a thermo couple loop and galvanometer was used to measure the cur~- rent at the movable end of the line. These two methods both have their respective advantages and disadvantages to be discussed later, The theory for the case in which the -8« current at the movable end is the quantity read has al~« ready been given by Me Raet), The theory for the case in which the voltage at the quarter wavelength point is the quantity read is given in the Appendices and will only be summarized here. ' The assumptions upon which the theory has been developed ae be. C)e are few, but important. It has been assumed: That no higher order modes of propagation exist in the line. In spite of the fact that the pre- sent line has a ratio of diameter to wavelength about three times that used by Mc Rae, the pree sent ratio of about 1:40 is well under that ree quired for the higher modes to become real*), The assumption is therefore justified. That the sample and sample holder and detector may be treated as lumped constants placed across the line at the point indicated, This assump- tion is justifiable on the grounds that the dimensions of these objects are very short com= pared with a wavelength, and that therefore the only effect of the field modifications they pro= duce is the introduction of some additional ad~ mittance and susceptance across the line, That certain higher order terms which arise in expansions in the analysis may be neglected.. These cases are treated as they arise and proved negligible in every case. (See Ap- pendix I). Assumptions a) and b) are important because they permit of a simple analysis based on four terminal network theory rather than a much more complicated solution using field theory. Assumption ec} is important because it per= mits the solution to be reduced to a very much simpler form than could otherwise be obtained. 203 Summary of Theory of Method The first step in the analysis is the derivation of the relation between the voltage measured at the sample by the detector and the driving voltage, the line length and the sample loss. If we define Kn such that eg = Kp eg where €@5 * voltage across line at sample eg = driving voltage supplied by coupling circuit, Kn, the "transfer constant", can be shown (See Appendix I) to be very closely given by 1 Bat + j(A + =) | “Ss Kp = (20) in which | A = a term representing all losses present in the line without a sample E sin pl, B = phase constant of line in radians per unit length. 4. = length at resonance of section of line between sample and movable shorted end. actual line length minus resonant length. o & = characteristic impedance of line, ES) 2 Ui desired equivalent shunting resistance of sample, j = operator v=I Now it wuld be possible to determine directly the value of At which makes % BAL = (A + a2 Rg and hence reduces Kp to L. times its maximum value. Thus, if the value of 4 whieh’ seduced the voltage at the center to 70.71% of its maximum value were determined both with the sample in place and removed, Rg could be calculated from these data very simply. However, such a determination rests upon the accuracy of only three readings of length » ll « and since these may be subject to slight statistical variations, the method is not very accurate. This fact was pointed out vy Mc Rae. Another method of obtaining R, which involves as . Many points as desired is given in Appendix II, There it is shown that / (=) o1 = a = (constant) x 4 Ate Rg where 6, = voltage at sample at resonance e = voltage at sample in general, Thus if / (=) ~ 1 be plotted as a function of M (or of 4 itself) for all the observed values of e, the points should lie on a straight line, which can therefore be drawn in by visual least-square weighting. The slope of this line, m, is then given by if a sample is present, and by B Myo = A if no sample is present. From these two equations it is easy to show that Rs = . | (24) This method of determining R,, while more laborious than the simple method first mentioned, has two important advantages, The fact that a great number of points are used in the determination minimizes the chance of error in the result due to the slight random error which may be present in any single observation. fFurther- more, the fact that over the range of variation of line length used in measuring any sample, these points should lie on a straight line when plotted as described, permits of an immediate check on the operation of the entire ap» paratus, In other words, if all the observed points, when plotted, obey the required straight line relationships, an entire class of errors: namely all those which would cause departure of the points from linearity, and which otherwise might be considered important, are automatically proved negligible by the experiment itself. These sources of error and many others will be discussed at some length in a later section. Having determined the magnitude of R, for any given sample, this may be translated into the effective resistivity and/or dissipation factor of the dielectric material itself provided the dimensions and/or capacity of the sample are/is known. This may be done by the re« lations: Ag P=R sa, and — s“s in which A, = area of sample (perpendicular to fiela)* d, = thickness of sample (in direction of fielda)* ® = angular frequency of applied field GC. = sample capacity, Both the effective resistivity and the dissipa+ tion factor have been calculated for all the dielectrics which have been tested. The value of the sample capacity CG was in each case determined by two methods, the mechan- ism of which will be more apparent when the procedure of taking readings is discussed but which should be described here. The first method, which was always used merely for a check or the results of the second, consisted of om oe we ee eel el relU ll rlU OCOUlUlUl lM UC lll lll lll lll *4 thin sample with two parallel, or nearly parallel plane faces is assumed. . “14 = varying the spacing of the sample«holding condenser till, without the sample present, resonance in the line was ob- | tained at the same line Length as with the sample present. From the two spacings of the sample condenser plates with and without the sample present it is possible to calculate an approximate value of the capacity of the sample. In Appendix (IIT) this capacity is shown to be given ap+ proximately by: ~Aog {1 ( As) 1 Cy ve E Q Z,) as Cis (29a) where Aj = area of sample condenser plates Ag = area of sample d, = plate separation without sample a, = plate separation with sample. This, for the constants of the actual apparatus, reduces to the convenient expression: ~|1l _ { As) 1 In the second method the spacing of the sample condenser plates is left equal to the thickness of the sample and the line length required to again establish resonance without the sample present is then, as shown in Appendix (III), given by 1018 | 1 ,As,| uufds Cc. = |j=z— (cot PL. ~ cot fl!) + & (28 (32a) in which — do = length of line from sample to movable end with sample present 44 = length of line from sample to movable end with sample absent, This second method has been taken to be the more accurate of the two for reasons to be discussed later. The two methods gave in every case results in close agreement. 2e4 Sensitivity of Method Obviously, there will be a maximum value of the equivalent sample resistivity, R,, which can be measured to some specified degree of accuracy. Neglecting all other sources of error, it may be shown (See Appendix IV) that this limit is rather sharply established by the losses in the line itself and the accuracy with which the slopes Wo, and mgs of the plots of the observed data can be de~ termined. This relationship is given by the expression: ( ) POS ae ohms, (38d) elf ~16< In which 4, = characteristic impedance of line A =a term proportion to the line logses. x 100 = maximum permissible percentage error in e max bm, ae x 100 = maximum possible percentage error in max determining m1, (and m,). From this equation it is apparent that the sen- sitivity of the method, i.e., its ability to measure ac- curately very low loss samples is directly proportional to the quantity ) A . Now as given in Appendix I, ato Bo A= sin? plo tat, + FF (18) where? a = attenuation constant of line B = phase constant. do, 44 = line section lengths. RL = equivalent resistance present at center of line by all other losses besides the sample and those represented by a. Therefore -17 = Bo 1 A L a ° 1 Bo sin® pty Su RE and we see that in order to make = as large as possible, =2 m must be maximized and all "extraneous" losses due to support insulation and measuring apparatus (proportional to gy) must be minimized. Terman”) has shown that —° Bo 9 is @ maximum when je) q 7 902 where @ = outer radius of inner conductor. b = inner radius of outer conductor, The conductor radius ratio of 9.2:1 is inconvenient for mechanical reasons, Fortunately, the maximum of =2 at this ratio of b to a is a very broad one, and the ratio of B= 428 which was actually used gives a value of =o only 12% below the maximum value. In view of the fact that the line losses were only about one half of the total loss without a sample, hardly more than a 6% gain could have been expected, had the optimum ratio of radii been used. It is interesting to rewrite the sensitivity equation by redefining our terms slightly. Thus we have Smo| _&aR Patol lel < © 1 mo! max | — Bo A (38c) in which | | Rg = equivalent resistance of loss in any “sample. e x 100 = maximum probable error of method (due to inaccuracies in measuring mo, m,, only). Substituting the values in this equation per~ taining to the apparatus used one finds that the maximum probable error is approximately given by le] bss Rg 4x 10° Thus an R, of 40,0008 could be measured with a probable error under 1%, an Rg of 400,000 with an error under 10% etc., the maximum probable error being propor tional to Rg. At low values of Rg, such as presented by sam~ ples with high losses, this error due to the fundamental sensitivity limitation of the method becomes negligible and is masked by other stray errors such as are inherent in any experimental procedure. Various sources of these stray errors will be discussed in the succeeding section -but it should be mentioned here that the values in the colums headed "aati mum Probable Error" in the tabulation of results were computed by allowing 5% in addition to 100 x €, for the probable maximum error due to all these other sources. (The Maximum Probable Errors listed for different samples of equal loss may not be the same, be- cause different sized samples were used). In view of the consistency of the results obtained, this value of 5% is believed to be conservative, but since in engineering ap- plications, it is seldom necessary to know the dielectric loss to any greater degree of accuracy, the great amount of analysis necessary in order to be certain of a closer tolerance was felt to be unwarranted, 205 Sources of Error As has been mentioned previously, all sources of error present in the apparatus can be divided into two classes: those which produce errors detectable in the data, and those which produce errors for which no check exists. The latter class we must prove negligible, The former class is shown to be negligible by the data, but must be considered, since as potential sources of error, the ef= fects involved impose certain requirements on the design and mechanical accuracy of the equipment. 2.51 Sources of Detectable Errors To be detectable, the error from any source must cause the experimental points taken to depart from a straight line relation when plotted as described in Section 2.3 and Appendix II, or the error must be such that it may be found by repeating the run. The principal sources of -error for which this is true are discussed below, one by One. a) Inaccuracies in measuring the small changes in line length required to pass through resonance could result in almost any kind of a non-linear plot, from a random scattering of the points above and below their proper positions, to a cy= clic shift resulting in a wavy line instead of a - straight one. Since in some of the runs the variation in line length from one point to the next was only 0,1 mm, it was imperative that the mechanism used be able to establish this interval with an accuracy of at least 10% or 0.01 m, This is the same order of magnitude as the expansion which can take place in the copper of the line with large changes in room temperature put this effect is largely balanced out as will pe explained later. b) Non=linearity in the response of the device used ad) as a detector (here a vacuum tube voltmeter) would cause the line passing through the observed points when plotted, to have a different slope for points near resonance than for points far from resonance. A marked S-curvature would therefore result in place of a straight line. The linearity of the detector was checked by independent means, thereby climinating the possibility of this error compensating some other. Extraneous coupling to the detector, would pro= duce a curvature in the plot of the data because of the change of phase of the voltage at the cen- ter of the line with respect to the stray coupled ' woltage as resonance is crossed. That no such coupling was present is evidenced by the fact that the meter gave no deflection with the line de- coupled from the feeding circuit and detuned. Any changes in the losses present in the line which might occur during a run would of course distort the data and be evident in the plotted ree sults. Such changes could only occur due to changes in the line temperature or variation in the contact resistance of the sliding ena short e) £) ciroui ting annulus. Care was taken to eliminate both of these sources, using methods to be de~ scribed. Since, particularly with low loss samples, the readings are very violently dependent upon fre- quency, it is essential that the frequency of the source oscillator remain constant. With a line length variation of only 0.007% between successive points with certain samples, the fre~ quency variations should be held below 0.0005%, This represents a stability in the oscillator such that the drift not exceed two parts in ten million. After a sufficient warm-up period, the oscillator used was found to possess the required stability, not with respect to an absolute fre- quency value but with respect to the resonant frequency of the line at any instant. What is meant by this is explained in the section de- scribing the oscillator. Fortunately frequency drift is particularly easy to check, simply by repeating the run. This was done in all cases when believed warranted. Two other sources of error involve the voltage supplied to the line and have been analyzed by = 23 ~ Me Rael), One is the reaction on the coupling circuit produced as the line is tuned through resonance. This effect is proved negligible if the current in the feeding circuit remains con- stant throughout the run, The reaction of the line on the coupling circuit might in turn proe duce a reaction on the oscillator and thus a fre« quency shift as a function of line length about resonance, even though no change be noticeable in the magnitude of the current in the coupling cir~ cuit. This is especially likely in view of the high frequency stability required. However, in the seteup actually used, both the coupling to the oscillator and the coupling between the feed~ ing circuit and line were so slight that no ef~ fect from this source was noticed. As a matter of fact, no trouble was experienced from any of the above mentioned sources ~- nor any others, such as stray fields from the oscillator. Provided the proper precautions were observed in taking the readings, the points all were found to line on a straight line within the limits of observational error. One effect did make itself manifest, an effect which was very confusing. It was found that if a run were taken with the feeding~circuit~to-line coupling reduced so that the voltage at resonance at the center of the line was only about 5 volts peak value, it was impossible to take data which would plot up to be a straight line. In« stead, a characteristic, broken about the resonant point, would be obtained such that the slope was greater for line lengths longer than the resonant length, than it was for shorter line lengths. Tests were made which showed that this effect was a function only of the voltage at the cen- ter of the line at resonance and not of the degree of coupling to the line (ordinarily less for low voltages) or of the load resistance in the detector circuit. Such a test run is given in Section 4.2. While not definitely proved, it may be that this effect was due to the electron transit time in the diode detector tube causing the device to present a reactance dependent upon the applied voltage. The effect was avoided by operating the line so that the voltage at resonance was about 50 volts peak value. 2.52 Sources of Non=Detectable Errors Most of the possible errors in the equipment used belong in the previous or detectable class, There are a few, however, for which no check exists. These are listed below. | a) Any change in the losses present in the line which occurs between the time the sample run is taken b) and the time the no sample run is taken would not show up in the results. Furthermore if this same change in losses occurred each time the experiment was repeated no indication of this error could ever be obtained. Temperature changes could of course bring about such a change in the line losses, but this same change could not be expected to occur each time. Only one alteration was made in the line between each run with a sample and the succeeding run without a sample. This was to adjust the spacing of the sample holding conden- ser till its capacity was returned to the same value as with the sample present. By so doing, the current distribution in the line was made very very nearly the same as with the sample present, and as a direct result of this the line losses should remain the same. The only place where any change in the current distribution might occur is on the surface of the condenser plates themselves, and this should represent a completely negligible change in loss, If the contact of the sample with the plates of the sample holding condenser is not complete the apparent equivalent resistance and the apparent capacity (as measured) will be greater and less than their true values respectively, due to the effect of the air capacity thereby placed in series with the sample. The observed resistivity and dielectric constant will therefore be in error, The errors in the two are reciprocal, however, and no error is introduced in the obe served dissipation factor. This source of error was eliminated as far as possible by a specially designed sample holder. c) Conversely anything which causes an error in the capacity determination alone will cause a similar error in the dielectric constant and dissipation factor, but no error in the resistivity. The me~ thod of capacity measurement has been described and is quite accurate, except for possible changes in the resonant length of the line and in the ap» parent spacing of sample condenser plates due to mechanical forces arising from the compression of the sample. The rigidity of the apparatus used was great enough so that not more than a 2% error should have been thus introduced, We see that the undetectable sources of error are comparatively few and small, and the method can be expected to be quite accurate within the limits previously given. ~ 27 = Let us. now consider some of the salient features of the apparatus actually used. - 28 ~ 3. DESCRIPTION OF THE APPARATUS The following section is a description of the ap- paratus actually used in carrying out the method described in the previous section. : Before considering the special details of each component let us look at the arrangement of the assembly as a whole in order that the function and location of each part may be more easily remembered. Figure 1 is a block diagram _of the entire apparatus which, as well as showing the func- tional relationships of the various parts, is a fairly ac- curate plan view of the room arrangement actually used. It should be noted that all high frequency sources and leads are completely shielded, and at all points where leads cross the boundary between these shielded regions and the outside world, filters have been used. Because of the very high frequencies involved this shielding and filtering presented no special problems. Almost any conductor looks opaque to a hundred megacycles. Sel The Resonant Line The coaxial line used consisted of two copper pipes about 6'6" long, the inner having an outer diameter of 5/8" and the outer an inner diameter of 3". Both had a wall thickness of 1/16". They were held in a coaxial one quemyenf pe | | mSuet euyt ov A OTT + | INGASONVEHY ONIMOHS rs) (( O r SoLvuvddy @uILNG JO wvEDyYId won —>——_ T mins fy ddns IQNOg : Multiplier Sample) and Biode Detector Ths porg TT (do48-4.1848 ) [| yourms Artddns eyetd ov A OTT IOVETTFO8oO roqeTnsey BBV4TOA 4 NOTTS ( ) JuTpeed C [/—_—_i nat. ad —_— QNIT NI ZOVId NI SAMTIONNV ONILINOID - LUO a awanol [ JOPONPUCO eUTT seEUUT {/~ eqn} MBIpD eTQuacH szezayy / ~ 4084009 f~ IoJONPUOS sUTT z94NnoO position, at each end by the short circuiting annuli, and in the center of the line by a Victron bridge (The tests show polystyrene would be better). The short circuiting rings were made from annu- lar discs of brass 1/4" thick. At the inner and outer cylindrical boundaries, short spring brass cylinders were soldered. These cylinders were turned thin except at the free ends, and then slotted to form a number of spring fingers lying on circles of nearly the same diameters as those of the line conductors. (See Fig. 2). Finally the entire piece was silver plated to increase the surface conductivity. Both of the short circuiting rings were movable although one (at the input end) was adjusted till the sam- ple and peak voltmeter were at a point truly one quarter wavelength from the sending end, and then left fixed at that adjustment. The length of the line was adjusted by sliding in and out the short-circuiting ring forming the "receiving" end of the line. To do this accurately, the ring was mounted on one end of a brass tube with flanges on each end (See Fig. 3) The other end of this tube was bolted to the nut of a special lead screw mounted in a cradle which . was securely clamped to the end of the outer line conductor. FIGURE 3 sdORT CIRCUITING RING MOUNTED ON DRAW TUBE (See Figures 4a and 4b). The pitch of this lead screw was ol millimeter, so that a dial on the end marked off in twenty divisions permitted the adjustment of the line length in steps of 0.05 mm. By careful turning of the screw on an accurate lathe, followed by long and tedious lapping of the screw with carborundum dust, then white lead, an accuracy of 0.005 mm over the required range of about 10 mm was ex- ceeded at all points along the screw. In order to cover the required range of line lengths used, two flanged tubes were made having lengths differing by twenty centimeters. This arrangement shortened the lead screw length necessary, and thereby considerably facilitated its construction. The change from one driving tube to the other could be brought about in a few minutes and was seldom necessary. The thrust of the lead screw was transmitted directly to the eradle by a collar near one end. This collar was turned at the same time as the screw itself so that the two would be accurately coaxial in order to avoid cyclic error which would be otherwise introduced if the plate ageinst which this collar bore were not exactly plane and perpendi- cular to the axis of the screw. As one of the first steps in the construction of the line, the copper pipe which was to form the outer con- ductor was cut into two pleces one about 3' long, and to ee as = a8 FIGURES 4 LEAD SCREW IN CRADLE = 3l « the two new ends thus formed were soldered brass rings _ which were then turned so that their exposed faces were plane, and perpendicular to axis of the tube. This formed a very accurate flange joint separable at any time by removing six screws. Access to the sample holder and peak voltmeter assembly inside the line was thereby facilitated. The joint was placed close to the sample holder on the input end side so that the currents across it were very small. The entire line was clamped firmly in three wooden yokes mounted on a heavy board. Figure 5 shows the complete line and its mounting. 5e2 The Sample Holding Condenser Because of the increased diameter of outer con- ductor used in the present line over that used by McRae, it became feasible to employ a sample holding condenser so constructed that the plates of the condenser and the flat dise samples used were all contained inside the line itself. This has several advantages, among which are a decreased loss due to the elimination of side connections, and increased accuracy due to the fact that the voltage actually impressed upon the sample is definitely the po-~- tential difference between the inside surface of the outer conductor and the outside surface of the inner conductor. FIGURE 5 COM PLETE LINE = 32 + Figure 6 is a section through the sample conden- ser assembly as mounted in the line. The upper plate of the condenser is formed by the capped end of a hollow cylinder threaded and recessed to screw snugly into a brass sleeve soldered in a hole in the line. This brass sleeve was undercut in back of the internal threads and then slotted in the same fashion as the short circuiting ring cylinders. After silver plating both parts, the fingers thus provided a tight, elastic, fit of the threads. The lower plate is a disk shaped electrode mounted on a boss on the inner conductor. A special feature of this electrode was the flexible construction which permitted it to align itself so as to lie flat against the lower face of the sample when the upper face was flat against the upper plate and the two faces were not parallel. This was accomplished by recessing the back of the plate and soldering to the rim thus formed a tightly stretched sheet of copper foil. To the center of this dise of foil was also attached the small dise with a threaded hole which serewed on the stud on the boss. This stud was allowed to penetrate and contact the back of the plate itself so that a firm point of support was established, about which the plate could be rocked by distorting the foil backing. High frequency currents to the plate must flow along the outside surface which accordingly was silver plated. Fig.7 Micrometer scale inscribed “ N on tube here Threaded Guide sleeve bearing spring contact fingers WA AAA SS VIA TIwAvstass Isa El Gas we oJ) fia) 3 SS S ——y, Inner line eo nductor Outer line conductor FIGURE 6 SECTION THROUGH SAMPLE HOLDING CONDENSER FIGURE 7 COMPONENTS OF SAMPLE CONDENSER FIGURE 8 SAMPLE CONDENSER alD VOLTMESTER shows the components of the sample condenser before assem- bly and Figure &, the complete condenser in place. 3.3 The Diode Detector Also visible in Figure 8 is the diode detector used to measure the voltage at the sample. This detector consists of a special small diode with its plate connected to the inner conductor just below the sample condenser, and its cathode connected through a small capacity to the inner surface of the outer conductor. Special features of this diode were the absence of internal support insulation and an extremely small element size and spacing. The cathode and heater leads were brought out through filter sections to the supply transformer, anda high resistance voltmeter was connected between the external cathode lead and the line. With a time constant in the load circuit long compared with the period of the frequency being measured, and with a voltmeter resistance high compared with the internal resistance of the diode, the voltage measured by the device is very marly the peak impressed voltage. As a result of this, the effective shunting ad- mittance across the line due to the voltmeter is twice the actual D.C. admittance of the meter. In parallel with this, of course, are the admittance due to the capacity and dielectric loss of the diode itself. Imer conductor AF 10 ,hen \\ 2) FIGURE 9 SCHEMATIC DIAGRAM OF VACUUM TUBE VOLTMETER A complete schematic diagram of the detector is given in Figure 9. The meter actually used was so sensi- tive that the shunting effect of the admittance of its multiplier resistances was negligible. The whole device was checked for linearity by varying the current in the feeding circuit, and for magnitude of reading (relatively unimportant) at low frequencies, and found to be entirely satisfactory. 5.4 The Input Coupling Circuit Input voltage to the line was secured by means of a very slight magnetic coupling to a tuned circuit driven by the oscillator. To achieve this coupling a slot was cut in the outer conductor of the line right at the short circuited input end, a slot 1/4" wide and about 2" long to allow for length adjustment. One finger of the short circuiting ring at that end was removed and the gap thus formed was rotated so as to coincide with the slot. A second slot in a long metal box was placed opposite the slot in the line. Inside this box, which served as a shield, was mounted a resonant circuit consisting of a pair of parallel copper tubes terminated in a variable tuning _ eapacity at one end and a loop of heavy wire at the other. See Figures 10 and 11. A shielded twisted pair from a one turn pickup coil, loosely coupled to the oscillator, was | precn ene nese ease T= -- 4 | I | Shielding case 7 Thermo couple meter CX ( From AA M oscillator | ns Comin Tmpedince ~~ coupling condenser match here loop a) SCHEMATIC DI4GR.M OF INPUT CIRCUIT Only flux passing through plane A - B provides coupling Loop bd) SHOWING COUPLING ACTION OF LOOP FIGURE 10 “=== 1 ——— — —— —- —) | — JO pug rr 3s{Try euT. go t_ FIGURE 11 FEEDING CIRCUIT WITH LID REMOVED ~ 35 « connected to this Loop at two points so chosen that the . twisted pair was properly terminated. By tuning the cir- cuit to resonance, a large current could be obtained in the loop end. By introducing this loop into the slot in the line, a small part of the flux due to the circulating current was allowed to link the inner conductor and thus induce a voltage effectively in series with the short cir- cuited end of the line. As a result of the low losses in the line, a surprisingly small amount of coupling was suf- ficient. With no sample present, it was found that a volt- age in excess of 100 volts could be obtained at the center of the line at resonance, with the end of the loop not even fully inside the slot. Resonance in this tuned feeding circuit was ine dicated by a thermocouple meter mounted in the lid of the shield box and inductively coupled to the tuned circuit (See Figures 10 and 11). This meter also served as a check on the constancy of input to the line and on the re- action of the line on the feeding circuits. It was found that this reaction was just noticeable with very high less samples requiring close coupling to the line to secure enough input, but this reaction was not apparent in the re- corded dates. - 36 = Seo The Frequency Source _ The frequency source used in the present work, i.e., the oscillator and its associated power supply and regulator did not differ materially from that used and described by McRae), The same pieces of equipment were used and only minor modifications in the wiring and ar- rangement of parts were made. As a result, only a brief description will be given here as a convenient reference. Seol The Oscillator A schematic diagram of the oscillator is given in Figure 12. The circuit consists of two Western Electric Type 304A triodes in a conventional self biasing push-pull connection. The resonant circuit to which the plates are connected is tuned to present a slightly inductive react- ance to the tubes, at the frequency of oscillation. ‘Energy is thus transferred into the grid circuit by the grid to plate capacity of the tubes and drives the quarter wave- length resonant line to which the grids are connected. This resonant line is the primary frequency controlling element of the system and accounts for the freedom from trouble due to frequency drifts arising from temperature changes. The required frequency stability of the oscillator was seen in Section 2.51 (e) to be on the order of 0.0005%. It may have occurred to the reader that since copper expands YOLYTIIOSO dO OSL +4 Thi -€ Thi AVYOVId OLLVWHHOS cr ro ! ; at wan la | ) rs i {~ eseo PTeTyS c-—--4--4 b- ———-—bL~4]p —~-yf——4])»- 4-—----~----—--_~- 1 | j | U ' | ! | | Ll V we orl Fe0T ! DFID TO13U00 | 1 __. Aouendbeazy | f~ eUTT 7. Usu0seYy } ! | wr ] | — | _™M | oot | V vor ; | 1 dn-yoTg = 37 © 0.0016% per degree centigrade, it would be necessary with a eonstant oscillator frequency to hold the ambient tem- perature variation to within 0.5° C. in order to avoid errors due to change in the line length with temperature. However, the stability requirement of 0.0005% is fixed solely by the sharpness of the line resonance, and it is therefore only the frequency of the oscillator relative to the resonant frequency of the line which must be held this closely. The absolute frequency of the oscillator can vary much more than 0.0005% provided the resonant fre- quency of the line vary isochronously. By making the fre- quency controlling resonant line of the oscillator also out of copper, this compensatory action was achieved. Such compensation is only exact if the time constants as well as the magnitude of the two counter-acting effects are equal. Actually the time constants were not the same and it was therefore necessary to avoid sudden temperature changes. Figure 13 shows the complete oscillator with the shielding case removed. oeo2 The Power Supply and Regulator The plates of the oscillator tubes were supplied with 750 volts from the output of a voltage regulator. The input of this regulator in turn was supplied by a conven- tional design full wave mercury vapor type rectifier and a EH 13 FIGURE ATOR WITH SHIELD REMOVED OSCILL & Fos COMPL filter. This voltage of this supply was adjustable and was nomally set to deliver 850 volts at full load to the regulator. The voltage regulator was absolutely essential to prevent changes in the oscillator frequency with changes in the A.C. line voltage. The reguiator also served as an additional filter on the power supply so that the hum present in the output was less than 0.01 volt. The regulation when properly adjusted was within 1 volt over long periods of time. A cireuit diagram of the power supply and regu- lator is given in Figure 14. *HOIVINOWA =FOVITOA ON’ Xlddns WaMOd dO OLLVAHHOS wt THNoLs "o°v °A OTT SLOT ITIL Jodea AM 197] ir a &{ddng aemog IOPsTNZey 9384TOA ~ 39 «= 4. PRELIMINARY TESTS AND ADJUSTMENTS 4.1 Tests of Components Before any attempt was made to use the apparatus as a whole, many preliminary measurements and adjustments were made on the individual components to insure their proper working. The line length controlling mechanism and its lead screw were checked in place by means of a micrometer indicator. The diode detector circuit and associated meter were checked as to magnitude of readings, and more especially as to the linearity of deflection, by means of the laboratory standard equipment. With the oscillator frequency roughly adjusted, and the device drawing its normal plate current, the voltage regulator was adjusted to operate in the middle portion of its con- trol range with the line voltage at its average value. The oscillator frequency was then adjusted by varying the length of the resonant line in the grid cirevuit, until the proper frequency was obtained with the shielding cover in place. The frequency was measured with a Lecher Wire system and the result obtained was in close agreement with the line length required (after allowing for the diode, and Victron bridge, and other stray capacity at the line center). - 40 « With the oscillator in operation but with no coupling to the line (which was detuned), a deflection was first noticeable on the diode voltmeter meter. A slight revision of the circuit, to the final form given, and the inclusion of more filtering in certain leads than was originally used succeeded in eliminating this effect. 42 Resonance Tests After all these adjustments had been made, the feeding circuit loop was brought near enough to the coup- ling slot to give the desired rectified voltage at reson~ ance, and a series of runs was made to test the symmetry of the line resonance under various operating conditions. The results of these test runs were extremely gratifying; for with the exception of those runs taken with an input to the line so slight that the voltage at resonance was on the order of only 5 volts, the plots of the rectified data (Ae/en)* - 1 asa function of Mt) showed no visible con- sistent departure from strict linearity. A sample reson- ance run “curve" is shown in Fig. 15. In Fig. 16, are given three curves representing a controlled test of the effect at low resonance voltages mentioned in Section 2.51. All three curves were taken using the 5 volt multiplier resistance (Ro Fig. 9) in the diode voltmeter circuit. As a result, the apparent line encase loss is higher than in Fig. 15. Curve A was taken with the meter shunted so that full scale deflection occurred with 50 volt peak voltage in the line instead of 5 volts. The couplings between oscillator and pickup coil and be- tween feeding circuit and line were those normally used to obtain a 50 volt resonance in the line. Curve B was taken by unshunting the meter and decreasing the oscilla- tor to pickup coil coupling till the voltage at resonance in the line was 5 volts. In Curve C, the oscillator to pickup coil coupling was restored to its original value and the feeding circuit to line coupling was reduced to lower the resonance voltage again to 5 volts. It will be noticed that both curves representing 5 volts at resonance in the line are substantially coin- cident and show the same departure from the linear 50 volt run, and that this departure is greater on one side of re- sonance than on the other, namely for line lengths shorter than the resonant length. (The slight separation of the curves laterally was intentional, to avoid confusion). It is this dissymmetry of the error which makes it so diffi- cult to explain, and which makes even the transit time ex- planation geem doubtful. With voltages at resonance of 25 volts or more the effect is no longer evident, and as a result all sample measurements were made with a voltage at resonance of between 40 and 50 volts peak in the line. 3B + = 42 = 5. OBSERVATION, RECORDING, AND CONVERSION OF DATA 5.1 Method of Taking Readings At the beginning of each series of tests on 4 group of samples, a considerable warm up period was allowed. — The first sample was placed in the line, the equipment turned on, and the line adjusted to resonance. An interval of about twenty minutes was normally required for thermal equilibrium to be established in the oscilla- tor and the frequency to become stable. The line was kept in resonance during this period as a check on the frequency drift. When drift no longer became apparent, the feeding circuit was again adjusted to resonance. Another ten minute period was then allowed to elapse during which any further frequency drift was observed. If none was found, the resonance curve was taken. Readings were normally taken from a half maximum value reading on one side of resonance, through resonance to a half maximum value reading on the other side, with a spacing such that a total of about twenty-five points was read. To eliminate effects due to backlash of the short- ing ring, the motion employed was always in the same direc- tion. The deflection of the thermocouple meter indicating the current in the feeding loop was observed at intervals during the run to make sure no change or reaction occurred. At the end of a run, the first few readings were rechecked - 43 - to insure that no frequency drift, or other change, had taken place during the run. _ The line was then reset at the resonant length, and after recording the thickness as given by the micro- meter scale on the sample condenser tube, the sample was removed. ‘the sample condenser cylinder was then replaced and screwed in until resonance was reestablished with no Sample present, and the plate spacing required to do this was also read from the micrometer scale. As this reson- ance was approached it wes usually necessary to reduce the feeding circuit to line coupling to keep the diode voltmeter on scale. After making the resonance run with no sample, the sample condenser plates were reset to the thickness of the sample (but with no sample present) and the line length required to reestablish resonance was re~ corded. With the recording of the sample dimensions and other characteristics, the run was completed. During all tests the temperature of the room was held to as nearly a constant value as possible. This made it convenient to make critical runs (on low loss samples) at night when the temperature was fairly stable, with no rapid fluctuations and therefore could be more easily con~ trolled. — In addition to the initial warm-up periods at the start of a series of tests, a ten or fifteen minute interval was allowed to elapse between successive runs, after having introduced the next sample and having made all necessary adjustments. This was done to allow the sample itself to come to thermal equilibrium with its surroundings. 5.2 Sample Data Sheet On the following page is reproduced as a typical case, the data as recorded for the test of a sample of cast Lucite. In the next section, this data will be treated, as an exemple, by the methods actually used to determine the Losses. MATERIAL: Cast Lucite ARBA: Dise 3/4" in Diameter dg: 3-85 mm (Sample thickness) do: 2.78 um (Plate spacing for same capacity) 463 63.15 om (Resonant length with d = dg, no sample) | 44 eg (wi th sample) dy ___ %& (no sample) 08 e2LleL Ay) 2e06 603.0 2267 604.0 24.5 oa 24.6 el 26.6 4 26-6 08 29-0 06 28.9 0d 31.9 8 O14 04 04.8 604.90 S4e1 5 58628 02 57 4 «6 41.6 6 43.0 8 47.7 8 45.0 oD 48.9 605.0 46.2 605.0 48.6 om 46-1 el 47.0 4 44.7 02 44.0 6 | 42.22 eo 40.1 8 39el1 04 07 0S 606.0 56.5 05 33.8 «4 30.7 - 9 28.3 «6 28-5 3 2567 68 26.0 mS) 25-6 607.0 24.0 606.0 21.9 ef 2225 ol 20-5 ~ 45 6 5-5 Conversion of Data - Example 5-51 Estimation of kesonance Reading As a first step in the conversion of the ob- served data, it is necessary to estimate the diode volt- meter reading at exact resonance with and without the sample present, since ordinarily no observed points cor- respond exactly to this condition. This is best done by plotting on an enlarged scale the points near resonance. By drawing a smooth curve through these points the maxi- mum can be accurately estimated. Thus for the case of east Lucite one obtains: Reading at resonance with sample = 46.3 Reading at resonance without sample = 49.0 Failure to estimate the reading at resonance with sufficient accuracy produces a detectable error in the plotted computed data whereby points which would other- wise lie on a straight line, lie instead on two rectangular half-hyperbolae as shown in Figure 17. 5.32 Computation of Equivalent Resistance of Sample Using the resonance readings obtained by the method described, the quantities cot bs, and cot 5 are obtained by means of the relations: cot ry _ EY - a al See aena Sennen Sie oe Soeeees : ep ne pd he i re. . T i] i. " 7 . TT ae Recents on cana Ste ppv otc pr pry pt tre ap ~ 46 = Thus for the cast Lucite, we obtain: , (46.3)2. 7 cot od, = {(e, ) Uf (42a 1 cot bo =v ( e@, ) The results of these computations are tabulated below: 4, cot Oo, 41 cot b, 04 -0.60 o? -0.43 8. 0.24 9 #0.06 605.0 - 05 605.0 0.12 or 10 el 0.30 04 0.26 02 0.49 6 0.45 0d 0.70 8 0.63 04 0.85 606.0 0.78 0D 1.05 08 0.95 06 1.24 04 1.13 7 1.41 26 1.28 8 1.62 8 1.47 09 1.82 607.0 1.65 606.0 2-00 02 1.82 ol 2017 The above computed data is then plotted as shown in Figure 18, and the slopes of the "curves" obtained graphically. We have, by this means: My (slope without sample) = 18.55/cem m, (slope with sample) = §.53/em from which Tio Msg ~ a (= «15.8/em MoM, Now for the present line, at the frequency used, p = isd radians/em = 1.2 degrees/cm. Therefore Bt, = 1.2 x 60.5 = 72.6° This gives 2 sin pty = 0.910 and B= B = * = 2.30x107" rad./om. sin“pd, 150 x 0.910 Ry» the equivalent sample resistance is now determined from the relation Rg = 32 Molly ams. mo -i, to be np. = 24 ohm=x om x 15.8/cm Ss 2.50 x 10 ~ rad R, = 64,500 ohms »~ 48 = 5-35 Computation of Sample Capacity (a) The recorded sample thickness, and plate spacing required to produce with no sample present the same total sample condenser capacity are, respectively, and dg = 2.80 mn. The sample diameter is 3/4", while the sample plates are 1-1/2" in diameter. Therefore the ratio of sample area A to plate area ~ 1/4, and from the relation (@] ( A | + -({i- As} 1. wpfds. GS: dy { Ao) d., C= lh eaeld 1 0.280 ( z) 0.385 ne 1.65 ppfds. (bd) The line length at resonance with the sample present at the line center was 4, = 60.51 cm. With the sample plates at the same spacing but the sample absent, the line length required for resonance was 43 = 63.15 om. From the relation ( in. A ) c, = ( 40 t BL. = cot BL' ) + §,8) . s 7 | we (cot BL, - cot BL, ) a (#5) juntas we get c. = | _104 8” | ix x92 (0.3135 = 0.2515) + 0.65 jantds. The two methods (a) and (b) just illustrated for finding the sample capacity were always in roughly the agreement indicated here. The discrepancy was never more than a few per cent, and was always greatest and in the same direction for large thick samples of high dielectric constants, since for these the edge effects in method (a) were large. Since method (b) involves no edge effects nor other serious approximations the result by this method was always used. 5.354 Results for Cast Lucite From the above calculations we have for cast Lucite: 1. Dissipation Factor = D.F. = SaR7 DF. = 1 2x x10° x1.70 x10" 125 64,500 - 50 « and Ae (5s (2-54) Resistivity p= —= R= ( 8 1 s 0.385 re 64,500 p = 0.48 megohm - em. The dielectric constant can also be calculated by the relation Ag r-4 e = Cc. K- d. 1.70 x 4 x 0.385 XL = 2.62 The values of the dielectric constant for the various samples tested and as calculated by this means have been tabulated along with the loss results. ~ 51 - S**y oF ¢gs°o OF S8700°0 (xeakg) sseTy oar OS- ‘OF+ - T°9OT OS~ ‘Ob+ 4%000°0 XBMm UTSerep T°s GF ¢8go°o SF OSZT"0 OYVIIFN SSOTNTTSO 9°¢ SF G4L0°O — St Sb90°O e4BZOOV SSOTNTTEO o*y GF $420°0 ct OZST*0 WETeIBO ge*g OF 8¢9°0 oF TZT0°O Xems oof yh oF 00S*°0 oF S800°0 (892 Nd) SSCT MOT 9°¢ GF ¥90°0 GF G940°O PTTos esuBto0 6°¢ GF T90°0 CF G940°O peyBUTMBT exuBrIO °F SF 42G0°0 GF #8L0°0 PTTOS Your S°P GF G640°0 SF OF80°O peqyeUtTueT YyoeTaq 6° oF 610°0 CF O6ST°O (qe0TO) 4evo ser; TeNEg 9¢g oF $28 °0 oF ~ 9¢800°0 Teangeu) requy qUBTSUOD {%) Toray (Wo-myosem) (%) T0117 IOVoRyT Tetzre_qeN eTdues OFIVOSTeTC *qorg ‘xem AQTATISTSOY *qorg *xeN uoT ed TEs Tq *3oGZ PUB “SSTOADBFOW OOT 38 sSoTasTreqoereyg oTiqZoeTetq T°9 SLTASHE HO NOILVINGVL °9 o°s =SB= fOG+ "PIT Ge ‘0S+ 280000°0 pesny ‘reeto (S*9) 3 (°a¢) 3 (6T000°0) Teqshig :z2qrend (O}ore Sot Bart Oot 96000°0 (SZ00T SNX) euerfqshTOg 9g GF TSs°0 GF GZTt0’O SSBIS= TXOTI GP°g oS~ ‘OOT+ *AG os- ‘OOT+ T000°0 uTJJBIEg ; o°F Ogt 43S0°0O CF Z180°O peyeuserduy touewd ou 9°S Ost 18°00 oF Tes00°0 Axem ‘fap ‘xesuepuoco :aredeg ' ats oF 6g°T oF 9%Z00°0 XOTBO TH aes oF GS*T oF 89¢00°0 BOTH 9° OF Z8°O OF SPI0°O (pesserd) peptow | 9°2 OF O8r°O oF SPTO°O 4680 204 TONT o°s GF &S0°0 GF 8L0T°O TBesor0y T°9 oF Z0°T oF 89¢00°0 | 09 FAUBTOST queqsuo0g (%) IOLIg (“mo-wYyosem) (%) LoIIg 107087 TVTzsyeN sTauwesg OFI2ZOOTOTC *qorg *xey AVTATISTSeH *qorg “xem uoTRedTSss tq ¥°S c+ 2v0°O SF PeT°O uyeis SuoTe a°g ot $e80°O CF 4260°O UfeIs ssoro0e a | (eutTd esorepuod) Doom, Shs StF ES°e OTF 48000°O MOTT OZ 9F°S STF g9°a STF ¢$8000°0 IBOTO wWOTQOTA 0°9 STF ST°9 6F 66000°0 snoyd.zoury *°S OF ‘0R+ “FT ge- ‘0S+ — gg000°0 MOTTEX :anydtng 6°S uF 969°0 L¥ G0600°0 (prey) reqqny Ley Gt T9P*0 Gt 2580°0 Touempey quejsuop (%) cOlig (“mo-myoseu) (%) Torrid 104 08,7 TeTLoveNy eTauesg OFIZIOTSTC *qorug*xew ATATISTssy *qorg*xey uomedtss tq - 54 « 668 Classification of Dielectrics as to their Dissipation Pactors at 100 Megacycles (a) Very High Loss D.F. > 0.1) Material | Cast Bakelite Catalan Cellulose Nitrate Koroseal Ponderosa Pine {along grain) (b) High Loss (0.1 > D.F. > 0.01) Material Ordinary Bakelite Beeswax Celiulose Acetate Lucite Pyranol Soaked Paper Plexi-Glass Redmenol Ponderosa Pine (across grain) (c) Low Loss (0.01 > D.F. > 0.001) Material Amber (natural) Low Loss Bakelite (BM262) Pyrex Glass 0.0084 0.0083 0.00485 - 55 = Material : D.F. Igolantite 0.0037 Mica ~ . 0,0027 Micalex 0.0025 Gondenser Paper (dry) 0.0033 Rubber (hard) 0.0090 (d) Ultra Low Logs (0.001 > D.F.) Material D.F. Ceresin Wax 0.00047 Paraffin 0.00013 Polystyrene (XMS10023) 0.00040 Quartz (fused, clear) 0.00005 Sulphur (yellow) 0.00035 (amorphous) 0,00049 Victron 0.00086 - 56 ~- 7. DISCUSSION OF RESULTS 7.1L Lew Loss Materials One of the primary objectives of any investiga-~ tion such as this is the discovery of those substances most ideal according to some definite criterion. Low loss is of course the goal usually sought for in a dielectric for high frequency application. (There are cases for which this might not be true: cases in which it might be desirable to introduce a loss proportional to frequency, and thus, for example, evade the loss-phase laws of "minimum phase™ net- works). Examination of the results shows that among the samples tested, those having really low losses are few in number, ‘Quartz in its usual role as an exceptional sub= stance has the lowest loss of all though there appears at present little reason to suppose that the loss it has is a theoretical minimum, Paraffin, too, is seen to have very little loss: roughly twice that of quartz. Next, and in a group, come Ceresin wax, Polystyrene plastic, and sulphur, all having Dissipation Factors about 8 times that of quartz. Last in this group of substances arbitrarily designated "Ultra Low Loss", is Victron, an earlier plastic than Polystyrene, and with a Dissipation Factor roughly twice as great or about 8 x 107*, -~ 57 - All of the above substances have Dissipation Factors so low as normally to be negligible (with proper mechanical design of parts) even at frequencies of 100 méegacycles per second. However the sad fact remains that with the exception of quartz, none of the substances in this group are capable of withstanding high temperatures, such as are involved in the construction and operation of a vacuum tube. It is not until we drop to Dissipation Factors ranging from 0.0025 to 0.005 that we begin to find substances, refractory, yet capable of being worked. Prin- cipal members of this group are Mica, and substances of high mica content, the high grade porcelains such as Isolantite, and the hard, high silica glasses such as Pyrex and Nonex. in view of the extremely low loss in quartz, it would seem that the hard glasses should be a likely group of substances with which to expsriment in an effort to de- velop new, refractory, low loss dielectrics. One such glass recently developed for other purposes is the new so- called “"shrunk-glass" in which the softer constituents of an original cast glass piece are leached out by an etching bath and the remaining mass (nearly pure silica) is refired, whereupon it shrinks to close up the interstices left after etching and leave a final article of substantially pure - 58 - quartiZe “This product should therefore have the low loss of quartz in addition to a workability approaching that of the ceramics. It was the author's hope to be able to obtain a Sample of this “shrunk glass" for test, but at the time, none was available from the manufacturer, * 7.6 Anomalies and Interesting Features in the kesults The reader may have noticed that the crystal quartz showed a much higher loss and dielectric constant than the fused quartz sample. In the author's opinion this was due to the piezo-electric effect in the crystal quartz causing a reflected reactance and resistance to appear in the electrical circuit as a result of mechanical motion. True, the frequency used was far from the frequency for which the crystal was ground, but there are more modes of vibration in crystals than there are styles in women's hats and it is possible that one of these higher modes lay near 100 megacycles. This is not necessary, however, for even without a nearby resonance an energy loss of the amount re- quired can be accounted for. | The anisotropic nature of wood was also apparent from the results for Ponderosa Pine (Normal Bridge Physics Laboratory Shop grade) which showed a higher loss when the *Gorning Glass Co, - 59 - field acted along the grain than when it was applied across the grain. This anisotropism in wood has been mentioned by others in connection with conductivity measurements, ©! Incidentally, the absence of any definite correla- tion between conductivity at low frequencies and loss at high frequencies is evidenced by the fact that while paraffin is both a good insulator and a low loss dielectric, both natural amber and Lucite which are better insulators have rather high losses. While the measurement of dielectric properties is hardly a suitable or adequate method of chemical analysis, it is interesting to look at a few of the results in this light. Thus the final properties of Lucite are seen to be remarkably independent of its method of fomation, while the two samples of Victron, though visibly very different were electrically identical, While the loss in Victron is over twice as great as the loss in Polystyrene, the di- electric constants as measured are seen to differ by less than 1%. This confirms other evidence (elasticity, brittle- ness, melting point, smell when hot etc.} of the molecular Similarity of the two substances. In fact it seems probable that Victron is merely impure Polystyrene. 7.3 Comparison of Resuits The results obtained admit of very little com- parison, as there is little other data available. Also the -~ 60 « large amount of variation between samples of substances of indefinite composition (as are porcelains, glasses etc.) make such data as is available hard to compare directly. Miller and Salzberg”! have published loss figures for a number of substances among them Polystyrene, and quartz. The figures they quote are DF. € Polystyrene 0.0006 Bed Quartz 0.0004 3.5 The agreement with the present work is fair in the case of Polystyrene but very poor in the case of quartz, for which the loss quoted is 8 times as great as that found by the author. This disagreement is in excess of the maximum probable error by the present method for the quartz sample. it is possible that there might be this much variation in fused quartz as a result of in- cluded impurities. (The sample used by the author was ex- ceptionally pure and optically perfect.) A discussion of the method used by Miller and Salzberg is given in Appendix VI and some possible sources of error in their method are mentioned, | Among the other substances for which data up to 10 megacycles are given elsewhere, the agreement obtained by extrapolation 1s as good as can be expected, - 61 ~ 8. SUGGESTED MODIFICATIONS, IMPROVEMENTS, AND FULURE RESEARCH USES. It seldom happens that an investigator, having concluded some research project, is completely satisfied with the adequacy of his results, and with every detail of the method and equipment used, It is always possible, in retrospect, to find faults (secretly, or openly) with the work, as it was done, and to suggest improvements and further applications. This is not necessarily an un- healthy symptom. Far from it. It may in fact be argued that it is out of just such unrest that the state of any art advances, in this section, a comparison is first made of the theoretical capabilities of the method with actual capabilities of the apparatus used. Two ways of improving the sensitivity are suggested, and some sug- gestions made for the use of the revised apparatus, 8.1 Comparison of Theoretical and actual Sensitivity AS has been pointed out, the sensitivity limit of the present method of loss measurement is fixed by the losses inherent in the line itself: were these halved, the sensitivity would be doubled. The theoretical lower limit for the losses in the line is the loss arising from the re- sistance of the line conductors themselves. The loss to be expected, were this the sole source, is calculated in Appendix V, where it is shown that oa =5x107*, The actual loss is also readily calculable, for example from Resonance Test #2, and was: A = 12.6 x 1074 Thus the line losses can account for only about 40% of the total loss and the theoretical sensitivity of the method with the line size used is roughly 2-1/2 times the realized sensitivity. 8.2 Localization of Other Losses Perhaps 10%, but hardly more, of the total loss may have been due to increased resistance at the movable end connections. Accordingly, about half of the total loss with no sample present must be attributed to the diode de- tector and the Victron support bridge at the center of the line. Since, however, the Vietron bridge was so constructed that the capacity it introduced was much less than 1 py fd, and since the Dissipation Factor of Victron is given by the measurements as 0.00086, the loss introduced by this bridge could not present an equivalent resistance across the line 6 of less than 2 x 10° ohms, which corresponds to an "A" of 0.5 x 107* or roughly 4% of the total loss. Apparently, therefore, the diode detector is responsible for at least 45% of this total loss. The effective load placed across the line by the meter multiplier resistance is equivalent to a resistance one half as large or 5 x 10° ohms for the 50 volt scale. This and the presence of the by pass condensers and insulating sleeves inside the line (see Figure 8) and the associated filter chokes outside the line can perhaps claim another 5% of the total loss. Around 35% then, must be due to the tube itself. This is not surprising, although it is rather disheartening, for the tube used was the best available at the time. 8.5 Origin, Magnitude and Reduction of Loss in the Diode Since the diode was operated as a peak wl1tmeter, with a load resistance very high compared with its plate resistance (Rpy:Rp > 1000:1), and since the spacing of the tiny plate and cathode was only about 1 mm, the electronic losses (including transit time effects) must have been but a small portion of the tube's loss. The major portion is easily accounted for by dielectric and resistance losses in the glass bulb (on the inside surface of which was a considerable film of magnesium “getter"), and by resistance losses in the lead wires which had to carry the currents due to the stray capacity of bulb and elements. A likely equivalent circuit of the losses in the diode is therefore that given in Figure 19(b) which at any particular frequency SSOI SLI dO NOLL’ LNGSaede CNV NOILONMLSNOO 4ddoId 6t ganols qINdITS epotp Uy ssOoT @potTp queTeatnbe petst{Tdmts (0 Jo yyNoryo yueTeatnby (q G2 noIG TOTES P T => a 7 Py Ty 4 a 4 (3 - 64 = can be converted to the equivalent circuit 19(¢c). It is to be remembered in computing these losses that the tube had applied to it at all times the total radio frequency voltage at the center of the line. In the tube used, the capacity was about 2.5 uu fds, of which approximately 1.5 uu fds, was due to the glass envelope. Taking C = 1.5 uw» fds, and the Dissipation Factor of the glass to be that found for Pyrex, we get Ry) = 215,000 ohms With the leads to the tube 0.02 om in diameter and a total of 2 om long, Rp = 0.1 ohm This proves negligible, and hence Re = 215,000 ohms which is equivalent to an "A" of 4.4 x 107%, or roughly 35% of the total loss, as expected, it is therefore possible with entirely reasonable values to account for all the “excess” loss present in the actual line as constructed. Since there was no internal support insulation present in the diode used, and since the loss in the leads was negligible, it seems that practically the only way to reduce the tube's loss would be to redesign the glass en- velope and construct it out of a lower loss glass, As to - 65 ~ this redesign of the envelope, some benefit could be ex- pected from a reduction in the wall thickness and in the lead in wire size as both of these changes would reduce the end to end bulb capacity. It is doubtful if the tube loss could be reduced by more than 30% by this means. A greater improvement could be obtained with a markedly lower-loss glass, and by the elimination of the getter film on the inside surface. By using all these means, it should be possible to reduce the tube loss till it be less than 10% of the total loss, in which case further improve« ment would be unwarranted, There are of course other methods for measuring the resonance in the line. McRae? used a thermocouple Loop and galvanometer to read the current at the movable end of the line. It should be equally feasible to use a pickup loop and amplifier, followed by a detector to do this. However, while these schemes may have somewhat less inherent loss than the simple method used by the author, the added complexity, and instability, and inconvenience involved are potential sources of error which completely negate any advantages they may have, Assuming success in reducing the diode loss, it would then be worthwhile to reduce some of the other losses by such means as silverplating the entire inside of the line, and then lacquering all current carrying surface to - 66 - which no contact need be made. By bending every effort to loss reduction it should be possible to very nearly double the sensitivity of the method over its present value. It should be mentioned that since the losses in the present type of transmission line at the frequencies used, or higher, are proportional to the square root of frequency (being controlled by skin effect) and since the loss in dielectrics is proportional to nearly the first power of frequency, the potentialities of the method are the greater the higher the frequency used, 8.4 Suggestions for Further Investigations AS well as for making continued measurements on many other deserving dielectrics, there are other applica-~ tions for which the apparatus is equally well suited. By constructing an additional, and very simple lower sample condenser plate in the form of a shallow cup, it would be possible to make loss measurements equally easily on liquid Samples such as oils. Series of runs could also be made to determine the variation of the dielectric loss with temperature in various substances, The measurement of the dielectric constants of other solids, liquids, and even gases is a possibility. - 67 = By bridging the line at the sample condenser lo~ cation with the proper elements of a vacuum tube, it should be possible to determine the admittance looking into these elements and thus provide an experimental check on transit time theory®), These are a few of the uses which suggest them- selves, uses for which the present apparatus could well be used now that it has been constructed, - 68 = 9. CONCLUSION AND SUMMARY . A method, based upon an earlier one used by McRae?) , has been developed for the measurement of di- electric losses and constants at ultra high frequencies, A large number of samples have been successfully tested by the method at a frequency of one hundred megacycles per second, and the results of these measurements are given. The theory of the method is presented and the theoretical limitations considered. Means for attaining very nearly the maximum sensitivity set by these limita- tions are suggested. - 69 - 10. ACKNOWLEDGMENT The author wishes to express his appreciation of the help given him in the work by Dr. S. S. Mackeown of the Electrical Engineering Department, and by the other members of this department who were of assistance from time to time. Thanks are due Mr. A. Le Samuel of the Bell Telephone Laboratories, who supplied the special diode used as a de~ tector; and due also the Bakelite Corporation which supplied several of the samples for test. The author also wishes to thank Mr. Arthur Harrison who assisted in making many of the readings, and whose concurrent difficulties in his own work were a source of vicarious psychological satisfac- tion. = 70 « APPENDIX I SENDING END=“TO«MIDPOINT TRANSFER CONSTANT Under the assumptions mentioned in Section 2.2, the resonant coaxial line used may be treated by the ordin« ary transmission line theory. We shall find it convenient, in the analysis, to break the line up into three sections each of which can be considered as a four terminal networks These sections are shown in the schematic diagram below: Section |< — Section three el to ~{~.—_ Section one ———» _o. O ° 7 R21 ¢ , ag 29 ayo Lo b =O ! O- | =) Az Bz ,Cz5Dz Ap sBo,Co Do Aq sy Cy sPy Fige 20 Section 1 is that part of the line lying between the sample condenser and the movable short circuited end of the line. Section 2 is simply the shunt admittances of é and jC representing the sample and holder and detector. Section 3 is the quarter wavelength long section from the _ gample condenser to the short circuited input end. The voltage and current and impedance looking into each section as well as the constants thereof (with the exception of the undenoted R, and C) are denoted by a subscript which is that of the section in which they lie. We desire to know the voltage at the center of the line, €p, as a function of the line parameters 41, Ry and C, with @z, the input voltage, held constant. By four~terminal network theory, we have: 1 1l*o 1*o ) (1) i = Cyeg + Dyiy ) By ®, = 0, so B) = Di (1a) 2 ByAotD7B @, = 0, so By = ine (2a) B1OgtD De @g = [Ag(AjAgiC1Bg) + BglayCo+CyD2) Jeg + [Ag(BjAgtD Bg) + Bg(ByCp+DyDe) Jig (3) ) ) ) ) ) ) ) + [Cg(ByAptDjBg) + Dg(ByCotD De) Ji, _ 4g (ByAgtD Bg) + Bg(ByC)+DjD2) 8 = 0 50 2s = . 03 (ByaAgtD Bg) + Dg(B,C]*D1D3) (3a) e Let us now define Kp = = « Then we have from equations 3 (2), (2a) ana (3): Fe) ByAptD Bo ene 2, | Po @g Ag(ByAgtD1 Bg) + Bg(ByCp*D D2) Kp = 2. ByCotD De Ll +B © BiAg*D, By Kp = —4 = (4) iti Bo Referring back to Figure 20, we see that: 1 1 i C, = — sinh 6 Co = = + Jud Cz = «= sinh 0 1” Bo i 2"gt be 3 Bo 5 Dy * cosh 0, Do =] Ds = cosh @5 where Z, = characteristic impedance of line. @ = hyperbolic propagation angle. Substituting the appropriate quantities in equation (2a), we get ~ 73 « > sinh 0) (~ + JoC) + cosh 04 1 ZB tanh 0; (5) 1 a2 ZR * Jot * | B Equation (5) is obvious directly since 4 = = = Z, tanh 0)< 1 Equation (5) now becomes: Kp = 4 an (6) cosh @5 +22 sinh Og + = a + joC By sinh 05 Now . Q, = at, + ity) in 85 = are, + jpts) where a # attenuation constant of line B = phase constant of line, and so, by trigonometric reduction, we may write: = coth 6) = tanh 6) (coth at, - j cot pt) l-j coth at) cot pty coth 6; = 1 coth al, (l= j tanh at, cot pt,) tanh of; [1+ cot@pl, » j(coth aty = tanh al ) cot pty] coth @= 1 + tanh@at, cot®ply But since ol, << 10°74 . (8) - & 6< Pi <3} we may safely neglect tanh=ot, cot"pl, with respect to unityo We then have (remembering that 1 + cot®x = cso”x and that 1 + tanh*y = sech“y) the relation tanh at; cot Bly coth 0, = sin® pl, cosh® aly Again because of relations (8), we may safely reduce this to oy sin” pL, coth 9) = - j cot ply (9) Also cosh 0, = cosh al, cos($ +8) + j sink abg sin(Z + 8) sinh 6, = sinh ode cos(=+8) + j cosh ats sin(S + 8) (10) where § is a small angle which may arise as a result of the section of line, day not being an exact quarter wavelength long. Since ats <x 1072 ) si} equations (10) reduce to: cosh 63 = j(ats + j sin 5) (11) sinh @, = j ) ~ 75 = Substituting the quantities given by equations (9) and (11) into our expression for Kp, we get: 1 JKy = Z & ats +%2 + —— + isin 8+ wl Bo - cot ne) sin*ptly - 1 (12) Rpt JQe Because of the relative magnitudes of the quanti-=- ties involved in the above expression can be still further simplified. Let us compute these quantities for the present line and at both extremes of the expected range of sample resistances For the line used > = 94 ohms | a = 363 x 10°6/om tee 8 55 rad/om as shown in appendix V. Since Pt. = és 4, = 75 om, and therefore Let us assume a 1" diameter sample, 1/8" thick, and for which € = 6. In this case, Cy * 865 ppFdo = V6 « Allowing 265 paFd for the tube capacity, and about 5 pyFd for stray capacity we find C = 16 ppfds. fhis higher than average value is accurate enough for the ‘present purpose, since variations in it will not affect the validity of our approximations, as we shall see. Neglect« ing sin & for the moment, we see that in order to make jKy real, cot BL, = w , = 1.0 ~ x phy ™ 45° = 4 Therefore sin®pl, = 0.5 and 44 = 37.5 Cte Depending on the sample R may be expected to lie anywhere between about 5000 ohms and 200,000 ohms (the upper limit being fixed by the voltmeter and support assembly). Hence we find by addition al, = 2.5 x 1074 a 5x 107% « = < 200 x 10°4 that = 2.5 x 1074 sin’pl, - 1075 <= Rp & 2x 10°8 -~ 77 = Thus (since jk, = ) anywhere from a 50 to a 1000 a Ry + Jaq fold rise in voltage can be expected with wp = 0. "Reson= ance" will be indicated when jKy is a maximum. Inasmuch as Rp = £(2,), the condition for resonance is not exactly that for which Qp = 0; but, as we shall see, the difference is negligibles Let 45 be defined such that cot BL, = wS Bo + sin & (13) Then in general, we may write 1, = 4, + Al and therefore, by ‘aylor's series: cot B(LotAt) = cot Bly - 9 * a. (Bab)? + 2s © (14) ° fe} thisgives for jKp _ 1 JKy = altgrsb) _ p. Bo] - 3B _ 90% Pe (pity sin*p(t,+ab) R sin®pt, sin®pl, ‘faking the lower extreme of 0.02 for Ry, we see that jKyp is reduced to the 70.71% value when { = 0,08 = YA - cot Plo ( ar)® + * © @ Sr sin@pl, sin*plo P which, for the case assumed (C = 16 ppfds) gives Bat = 0.01 fhe omission of all terms in the expansion of a power of (Bat) greater than the first can introduce an error of 1% at most, and is therefore permissible. We then have 1 jKn (15) (a (tort) + at er ats sin®p(t +A) Bo) |, fat ° R) : sin®pt Again, by Taylor's series: a(t+at) abo ink BL, cot Blo sin®p(L,+at) sin®pt, sin*pb, (att) + oo @ {16) =Yg + Brg If we let BAl = 0.02 to get the maximum variation in Re from one 70.71% point to the other, we get: “te (4) +> (3e2 x 10%°)(0.02) = - 7.3 x 107 bro * This is less than 0.001% of Ry. The variation is, as a matter of fact, even less for Bly > i and zero when BL, cot pl, = ‘ « As & result we can neglect all changes in Rip over the resonance range, as predicted, and write simply Bat, (i tto , al, + 52) sin®pl,, (sin®pl, ) in the actual arrangement mle wotiy dt R, Ro where R, = effective resistance of sample R, * effective resistance of all loss at line center with no sample Therefore, if we let att 3 Ae — 2 + ah, + 2 (18) sin*Bl, Ro Be —b_ (19) sin®pl,, We may write Kp = i (20) pat + jla + 22) | Rg fhe quantity "A" is seen to be a quantity which includes all the loss present in the line without a sample and with dizto: and can be determined experimentally by taking such &@ Truno The method used to determine A and Rg from the experimental data is given in Appendix If, - 80 ~ APPENDIX II CONVERSION OF DATA In Appendix I we saw that Ky = — x Zz (20) BM + j(A + 2%) s Writing this in polar form, we have: Ky = 1xpt lb = — Lo (21) 45,2 [sten? + (A +2) Rg where d = cot BAL a+ 22 Rg Thus if cot $ be plotted as a function of M, the result should be a straight line having a slope, m, given by m=. cotd. B 22 a” 8s (22) . Rs If m, = slope without sample present m, = slope with sample present we see that Mm =F = B and Mm, —z A+R . B from which A= = (23) My 4 %, and Re = 2 = =2 ots (24) Bea Mo ~ Ms Ig in which B® _ 8B sin*BL,, In order to determine Rg by this method there~ fore, it is necessary to know the slopes m,, and mg, found by plotting cot 6 as a function of M (or 41). If we let Kr. = value of Kp at resonance, we see from equation (21) that ~ 82 - = t z cot 0 At= But 2 a (&r) (se) 72 (25) where &, = voltage read on diode detector at resonance e ™ voltage read on diode detector at any point. So that a cot ) = /\=) ~1 (26) and in order to find M,, OF Mg, it is merely necessary to convert the appropriate data by the above equation, plot cot 6 as a function of AL (or 44) and measure the slope. The sample resistance is then given by equation (24). ~ 83 = APPENDIX ITI DEVELOPMENT OF SAMPLE CAPACITY FORMULAE Methed a) Consider the parallel plate sample condenser be- tween the plates of which is a slab of dielectric, small enough so that no portion extends to the edges of the plates. By the parallel plate capacity equation, then: where C OQ aQ ar ta oe a. By removing = (A A ) o *s and, + Og + Co} om (27) total capacity at line center capacity of dielectric excess stray capacity at line center plate area in em” dielectric area in om” dielectric thickness ~ plate spacing in cm the dielectric, the plate spacing may be de- creased till the capacity is again the same. Then: (_4o (4nd, + Co) em (28) d, ™ plate spacing for same capacity with no sample present. Therefore from equations (27) and (28) 3) cm 29 Ax dy 4nd, (29) A A | sfoll wt, 28) 2 or Cy ° is ~ a ie) ay om (29a) A 0 1 ( As) 1 Cs * (B.6)x }fo ~ (7 7 Bg) Ge] PFGE (28) For the apparatus used: A _ «(0.75 x 2.54)? (S6)x Be6 tt = 1 cm pefds and therefore ~}i _ ( Ag) 1 Cg = (=~ 1 + —, = ippfds (30) The method is approximate because of the pres- ence of edge effects around the parallel plate condenser, Method b) From equation (13) (Appendix I) we have (with CG in farads): cot Bl, = oC & + sin & (13) If we let C* = capacity (in farads) of sample condenser without dielectric present but at plate spacing of d, as = resonant length (of 4) under these con- _ ditions. Then cot 24) = who (Ct + C5) + sin 5 (32) Subtracting from equation (13): cot 84, = cot BL, = wy (C -Ct=C,) But t mAs 1 ) C - Cc *o ) farad = + + areas (8 “9 48ds 9x 1014) t Ag 1 Gt = 4ndg 9x i911 farads where AS = effective area of sample condenser plates including edge effects. Hence C=C eC t *s i farad o 4 4x45 954911) Substituting, we get: ( A ) c. = (~L (cot st. mcot af") +—8 i} farads (32) s (Wiky ° Oo 4nd 9 x1024) This expression is exact since there are no edge effects around the boundary of A,, provided this boundary is well inside the boundary of A,, as specified. For the appara- tus used, equation (32) reduces to (4912 e (As) i} (Zo (cot B4.=cot 4.) + (Zo) as} pnfds (32a) Cg * APPENDIX IV BASIC SENSITIVITY OF THE METHOD We have seen (Appendix II) that the equivalent resistance of the sample, R,, is given by m 5 os Mo - Ms Rg =>" (24) In which %. = characteristic impedance of line B= —£— sin“pl, B = phase constant of line ho = length of section 1 of line at resonance m. = slope of plotted data without sample m, = Slope of plotted data with sample In practice it is only possible to determine m, and m, within a certain maximum probable error, and a correspond~ ing error may thus be present in Rg. Quantitatively: OR, ORg SR, = amy Sm, + on, Sm, (in _ . ) SR. = Bq ( (Mg Mg )M, ~ MMs Sm + (mo-ms)M + Molls sm. } which reduces to - B83 = 2 : 4, My) Mg ~ Ms"6M, SR, = 5 (33) 8 Bz (my - mg) Dividing through by Ry: we get 2 SR, _ modmy - mg’dm, Rg MoM,g(mo - Mg) SRs _ s ie) Rg (m, ~ mg) (34) om, 6m, This expression is largest when a and are of oppo~ 8 site sign; in other words, if one slope is estimated too large, and the other too small. Thus ve) 8 8R, ™s' max *o!' max = = (35) 8! max My ~ My om, Sm, where 100|-—— end 100|—— are the maximum probable S|max Mo |max percentage errors in estimating mg and m,. For given Sm 5m values of |---| and |—*| » equation (30) is the greater, s the nearer m, approaches m,. if we define: 2m = m, “~ Mg 6 = Rg max we may rewrite equation (350) thus: ( 5m ) ém (| @sgl pax "oO Olmax ) As mM, > M,, <= + 0, and we have c=" (18me} + [Sto] ém (| ™simax Mo|max ) and accordingly m, (lem am, | ) | € (| ™s|max Molmax ) But from equation (24) 2 ~ Zo mo” (1 me R ss asm s B dm and again as M, > Mo, we have 2 6 2 (37) m ~ 59 R aguas queer s” B fm - 90 ~ Combining equations (31) and (32) we get % ~ ) R, = 2m, (— £ {}™o|mazx ms|max } but since from Appendix II, B A= Mo we may write Zo § R. s— ( £ ) 3 SA | | Sel + | Sa} ) 98) Mo! max Mg Now this expression has been developed for the case when the loss is low and therefore form, =m,. In this case it is reasonable to assume that do] 3] Bg Do!{ max Ms} max and hence that: ~ A Si, a Oo! max Thus we have a relation between the maximum probable error in reading the slopes n, and m., the sample s? resistance and the error in the result. - 91 - APPENDIX V CALCULATION OF LINE CONSTANTS a) Characteristic Impedance, Since in the line used, the resistance and leak- age were negligibly small compared with the inductive re- actance and capacitive susceptance, we have for the char- acteristic impedance of the line Ay» 4, * > where A = inductance per unit length lr = capacitance per unit length now A = Zp log 8 = (2x 107%)p log 8 honries £ E farads 2 log 8 (18 x 1044) log B om Hence , b Zo = 60 /* log gq ohms. oo For the present line, » = 1, e€ =1, 2 = 4.8 and we get fa Bo * 94 ohms ob) Phase constant of Line, Bp. In a transmission line with negligible dissipa- tion, the velocity of propagation is given by -~ 92 + where e = velocity of light bh = permeability of medium e = dielectric constant of medium, In our case therefore vec }f where } = wavelength f = frequency 2 But p =<", so = Hf 2 B= “o- "6 8 Since w = 2x x 10° rad/sec c = 3 x 1019 on/see rad we get B= Ted “on om ° ¢) Attenuation constant of line, a. The loop resistance of a copper coaxial line at high frequencies is very nearly”): -9 ohms Ry, = 41.6 VF (4 +d) x 10 on where a= outer radius of inner conductor in cm. b = inner radius of outer conductor in cm, and the attenuation constant is given by For the present line: Ry, = 41.6 x 10° x $255 5 Ry = 62,1 x 10° ohms/cm, and thus _ 62.1 x 107° 2x 94 = 3.3 x 107°/om, For the whole line therefore atzF aq (44 + tz) =qxi150=5x 107" - 94 ~ APPENDIX VI METHOD USED BY MILLER AND SALZBERG A method of measuring admittances at ultra high frequencies, and one which also makes use of a tuned trans-~ mission line, has been described by Miller and Salzberg"), In their method a two wire transmission line considerably less than a quarter wavelength long was used; one end of the line being short circuited and the other loaded with the sample condenser and sample. across the "open" (condenser) end was a vacuum tube voltmeter. To measure a sample, a reading of the voltmeter was first made with the sample in place and the line tuned to resonance. The sample was then removed and the line was again tuned to resonance by the terminal capacity, but with a calibrated (7) resistor shunting the line at some point such that the same reading was again obtained on the vacuum tube voltmeter. From the position on the line of the re- si stor relative to the short-circuited end, and from the value of the resistance used, the equivalent resistance of the sample was computea by a simple relation, This method, though convenient, has, in the author's opinion, several notable disadvantages, First: because of a fundamental sensitivity limitation imposed by -~ 95 « the losses in the line itself (similar to that derived in Appendix IV) and the fact that these losses are higher on a two-wire line (due to radiation), the method is inherent- ly less sensitive than that used by the author. Second: being unshielded, the apparatus used is more susceptible to errors due to stray capacities and couplings. Third: the measurements rest upon the validity of but two observations, and hence all the errors which may affect a single reading are not eliminated. Fourth: Bi€@th, and perhaps most im- portant, the current distribution in the line itself is not the same with and without the sample as a result of the stray capacity and loss present in the "standard" resistor placed across the line at an intermediate point. The ef+ fect of this change in current distribution is in such a direction as to alter the loss contributed by the line itself, between the sample and no-semple runs, This, and the other effects listed, could be expected to introduce an error into the results obtained by this method: an error large for low loss samples. In addition the method is not absolute, as it depends upon the accuracy of the standard resistor with respect to which all measurements are made, and a standard resistance accurate at ultra high frequencies is difficult to obtain. le Be Se De 4. De 6. ?. 8. - 96 «~ REFERENCES McRae, J. W.: "The Measurement of Losses in Solid Dielectrics at Very High Frequencies" «+ Ph.D Thesis, C.I.T., May 1937. Doll, EZ. B.: “Radio Field Strength Measurements at 41 Megacycles" «= Ph.D. Thesis, C.I.T. May 1938. a} Morgan, S.0.: “Dielectric Losses in Polar Liquids and Solids ~ B.T.L. Monograph B-1066. b} Muller, f., H.: "“Dielectrische Verluste im polaren Aufbau der Materie" - Ergebnisse der Exakten Naturwissenschaften, Vol. 17, Julius Springer, Berlin. Schelkunoff, S. A.: "The Blectromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields" - B.S.T.J. Oct., 1934. Terman, F. E.: “Resonant Lines in Radio Circuits" ~ Blec. Eng. July, 1934. Schwaiger, Sorensen: "Theory of Dielectrics". (Wiley) Miller and Salzberg: "Measurement of Admittances at Ultra High Frequencies" - RCA Review, April, 1939. Uewellgn, F. B.: "Operation of Ultra-High Frequency Vacuum Tubes - B.S.T.d. Oct., 1935.